Decisions, Risk and Reward (Routledge Studies in Business Organizations and Networks)

Decisions: Risk and Reward

In recent years leading figures in a variety of fields – political, financial, medical and organizational – have become acutely aware of the need to effectively incorporate aspects of risk into their decision-making. This book addresses a wide range of contemporary issues in decision research, such as how individuals deal with uncertainty and complexity, gender-based differences in decision-making, what determines decision performance and why people choose risky activities. This book presents results from academic research carried out over the last 20 years. A common theme is the study of decisions made in horse-race betting markets, a research medium which offers a rich insight into decision-making in general and one which enjoys particular methodological advantages over laboratory-based simulations. This set of naturalistic studies explores the variety of individual motivations for betting, how people perceive and respond to the presence of uncertainty, the challenges of complex and turbulent information and the use of heuristics as a response, how decision-making performance is affected by structural or process-related features of the decision environment, and how men and women differ in their decision behaviour. The authors’ interesting and novel findings offer a richer understanding of the psychological and economic underpinnings of betting behaviour which should inform practitioners, policymakers and regulators in an industry which is undergoing unprecedented global growth. This book is also relevant to courses covering subject areas such as financial markets, decision-making and behavioural finance. Johnnie Johnson is Professor of Decision and Risk Analysis and Director of the Centre for Risk Research at the University of Southampton. Alistair Bruce is Professor of Decision and Risk Analysis at Nottingham University Business School.

Routledge studies in business organizations and networks

1 Democracy and Efficiency in the Economic Enterprise Edited by Ugo Pagano and Robert Rowthorn 2 Towards a Competence Theory of the Firm Edited by Nicolai J. Foss and Christian Knudsen 3 Uncertainty and Economic Evolution Essays in honour of Armen A. Alchian Edited by John R. Lott Jr 4 The End of the Professions? The restructuring of professional work Edited by Jane Broadbent, Michael Dietrich and Jennifer Roberts 5 Shopfloor Matters Labor-management relations in twentieth-century American manufacturing David Fairris 6 The Organisation of the Firm International business perspectives Edited by Ram Mudambi and Martin Ricketts

7 Organizing Industrial Activities Across Firm Boundaries Anna Dubois 8 Economic Organisation, Capabilities and Coordination Edited by Nicolai Foss and Brian J. Loasby 9 The Changing Boundaries of the Firm Explaining evolving inter-firm relations Edited by Massimo G. Colombo 10 Authority and Control in Modern Industry Theoretical and empirical perspectives Edited by Paul L. Robertson 11 Interfirm Networks Organization and industrial competitiveness Edited by Anna Grandori 12 Privatization and Supply Chain Management Andrew Cox, Lisa Harris and David Parker

13 The Governance of Large Technical Systems Edited by Olivier Coutard

21 Workaholism in Organizations Antecedents and consequences Ronald J. Burke

14 Stability and Change in HighTech Enterprises Organisational practices and routines Neil Costello

22 The Construction Industry An international comparison Edited by Gerhard Bosch and Peter Philips

15 The New Mutualism in Public Policy Johnston Birchall 16 An Econometric Analysis of the Real Estate Market and Investment Peijie Wang 17 Managing Buyer-Supplier Relations The winning edge through specification management Rajesh Nellore 18 Supply Chains, Markets and Power Mapping buyer and supplier power regimes Andrew Cox, Paul Ireland, Chris Lonsdale, Joe Sanderson and Glyn Watson 19 Managing Professional Identities Knowledge, performativity, and the ‘new’ professional Edited by Mike Dent and Stephen Whitehead 20 A Comparison of Small and Medium Enterprises in Europe and in the USA Solomon Karmel and Justin Bryon

23 Economic Geography of Higher Education Knowledge, infrastructure and learning regions Edited by Roel Rutten, Frans Boekema and Elsa Kuijpers 24 Economies of Network Industries Hans-Werner Gottinger 25 The Corporation Investment, mergers and growth Dennis C. Mueller 26 Industrial and Labour Market Policy and Performance Issues and perspectives Edited by Dan Coffey and Carole Thornley 27 Organization and Identity Edited by Alison Linstead and Stephen Linstead 28 Thinking Organization Edited by Stephen Linstead and Alison Linstead 29 Information Warfare in Business Strategies of control and resistance in the network society Iain Munro

30 Business Clusters An international perspective Martin Perry

37 Business Networks Strategy and structure Emanuela Todeva

31 Markets in Fashion A phenomenological approach Patrik Aspers

38 Universities, Innovation and the Economy Helen Lawton Smith

32 Working in the Service Sector A tale from different worlds Edited by Gerhard Bosch and Steffen Lehndorff

39 Developments in the Call Centre Industry Analysis, policy and challenges Edited by John Burgess and Julia Connell

33 Strategic and Organizational Change From production to retailing in UK brewing 1950–1990 Alistair Mutch

40 Government Managing Risk Income contingent loans for social and economics progress Bruce Chapman

34 Transportation Economics Towards better performance systems Edited by Bart Jourquin, Piet Rietveld and Kerstin Westin 35 Knowledge Flows in European Industry Edited by Yannis Caloghirou, Anastasia Constantelou and Nicholas S. Vonortas 36 Change in the Construction Industry An account of the UK construction Industry Reform Movement 1993–2003 David M. Adamson and Tony Pollington

41 Formula Funding of Public Services Peter C. Smith 42 Location Behaviour and Relationship Stability in International Business Networks Evidence from the automotive industry Bart Kamp 43 Privatization and Financial Collapse in the Nuclear Industry The origins and causes of the British energy crisis of 2002 Simon Taylor 44 Decisions: Risk and Reward Edited by Johnnie Johnson and Alistair Bruce

Decisions: Risk and Reward

Edited by Johnnie Johnson and Alistair Bruce

First published 2008 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Ave, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group, an informa business

This edition published in the Taylor & Francis e-Library, 2008. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2008 Selection and editorial matter, Johnnie Johnson and Alistair Bruce; individual chapters, the contributors All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-93281-1 Master e-book ISBN

ISBN10: 0-415-42628-6 (hbk) ISBN10: 0-203-93281-1 (ebk) ISBN13: 978-0-415-42628-2 (hbk) ISBN13: 978-0-203-93281-0 (ebk)

Contents

List of illustrations Notes on contributors Preface Acknowledgements

x xiii xiv xxi

PART I

Motivation for betting and risk taking

1

1

5

Towards an explanation of betting as a leisure pursuit A.C. BRUCE AND J.E.V. JOHNSON

2

Costing excitement in leisure betting

25

A.C. BRUCE AND J.E.V. JOHNSON

3

Successful betting strategies: evidence from the UK off-course betting market

42

J.E.V. JOHNSON AND A.C. BRUCE

PART II

The impact of complexity on decision-making behaviour

59

4

63

The complex decision: insights from naturalistic research A.C. BRUCE AND J.E.V. JOHNSON

5

An empirical study of the impact of complexity on participation in horse-race betting

74

J.E.V. JOHNSON AND A.C. BRUCE

6

A probit model for estimating the effect of complexity on risk taking J.E.V. JOHNSON AND A.C. BRUCE

86

viii

Contents

7 Risk strategy under task complexity: a multivariate analysis of behaviour in a naturalistic setting

96

J.E.V. JOHNSON AND A.C. BRUCE

8 Decision-making under risk: effect of complexity on performance

117

A.C. BRUCE AND J.E.V. JOHNSON

PART III

Gender differences in decision-making behaviour

127

9 Gender and DSS design: the research implications

131

P.L. POWELL AND J.E.V. JOHNSON

10 Male and female betting behaviour – new perspectives

172

A.C. BRUCE AND J.E.V. JOHNSON

11 Gender-based differences in leisure behaviour: performance, risk taking and confidence in off-course betting

184

A.C. BRUCE AND J.E.V. JOHNSON

12 Decision-making, risk and gender: are managers different?

198

J.E.V. JOHNSON AND P.L. POWELL

PART IV

The use of information by decision-makers and deviations from rational economic behaviour

221

13 A violation of dominance and the consumption value of gambling

229

J.E.V. JOHNSON, R. O’BRIEN AND H.S. SHIN

14 Exploring decision-makers’ use of price information in a speculative market

250

J.E.V. JOHNSON, O. JONES AND L. TANG

15 Gluck’s Second Law: an empirical investigation of horse-race betting in early and late races

269

J.E.V. JOHNSON AND A.C. BRUCE

16 Investigating the roots of the favourite–longshot bias: an analysis of decision-making by supply- and demand-side agents in parallel betting markets A.C. BRUCE AND J.E.V. JOHNSON

277

Contents 17 Market efficiency analysis requires a sensitivity to market characteristics: some observations on a recent study of betting market efficiency

ix

300

A.C. BRUCE AND J.E.V. JOHNSON

18 Efficiency characteristics of a market for state-contingent claims

305

A.C. BRUCE AND J.E.V. JOHNSON

19 Market ecology and decision behaviour in state-contingent claims markets

311

A.C. BRUCE AND J.E.V. JOHNSON

20 Calibration of subjective probability judgements in a naturalistic setting

333

J.E.V. JOHNSON AND A.C. BRUCE

Index

359

Illustrations

Figures 2.1 7.1 7.2 7.3 7.4 13.1 13.2 13.3 13.4 13.5 14.1 14.2 14.3 14.4 14.5 14.6 14.7 16.1 16.2 19.1 19.2 19.3 20.1

Significant events in a typical betting office day Dependence of mean LODS on HCP and WEW Dependence of mean LODS on HCP and RUN Dependence of mean LREL on HCP and WEW Dependence of mean LREL on HCP and RUN Percentage of bets with tax paid on wager Probability of paying tax on the wager for a given outlay Slope of ψ when t = 0.1 and p/π =1 Consumption value of gambling. Consumption value of gambling as p/π varies Orthogonal polynominal decomposition of a price curve Late-change predictor Natural logarithm of cumulative wealth using the Kelly strategy Histogram of log error Analysis of bets on winning horses Profit obtained from winning horses Influences of predictor variables for winning horses Predicted win probabilities (post-normalization) Predicted win probabilities (prior to normalization) Favourite–longshot bias in Tote versus bookmaker markers (all races) Favourite–longshot bias in Tote versus bookmaker markets (Class A–C races) Favourite–longshot bias in Tote versus bookmaker markets (non-handicap, Class D–H) Comparison of objective probabilities with bettors’ subjective judgements

29 105 105 106 107 240 243 245 246 247 253 256 260 263 264 265 266 288 290 327 327 328 347

Tables 1.1

Off-course bookmakers’ turnover on horserace betting

6

Illustrations xi 1.2 1.3 1.4 1.5 1.6 2.1a

Motivationally-distinct subsets 15 Measures of financial return to motivational subsets S1–S4 18 Average stake in each motivational subset 19 Stakes on profitable and unprofitable bets by motivational subset 19 Measures of risk taking across motivational subsets 21 Performance of bets placed in the pre-racing versus active racing periods (definition 1) 32 2.1b Performance of bets placed in the pre-racing versus active racing periods (definition 2) 33 2.2 Performance and staking: ‘cold’ pre-racing versus ‘hot’ active racing periods 35 2.3 Performance of bets placed in the first half of the show period versus second half of the show period 36 2.4 Average staking levels in different time periods 37 3.1 Indicators of bet performance in different time periods 48 3.2 Indicators of bet performance in different time periods, disaggregated by BP and SP 53 3.3 Return/stake 54 3.4 Average stake 55 5.1 Participation in decision-making according to complexity, defined in terms of alternatives (numbers of runners) 79 5.2 Participation in decision-making according to complexity, defined in terms of alternatives (handicap/non-handicap status) 80 6.1 Results of probit estimation 91 6.2 Tests of goodness of fit of probit estimation 92 7.1 Observed data 100 7.2 ANOVA for dependent variables LODS, LREL, and LSTAK (parsimonious models) 104 8.1 Comparative performance on races of different complexity, defined in terms of number of runners 121 8.2 Comparative performance on races of different complexity, defined in terms of handicap/‘non-handicap’ status 123 9.1 Appendix: Summary of literature 153–65 10.1 Comparison of male and female bet performance 176 10.2 Comparison of bet type preferences of males and females 177 10.3 Comparison of male and female propensity to select ‘straight’ or ‘reverse forecasts’, ‘doubles’ or ‘trebles +’, and ‘win’ or ‘each-way’ 177 10.4 Comparison of male and female staking levels 178 11.1 Comparative male and female performance on single bets 190 11.2 Comparative patterns of male and female betting on horses 191 11.3 Comparative patterns of male and female betting on horses 193 11.4 Comparative staking behaviour: males and females 194 12.1 Comparison of betting shop clientele with general population in the UK 208

xii 12.2 12.3 12.4 13.1 13.2 13.3 14.1 15.1 15.2 15.3 15.4 15.5 16.1 16.2 16.3 18.1 18.2 19.1 19.2 19.3 19.4 20.1

20.2

Illustrations Indicators of male/female decision quality (betting study) Indicators of male/female risk propensity (betting study) Indicators of risk propensity, decision quality and locus of control (managerial population) Tax paid on the wager or the return by size of outlay Results of probit estimation Consumption value of gambling as outlay and p/π varies Estimated coefficients of the model Mean odds of bets placed during the show period on races at different stages of the racing day Mean ‘odds of bets placed/number of runners’, during the show period, on races at different stages of the racing day Percentage of bets placed on favourites, during the show period, on races at different stages of the racing day Mean staking levels (£) of bets placed on races at different stages of the racing day Performance of bets placed, during the show period, on races at different stages of the betting day Comparison of mean Tote odds and mean bookmaker odds Results of logit estimations for model 1 and model 2 Predicted probabilities of success arising from bookmaker and Tote odds Truncated comparisons of pari-mutuel and bookmaker odds Categorized comparisons of pari-mutuel and bookmaker odds Pari-mutuel and bookmaker markets: ecological distinctions Results of conditional logit estimations and curve-fitting procedures for models 1 and 2 (all races) Results of conditional logit estimations and curve-fitting procedures for models 1 and 2 (Class A–C races) Results of conditional logit estimations and curve-fitting procedures for models 1 and 2 (non-handicap, Class D–H races) Comparison of bettors’ aggregate subjective probability judgements and horses’ observed (objective) probability of success Results of conditional logit estimation

209 210 215 239 241 247 257 272 273 273 273 274 282 287 289 307 308 318 324 325 326

344 346

Contributors

Owen Jones gained his PhD at the Statistical Laboratory, Cambridge, and now lectures in Mathematics and Statistics at the University of Melbourne. He undertakes research in the fields of statistics, stochastic processes and operational research. Raymond O’Brien is a senior lecturer in the Economics division of the School of Social Sciences. His interests are econometric theory, Bayesian econometrics, numerical analysis and econometric computing. Philip Powell is Deputy Dean of the School of Management at the University of Bath. He is also honorary professor of Operational Information Systems at the University of Groningen. He is the author of six books on information systems and financial modelling and his work has appeared in over 90 international journals. He has been Managing Editor of the Information Systems Journal for over a decade and is a past President of the UK Academy for IS. Hyun Song Shin is Professor of Economics at Princeton University, affiliated with the Department of Economics and the Bendheim Center for Finance. Before going to Princeton in 2006, he held positions at the London School of Economics, Oxford University and the University of Southampton. Professor Shin’s research has focused on financial economics, especially on financial crises, risk and asset pricing. Leilei Tang is a lecturer in Finance at the University of Strathclyde. Prior to joining the University of Strathclyde in 2006, he held academic appointments at the University of Southampton and at CASS Business School. His research interests and publications are primarily focused on financial econometrics and risk management.

Preface

Decision-making matters. Whether our decisions are made by luck, wit or wisdom, their consequences, the rewards and penalties which flow from them, can have a profound effect at a personal, organisational, national or global level. Ultimately, our decision-making, in particular our ability to make effective decisions in the face of risk and uncertainty, will determine the future of the human race. The aim of this book is to shed light on what motivates us to engage in risk taking, how we make decisions in the face of uncertainty and how we can improve our decision-making. The book comprises a set of chapters, derived from previously published papers, which explore decision-making behaviour in a risky environment. In particular, the work presented here addresses why individuals undertake risky activities such as betting, the impacts of complexity on both risk taking and performance, to what extent gender impacts decision-making behaviour, what use individuals make of information in their decisions and to what extent these decisions deviate from rational economic behaviour. Much of the existing literature in this area has been derived from research conducted on naive subjects under laboratory conditions. A central argument underlying the motivation to develop the chapters presented in this book is that this experimental research fails to reproduce the conditions faced by experienced decision-makers in their normal risky environments. Consequently, the results of these earlier studies may not be applicable to real-world contexts. This book seeks to address these concerns by exploring the behaviour of individuals with relevant knowledge or experience of tasks in a naturalistic setting. In particular, the decision-making behaviour of horserace bettors is analysed. Consequently, the central aim of the research presented here is to develop a better understanding of the behaviour of individuals engaged in horserace betting, and as a result, to provide a window on how individuals might be expected to behave in wider decision-making environments. One of the more evident economic and social phenomena of the past two decades in the UK has been the remarkable growth in gambling as a pastime. This growth in the appetite for gambling has brought a vigorous response from suppliers, in terms of the volume and scope of gambling opportunities on offer. The range of events on which bets can be placed has diversified from its

Preface xv traditional focus on horse and greyhound racing to embrace the full breadth of sporting activity, financial markets and the outcomes of reality TV shows. Gamblers are now routinely able to access new forms of betting market, such as spread betting, simulated events and new betting interfaces such as betting exchanges and Internet gambling. The growth of gambling embraces wider forms of gaming beyond betting. There is an evident market for participation in lotteries and a growing interest in gaming, with vigorous growth in Internet and casino-based activity. Gambling has moved at a remarkable rate from being an activity relatively close to the social margins to a mass participation mainstream leisure activity. Unsurprisingly, as well as provoking a vigorous response from the gambling industry, this sustained surge in interest has engaged the attention of policymakers and regulators. The more liberal attitudes to gambling which have, in part, been responsible for its growth are balanced by concerns associated with the proliferation of gambling and the negative economic and social consequences which can follow from it. The chapters presented here focus on a particular form of gambling, horserace betting, which has, over the last two decades, shared in the general boom. Whilst not as overwhelmingly dominant as it once was, horse-race betting remains easily the biggest single sector of the UK betting market as a whole. As such, it offers both an invaluable window on the world of betting and gambling more generally and an insight into risk and decision-making behaviour in wider market contexts. As gambling has increased in significance as a social and economic phenomenon, so has its investigation across a range of disciplines. The theoretical and empirical analysis of multiple aspects of betting behaviour has proliferated in the economics, finance, decision-making, psychology and sociology literatures. There is a greater acceptance of and interest in gambling behaviour as a legitimate medium for enquiry which can illuminate wider human behaviour and increasing evidence of multidisciplinarity in gambling research. As such, the publication of this collection is timely. It offers an insight into the rich variety of questions and issues associated with decision-making in a risky environment which betting research can illuminate and the range of methods and techniques which can be applied to data drawn from betting markets.

Laboratory v. naturalistic research The impetus for the research presented here lies in the apparent contradiction between the large volume of literature (largely derived from laboratory research) which suggests that human reasoning is badly flawed and the results of studies which demonstrate the notable ability of experienced individuals to solve complex problems associated with their familiar decision-making environments. It is argued here, with corroborating research evidence, that the disparity between these findings may have arisen because decision-making behaviour differs significantly between: (1) laboratory and naturalistic settings and (2) subjects who have relevant knowledge and experience of a task and those who are

xvi

Preface

relatively naive in the context presented. Laboratory investigations have largely failed to reproduce the conditions faced by decision-makers in their normal risky environments. Such conditions might include an informationally turbulent setting, varying time constraints and multi-event, multi-decision contexts. Under these naturalistic conditions, prior outcomes may influence subsequent decisions, the decision-maker often has multiple, ill-defined or competing goals and the outcome generally has real welfare implications for the decision-maker. Laboratory studies have by contrast often involved naive subjects, performing artificial tasks which lack meaningful consequences. As Yates (1992) observes, ‘there is reason to suspect that the actual risk-taking behaviour observed in comfortable, low-stakes, laboratory settings differs in kind, not just in degree from that which occurs in often stressful, high stakes, real-world contexts . . .’. In addition, there is increasing evidence that greater familiarity with a task results in the employment of different means of selecting and coding information, interpreting ambiguous cues, assessing options and reaching decisions. It is argued, therefore, that in order to better understand decision-making behaviour in everyday, complex, risky environments, an approach is required which incorporates an examination of individuals within their familiar, naturalistic decision-making environments. Despite the criticisms indicated above, a clear advantage of laboratory investigation is that it offers the prospect of effectively controlling for potentially distorting phenomena present in real-world situations. To a large extent, therefore, laboratory and naturalistic studies may be regarded as complementary. Indeed, Baars (1990) notes that ‘without naturalistic facts, experimental work may become narrow and blind: but without experimental research, the naturalistic approach runs the danger of being shallow and uncertain’. Consequently, the research method employed in the chapters presented here is one in which hypotheses are derived largely from the findings of previous laboratory studies and these hypotheses are then tested in a naturalistic setting. The analysis of decisions made by bettors represents a valuable contribution to the decision-making literature and provides a number of important methodological advantages: 1

2

3

4

A comprehensive documentary record of a large number of real betting decisions can be obtained, in the absence of researchers, thereby avoiding observation effects. Additional complementary information is readily available, such as precisely timed transcripts of the evolving betting market, which enable an accurate picture of the decision-making environment to be developed. The decisions which are analysed are made by individuals who have chosen to engage in betting activity, the majority of whom possess some degree of experience and knowledge associated with the betting task. Data available from betting markets provide the opportunity for developing quantifiable measures of impact, associated with various factors (e.g. complexity, gender, etc.), on the nature of the decision.

Preface xvii 5

Decisions made in betting markets share many features in common with decisions made in other uncertain decision environments: • •

•

•

They are made within a complex, multi-event, multi-cue, informationally-turbulent setting, described above. Each decision is essentially a speculative venture, involving financial commitment and an implicit judgement on the future states of the world. The accuracy of these judgements determines the future reward and the outcome of the decision has real rather than notional welfare implications. The decisions involve the following features: the assessment of risk, the analysis of quantitative and qualitative information from a variety of sources (including the interpretation of evolving information sets), the consideration of precedent, formulation of expectation, use of ‘gut feelings’ and expert opinion, the selection of decision strategies (including risk hedging strategies) and the ability to seek multiple goals within a stimulating decision environment.

In addition, behaviour in betting markets may provide insights into behaviour in other financial markets since they share many features in common, such as a large number of participants, extensive market knowledge, ease of entry and a considerable element of skill which is required to achieve profitable trading. In summary, it is argued that the research method employed provides the opportunity for developing a clearer understanding of the decision-making behaviour of bettors and, in addition, offers an insight into decision-making under uncertainty in broader contexts.

Structure of the book The remainder of this book consists of 20 chapters, arranged in four parts. Each part explores a different aspect of decision-making behaviour and a common finding is that the behaviour of individuals in their naturalistic environment differs from the reported behaviour of naive subjects involved in laboratory investigations. The extent to which different motivations for risk taking in general and betting in particular can be discerned from bettors’ behaviour is discussed in Part I and the betting characteristics of those primarily pursuing excitement and financial gain are explored in some detail. These issues are considered in Part I since motivation is of primary importance in helping to explain individuals’ subsequent decision-making behaviour. Once they have decided for whatever reason to engage in risk taking, the degree of environmental complexity to which decision-makers choose to expose themselves is an important element of their decision strategy. Part II analyses the impact which different types and degrees of task complexity have on decision-making behaviour. The research

xviii Preface method employed in Parts I and II necessarily prevented most individual characteristics of the decision-makers from being discerned. Part III comprises chapters which seek to focus on one potentially important characteristic of decision-makers which can be discerned without compromising the research method – their gender. Consequently, gender differences amongst horserace bettors in terms of performance, risk-taking and confidence are explored. The empirical research discussed in the first three parts suggests that bettors do not always behave in a manner consistent with rational economic objectives. The chapters in Part IV explicitly identify and examine examples of non-rational economic behaviour, and the incidence of such behaviour is used to relate these results to the motivation for betting, by explicitly assessing the consumption value of gambling. In addition, the chapters presented in the final part more broadly examine to what extent individuals effectively use information to help improve the quality of their decisions.

Conclusions In terms of the four related themes addressed in the book the following conclusions emerge: 1

2

3

The chapters in Part I suggest that there are a number of motivations underlying horserace betting and the betting population appears to consist of subsets of bettors pursuing different objectives. Individuals in these subsets are discernable from the timing of their betting activity and the price-taking strategy they employ. Significant differences exist between the betting behaviour of these subsets, including their risk-taking strategies, the information they employ to make their decisions, the manner in which they react to the excitement generated by the betting activity and the financial rewards which they reap. It is clear from Part II that different types and degrees of complexity induce different behavioural responses from bettors. Contrary to previous laboratory findings, alternative-based complexity does not appear to trouble decision-makers in betting markets as much as attribute-based complexity – both performance and participation increase as alternative-based complexity increases, whereas bettors avoid attribute-based complex conditions (even though little difference in performance can be discovered between low and high attribute-complex situations). The two forms of complexity exert an interactive effect on the risk strategy employed by bettors but the complexity/risk strategy relationship is influenced by the risk measure employed and the availability of risk hedging mechanisms. The relationship between gender and decision quality, risk propensity and confidence is not as straightforward as previous research suggests. The relative decision performance of males and females appears to depend on the performance criteria employed and there appear to be gender differences in the definition and perception of what constitutes risk. Established views,

Preface xix

4

that males demonstrate greater confidence in their decisions, are not supported in the research presented in Part III, although the results suggest that some caution should be exercised in directly translating gender differences in betting behaviour to gender differences in decision-making behaviour in organisational contexts. The chapters in Part IV demonstrate that bettors, under certain circumstances, deviate from rational economic behaviour. Whilst this might be expected from individuals pursuing a variety of non-economic objectives, it is observed that some bettors will even pursue strategies that violate dominance, a rarely observed phenomenon. Suppliers of betting products are shown to exploit this non-rational economic behaviour amongst bettors to their financial advantage. However, the chapters demonstrate that the well documented favourite–longshot bias, which has often been attributed to the biased behaviour of bettors, may, at least in the UK, have its origins in the behaviour of bookmakers. Despite this, the chapters provide evidence that often bettors do not discount all useful information in the final odds. It is clear that individuals are able to handle transparent information when making decisions, but they often fail to employ more opaque information; individuals fail to make even simple transformations of data in certain situations, despite the fact that these can significantly improve their decision performance. A clear theme to emerge from the chapters in this part is that the environment in which decisions are made has an important influence on the manner and degree to which information is used, which in turn influences the accuracy of judgements. Certain environmental conditions appear to enable decision-makers to focus on the decision task and as a result they can make remarkably accurate judgements, yet only limited changes to these environments can cause a significant reduction in accuracy and decision performance.

The conclusions which are drawn relate specifically to the behaviour of horserace bettors, but, as argued in several of the chapters presented here, these results may also be seen as providing a window on decision-making behaviour in wider environments. The research method, which concentrates on observing behaviour in a naturalistic environment, to some extent, lacks environmental control. However, this is a common feature of naturalistic studies and it is argued that the advantages of the research method significantly outweigh its disadvantages. Opportunities clearly exist for development of the research method employed here, to combine data on an individual’s betting decisions with information drawn from post-betting interviews, on their economic and social circumstances and their declared motivational drives. These data would permit a further refinement of the conclusions drawn from the chapters presented here. In addition, there exist opportunities for further naturalistic research, employing a similar research strategy to that advocated here, in other betting environments, and in broader decision-making contexts, such as financial markets. Comparing the results from these studies with those reported here

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would offer important clues to the degree to which the conclusions may be generalised. In the absence of such studies the extent to which the results reported here offer a window on how individuals might be expected to behave in wider decision-making environments remains a matter of opinion. This seems fitting, since as Mark Twain observes in Puddin’ Head Wilson’s calendar (2001): ‘It were not best that we should all think alike; it is a difference of opinion that makes horseraces’.

References Baars, B.J. (1990) Eliciting predictable speech errors in the laboratory. In Fromkin, V. (ed.) Errors in Linguistic Performance: Slips of the Tongue, Ear, Pen and Hand, Academic Press: New York. Twain, M. (2001) The Tragedy of Puddin’Head Wilson, Quiet Vision Publishers: Sandy, UT. Yates, J.F. (ed.) (1992) Risk Taking Behaviour, John Wiley: Chichester.

Acknowledgements

Chapter 1: ‘Toward an explanation of betting as a leisure pursuit’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Leisure Studies, 11(3), 1992, pp. 201–18 and is reprinted with kind permission of Routledge. Chapter 2: ‘Costing excitement in leisure betting’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Leisure Studies, 14, 1995, pp. 48–63 and is reprinted with kind permission of Routledge. Chapter 3: ‘Successful betting strategies: Evidence from the UK off-course betting market’, by J.E.V. Johnson and A.C. Bruce. This paper first appeared in Eadington, W.R. & Cornelius, J.A., eds: Gambling and Commercial Gaming: Essays in Business, Economics, Philosophy and Science, Reno, Institute for the Study of Gambling and Commercial Gaming, 1992, pp. 635–56 and is reprinted with kind permission of The Institute for the Study of Gambling and Commercial Gaming, Reno. Chapter 4: ‘The complex decision: insights from naturalistic research’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in The International Journal of Project and Business Risk Management, 1, 1998, 403–15. Chapter 5: ‘An empirical study of the impact of complexity on participation in horserace betting’, by J.E.V. Johnson and A.C. Bruce. This paper first appeared in Journal of Gambling Studies, 13(2), 1997, 159–72 and is reprinted with kind permission of Springer Netherlands. Chapter 6: ‘A probit model for estimating the effect of complexity on risk taking’, by J.E.V. Johnson and A.C. Bruce. This paper first appeared in Psychological Reports, 80, 1997, 763–72 and is reprinted with kind permission of Ammons Scientific Ltd. Chapter 7: ‘Risk strategy under task complexity: A multivariate analysis of behaviour in a naturalistic setting’, by J.E.V. Johnson and A.C. Bruce. This paper first appeared in The Journal of Behavioral Decision Making, 11, 1998, 1–18 and is reprinted with kind permission of John Wiley & Sons.

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Acknowledgements

Chapter 8: ‘Decision making under risk: effect of complexity on performance’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Psychological Reports, 79, 1996, 67–76 and is reprinted with kind permission of Ammons Scientific Ltd. Chapter 9: ‘Gender and DSS design: the research implications’, by P.L. Powell and J.E.V Johnson. This paper first appeared in Decision Support Systems, 14, 1995, 27–58 and is reprinted with kind permission of Elsevier Science. Chapter 10: ‘Male and female betting behaviour – new perspectives’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Journal of Gambling Studies, 10(2), 1994, 183–98 and is reprinted with kind permission of Springer Netherlands. Chapter 11: ‘Gender-based differences in leisure behaviour: performance, risktaking and confidence in off-course betting’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Leisure Studies, 15, 1996, 65–78 and is reprinted with kind permission of Routledge. Chapter 12: ‘Decision-making, risk and gender: are managers different?’, by J.E.V Johnson and P.L. Powell. This paper first appeared in British Journal of Management, 5(2), 1994, 123–38 and is reprinted with kind permission of Blackwell. Chapter 13: ‘A violation of dominance and the consumption value of gambling’, by J.E.V Johnson, R. O’Brien and H.S. Shin. This paper first appeared in Journal of Behavioral Decision-Making, 12, 1999, 19–36 and is reprinted with kind permission of John Wiley & Sons. Chapter 14: ‘Exploring decision makers’ use of price information in a speculative market’, by J.E.V Johnson, O. Jones and L. Tang. This paper first appeared in Management Science, 52, 2006, 897–908 and is reprinted with kind permission of INFORMS. Chapter 15: ‘Gluck’s Second Law: an empirical investigation of horserace betting in early and late races’, by J.E.V. Johnson and A.C. Bruce. This paper first appeared in Psychological Reports, 72, 1993, 1251–8 and is reprinted with kind permission of Ammons Scientific Ltd. Chapter 16: ‘Investigating the roots of the favourite–longshot bias: An analysis of decision-making by supply and demand-side agents in parallel betting markets’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Journal of Behavioural Decision Making, 13, 2000, 413–30 and is reprinted with kind permission of John Wiley & Sons.

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Chapter 17: ‘Market efficiency analysis requires a sensitivity to market characteristics: some observations on a recent study of betting market efficiency’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Applied Economics Letters, 7, 2000, 199–202 and is reprinted with kind permission of Routledge. Chapter 18: ‘Efficiency characteristics of a market for state contingent claims’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Applied Economics, 33, 2001, 1751–4 and is reprinted with kind permission of Routledge. Chapter 19: ‘Market ecology and decision behaviour in state-contingent claims markets’, by A.C. Bruce and J.E.V. Johnson. This paper first appeared in Journal of Economic Behavior and Organization, 56, 2003, pp. 199–217 and is reprinted with kind permission of Elsevier Science. Chapter 20: ‘Calibration of subjective probability judgements in a naturalistic setting’, by J.E.V. Johnson and A.C. Bruce. This paper first appeared in Organizational Behavior and Human Decision Processes, 85, 2001, 265–90 and is reprinted with kind permission of Elsevier Science.

Part I

Motivation for betting and risk taking Introduction An understanding of the decision to engage in risk-taking activity such as betting is central to helping to explain subsequent decision-making behaviour. To this end the chapters in this part attempt to disentangle the decision-making characteristics of those with motives such as financial gain, excitement, peer esteem and intellectual challenge. The damaging impact of excitement on decision-making in a risky environment is also highlighted and illustrated. This part of the book represents one of the few attempts to assess the impacts of motivation for risk taking on decision-making behaviour in naturalistic environments. In particular, the chapters in this part consider issues associated with the motivations underlying horse-race betting by exploring, empirically, whether subsets of the aggregate betting population are associated with particular motivational factors. The distinctive betting behaviour of these subsets of bettors is also addressed. This part also explores the extent to which the motivations of financial gain, intellectual challenge, social interaction and excitement can be discerned from the behaviour of bettors. The betting characteristics of those motivated by excitement and financial gain are discussed in depth. Chapter 1 examines the proposition that the motivation to bet varies between individuals. The chapter introduces and explores the concept of the off-course betting office as a population characterised at different times by different densities of bettors with varying motivations. Classifying subgroups of bettors by the time they place their bet is a novel approach to the discernment of betting motivation. A rationale is presented for expecting individuals’ betting motivations to be reflected in the nature and timing of their betting activity. A large sample of decisions made in off-course betting offices is analysed to test for differences in betting behaviour between these subgroups. An important contribution of the chapter lies in its identification of clear differences in the financial performance, staking and risk taking associated with subsets of bettors. These subsets are clearly defined by time-specific and bet-related variables. It is argued that these differences in behaviour offer strong support for the possibility of drawing clear motivational distinctions between time-defined subsets of the betting population.

The results provide an important step towards a better understanding of betting behaviour and in particular they offer support for the existence of four specific betting motivations. They represent an advance on previous laboratory-based research or questionnaire/interview surveys since they utilise the actual betting decisions of a large, geographically dispersed sample of bettors made in the naturalistic environment of the betting shop, where subjects were unaware that their behaviour was being monitored. Chapter 1 indicates that excitement represents an important motivation for betting and this theme is explored further in Chapter 2. In particular, this chapter explores the effects which excitement has on the nature of betting decisions and the financial penalties which can attend excitement. A literature survey reveals that, whilst a number of studies have identified excitement as an important motivational drive in explaining betting behaviour, few attempts have been made to measure the specific impacts which excitement has on betting behaviour in a naturalistic environment. Chapter 2 addresses this neglected area. The notion of distinct time periods in the off-course betting office is introduced where factors which could be expected to generate excitement are most prevalent. The coincidence of these time intervals with periods of maximum information availability is also noted. A large sample of betting decisions made in off-course betting offices throughout the UK was divided into a number of time-defined periods, representing periods offering relatively great or little scope for excitement. An important finding of the chapter was that despite informational advantages associated with the periods of maximum excitement potential, the consumption of excitement involves a substantial financial penalty and significantly higher staking levels. This issue is further explored in Chapter 6. The results are found to be robust, since controls were applied to discount the possibility that the results were attributable to the effects of information complexity or other non-motivational influences such as alcohol consumption. The chapter clearly confirms the importance of excitement as an influence on betting behaviour and makes an important contribution in attempting to cost the ‘consumption’ of excitement. Arguments are presented which suggest that these findings could provide an insight into the impact of excitement in wider decision-making contexts. Chapter 3 explores financial gain as a potential motivational force for betting activity; in particular, it examines the extent to which enhanced financial performance can be achieved by subsets of bettors. A large sample of betting decisions made in off-course betting offices was separated into time-defined subsets, associated particularly with differential exposure to market information. Significant differences in financial performance of bets placed in these time periods is explained in terms of information complexity, environmental stimuli which increase excitement and completeness of the information set required to make effective betting decisions. A particular subset of bets, which is demonstrated to be associated with significantly superior financial performance, is argued to be associated with qualitative and quantitative informational advantages. It is argued that there are a priori grounds for believing that individuals

whose bets are associated with this subset (bets placed late in the market) are most likely to be those who are primarily motivated by financial return. The research presented in Chapter 3 also represents an important contribution to the market efficiency literature. Previous literature has focused on identifying profitable opportunities for bettors. However, the research outlined in this chapter identifies opportunities for financial gain and quantifies the extent to which they are exploited in a naturalistic betting environment. This chapter is the first to examine the financial gains actually achieved by subsets of bettors in non-pari-mutuel betting markets. The results also provide a valuable insight into the response of betting behaviour to market-generated information. The chapter integrates economic and psychological perspectives on the use of information – issues which to date have largely been explored in isolation; as such the chapter provides rich insights into betting behaviour, in particular the potential for achieving financial gain through this activity. In summary, the chapters in Part I contribute a novel means of identifying relative densities of bettors in off-course betting offices with particular motivations and an insight into the betting behaviour of those primarily motivated by: financial gain, excitement, intellectual challenge and social interaction. Few attempts have been made to assess the impact of motivations for betting on behaviour in naturalistic environments. Consequently, the clear differences in financial performance, staking and risk taking observed in the studies reported here, which were conducted in a non-laboratory setting, represent a valuable contribution towards a better understanding of betting behaviour. In addition, the chapters focusing on the performance of those motivated by financial gain make an important contribution to the market efficiency literature. The work reported in this part quantifies the extent to which opportunities afforded by qualitative and quantitative informational advantages are exploited by bettors in real-world settings to achieve significantly superior financial performance.

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Towards an explanation of betting as a leisure pursuit A.C. Bruce and J.E.V. Johnson

This chapter uses an analysis of betting decisions to explore the motivations underlying off-course horse-race betting – a leisure activity which accounted for a turnover of £4.3 billion in the UK in 1989–90. Specifically, four possible motivations are considered: financial gain, intellectual challenge, social interaction and excitement. A testable proposition is developed, linking each motivation to a particular time period in which the bet is placed and as to whether the bet is placed at starting price. Hence, four distinct subsets of the aggregate betting population are defined. The proposition is tested by examining betting behaviour in each subset according to three bet characteristics–financial return, average stake and degree of risk taken, where the value of each characteristic is held to be indicative of an underlying motivation. The results indicate significant support for the proposition that individuals vary in their motivation to bet which is reflected in the nature and timing of their betting activity.

Introduction The objective of this chapter is to explore the pattern of motivations underlying horse-race betting as a leisure activity in the UK via the analysis of a large sample of real betting decisions in betting offices throughout the country. Following this brief introduction, the chapter proceeds in five sections. The first explores the various motivations associated with betting and reviews the literature in this area; the second describes the characteristics of the database from which the subsequent results are derived, stressing its incorporation of real betting decisions from throughout the UK and its ability to locate precisely the time at which bets were placed and the exact time profile of evolving betting markets. This leads to a discussion of the degree to which betting associated with particular motivations is likely to be time-specific in nature. In addition, the motivational aspects of the board price/starting price decision are discussed. Punters may elect to have their bet, on a particular horse, settled at the odds prevailing in the market when the bet is struck (board price). If they do not elect to do this, the bet is settled at starting price, the official, independently estimated average odds prevailing in the betting market at the start of the race. It is argued that the taking of board price or the acceptance of starting price is indicative of particular betting

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motivations. The material on betting motivation is formalized by developing the proposition that there exist distinct subsets of the betting population, each characterized by a different dominant motivation and defined in terms of timing of bet placement and, in one case, position on the board price/starting price decision. This proposition is tested, using analysis of bet-specific variables which are indicative of the underlying motivation to bet. The results appear to offer an encouraging degree of support for the proposition in general and strong support for particular features of motivational subset distinctions. Lastly the approach adopted and the contribution of the chapter are summarized. The examination and analysis of betting, and in particular horse-race betting, as a legitimate area of interest within the leisure studies domain springs from its significance as a leisure activity in the UK. The 1991 Mintel Gambling Report gives the total UK turnover on all betting and gaming in 1989–90 as a little over £9.8 billion, of which just over £6.5 billion (66 per cent) was accounted for by on- and off-course bookmaking turnover. The Racing Industry Statistical Bureau reports off-course turnover on horse-race betting alone in 1989–90 as £4.3 billion, this figure forming approximately 80 per cent of total off-course turnover. In financial terms then off-course horse-race betting clearly constitutes a major industry. In terms of participation levels, it has been suggested (Filby and Harvey, 1988) that the number of regular betting shop punters in Britain may be close to five million. MAS Omnibus, in a report prepared for Ladbroke Racing in 1990, found that this level increases markedly for particular events. For example, about eight million people (19 per cent of the adult population) placed bets on the 1990 Grand National, a figure which rose to around 11 million (26 per cent of the adult population) when account was taken of the fact that some bets were placed, in part, on behalf of others. As regards the recent development of the popularity of horse-race betting in off-course bookmakers, Table 1.1 illustrates nominal and real (1990 prices) turnover figures since 1984–5. These figures illustrate the continued popularity of the activity, with increasing real turnover throughout the period, apart from a slight downturn in 1989–90, a financial year characterized by very high interest rate levels and the end of the vigorous consumer boom of the late 1980s.

Betting motivation There is a considerable and diverse literature relating to individual betting motivations. This embraces several branches of the social sciences; notably psychology, Table 1.1 Off-course bookmakers’ turnover on horse-race betting (£ millions to nearest million)

Nominal 1990 prices

84/5

85/6

86/7

87/8

88/9

89/90

2,746 3,566

2,965 3,633

3,242 3,851

3,550 4,057

4,172 4,496

4,301 4,301

Source: The Racing Industry Statistical Bureau Statistics, 1986–1990, Weatherbys.

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sociology and economics. Similarly, there are a number of surveys of the literature on betting motivation. For the purposes of this study, we focus on four aspects of the motivation to bet: betting for financial return, betting as an intellectual challenge, betting to experience excitement and betting as a medium for social interaction. This set of motivations does not claim to be exhaustive; at the same time it recognizes that much betting activity by individuals is likely to be accounted for by a blend of motivational impulses. As Furnham (1985) notes ‘the types of motivation for, satisfaction derived from, attitudes to and habits of gambling are interrelated and multidimensional’ (p. 501). In the interests of clarity, however, the motivations are considered separately in this section. Financial gain An essential feature of placing a bet is the commitment of current funds in the hope of collecting a financial return in the future. A major survey reported by Cornish (1978) found that 70 per cent of those who gambled gave financial gain as their primary motive. As such, it seems reasonable to suggest that the prospect of financial gain will form part of the motivation to bet. At the same time, there is evidence from large samples of actual betting decisions (Filby and Harvey, 1988) to suggest that successful bets (bets generating a positive return) form only about 25 per cent of all bets placed. This clearly presents problems for economic approaches which seek to explain betting as an activity pursued by rational agents in the pursuit of financial gain. In reality, of course, those whose betting is predominantly motivated by the prospect of financial gain may be prone to developing optimistic subjective perceptions of their betting performance so that the financial gain motivation, justified or not, may be intact. Alternatively, Downes et al. (1976) observe that ‘few gamblers realistically suppose that gambling will truly be for them a short-cut to wealth, though it is a convenient pretext for fantasy along these lines’ (p. 24). For certain types of bettor, such as the so-called professional gamblers who bet according to strict disciplines and systematic rules, positive financial returns in the long term may genuinely be a more realistic proposition. Intellectual challenge A second aspect of the motivation to bet may relate to the notion of betting as an intellectual challenge, where a horse race represents a soluble problem of considerable and diverse complexity. As Downes et al. (1976) state: ‘Gambling, like crossword puzzles and chess, . . . provides artificial, short-term, miniature, “capsule” problems – and their resolution – for those who enjoy them’ (p. 25). Downes et al. further suggest that those who lack decision-making in their work seek it in the form of gambling. An important element in this motivation is that a successful bet is regarded as the result of intellectual or analytical skill. Scott (1968) observed that ‘the

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regular (racegoer) comes to see himself as one who can rationally cope with the complexities of picking winners’ (p. 86). In addition, research into off-course horse-race betting in the UK by Downes et al. (1976) reported that 65 per cent of male bettors cited ‘skill’ as the sole basis for the selection made. Though this may be difficult to sustain in an area characterized by significant and complex uncertainty, so long as the illusion of having skillfully solved the puzzle exists, then the motivation may remain important. Langer (1983) introduced the idea of an ‘illusion of control’ which tends to reinforce individual involvement in areas which are perceived to demand skill and this would appear to support the ‘intellectual challenge’ motivation for gambling. The results of laboratory-based studies conducted by Letarte et al. (1986) suggest that such perception of control tends to increase in line with the frequency of successful decisions. Excitement Gilovich and Douglas (1986) note that ‘for many people, gambling offers excitement that is matched in few other areas of life’ (p. 239). In the case of horse racing, there are many aspects to this excitement. There is excitement associated with the build-up to a race, culminating in the rarefied and condensed drama of the race itself. The excitement experienced by bettors with an interest in the race is naturally heightened by the risk to which they have exposed their stakes and the anticipation of possible success. Downes et al. observe that ‘even if loss ensues, the pleasures of anticipating a win can be seen as worth the effort’ (1976, p. 25) and gambling involves a cycle of tension, accumulation and resolution. The respectable can experience the ‘safe deviance’ involved in acting out the counter mores of daring and risk-taking in a segregated setting, which renders its insecurities ‘less real’ than that of everyday life. Even the most casual empiricism suggests the significance of this type of motivational impulse to many betting office customers. It is reasonable to suggest that the recently increased sophistication of the UK betting office environment may serve to enhance this phenomenon, most notably, perhaps, via the live televised transmission of races. As Saunders and Turner (1987) note (p. 293): ‘Cable communications plus changes in legislation now provide the potential for visual monitoring of the odds that are automatically adjusted throughout the pre-race period – not to mention the added excitement of actually seeing the race being run’. The concepts of ‘sensation-seeking’ and ‘arousal’ form important elements of the psychological explanation of betting. Prominent in this area is the work of Anderson and Brown (1984), who characterize ‘sensation-seeking’ in terms of the regular bettor’s responses to various stimuli regularly present within the

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betting office prior to each horse race. Further, as Brown (1986) observes ‘. . . some form of arousal or excitement is a major, and possibly the major, reinforcer of gambling behaviour for regular gamblers . . .’ (p. 1001). Dickerson (1979, p. 322) has also pointed to this type of phenomenon as a distinct factor likely to detain the bettor in the betting office: ‘Excitement is not generated by cognition of cash won, but the very process of the gambling behaviour and environmental changes’. A further element of excitement associated with betting may be that which derives from pursuit of an activity which is still regarded in certain circles as on the margin of respectability or morality. Social interaction As a motivation for betting, any opportunity which it provides for social interaction is clearly not attributable to all betting behaviour. Betting may be a solitary activity. For many it is a personal and private pastime, where interaction with other bettors is actively avoided. For the purposes of this study, however, which is confined to betting which takes place within betting offices, it seems reasonable to suggest that the social dimension which betting offers may be a significant motivational factor. Downes et al. (1976) observed that the betting office is often used as a place to meet and socialize with others with similar interests and, from their research into the off-course betting shop, Filby and Harvey (1989) suggest that ‘there is also a good deal of “social” work involved . . . in establishing oneself as a member rather than simply as a client with the staff and other habitués’ (p. 226). A variety of forms of social satisfaction may be important. These might include the common pursuit of a shared enthusiasm and the scope this provides for discussion of the prospects and performance of racehorses, the opportunity for receipt and passing on of information. A further social payoff may be the shared enjoyment of a common success or the opportunity to share disappointment over a common betting loss. On an individual level, the successful bettor who makes known this success may expect to receive, for at least a short period, peer-group esteem associated with perceived ‘skill’. As Saunders and Turner (1987) note (p. 293): ‘They become virtual legends and stars’. Additionally, for those bettors who are less inherently interested in betting per se, the betting shop may be regarded as embodying some of the characteristics and social functions of pubs or clubs. In this respect, horserace betting may be similar to the playing of bingo. Dixey and Talbot (1982) observe that bingo provides players with a source of companionship–in fact they argue that ‘the bingo club provides a valuable social network’ (p. 165). In relation to most of these aspects of betting as social interaction, recent legislative modifications may tend to enhance this motivation for the betting office punter. In particular, the right of betting offices to sell refreshments, provide more extensive seating and offer televised race coverage may be important in this context.

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It is important to reiterate that this section has dealt with the various betting motivations identified as distinct and separate in the interests of expositional clarity. As noted above, it is understood that an individual’s betting activity is likely to be best explained by an equally individual blend of motivational factors. Later, the definition of subsets of the aggregate database in terms of time and price-taking behaviour suggests that there is some scope for isolation of motivationally distinct subgroups thereby supporting the appropriateness of the broad quantitative data approach used in this chapter. Nevertheless, it is acknowledged that a large-scale statistical analysis of betting activity cannot expect to offer a full, qualitative explanation of each individual bettor’s experience. Indeed, some of the problems inherent in this type of exercise are specifically addressed in this chapter. Whilst there is clearly scope for further corroborative work of a more qualitative and individual nature, it should equally be recognized that the database and procedures outlined in the following sections represent an unprecedented empirical insight into actual betting behaviour.

The database The principal source of information for the database used in this study is the betting slip, which provides the main characteristics relating to each bet placed in a betting office. Most importantly, this includes the selection made, the stake wagered, the type of bet (single, accumulator, forecast, etc.) and the exact time and location at which the bet was placed. The results reported below are based on approximately 1,200 bets, randomly selected from a larger sample of betting activity throughout the UK in March and April 1987. All bets included in the database are ‘singles’, the simplest form of bet, where the stake is placed on an individual horse and the ‘winnings’ are determined by the performance of that horse. Singles were chosen since they constitute the most common type of bet placed. In addition, the selection in a single bet relates to an individual race and consequently provides an unambiguous picture of the bettor’s motivation. Difficulties of interpreting the relative weight to attach to selections in a multiple bet, perhaps consisting of singles, doubles, trebles, forecasts, etc., were thus avoided, as were problems of comparing the relative risk inherent in multiple forecast or accumulator bets. An important feature of this database is that it comprises real betting decisions, selected randomly by betting office staff following close of business. This ensures that the data are collected without the knowledge of the bettor, thus avoiding possible ‘observation effects’. This feature, made possible through the collaboration of Ladbroke Racing plc, represents an improvement both over those studies which have involved observable researcher presence in the betting office (e.g. Dickerson, 1979) and those which have relied on data obtained from laboratory simulations of the betting environment. In relation to the latter type of study, Anderson and Brown (1984) note that ‘It appears that gambling behaviour . . . differs to a significant degree in the real and the laboratory situations’ (p. 407).

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For each betting slip decision recorded, a further set of relevant information was compiled. Most significantly, by using precisely timed transcripts of the betting information transmitted to betting offices by Extel, an accurate picture was assembled of the exact nature and extent of information available to the bettor at the time of the bet. The addition of the relevant results enabled the calculation of returns to each bet. Taken as a whole, the database offers a comprehensive documentary record of a large number of real betting decisions. This enables the testing of a range of hypotheses regarding bettor behaviour. For the purposes of this investigation into betting motivation, an important feature of the data is the detailed information relating to the timing of bets and of changes in the relevant betting markets which enables investigation as to whether betting activity in different time periods is induced by differing motivational impulses or, alternatively, whether certain motivations to bet are more time-sensitive than others. A further feature which is of particular value in the context of this study is the fact that each bet may be identified as having been placed either at starting price or at board price.

Motivation, the timing of bet placement and the price decision In the last section the four motivations which might be expected, individually or collectively, to contribute to the explanation of betting as an activity were discussed. Here the earlier discussion is extended by considering the degree to which the presence of particular motivations might be expected to influence two important aspects of the betting decision–the time at which bets are placed and whether the bet is placed at board price or starting price. This allows the development of insights into the manner in which bettors with different motivations bet and forms the basis for the framing of more specific testable hypotheses. Time Clearly, the time at which bets are placed may to some degree be constrained by individuals’ non-betting activities and commitments. Some individuals must, therefore, necessarily place their bets at particular times of the day. This is probably likely to be more significant during weekdays, when work commitments may be an important constraint. Bearing this reservation in mind, the principal proposition to be developed here is that of the four motivations identified, three–betting for excitement, betting for social interaction and betting for financial gain–are more likely to stimulate betting during particular periods. The intellectual challenge motivation is, it will be argued, more likely to be neutral in terms of its influence on bet time. Those whose betting is primarily motivated by social interaction are likely to maximize their satisfaction during periods when the betting shop is relatively densely populated, that is to say the afternoon period during which horse races

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and their associated audio and visual broadcasting take place. During this period, the opportunity for ex ante speculation relating to and ex post analysis of broadcast events is at its peak. By contrast, customer density in the morning, pre-race period is likely to be considerably less. During this period there are no live horse races to detain customers, whose visits to the betting shop are therefore likely to be of shorter duration, hence reducing the scope for social interaction. The motivation relating to excitement may be expected to have a similar influence on the timing of bets. Excitement will tend to increase during the build-up to the relevant racing event, to be intensified during the race itself and, where a successful bet has been made, to be sustained through to the collection of returns to the bet and possibly beyond. Those who place their bets in the morning are necessarily temporally remote from the events to which their betting relates and hence excitement levels during this period are likely to be relatively low. Where the principal motivation for betting is financial return, there are both a priori and empirical reasons for suggesting that such activity may tend to be more rather than less time-specific. On a priori grounds, the rational bettor motivated principally by financial gain might be expected to concentrate betting activity in the period immediately prior to the relevant betting event. By doing so, maximum exposure to event-specific information is assured. This would include, in the context of horse racing, such information as late changes of ‘going’, jockey or weight, information regarding the horses’ behaviour and appearance prior to the event (in the parade ring, ‘going down’ to the start and at the start) and most importantly, perhaps, information generated by the betting market as seen through the continual changes in the pattern of prices in the 10–15 minutes (typically) of the active betting market prior to the event. Assuming that this information is received and used ‘rationally’ it should constitute a valuable resource in the making of a decision under conditions of uncertainty. Empirically, there is evidence to suggest that in pari-mutuel betting markets, there are performance advantages associated with bets placed closer to the relevant event. Explaining the superiority of returns to those bets placed later rather than earlier, Asch et al. (1984) suggest that: ‘bettors with true inside information will prefer not to signal that information to the public until late in the betting cycle to minimise “following” behaviour on the part of other track bettors’ (p. 168). This specific argument, of course, applies only in pari-mutuel betting markets, where the exact return to a given bet cannot be determined until after the event since the return to a stake on the winning horse is calculated by dividing the total money staked on a given race (less the operator’s profit and expenses) by the total amount wagered on the winning horse. Consequently, in pari-mutuel betting markets the returns to inside information cannot be guaranteed by the taking of a board price, as in bookmaker-based markets. As regards the motivation to bet resulting from the inherent intellectual challenge, it may be argued that the timing of bet placement is, prima facie, less important. For example, there may be grounds for suggesting that placing a bet

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well in advance of an event represents a greater intellectual challenge given the paucity of information and that a correct selection under such circumstances may generate a consequently greater sense of intellectual satisfaction. Equally, it could be argued that a bet placed closer to the event represents more of an intellectual challenge as it involves the analysis of a fuller and more turbulent information set. On balance, therefore, it is difficult to conclude that any particular period is likely to be dominant in determining the timing of activity of those whose motivation lies principally with intellectual challenge. What we may suggest, however, is that there may be a greater density of the intellectual challenge motivation in any defined subset of bettors where the conditions for the satisfaction of the other motivations are absent. In this sense, it could be argued that the subset of bets placed during the morning is likely to be more closely associated with the intellectual challenge motivation. The board price/starting price decision This section considers whether the decision to take the prevailing board price (BP) or the starting price (SP) when placing a bet may be seen as indicative of a particular motivational bias. The significance of the pricing decision lies principally in the potential impact of the decision on the financial return to a successful betting decision. Simply, in a bookmaker-based market, the taking of a board price sets the rate of return to a win, while the acceptance of starting price means that the ultimate return is dependent on the market. It is important to stress that the board price/starting price decision is fundamental to each bet placed in a betting office and as such is an issue on which each bettor, for each bet, must take a position. It is suggested that for three of the four motivations discussed, it is difficult to justify the likelihood of a systematic connection between motivation and the price decision. Hence, where the bettor is principally motivated by excitement, social interaction or intellectual challenge, it is difficult to see how the BP/SP decision could be expected materially to affect achievement of the aim inherent in the motivation, at least in a consistent way. For the bettor who is motivated by the prospect of financial return, however, there are grounds for suggesting a greater tendency to take board price rather than starting price as a rational return-maximizing strategy. In part, in bookmakerbased markets, this relates to the fact that bettors who believe themselves to be in possession of superior information are able to guarantee the returns to that information by taking board price. Any subsequent followship behaviour by other market participants cannot erode the returns to a bet struck at board prices. In contrast, returns to a bet placed at starting price would be vulnerable to such replication. Awareness of the tendency for large on-course wagers to be placed very late in relation to the event would suggest that the taking of board price remains a rational strategy even immediately prior to the event, in spite of the then limited scope for replication. The reasoning here relates to the lag between price changes on-course and reported price changes in betting offices. By taking a

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price, even immediately before the event, the bettor can guarantee that very late transmitted price changes (reflecting late support for the selection on-course) do not erode returns. Again, this protection is unavailable to starting price bets.

Motivationally distinct subsets – rationale and tests Motivational subset definition Taken together, the influences of bet time and the SP/BP issue suggest that there may be a basis for examining subsets of bettors, defined by bet time and pricetaking behaviour, in order to shed light on the distribution of motivations within the aggregate betting population. In moving towards a specific testable proposition, it is necessary to re-emphasize that both the time constraints on individuals’ ability to bet at particular times and the fact that the betting of many individuals is explained by a cocktail of motivations may inhibit the emergence of highly significant distinctions between defined subgroups. If the above observations relating to the nature of motivations are reasonable, however, then evidence for the existence of different densities of individual motivation across subgroups is a reasonable expectation where large numbers of individual betting decisions are involved. In synthesizing the above observations relating to betting motivation, bet timing and the price decision, it is useful to split the aggregate sample into four subsets, where it is suggested that the aggregate of bets in each subset is likely to be characterized by a different dominant motivation. This then forms the basis for testing the robustness of the alleged motivational distribution, in terms of differences in financial performance, staking and risk-taking behaviour across the subsets. The four subsets are defined as follows: S1 All bets placed prior to 12 noon. This subset is defined as likely to be relatively heavily populated with bets where intellectual challenge is a dominant motivation. The alternative motivations are likely to be less densely present due to the absence of opportunities for excitement or interaction and the informational disadvantages associated with this time period, which would tend to deter the social interaction-seeker, the excitement-seeker and the financial returns-seeker respectively. S2 All bets placed after 12 noon, but prior to the first betting show of the event to which the bet relates. During the betting show period odds available at the racecourse (the betting show) are transmitted to the betting shop. This subset, therefore, excludes bets placed during the betting show period which generally takes place 10–15 minutes prior to the start of the race. Subset S2 is, consequently, defined as likely to be relatively heavily populated with bets where social interaction is a dominant motivation. The argument here is that the bets in this subset are placed during the relatively heavily populated afternoon period, where the scope for social interaction is maximized.

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Importantly, however, the bets are placed before the active betting period of the relevant betting event. As such the bets are relatively temporally remote from the event and the bettors are less exposed to the excitement associated with the immediate build-up to the event than those in the following subset. S3 All bets placed following the first show of betting related to the relevant event, but excluding bets placed in Subset S4 (see below). Bets in S3 are placed during the active build-up to the race, where the betting office customer is subjected to regular transmissions of event-specific information, perhaps accompanied by television pictures of the preliminaries. As such, it is argued that this is a period during which the bettor motivated principally by excitement is likely to be active. S4 All bets placed at board price in the final 30 seconds prior to the commencement of the relevant betting event (the ‘off’) or in the short, arbitrary period following the ‘off’ during which bets are accepted. This pattern of betting could be expected to be associated with financial gain as a motivation in two respects. First, considering the time dimension of S4, bets in this subset are exposed to the fullest possible amount of market-generated information as a basis for the betting decision. Second, regarding the price-taking aspect, such behaviour insulates the bettor from the erosion of returns by late oncourse betting which could affect starting price after off-course betting opportunities cease. Formalizing this gives us Table 1.2, which constitutes a testable proposition relating to distribution of motivations. Hypothesis testing – introduction In testing the explanatory strength of the above distribution of motivations, three variables which characterize all bets in the aggregate sample are examined. These variables are financial returns, level of stake and the degree of risk associated with each bet. The contention of this chapter is that if the proposition relating to the distribution of motivations offered above is accurate, it should be reflected in differences between the subsets in terms of these three further variables, the Table 1.2 Motivationally-distinct subsets Subset

Bet population

Dominant motivation

S1 S2

All bets placed pre-12 noon All bets placed post-12 noon but pre-first betting ‘show’ of relevant race All bets placed post-first betting ‘show’ of relevant race excluding S4 All bets placed in last 30 seconds before ‘off-time’ of relevant race or later

Intellectual challenge Social interaction

S3 S4

Excitement Financial gain

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values of each of which are held to be indicative of the underlying motivation to bet. Before considering the nature of differences required for confirmation of the proposition and the actual results, it is important to stress again that highly significant differences across subsets are difficult to anticipate given the existence of both non-motivation-related constraints (e.g. work commitments) on the timing of bets and the contention that any individual bet is likely, generally, to be characterized by a mixture of motivational factors. The likelihood of observable distinctive differences is further affected by the fact that it is impossible to guarantee that the individual subset populations are comprised purely of bettors whose motivations conform to the subset label. For example, bets placed by those motivated by intellectual challenge could appear in any subset. Equally, the subset relating to excitement could include some bets placed by those with a social interaction motivation, given that the two groups each occupy the betting office during the afternoon period. Nevertheless, over a large number of recorded bets, the contention inherent in the classification’s design is that the majority of bets in each subset will be placed by those individuals within the distinct motivational group. For example, for those seeking to maximize financial gain, there would be little rationale in placing a bet in any subset other than S4. Given this cautionary note, the three further variables noted above are now considered in turn. Financial returns In terms of financial returns, it seems reasonable to suggest that the subset which is held to be dominated by financial gain as a motivation would be expected to outperform the other three subsets. Such an expectation is attributable to the fact that subsets S1, S2 and S3 are less focused on financial gain and more motivated by alternative, non-financial payoffs. As regards the comparative performance of these remaining groups, there is some evidence to suggest that those bets placed in subset S3, where excitement is the dominant motivation, may tend to perform worse than either S1 or S2 due to the documented effects of what Eiser and van der Pligt (1988) term ‘noncognitive constraints on effective decision-making’ (p. 100). Bettors in S3 are subject to rapid and continual changes in the information set (e.g. prices of horses, horses’ pre-race behaviour). In this complex informational environment, previous research has suggested that rational cognitive processes may be suspended. Eiser and van der Pligt (1988, p. 101) note firstly, individuals tend to use simpler and less optimal choice rules as the information load increases. Usually accuracy declines considerably when the number of features or the number of alternatives increases. Secondly, the reliability with which choice rules are used tends to decrease as the decision-maker’s information load increases.

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Additionally, S3 bettors may be affected by what Janis and Mann (1977) describe as ‘hypervigilance’ – there is an overactive search for information and inability to distinguish between irrelevant and relevant information. This frequently leads to ‘decision paralysis’. Janis and Mann (1977) argue that in countering this, the decision-maker may tend to distort the meaning of information, suspend vigilant search and be characterized by selective inattention. It is less easy to postulate the likelihood of significant differences in performance between those in subsets S1 and S2. While it could be argued that S2 bettors, given the timing of their bets, may be able to benefit from a slightly fuller set of race-specific information in making their decisions, they may equally be deflected from objective, rational analysis by the influence of fellow bettors with whom they are interacting. The concept of ‘groupthink’, coined by Janis (1972, 1982), may be such a distorting influence. Thus, within close, cohesive groups there is a powerful psychological pressure for agreement and suppression of dissension. In other words, group members’ ability to employ a logical, cognitive approach to decision-making is inhibited by group pressure. As such, there exist factors which could account for performance advantages for either S1 or S2. It is tempting to suggest that these may tend to balance out to some degree, so that the most rational expectation may be that S1 and S2 would be broadly similar in terms of financial returns. The results relating to financial returns are presented in Table 1.3. Clearly, the most striking feature of these results is the superiority of those bets placed in S4 over those placed in each of the other subsets. This feature is consistent across the five performance measures considered and offers strong support for the proposition that S4 bets feature financial gain as a dominant motivation. Similarly consistent evidence supports the inferiority of those bets placed in S3. This appears to be suggestive of the negative influence on cognitive rationality associated with high levels of excitement. S1 and S2 are closer in performance terms, though the ranking of performance differs across the various measures. Again, this result tends to conform to our a priori expectations of little systematic distinction between these subsets. A further measure of comparative financial return across subsets is the ratio of return to stake, expressed as a percentage, for all bets in each subset. This measure offers confirmation of the patterns discussed above, with ratios of 72.5 per cent, 79.8 per cent, 53.8 per cent and 147.3 per cent across groups S1 to S4, respectively. Taken together, the financial performance data offer an encouraging degree of support for the proposition relating to the distribution of motivations, most significantly in relation to subsets S3 and S4. Staking level The second variable to be considered in testing the proposition is staking level. Here it is suggested that the pattern of staking across subsets which would be

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Table 1.3 Measures of financial return to motivational subsets S1–S4

% of bets with a positive returna % of stakes with a positive returnb % of bets with a profitc % of stakes with a profitd

S1

S2

S3

S4

24.6S3,S4

22.3S3

16.9(S4)

50.0(S2)+

26.4(S4)

20.1S3

16.3(S4)

52.4S2+

17.0(S3),S4 24.4(S3),S4

19.6 17.9S3

13.4(S4) 11.8(S4)

43.3(S2)+ 50.6(S2)+

Notes a Number of bets (irrespective of stake size) producing a positive return, which may be less than the amount staked, divided by the total number of bets placed. b Number of bets (irrespective of stake size) producing a return greater than the amount staked, divided by the total number of bets placed. c The total amount staked which produced a positive return, divided by the total amount staked. d The total amount staked which produced a return greater than the amount staked, divided by the total amount staked. e.g.

Bet 1 2 3

Stake (£) 10 4 6

Return (£) 25 0 2

% of bets with a positive return = 2/3 = 66.7% % of stakes with a profit = 10/20 = 50% + = Significant difference between the four statistics at the 0.05 level. Si (where i = 1,2,3,4) is significantly different from time period Si at the 0.05 level. All Si’s in parentheses indicate where (conservative) multiple comparison procedures also suggest significantly different from time period Si at the 0.05 level.

necessary to support the proposition would involve the highest stakes for those motivated by financial gain on the basis that the higher the stake, the greater the (absolute) financial return to any given successful bet. Conversely, where payoffs to betting are largely non-financial in nature, the expectation would be of generally lower stake levels. It could also be argued, however, that staking levels allow us to distinguish between bettors motivated by intellectual challenge (S1) and the two intermediate groups (S2 – social interaction and S3 – excitement). If these subsets are reliable, there are grounds for suggesting that stakes in S1 would be expected to be lower than stakes in either S2 or S3. The rationale for this expectation lies in the suggestion that both social interaction and excitement (absent in S1) may positively influence stake size. Such influences may reflect, on the one hand, status accorded to perceived ‘large stakes’ bettors in S2 (see, for example, Dickerson, 1979, p. 321) and, on the other hand some suspension of normal notions of ‘appropriate’ or ‘sensible’ staking levels in S3, in line with the ideas of Dickerson (1979) and others noted above. Table 1.4 details average stake sizes for the four subsets. These results offer a strong confirmation of the nature of motivations in S4, where the average stake size is significantly in excess of all other cells. Though this is the most

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Table 1.4 Average stake in each motivational subset (£)

Average stake

S1

S2

S3

S4

1.25(S2)(S3)

2.67(S3)(S4)

4.85(S4)

12.24(S1)+

Notes + = Significant difference between the four statistics at the 0.05 level. Si (where i = 1,2,3,4) is significantly different from time period Si at the 0.05 level. All Si’s in parentheses indicate where (conservative) multiple comparison procedures also suggest significantly different from time period Si at the 0.05 level.

striking feature, the stake sizes in the other subsets are supportive of the proposition as a whole. The low level of staking in S1 is suggestive of a class of bettor content with a token level of financial commitment. Arguably this level of staking may be viewed as analogous to an entry fee to participate in the intellectual challenge. The results relating to subsets S2 and S3 offer further support for the classification. Each subset’s average stake exceeds that of S1, suggesting the possible influence of some positive interactive or excitement-related influence on stake, while the comparison between S2 and S3 invites the suggestion that S3 stakes may be subject to both interaction and excitement-related stimuli. (Note here that, by definition, bets placed in S2 are not subject to the potentially distortive effects on rationality associated with S3, whilst bets placed in S3 are still subject to the potential influence of stimuli related to interaction.) A further related set of results which reinforces the notion of S4 bettors as more financially ‘sophisticated’ splits average stakes across the subsets according to whether or not bets yield a profit. Table 1.5 presents these results. Though not statistically significant, these results are suggestive of the proposition that, at least in relation to S2 and S3, the financial return-motivated group S4 has a more refined awareness of the probability of success in that the stake size is larger for profitable as against unprofitable bets, whereas it is the unprofitable bets in S2 and S3 which carry higher average stakes. Bets placed in S1 also feature higher staking for profitable than for unprofitable outcomes. This result is less easy to explain in positive terms, but may be accounted for by the absence of previously discussed influences which affect behaviour in subsets S2 and S3 (e.g. groupthink, hypervigilance). Table 1.5 Stakes on profitable and unprofitable bets by motivational subset (£)

Average stake on bets producing a profit Average stake on bets not producing a profit

S1

S2

S3

S4

1.81

2.43

4.25

14.30

1.15

2.73

4.94

10.67

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Degree of risk The final variable to be considered in testing the proposition relating to the distribution of motivations is the degree of risk inherent in the bet. For the purposes of this analysis, three measures of risk are used. These are: 1 2 3

The propensity to select horses which, at the time of bet placement, are first or second favourites for the relevant race. The propensity to select horses which, at the time of bet placement, do not occupy the first three positions of favouritism in the betting market. The propensity to select ‘outsiders’, horses which carry odds of 20/1 or greater at the time of bet placement.

It is argued that the pattern established by these variables enables further evaluation of the proposition. Its ability to do so relates to observed and documented phenomena concerning the actual probability of success of horses occupying particular positions relative to favouritism in the betting market and, relatedly, horses carrying particular ranges of odds. Dowie (1976) and Henery (1985) have separately demonstrated that over large numbers of betting events, there is a systematic tendency for the actual probability of success for horses with longer odds to be considerably overstated by the probability inherent in the odds. By contrast, short-priced horses’ odds are a much closer reflection of actual probability of success. Consequently, a strategy which focused exclusively on betting on all first and second favourites would, over a large number of betting events, significantly outperform a strategy which involved betting on all other horses. Given these phenomena, a natural expectation, assuming the proposition regarding motivational distribution to be acceptable, is that compared with other subsets, S4 bettors would tend to concentrate on selections which are both in prominent positions of favouritism and which carry relatively short prices. Equally, the expectation is that S4 bettors would tend to ignore long-priced selections as ‘bad value’ investments. Though this naturally suggests that the other subsets would be likely to be less conscious of, or concerned with, the need to focus on favouritism and shorter prices, it is difficult to offer confident predictions of distinctive patterns of risktaking behaviour between these groups. For example, so far as those motivated by intellectual challenge are concerned, their risk-taking behaviour may depend largely on the role of precedent, compared with other factors, in their problemsolving approach. Thus, for example, if previous statistical patterns of winning favourites were accounted for in the formulation of the decision, one would expect S1 bettors to focus their betting on short-odds, favoured horses. For the subset in which social interaction is a dominant motivation, there could be grounds for suggesting that group esteem may be positively related either to the choice of risky selections (less chance of success but better meeting the classic image of the gambler) or to the choice of low-priced or

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near-favourite selections (more chance of success, enhanced reputation as a ‘skilful’ gambler). Where excitement is allegedly dominant in S3, there are similarly conflicting potential influences on risk-taking behaviour. Much may depend on whether excitement derives from the remote prospect of successfully selecting a ‘long shot’ or from the greater likelihood, with a short-priced or favoured horse, that the selection will sustain the excitement throughout the course of the event. That is to say, in general one could expect this type of selection to feature prominently for a significant proportion of the race. A factor which may lead us more towards the idea of the S3 bettor having a preference for less risky selections relates to the S3 bettor’s presence in the betting office during the transmission of prices in the evolving betting market. It may be argued that there is considerable excitement to be derived from being part of a significant gamble on a particular horse. To the extent that this is the case, one might expect some bias in S3 towards horses with shorter prices and greater degrees of favouritism, compared with bets placed in S1 and S2. The results relating to risk taking across subsets are presented in Table 1.6. These results serve to reinforce the notion of the S4 subset as the most sophisticated in terms of awareness of and focus on financial gain. Bettors in this subset have an unambiguous preference for horses with a higher degree of favouritism and are evidently reluctant to make selections outside the first three in the betting or with odds of 20/1 or greater. In all three measures of risk, the S4 class differs from the other groups. An interesting additional detail relates to average staking on first favourites versus non-first favourites by this subset. Average stakes on first favourites are £22.33, and only £6.40 on non-first favourites, emphasizing again the subset’s awareness of comparative profit opportunities. Of the remaining results, perhaps the most interesting and consistent are those which appear to confirm the existence of a distinction between S2 and S3. Table 1.6 Measures of risk taking across motivational subsets

% of bets on first and second favouritesa (at time of bet) % of bets on horses not first three positions of favouritisma (at time of bet) % of bets on horses with odds ≥ 20/1 (at time of bet)

S1

S2

S3

S4

26.4(S2)

35.3(S3)

46.8(S1)

60.0(S1),S2+

62.0(S3),(S4)

53.4(S3)

37.7(S4)

16.7(S2)+

17.0(S4)

16.1(S3)

8.7(S1)

3.3+

Notes a Including, where applicable, joint first, second, third favourites. + = Significant difference between the three statistics at the 0.05 level. Si (where i = 1, 2, 3, 4) is significantly different from time period Si at the 0.05 level. All Si’s in parentheses indicate where (conservative) multiple comparison procedures also suggest significantly different from time period Si at the 0.05 level.

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Over all three indicators, the excitement-motivated subset, S3, demonstrates a reluctance to assume the levels of risk accepted by S2, the interaction-motivated group. In the case of each measure of risk, the difference between the groups is statistically significant, suggesting that there may be some substance in the idea that excitement in S3 derives in part from association with horses likely to feature prominently in the race. S2 punters, being primarily motivated by social interaction, may be more prone to the ‘risky shift’ phenomenon in which individuals acting in cohesive groups have been shown to make riskier decisions than when acting alone (Teger and Pruitt, 1967). This clear difference between S2 and S3 reinforces the evidence of a legitimate distinction which was suggested by the results relating both to financial returns and to staking levels. The S1 figures appear to indicate a marked preference, across all three indicators, for riskier selections. Whilst this result is not easily explained as a systematic phenomenon, it may be the case that this group’s acceptance of riskier selections is related to its low staking levels (higher risk, but smaller potential loss). In any case, the existence of a radically distinct attitude to risk appears to confirm the legitimacy of the separate identification of this subset.

Conclusions This chapter has attempted to shed light on the composition of the aggregate betting shop population in terms of differing densities of betting motivation across subsets defined by the time of bet placement and price-related behaviour. The first stage in this process introduced the principal motivations generally associated with betting and suggested that, by considering the time-specificity and price decision characteristics of each motivation, a tentative segmentation of the aggregate betting population could be developed. After establishing a specific proposition suggesting four subsets, each defined in terms of a different dominant motivation, the proposition was tested using a database of actual betting decisions from betting offices throughout the UK. Specifically, variables relating to three aspects of the individual bet – financial return, stake, inherent risk – were selected as important indicators of underlying betting motivations. Consideration of the values taken by these variables for each subset suggests that the motivational distinctions inherent in the proposition are at least reasonably robust. Undoubtedly, the most striking conclusion relates to the unambiguous confirmation of the existence of a subset motivated by financial returns. Less dramatic, but quite distinct behavioural differences are evident between those subsets motivated principally by intellectual challenge, social interaction and excitement. The patterns of difference appear to offer an encouraging degree of support for the validity of the subsets’ motivational ‘labels’. These results emerge in spite of the acknowledged existence of nonmotivation-based constraints on the time pattern of betting and of the belief that most individual betting decisions spring from a blend of motivations specific to the bettor.

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By demonstrating the possibility of drawing clear motivational distinctions between subsets of the betting population, these results represent an important step towards a fuller understanding of the nature of betting behaviour.

Acknowledgements The research reported here was made possible by grants from Ladbroke Racing and the co-operation of Ladbrokes and Extel, to whom we are most grateful. Special thanks to Colin Walker and Douglas Hunter.

References Anderson, G. and Brown, R.I.F. (1984) ‘Real and laboratory gambling, sensation-seeking and arousal’, British Journal of Psychology, 75: 401–10. Asch, P., Malkiel, B.G. and Quandt, R.E. (1984) ‘Market efficiency in racetrack betting’, Journal of Business, 57: 165–75. Brown, R.I.F. (1986) ‘Arousal and sensation-seeking components in the general explanation of gambling and gambling addictions’, The International Journal of the Addictions, 21: 1001–16. Cornish, D.B. (1978) Gambling: A Review of the Literature, London: HMSO. Dickerson, M.G. (1979) ‘F.I. Schedules and persistence at gambling in the UK betting office’, Journal of Applied Behavioural Analysis, 12: 315–23. Dixey, R. and Talbot, M. (1982) Women, Leisure and Bingo, Leeds: Trinity and All Saints College. Dowie, J. (1976) ‘On the efficiency and equity of betting markets’, Economica, 43: 139–50. Downes, D.M., Davies, B.T., David, M.E. and Stone, P. (1976) Gambling, Work and Leisure: A Study Across Three Areas, London: Routledge & Kegan Paul. Eiser, J.R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Filby, M.P. and Harvey, L. (1988) ‘Recreational betting: everyday activity and strategies’, Leisure Studies, 7: 59–72. Filby, M.P. and Harvey, L. (1989) ‘Recreational betting: individual betting profiles’, Leisure Studies, 8: 219–27. Furnham, A. (1985) ‘Attitudes to, and habits of, gambling in Britain’, Personality and Individual Differences, 6: 493–502. Gilovich, T. and Douglas, C. (1986) ‘Biased evaluations of randomly-determined gambling outcomes’, Journal of Experimental Social Psychology, 22: 228–41. Henery, R.J. (1985) ‘On the average probability of losing bets on horses with given starting price odds’, Journal of the Royal Statistical Society, 4: 342–9. Janis, I.L. (1972) Victims of Groupthink, Boston, MA: Houghton Mifflin. Janis, I.L. (1982) Groupthink, 2nd edn, Boston, MA: Houghton Mifflin. Janis, I.L. and Mann, L. (1977) Decision Making: a Psychological Analysis of Conflict, Choice and Commitment, New York: Free Press. Langer, E.J. (1983) The Psychology of Control, London: Sage. Letarte, A., Ladouceur, R. and Mayrand, M. (1986) ‘Primary and secondary illusory control and risk-taking in gambling’, Psychological Reports, 58: 299–302. MAS Omnibus (1990) Betting survey, unpublished research paper prepared for Ladbroke Racing Ltd.

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Mintel (1991) Gambling, Mintel Special Report, London, 3. Saunders, D.M. and Turner, D.E. (1987) ‘Gambling and leisure: the case of racing’, Leisure Studies, 6: 281–9. Scott, M.B. (1968) The Racing Game, Chicago: Aldine. Teger, A.I. and Pruitt, D.B. (1967) ‘Components of group risk taking’, Journal of Experimental Social Psychology, 3: 189–205. Weatherbys (1991) The Racing Industry Statistical Bureau Statistics 1985–90, Wellingborough, Northants.

2

Costing excitement in leisure betting A.C. Bruce and J.E.V. Johnson

The objective of this chapter is to explore the effects of excitement on the nature of betting decisions. As such, it addresses an area of inquiry, the relationship between excitement and leisure, which has received only limited attention in the literature. A distinctive feature of the chapter is its use of a large and geographically dispersed sample of real betting decisions made in UK betting offices. Two procedures are employed to test the existence and magnitude of the effects of excitement. Those subgroups of the aggregate population which are most subject to excitement are shown to display significantly inferior decision-making performance, despite apparent informational advantages. Evidence is also presented which suggests that they bet with significantly higher stakes and it is argued that the results support the notion that the consumption of excitement involves a financial penalty. Betting, in its various forms, is widely acknowledged as an important leisure pursuit (e.g. see Filby and Harvey, 1988). This may in large part relate to the fact that, as Saunders and Turner (1987) note, betting is: ‘a form of risk taking that involves the material commodity of money and the emotional experience of excitement’. It is the principal objective of this chapter to measure the effects of this excitement on individuals’ leisure betting via an empirical study of a large number of horserace betting decisions made in UK off-course betting offices. As such, the chapter offers an extension to the authors’ earlier work (Bruce and Johnson, 1992) which investigated the various motivations behind the individual decision to engage in betting. This chapter’s focus on excitement and its effects reflects not only the importance of excitement in relation to leisure betting, but also its wider significance in other leisure contexts. It is important to note here the paucity of studies addressing issues relating to excitement in leisure. Elias and Dunning (1986) observe that though the area appears accessible to investigation from three distinct disciplinary bases, the physiological, psychological and sociological literatures, taken together, have offered at best only limited insights into aspects of leisure excitement. The chapter proceeds in four sections. The first section reviews briefly the literature relating to the role of excitement in leisure, generally, and betting in particular. The second section explains the methodology used, the nature of the

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database and its suitability for exploring the effects of excitement. The third section introduces specific hypotheses, outlines the procedures which permit their investigation and reports and analyses the results, which are related to existing literature in the final section.

Existing literature The importance of excitement as a motivational factor in explaining participation in leisure activities has received considerable attention in recent years. A synthesis of the issues, and specifically of the work of two of the more important contributors in this area, is provided in Elias and Dunning (1986). Here, an important theme is the increasing importance of leisure activities as a context for the experience of and expression of excitement. This is explained in terms of the suppression of excitement, particularly overt manifestations of excitement, in other areas of modern society. Leisure is viewed as offering an ‘enclave’ for excitement. As Elias and Dunning (1986, p. 72) observe: ‘In a society in which the propensities for the serious and threatening type of excitement have diminished, the compensatory function of play-excitement has increased’. Elias and Dunning (1986) analyse the experience of excitement in leisure via a focus on so-called ‘mimetic’ activities, where participants experience emotional arousal which, while related to similar forms of arousal in other (e.g. nonleisure) spheres, retains distinctive characteristics. They note (p. 80): ‘In serious, non-mimetic excitement people are liable to lose control over themselves and to become a threat, both to themselves and to others. Mimetic excitement is socially and personally without danger and can have a cathartic effect’. Important components in mimetic excitement may include surprise, tension and climax or ‘. . . a gradual rising of tensions leading, through a climax, to a form of tension-resolution’ (Elias and Dunning, p. 83). Such characteristics are strongly suggestive of the environment encountered by those who choose to engage in horse-race betting. Indeed, Elias and Dunning note, explicitly (p. 84): a strong element of pleasurable excitement and, as a necessary ingredient of the pleasure, a degree of anxiety and fear, is always present whether it is the tension-excitement derived from going to the races, especially when one has a little flutter on the side, or the much quieter but more profound excitement one may derive from listening to Beethoven’s Ninth Symphony. More recently, Murphy et al. (1990, p. 5) observe, in the context of soccer: to experience excitement at a soccer match one has to care. In order, as it were, for the ‘gears’ of one’s passions to engage, one has to be committed, to identify with one or another of the teams and to want to see it win. The question of identification is an issue of critical importance.

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The parallels between this commitment and identification associated with soccer supporters and that associated with a bettor who has selected a particular horse in a horse race is compelling. The placing of a bet is for many, arguably, the act which ‘engages the gears of passion’, thereby exposing the bettor to the experience of excitement. Further contributions to the literature have addressed more specifically the link between excitement and betting. Downes et al. (1976) and Kusyszyn (1984), for example, suggest that excitement plays an important role in betting activity. Studies by King (1985) and Gilovich and Douglas (1986) suggest that for many people the excitement offered by gambling exceeds that available from most other areas of their lives. The term ‘arousal’ is used by Brown (1986) and Anderson and Brown (1984) to describe the psychological appeal of betting. Brown (1988), in summarizing this work, suggests (p. 165): ‘(1) gambling is very exciting; (2) some form of arousal or excitement is a major, and possibly the major, reinforcer of gambling behaviour for regular gamblers’. These observations are in line with field surveys carried out by the US National Commission on Gambling (1976) indicating that excitement is a major motivation to gamble. Dickerson (1979) modifies these observations, by suggesting that excitement is generated not by the cognition of cash won but by the process of gambling behaviour and the attendant environmental changes. Bruce and Johnson (1992) discuss the role of excitement as a motivational factor in the exploration of betting as a leisure activity and identify periods of the betting day during which factors promoting excitement are more apparent. Taken together, these contributions suggest that excitement is an identifiable motivational drive in explaining betting behaviour. This invites consideration of the central question to be addressed by this chapter; that is, given its motivational significance, what effects does the experience of excitement have on the nature of betting decisions? It might be expected that the experience of feelings of excitement may inhibit sober, rational judgement. A tentative a priori expectation would therefore be that this might affect performance negatively and might lead to higher staking levels than would be considered judicious in the absence of such influences. As such, bettors who experience excitement may be expected to bear some associated financial cost. The specific hypotheses to be tested, therefore, are that those bettors who are most exposed to excitement will: 1 2

display significantly inferior financial performance; and place higher stakes. These issues are investigated in the following sections.

Methodology While the phenomenon of excitement in the context of betting has received attention in the literature, there has been little attempt to verify empirically the existence, and to measure the explicit cost, of excitement. Most of the work to

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date has been either at the theoretical level or has involved laboratory-based simulation of real betting behaviour (see, for example, Cornish, 1978 and Dickerson, 1974 for surveys of relevant studies). The limitations of laboratory-based studies are well documented. Slovic (1969), Lafferty and Higbee (1974) and Watson (1985) each identify particular areas of difficulty associated with laboratory-based models. Equally Dickerson et al. (1990) note that real-world gambling has been demonstrated to differ to a significant degree from behaviour observed in laboratory games. Anderson and Brown (1984, p.408) conclude that the most appropriate strategy for the study of gambling, risk-taking and other behaviours involving high degrees of arousal and/or emotional involvement is not necessarily primarily the laboratory-based experiment followed by secondary checks on the viability of findings from it in field studies, but may rather be the exact reverse – primarily naturalistic or field studies supported by secondary checks in the laboratory on the validity of the measuring instruments and on the method used in the field. A significant methodological advantage of the study reported here is that it is conducted in a natural setting. It therefore addresses the need for empirical investigation based on real decision data. The following section outlines the particular advantages associated with the analysis of decisions made in offcourse betting markets to explore the financial cost associated with the consumption of excitement. The scope of betting data An investigation into the specific impacts of excitement on betting behaviour is facilitated by the fact that within the off-course betting office ‘betting day’ there is scope for the identification of particular subperiods which are distinct in terms of the presence of factors which could be expected to generate excitement. In order to explain this, it is necessary to outline briefly the structure of the betting day (Figure 2.1). Betting offices generally open for business at around 10 am. All horse races take place in the afternoon. Consequently, during the morning period, bets placed are to a greater or lesser extent temporally remote from the events to which they relate. By contrast, bets placed in the afternoon can be placed right up to the time of the start of the relevant event (‘the off’) and perhaps immediately after the start. For a period of, typically, 10 to 15 minutes prior to each race (the ‘show’ period), information relating to the development of the active betting market for that race will be transmitted from the racecourse into the betting office, together with either sound or televisual coverage of the build-up to the race (horses parading, changes in race-specific information, etc). Sound or televisual coverage of the event itself is then transmitted. There would appear to be a reasonable case for suggesting that, in general, the scope for excitement is likely to be less during the morning period. This was

Costing excitement in leisure betting Pre-racing period

Show periods

Pre ʻfirst-showʼ of the day

29

Active-racing period Show period of race 1

Show period of race 2

Show period of race 3 etc.

Real time

10 am Betting shop opens

12 noon

Approx. 5 pm Betting shop closes

Odds available on race 1 first broadcast in shop

Odds movements on race 1 broadcast in shop

Race 1 starts

(Relative values)

Environmental and related factors

Amount of information available to bettor

Small (e.g. previous form of horses, betting forecasts)

Large (previous form, betting forecasts, going, horsesʼ condition in paddock and going to post, results from previous races, odds movements, etc., audio/visual coverage of races in progress)

Turbulence of information available to bettor

Stable (occasional jockey changes, going changes, withdrawals)

Turbulent (often rapid changes in odds, previous results indicating jockeys/trainers in form, going changes, late withdrawals, etc.)

(Relative values)

Figure 2.1 Significant events in a typical betting office day.

explored by Bruce and Johnson (1992) and relies on the contention that proximity of the relevant race and the stimuli present in the betting office are significant in determining the degree of excitement and are greater in the afternoon. More specifically the afternoon period immediately prior to the ‘off’ is characterized by increasingly regular transmission of betting market price changes which may be indicative of on-course market moves. These are augmented by audio-visual transmissions from the racecourse including expert analysis, television pictures of horses in the parade ring, announcements of horses ‘going to post’, ‘going behind the stalls’ and ‘under starters orders’. All of these factors, Dickerson (1979) suggests, serve to enhance the remote bettor’s sense of involvement and attendant excitement in the unfolding event. This view is reinforced by the emotionally charged atmosphere observed within the betting shop during the afternoon racing period, which is in sharp contrast to the calmer, more sober morning period. Additionally, of course, observation of the televised races themselves in the afternoon generates further excitement as does the expectation of imminent financial reward or penalty. These considerations will be important in justifying the particular procedures to be developed in the following section. A major advantage of using real betting decisions is the richness of the data in terms of informational content. Of central importance here is the fact that each decision made in off-course betting offices is necessarily recorded on a ‘betting slip’. As a minimum, the betting slip will detail the selection made and the relevant race, the value of the investment (‘the stake’), the exact time at which the bet was placed and the inherent ‘riskiness’ of the bet, as evidenced by

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the type of bet placed and the probability of success implicit in the ‘odds’ relating to the selection at the time of bet placement. The precise timing of each decision is of particular significance in facilitating comparison across timedefined subgroups of the betting population. It also enables identification of an accurate profile of the range of odds in the betting market at the time the decision was registered. One further aspect of the evolution of the betting day deserves attention at this stage as it features in the interpretation of results in the final section. This is the way in which the information environment develops. In terms of information relevant to a particular event, the morning period may see the emergence of some new information relative to that available in the morning specialist media. For example, there may, during the morning, be announcements of jockey changes, non-runners, etc. As race proximity increases in the afternoon period, further such announcements may modify the information set. Additionally, the results of early races may yield information which those betting on races later in the afternoon may wish to take into account (e.g. the form of particular stables, jockeys). For any particular race, however, it is the time from the start of that race’s show period which is marked by the most significant input of race-specific information, in the form of the evolving pattern of odds in the betting market (reflecting the degree of confidence in the chances of various horses), the opportunity to witness the condition and behaviour of horses, etc. This is a period during which the various types of race-specific information are subject to considerable turbulence. Clearly, then, there is a positive correlation between the passage of time and size and completeness of the information set relating to a particular race. In terms of our investigation of excitement-related influences on decision-making, it is necessary to be aware that those periods which suggest the maximum potential for such influences are likely to coincide with the periods of maximum information availability. The implications of this will be considered in interpreting the results of the procedures outlined in the following section. The database The database used in the analysis which follows comprises full details of over 1,200 individual betting decisions, made in betting offices throughout the UK during 1987. The population from which the sample was taken consisted of all bets placed in UK betting offices owned by Ladbroke Racing (the largest offcourse bookmaker in the UK) during March and April that year. A systematic random sample was selected according to the serial numbers of betting slips (which are chronologically arranged) thus ensuring a spread of bets throughout the betting day. Only horse race ‘single’ bets were selected. The ‘single’ is the simplest form of bet, where the return to the bet is wholly dependent on the performance of one horse in one race. Hence the database is homogeneous in terms of bet type. All randomly selected betting slips were isolated by betting office staff after close of business, thereby ensuring complete absence of ‘observation’ effects on bettors. For each betting decision selected, further information

Costing excitement in leisure betting

31

relating to the relevant horse race and its associated betting market was collated. Specifically, the inclusion of precisely timed information relating to all changes of odds reported in the betting market permits an accurate picture of the exact nature of the relevant betting market at the time of each decision.

Procedures and results The previous section outlined the potential of the analysis of betting in testing the impacts of excitement on the nature of betting decisions. The main objective of this section is to explain the rationale for, and present and analyse the results of two procedures to test explicitly the existence and magnitude of such impacts. The procedures Discussion of the evolution of the betting day suggested that it is possible to identify a range of time-defined periods with substantially differing potentials for excitement, thereby enabling informative cross-period comparisons. The remainder of this section presents and analyses the results of two cross-period comparisons. In each case, the characteristics considered in comparing betting behaviour across time periods are bet performance (variously measured) and staking behaviour (indicating the degree of commitment to the decision). The main aim of these procedures is to distinguish, as far as possible, those periods throughout the betting day in which relatively significant excitement influences might exist, from those periods where these phenomena are less prevalent. The betting behaviour observed in these periods will be used to test the hypotheses that individuals subjected to the greatest amounts of excitement will make inferior financial decisions and will demonstrate greater commitment to their decisions (by betting with larger stakes) than individuals subjected to lesser amounts of excitement. Hypothesis 1 – performance Procedure 1 compares the characteristics of all bets placed ‘prior to the first betting show of the afternoon’s racing programme’ with all bets placed ‘subsequent to the first show of the afternoon’s racing programme, excluding bets placed later than 30 seconds prior to the off-time of the relevant race’. As such, it compares two periods which are temporally adjacent. The exclusion of bets placed immediately prior to (or after) the ‘off’ requires explanation. Johnson and Bruce (1992) demonstrated that bettors in this late period distinguished themselves as an elite in terms of betting performance and as atypical in their propensity to stake large amounts. These bettors, they argue, have an awareness of the value of both quality and quantity of information and make rational use of each in arriving at a decision. This group of bettors’ awareness, it is argued, and their motivation for financial gain (Bruce and Johnson, 1992) allows them to insulate themselves from the potentially distortive effects of excitement. This notion of

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an ‘informed class’ of bettors is in line with research carried out by Asch et al. (1982) which suggested that bets placed nearer to the ‘off’ provided a much better prediction of outcomes than those placed earlier in the ‘show’ period. In order to focus on the behaviour of those bettors who remain susceptible to excitement, Procedures 1, 2 and 3 omit this ‘informed class’. Procedure 1 allows us to investigate whether identifiable performance differences exist between decisions made in the pre-racing period and the active racing period. The importance of this lies in the contention that, in the active racing period, the potential for excitement is greater. As such, in line with the observations made in the first section, there might be grounds to expect an improved performance where cognitive processes are relatively unexposed to excitement. Different definitions of the pre- and active racing period are presented in Tables 2.1 a and b, with the division between each given, respectively, by the time of the first show of betting of the afternoon and by a point 15 minutes prior to the first betting show of the afternoon. The results relating to bet performance (variously defined) are somewhat ambiguous. There is limited support for superior performance in each of the earlier periods but the cross-group distinctions are considerably less marked than ex ante expectations would have suggested. For example, comparing ‘pre-first show’ with ‘post-first show’ groups yields a statistically significant superiority for the former only in terms of the number of bets generating a return. Three of the remaining four performance-related measures indicate superior performance, Table 2.1a Performance of bets placed in the pre-racing versus active racing periods (definition 1) Pre-first show of afternoon N = 394 Bets with returna Bets with profitb Stakes with returnc Stakes with profitd Return/stake

0.254 0.180 0.208 0.153 0.472

Post-first show of afternoon N = 628 **

0.191 0.153 0.190 0.139 0.655

Notes a Number of bets (irrespective of stake size) producing a positive return, divided by the total amount staked. b Number of bets (irrespective of stake size) producing a return greater than the amount staked, divided by the total number of bets placed. c The total amount staked which produced a positive return divided by the total amount staked. d The total amount staked which produced a return greater than the amount staked, divided by the total amount staked. ** Significant difference between the two statistics at the 0.01 level. (For performance criteria a, b, c, d above, the statistical significance of the difference between the pre- and active racing period is tested using a one-tailed, large sample test for differences between proportions. For the return/stake performance criteria a standard t test is employed, with no assumption of equality of variance. Since it is hypothesized that those individuals subjected to the greatest amount of excitement (i.e. betting in the active racing period) will make inferior financial decisions, one-tailed tests are employed in all cases).

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Table 2.1b Performance of bets placed in the pre-racing versus active racing periods (definition 2) Pre (first show of afternoon –15 minutes) N = 347 Bets with returna Bets with profitb Stakes with returnc Stakes with profitd Return/stake

0.254 0.176 0.246 0.181 0.559

Post (first show of afternoon – 15 minutes) N = 674 * ** *

0.194 0.157 0.185 0.135 0.635

Notes a, b, c, d See Table 2.la for definition of performance criteria. * Significant difference between the statistics at the 0.05 level. ** Significant difference between the statistics at the 0.01 level. (See Table 2.la for details of statistical tests employed.)

though not at statistically significant levels. The fourth, ‘returns as a percentage of stakes’, indicates superior performance for the later group. By contrast, comparison of the ‘pre-first show – 15 minutes’ group with the ‘post-first show – 15 minutes’ group indicates statistically significant superiority for the earlier bettors in three of the five performance measures. In seeking to explain this lack of conclusive performance differences across groups, it may be instructive to recall the role of information and, specifically, its comparative availability in the various time frames. It may be the case that the inferior informational base (incomplete and remote from the race) with which the pre-racing groups must necessarily work tends to balance the advantages of a decision environment less affected by conditions which tend to generate excitement. Similarly, the active racing groups’ superior information may compensate for the negatively distortive environmental disturbances. However, a more powerful explanation of the lack of more significant performance differences may lie in the nature of the groups themselves. Both the pre-racing and active racing groups comprise a large number of individual decisions made in an equally large and heterogeneous range of settings in terms of excitement influences and information availability. For example, the pre-racing groups cover bets made, typically, over a three-hour period. The active racing periods are arguably even more heterogeneous in comprising decisions made both outside and within the show periods of the relevant events, with correspondingly greater levels of variation in the factors which might generate excitement. Additionally, the temporal contiguity of the preand active racing groups suggests that an area of similarity around the margin is likely. Taken together, the observations regarding the characteristics of the groups featured in Procedure 1 and the more significant differences observed when comparing results in Table 2.1b invite a refinement of the way in which groups

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are defined. In particular, given the relatively extended timescales of the groups and the consequent range of environments within each group, it may be argued that the groups as defined are most appropriately regarded as either ‘cool’ or ‘warm’ environments in terms of the scope for excitement. In order to provide a clearer indication of the impacts of excitement, the betting periods under consideration need to be modified to allow a ‘cold/hot’ rather than a ‘cool/warm’ comparison. Specifically, this should involve the ‘ring-fencing’ of more tightly time-defined periods where it can be established with confidence that excitement is either largely absent or strongly present. A clue to the basis for this redefinition emerges from the comparison of results between the two variants of pre- and active racing periods given in Procedure 1. It has been noted that the distinction between pre- and active racing groups is statistically stronger where the pre/active distinction is set 15 minutes prior to the first show of the afternoon, rather than by the time of that first show. This appears to suggest a tendency for performance to improve, the more remote the placing of the bet relative to the active racing period, with its associated excitement-related influences. Procedure 2 involves a modified definition of groups designed to isolate environments which can, with confidence, be regarded as ‘cold’ and ‘hot’ in terms of their scope for excitement. This results in the following reformulation. Group C comprises all bets made prior to 11:30 am. As such, bets are temporally remote from the commencement of the afternoon racing programme and are made in a thinly populated betting office environment. Equally, they cover a relatively tight time-period of, on average, an hour and a half. It is reasonable to suggest that bets within this group are placed in an environment where excitement is likely to be minimal. Group H contains all bets placed in the second half of the show period, but excludes those bets placed after a point 30 seconds prior to the off-time of the race. As such, it excludes the cell of atypical behaviour identified from Procedure 1. Clearly, this time frame captures bets placed during the immediate prerace period where excitement and related factors are likely to be at their most evident. The a priori expectation regarding the comparative characteristics of decision-making across these groups is that if excitement-related pressures are influential, group C will significantly outperform group H. The results of Procedure 2 are given in Table 2.2. These results corroborate the expectation outlined above. In terms of comparative performance, the group whose bets were placed during the period with maximum scope for excitement performs markedly worse than the pre-11:30 group on all five performance measures. These results emerge in spite of the apparent informational advantages enjoyed by group H bettors and are indicative of some negative impact on performance associated with excitement. Procedure 3: It could, of course, be argued that the poor performance of group H bettors is due to factors in addition to excitement. For example, the inferior performance of those who place their bets in the later period could

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Table 2.2 Performance and staking: ‘cold’ pre-racing versus ‘hot’ active racing periods Group C (pre- 11.30 am) N = 130 Bets with returna Bets with profitb Stakes with returnc Stakes with profitd Return/stake

0.238 0.192 0.294 0.286 0.847

Group H (second half of show period) N = 247 * * ** **

0.150 0.117 0.184 0.089 0.403

Notes a, b, c, d See Table 2.la for definition of performance criteria * Significant difference between the statistics at the 0.05 level. ** Significant difference between the statistics at the 0.01 level. (See Table 2.la for details of statistical tests.)

partially be explained if this group of bettors were exposed to additional potentially distortive influences. A prime example of such an influence might be the consumption of alcohol, with its associated potentially negative impact on the formulation of decisions. The desirability of controlling for this factor derives first from the observation that alcohol consumption often appears as a feature of the betting office customer’s leisure activity and second from the fact that the opportunity for consumption of alcohol in public houses differs across earlier and later period bettors. Clearly, a considerable volume of earlier period betting takes place prior to the late morning opening of public houses, whilst later period bettors have had at least the opportunity for alcohol intake. The control for the potential impact of alcohol is achieved by comparing the performance of those who place bets in the first half of the show period (group L) with those who place bets in the second half of the show period (group H). Since these groups place their bets within a fairly tight time frame (the duration of the whole show period is generally about 15 minutes) similar exposure to alcohol can be safely assumed. However, as the time of the race approaches the level of excitement is likely to increase. If excitement-related pressures are the primary cause of poorer performance then group L bettors would be expected to outperform group H bettors. The results indicated in Table 2.3 clearly confirm this expectation, with bets placed in the period of maximum excitement performing worse than those placed in the period of lesser excitement using four of the five performance measures. Hypothesis 2: staking In terms of comparative staking levels, there is clear evidence to support the distinctions between bets placed in the periods of relatively greater and lesser excitement outlined in Procedures 1, 2 and 3. These differences are most acute when comparing the periods identified as ‘cold’ and ‘hot’ in terms of excitement

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Table 2.3 Performance of bets placed in the first half of the show period versus second half of the show period Group L (first half of show period) N = 347 Bets with returna Bets with profitb Stakes with returnc Stakes with profitd Return/stake

0.207 0.147 0.154 0.131 0.623

Group H (second half of show period) N = 247 * *

0.150 0.117 0.184 0.089 0.403

Notes a, b, c, d See Table 2.la for definition of performance criteria. * Significant difference between the statistics at the 0.05 level. (See Table 2.la for details of statistical tests employed.)

potential and are therefore consistent with expectations regarding the impact of excitement on staking levels (see Table 2.4). It should also be observed that there is a correlation between higher staking and poorer performance which suggests a further form of irrationality relating to decisions taken by bettors exposed to higher levels of excitement.

Discussion The procedures described in the previous section clearly demonstrate the distinct differences between betting behaviour in different time periods in terms of performance, variously measured, and staking. These cross-period differences are most significant when comparing environments which are defined, respectively, as ‘hot’ and ‘cold’ (Periods H and C) in terms of the presence or absence of environmental conditions which might generate opportunities for excitement. Specifically, the inferior performance and higher staking levels evident in Period H support the hypotheses that the presence of excitement materially affects performance and staking behaviour. As such, the results corroborate and extend earlier contributions in this area. In essence the results support the notion that the consumption of excitement involves a financial penalty. This cost can be measured in a variety of ways. For example from Table 2.2 it appears that a pound staked by a ‘cold’ period bettor has three times the prospect of generating a profit as compared with a pound staked by a ‘hot’ period bettor. Alternatively the ‘return/stake’ for ‘cold’ period bettors is more than twice that for ‘hot’ period bettors. The full cost of consuming excitement must additionally take account of the relative staking levels. Since the data indicate that, on average, ‘cold’ and ‘hot’ period bettors lose, the magnitude of loss in absolute terms will be magnified by higher staking levels. Table 2.4 indicates that ‘hot’ period bettors place stakes which are, on average, more than three times greater than ‘cold’ period bettors.

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Table 2.4 Average staking levels in different time periods (£) Periods of:

Average stake (£) (SD)

Lesser excitement

Greater excitement

Pre-first show of afternoon N = 394 1.43 (4.53)

Post-first show of afternoon N = 628 4.46 (11.93)

Pre-(first show of afternoon – 15 minutes) N = 347 1.33 (2.57)

**

**

Group C (pre-11.30 am) N = 130 1.37 (3.0)

**

Post-(first show of afternoon – 15 minutes) N = 674 4.30 (11.90) Group H (second half of show period) N = 247 4.22 (7.23)

Notes ** significant difference between the statistics at the 0.01 level. Since the above data are not normally distributed, a t test for the difference between mean staking levels was not appropriate. A logarithmic transformation of the data was therefore employed which created normally distributed data. A t test was then conducted on the transformed data. The transformed means and standard deviations are, respectively, as follows: –0.80 (1.43) –0.75 (1.37) –0.81 (1.40)

0.63 (1.31) 0.26 (1.56) 0.37 (1.51)

Since it is hypothesized that the individuals subjected to the greatest amount of excitement will commit higher stakes, one-tailed tests are employed.

It appears, therefore, that the exposure to excitement imposes a substantial financial cost on those who choose to consume it. It should however be noted that bettors, in maximizing their utility, may regard the financial cost as an acceptable price to pay for their excitement. Their continued participation in this leisure activity would tend to support this view and is in line with the findings of Filby and Harvey (1988) who conclude (p. 171): ‘For the majority of punters, then, it would seem that betting makes sense primarily as a recreational activity for which they are prepared to pay their own personal tariffs’. The remainder of this section explains the relationship between the findings of this study and existing work on the impact of excitement, before offering a brief reconsideration of the role of information in betting behaviour. This

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reconsideration is prompted by the fact that subsets of bets characterized by inferior performance (especially in Procedure 2) are associated with high levels of information availability – an intuitively unusual result. Finally, the possibility of interaction between separate areas of influence on decision-making is addressed. In relation to excitement, Brown (1986) has indicated that its presence accompanies markedly different gambling behaviour. Specifically Dickerson (1979) notes a relationship between size of stake and physiological manifestations of excitement. Similarly, Anderson and Brown (1984) record highly significant correlations between mean bet size and heart rate increases in a real gambling situation. The higher average staking levels noted in the current study for bets placed in time periods when excitement is most likely to be present confirm these findings. The results relating to comparative performance between bets placed in earlier and later time periods emerge in spite of the apparent informational advantages enjoyed by the latter groups, particularly in Procedure 2. While, prima facie, this appears to emphasize the distortive influence of excitement in the later periods, it also invites a reconsideration of the role of information in decision-making, where the rationalist view would regard more rather than less information as an asset. For example, Etzioni (1985) observes (p. 758): ‘Rationalist models of decision-making assume very high capacity of the actors to collect information, to process it, and to draw proper conclusions from the information and its interpretation’. By contrast, a number of studies point to the limitations on the ability of humans to process information effectively under certain circumstances. Complexity of the relevant information set may result in reliance on heuristics, non-rational strategies and biases (see, for example, Kahneman et al., 1982; Agnew and Brown, 1986; Eiser and van der Pligt, 1988; March and Simon, 1958; Keren and Wagenaar, 1985). Onken et al. (1985) indicate that as information load increases a decreasing proportion of additional information is processed. They argue that when task complexity is high, decisionmakers simplify their task by rejecting alternatives on the basis of little information. It is worth noting, in relation to ‘task complexity’, the qualitatively diverse nature of information to which betting office clients are exposed. In the immediate pre-race period, for example, the profile of odds available is subject to continual change. Other types of information to be considered are the appearance of horses prior to the relevant race (e.g. negative signs such as sweating, lameness, dislike for conditions underfoot as the horse canters to post) and the varying views of broadcast expert opinion. Clearly, there are ways in which increased information may simultaneously be regarded as an asset and a liability to the decision-maker. The net effect on any individual depends largely on that individual’s cognitive capacity. Given this, a reasonable assumption might be that the influence of differential information across excitement and nonexcitement periods might be neutral over a large number of individual decisions.

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Excitement in other leisure contexts The validity of using betting decisions as a window on decision-making in a broader leisure context has been widely supported, most notably in terms of the similarity between the characteristics of the betting decision and decisions made in other settings. Hence, factors which are likely to be influential in the betting decision include precedent, expectation, the assessment of risk and the analysis of a variety of forms of qualitative and quantitative information from various sources. Equally, each betting decision is essentially a speculative venture, involving financial commitment and an implicit judgement as to the future state of the world, the accuracy of which determines the future reward. Several authors have noted the value of betting markets in providing insights into wider decisionmaking under uncertainty. For example Gabriel and Marsden (1990) and Metzger (1985) confirm the ecological validity of the betting office as a setting for the observation of risk-taking behaviour. Snyder, discussing the validity of using betting data to explore wider decision-making behaviour, observes: If security markets and horse racing seem worlds apart, the difference is more apparent than real and can be explained largely by the social stigma society attaches to the latter. Both have common characteristics including . . . large numbers of participants, extensive market knowledge and ease of entry. Also . . . horse racing offers an opportunity to study economic decisionmaking under conditions of risk and uncertainty. (1978, p. 1109) This insight indicates the potential significance of the phenomena observed here for the understanding of the impact of excitement in a wider context. Further research, therefore, in other leisure contexts might be used to explore the extent to which individuals are prepared to incur a financial penalty for the privilege of consuming excitement.

Conclusion In summarizing the contributions of this chapter to the development of the literature on leisure betting, five should be emphasized. First, from a methodological viewpoint, its use of a large sample of real betting decisions, made in nonexperimental conditions, represents an important innovation. Second, in terms of the empirical results, it identifies clear behavioural distinctions between subgroups of the aggregate population, notably in decision performance and patterns of staking. Third, it argues that these distinctions are strongly suggestive of the importance of excitement as an influence on betting behaviour. Fourth, an attempt is made to cost the consumption of excitement. Finally, while the current chapter provides some insights into the impacts of excitement on betting behaviour, it also suggests that application of this form of investigation in other leisure contexts offers fruitful opportunities for further research.

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Acknowledgements The research reported here was made possible by grants from Ladbroke Racing and the co-operation of Ladbrokes and Extel to whom we are most grateful. Special thanks to Colin Walker, Douglas Hunter and the anonymous referees.

References Agnew, N. McK. and Brown, J.L. (1986) ‘Bounded rationality: fallible decisions in unbounded decision space’, Behavioural Science, 31: 148–61. Anderson, G. and Brown, R.I.F. (1984) ‘Real and laboratory gambling, sensation-seeking and arousal, British Journal of Psychology, 75: 401–10. Asch, P., Malkiel, B.G. and Quandt, R.E. (1982) ‘Racetrack betting and informed behaviour’, Journal of Financial Economics, 1: 187–94. Brown, R.I.F. (1986) ‘Arousal and sensation-seeking components in the general explanation of gambling and gambling addictions’, International Journal of Addictions, 21: 1001–16. Brown, R.I.F. (1988) ‘Arousal, reversal theory and subjective experience in the explanation of normal and addictive gambling’, in W.R. Eadington (ed.), Gambling research: proceedings of the Seventh International Conference on Gambling and Risk Taking, vol. 3: 165–87. Reno: University of Nevada. Bruce, A.C. and Johnson, J.E.V. (1992) ‘Toward an explanation of betting as a leisure pursuit’, Leisure Studies, 3: 201–18. Commission on the Review of National Policy Towards Gambling in America (1976) Washington, D.C.: United States Government Printing Office, (Stock No. 52–003–00243–4). Cornish, D.B. (1978) Gambling: A Review of the Literature and its Implications for Policy and Research, London: Home Office. Dickerson, M.G. (1974) ‘The role of the betting shop environment in the training of compulsive gamblers’, Behavioural Psychotherapy, 1: 24–9. Dickerson, M.G. (1979) ‘FI schedules and persistence at gambling in the UK betting office’, Journal of Applied Behaviour Analysis, 12: 315–23. Dickerson, M., Walker, M., England, S.L. and Hinchy, J. (1990) ‘Demographic, personality, cognitive and behavioural correlates of off-course betting involvement’, Journal of Gambling Studies, 6: 165–82. Downes, D.M., Davies, B.P., David, M.E. and Stone, P. (1976) Gambling, Work and Leisure: A Study Across Three Areas, London: Routledge and Kegan Paul. Eiser, J.R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Elias, N. and Dunning, E. (1986) Quest for Excitement: Sport and Leisure in the Civilizing Process, Oxford: Basil Blackwell. Etzioni, A. (1985) ‘Guidance rules and rational decision making’, Social Science Quarterly, 66: 755–69. Filby, M.P. and Harvey, L. (1988) ‘Recreational betting: everyday activity and strategies’, Leisure Studies, 7: 159–72. Gabriel, P.E. and Marsden, J.R. (1990) ‘An examination of market efficiency in British racetrack betting’, Journal of Political Economy, 98: 874–85. Gilovich, T. and Douglas, C. (1986) ‘Biased evaluations of randomly determined gambling out-comes’, Journal of Experimental Social Psychology, 22: 228–41.

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Johnson, J.E.V. and Bruce, A.C. (1992) ‘Successful betting strategies: evidence from the UK off-course betting market’, in W.R. Eadington and J.A. Cornelius (eds) Gambling and Commercial Gaming: Essays in Business, Economics, Philosophy and Science, Reno, US: Institute for the Study of Gambling and Commercial Gaming. Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgement under Uncertainty: Heuristics and Biases, New York: Cambridge University Press. Keren, G. and Wagenaar, W.A. (1985) ‘On the psychology of playing blackjack: normative and descriptive considerations with implications for decision theory’, Journal of Experimental Psychology: General, 114: 133–58. King, K.M. (1985) ‘Gambling: three forms and three explanations’, Sociological Focus, 18: 235–48. Kusyszyn, I. (1984) ‘The psychology of gambling’, The Annals of the American Academy of Political and Social Sciences, 474: 133–45. Lafferty, T. and Higbee, K.L. (1974) ‘Realism and risk-taking’, Psychological Reports, 34: 827–9. March, J.G. and Simon, H.A. (1958) Organisations, New York: Wiley. Metzger, M.A. (1985) ‘Biases in betting: an application of laboratory findings’, Psychological Reports, 6: 883–8. Murphy, P., Williams, J. and Dunning, E. (1990) Football on Trial: Spectator and Development in the Football World, London: Routledge. Onken, J., Hastie, R. and Revelle, W. (1985) ‘Human perception and performance’, Journal of Experimental Psychology, 11: 14–27. Saunders, D.M. and Turner, D.E. (1987) ‘Gambling and leisure: the case of racing’, Leisure Studies, 6: 281–99. Slovic, P. (1969) ‘Differential effects of real versus hypothetical payoffs on choices among gambles’, Journal of Experimental Psychology, 80: 434–7. Snyder, W.W. (1978) ‘Horse racing: testing the efficient markets model’, Journal of Finance, 33: 1109–18. Watson, J.S. (1985) ‘Volunteer and risk-taking groups are more homogeneous on measures of sensation seeking than control groups’, Perceptual and Motor Skills, 61: 471–5.

3

Successful betting strategies Evidence from the UK off-course betting market J.E.V. Johnson and A.C. Bruce

The objective of this chapter is to conduct an empirical investigation of betting decisions made by individuals in the UK non-parimutuel betting market. More specifically, it investigates the existence of evidence for identifiable subclasses of bettor, characterized by their superior performance in terms of quality of betting decisions made and associated financial returns. A distinctive feature is the use of documented evidence of actual decisions made in a large number of betting shops throughout Great Britain. This allows important extensions to earlier work which seeks principally to identify profitable betting opportunities within markets, but which is unable to offer an analysis of the nature of bettors’ individual decisions. A significant and novel feature of this study is its ability to assess whether profitable opportunities are identified and exploited by bettors and to quantify the profit opportunities available by comparing the performance of betting across different groups. These features are in large part a function of the unique database employed within the study, which is described in detail. In explaining differential performance, the authors draw both on the literature relating to information and market efficiency, and that relating to the effects of environmental stimuli on the nature and quality of decision-making under uncertainty, thus integrating perspectives on the issue which have to date remained separate.

Betting: opportunities for gain – a brief review There has been considerable interest in the analysis of betting markets over the last decade. Much of the interest has been generated by a belief that betting market analysis may offer important insights into the functioning and efficiency of wider financial markets and the decision-making behaviour of agents within such markets, given that betting and other financial markets share many common characteristics. In providing a brief review of the literature as a context for this study, the emphasis is placed on those studies which have sought to identify opportunities for profitable betting behaviour within the aggregate betting market. The approaches adopted, together with the results of these studies, will be evaluated. This evaluation forms an important basis for the development of the method employed in this study.

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Much of the literature relating to the notion of a class of bettor characterized by superior performance involves testing for the existence of differential opportunities for financial gain across different segments of the aggregate market relating to a particular betting event. Identification of such ‘cells of opportunity’ suggests some degree of market imperfection, in the sense that a perfect market would feature perfect dissemination of information and the erosion of profit opportunities. An important contribution in this area which merits extended consideration is that of Asch et al. (1982). This paper investigates, inter alia, the notion of an ‘informed’ subset of bettors via an analysis of minute-by-minute changes in pari-mutuel odds for the 729 horse races which took place at Atlantic City during the 1978 season. Subgroups of the aggregate betting population are defined by the proximity of their wager to the race time. Asch et al.’s procedure involves initially calculating the ratios of ‘marginal’ to ‘morning line’ odds for a variety of time-defined subgroups of the betting population. ‘Marginal’ odds are those which describe the betting activity on a particular horse within a particular time frame or cycle during the betting period. Morning line odds are those estimated by the racetrack’s professional handicapper and are published in the race card. The ratios of marginal to morning line odds are then compared with the ratios of final pari-mutuel to morning line odds for horses occupying the first four positions in each race. Where the ratio of marginal odds to morning line odds is less than the ratio of final odds to morning line odds, then those bettors within that time frame are identified as superior predictors of outcome compared with the aggregate market (reflected in final odds to morning line odds). Asch et al.’s results show that for horses placed first, the ratio of marginal to morning line odds for those betting in (1) the last eight minutes, and (2) the last five minutes before the race are 0.79 and 0.82, respectively, compared with a final odds to morning line ratio of 0.96. These results are suggestive of superior betting decisions by those in the latter stages of the betting market, which Asch et al. cite as typically lasting for around 25 minutes prior to the race. The rationale offered for this pattern is that ‘informed’ bettors place their bets late in order to minimize the amount of time available for the wider betting public to observe support for a particular horse, which would be likely to result in replica bets, which would in turn drive down the return to all who had made that selection. Subsequent contributions from Asch et al. (1984, 1986) explore further the opportunities for the development of profitable betting strategies. Their conclusions are largely unsupportive of the existence of profitable win betting strategies and sceptical as to the existence of profitable place betting strategies. Crafts (1985) presents a modification of the methodology developed in Dowie (1976) which had concluded that the UK betting market was not ‘strongly inefficient’. Crafts focuses on the performance of horses where the price forecast in the specialist media (i.e. The Sporting Life) is substantially greater than the starting price (suggesting an increased probability of success as perceived by market behaviour). He demonstrates significant profitable

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opportunities for a betting strategy based on backing all such horses for bets placed at the forecast price. The opportunity for profit becomes negligible, however, for the same selections if bets are placed at starting price. Consideration of horses, the prices of which fall substantially in the on-course market, offers results which support the view that those with prior information relating to these horses are in a position to make a profit. This opportunity arises since their opinion of these horses’ chances of success is superior to that taken by oncourse bookmakers at the start of trading. Bird and McCrae (1988a) analyse non-parimutuel Australian betting markets and conclude that in terms of the movement in bookmaker odds through the course of a betting market, the market is efficient and profitable strategies are unavailable. However, given prior knowledge of subsequent price movements, profitable strategies would be available. This ‘prior knowledge’ could be assumed to reside with those bettors who have private information at the commencement of betting and who are aware of the impact on subsequent prices which the use of that information will have. This conclusion is very similar to that offered by Crafts (1985) and is confirmed by Bird and McCrae (1988b). They additionally suggest that the market is also efficient in its use of information supplied by newspaper tipsters. In assessing the recent literature relating to betting market efficiency and the possibility of information-related opportunities for profitable betting strategies, a number of observations may be made: 1

2

3

There is a reasonable consensus that betting markets are, in the main, relatively efficient. On the evidence available, this would seem to apply to both pari-mutuel and bookmaker-based markets. There is some support for the notion that cells of profit opportunity may exist in theory (e.g. Asch et al.’s place betting, Crafts’ informed ‘insiders’) but that in practical terms they are unlikely to be exploitable. Crafts (1985), however, suggests that the observation of publicly available price changes by bettors without inside information would allow them to discount horses with lengthening prices from their consideration, so allowing a markedly improved performance relative to bettors in general. In the absence of data relating to actual individual betting decisions, most studies focus on identifying profitable opportunities within the aggregate betting market. Though Asch et al. (1982) deal in aggregated actual decisions in different time-defined cells of the market, they are unable to say anything about the composition of betting behaviour within each cell (e.g. is the betting activity in the last five minutes of the market accounted for by many small wagers or, at the limit, one very large wager?). In the absence of individual bet information, our understanding of the nature of the ‘informed’ bettors’ behaviour is necessarily very limited. The previous studies are unable to quantify rates of return to actual betting behaviour. Asch et al. (1982) conclude that ‘the data contain a suggestion that there is an “informed” class of racetrack bettors’ but concede that ‘it is

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4

5

6

45

not possible, however, to define the rates of return that may be earned by this group’. Those studies which focus on the identification of profitable opportunities provide hypothetical rates of return, but in the absence of analysis of actual decisions made, we cannot say whether these rates are actually earned. Each of the studies considered is fairly limited in terms of the locations considered. A number focus on activity at a particular racetrack, for example. There may be a tendency for some degree of bias within such studies. For example, in a British context, one might have grounds for expecting a betting market at a training centre such as Newmarket to be considerably more ‘informed’ than a market at, say, Wolverhampton. There is little discussion of the impact of environmental stimuli on betting behaviour and performance. Consideration of the literature relating to the psychology of decision-making under uncertainty would suggest that environmental factors may be influential in explaining, for example, different levels of performance across time- or location-defined subgroups of the aggregate betting market. The literature considers both pari-mutuel and bookmaker systems of betting markets, but significant differences in the use and the value of information between the systems is generally understated. For example, while Asch et al.’s explanation for the late betting of their informed class of bettors is plausible in the pari-mutuel system, it would be less convincing in a bookmaker system. The different roles of information in the two market systems are discussed further below.

In summary, the contributions cited in this brief review offer a number of interesting insights into the role of information in betting markets, its implications for maker efficiency and the opportunity for the development of profitable betting strategies. The above observations would, however, suggest a case for a methodology which is able to: 1

2

3

Collate and analyse actual betting decisions made by individuals within betting markets. This would enable the research to go beyond the identification of theoretically profitable betting opportunities and to conduct direct empirical tests for the existence of cells of profitable betting activity. The characteristics of such cells could be isolated and the rates of return to variously defined subpopulations of the aggregate betting market could be quantified. Provide a geographically broad survey of betting behaviour, less sensitive to location-specific effects than earlier studies, which have been confined to betting activity at a single racetrack. Accommodate the possible influence of environmental stimuli in seeking to explain betting behaviour and performance. This would broaden the current explanatory base which focuses on considerations of the bettor’s attitude to profit and risk.

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The following section describes how this study has attempted to develop a methodological approach which seeks to incorporate the above features.

Database and methodology This section describes the database and methodology associated with the results which follow. It will be seen that the approach draws on the lessons offered by earlier studies in the area and offers the potential for a more detailed insight into the nature of individuals’ betting behaviour and performance. Before outlining in detail the nature of data collected for this analysis, two general features need to be mentioned. First, the data relate to bets made in a non-pari-mutuel betting market. This carries potentially important implications for the subsequent analysis. In non-pari-mutuel markets, the bettor has the opportunity to determine the odds at which the bet, if successful, will be settled. In other words, where a bet is placed on the basis of information known to the bettor, they may choose to appropriate fully any returns to that information by ‘taking’ the price on offer (the board price) when the bet is placed. Where the price is not taken, then the bet is settled at starting price, which is determined by the full weight and distribution of money bet at the course. Clearly in this system, whether or not to take the price becomes a necessary and critical aspect of the decision. The implications of this are discussed further in the next section. As observed earlier, this contrasts with the pari-mutuel system, where the ultimate odds at which the bet is settled are necessarily a function of the weight of money placed on a particular selection by both the ‘informed’ bettor and all others who bet on that particular horse. In other words, the returns to information in a pari-mutuel system are not wholly appropriable. This would suggest that the informed bettor in the non-pari-mutuel market is likely to be less sensitive to the possibility that his betting behavior may induce replication. So long as a price is taken, replication is costless to the informed bettor. Consequently, for non-pari-mutuel markets, the emphasis should shift away from the idea that betting behaviour is largely influenced by the signals the informed bettor sends to the market, via his actions. Rather, it should focus on the notion that betting behaviour is principally influenced by the information which the bettor perceives from the price changes in the evolving market. A second broad feature of the data is that, in contrast to earlier studies, it relates to bets placed in betting shops rather than at the racetrack As such, it may be desirable to seek to incorporate the possible influence of the betting shop environment into the analysis of decision-making behaviour. There is a considerable literature relating to environmental impacts on the nature and performance of decision-making and the analysis which follows will suggest that the understanding of betting behaviour may be enriched if economic and psychological perspectives on the decision-making process are combined.

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The basic raw material of the database is the betting slip which provides detailed characteristics of each bet placed in a betting office. This includes the level of risk, as evidenced by the type of bet and the ‘risk’ implicit in the odds; the size of the investment; the exact time of the investment; and the location of the betting shop. Approximately 1,200 bets, randomly selected from a larger sample and representing betting decisions made in offices throughout Great Britain during March and April 1987 form the basis for the results reported below. All of the bets in the database prepared for this study are ‘single’ bets on horseraces. More complex bets, for example accumulators or forecasts, have been set aside for separate analysis. The most important and distinctive feature of this data set is that it comprises real betting decisions, each selected randomly and without the knowledge of the bettor involved, thereby avoiding any ‘observation’ effects. This was achieved by the betting office staff removing a random selection of betting slips following the close of business.1 This was an arrangement made possible by the co-operation of Ladbroke Racing, the largest single bookmaking organization in Great Britain, and involved all their betting offices. As such, it is suggested that the data in this study have clear advantages over both laboratory-based simulations of the betting shop and those studies which have used actual betting shop data, but which have involved the presence of the researchers in the betting shop (e.g. Dickerson, 1979, and Shewan and Brown, 1988). For each decision recorded, a further range of relevant information was assembled. Most significantly, the use of precisely timed transcripts of betting information transmitted to betting offices by Extel2 allows an accurate picture of the exact nature and range of information (most notably price information) available to the decision-maker at the time that the decision was made. This is clearly of importance in evaluating the response of bettors to information as it emerges through the price mechanism. Rates of return to each individual betting decision are calculable by referring to the results of the relevant events. These may be aggregated in various ways to provide average rates of return to bettors within particular cells of the aggregate market. Similarly, the database allows comparison of different groups’ success rates – both in terms of the percentage of correct decisions as well as rates of return. Analysis of further characteristics of each betting decision or group of decisions (e.g. propensity to bet to win – rather than each-way, propensity to ‘take’ the price offered, propensity to select short-priced horses, to bet high stakes, to pay tax on the bet, etc.) may offer insights into the reasons for any identified performance differentials across subgroups of bettor. In summary, this database allows the research programme in this area to go well beyond the identification of profitable opportunities within betting markets and to analyse directly actual betting behaviour and performance from a variety of perspectives. Necessarily, for the purposes of this chapter, the authors have focused on a small set of related investigations. These, together with their associated results are outlined and analysed below.

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Results and analysis The initial line of investigation relates to the comparative performance of betting sub-populations, defined by the time at which bets were placed relative to the start of the relevant betting event (horse race). As such, it addresses the issue raised by Asch et al. (1982), albeit in the context of a bookmaker, rather than a pari-mutuel betting market. More specifically, the aggregate population was split between those who placed bets in advance of the first ‘show’ of betting reported to betting offices (T1),3 those who placed their bets during the ‘show’ period (T2)4 and those who placed their bets in the last 30 seconds prior to the start of the race or in the period immediately after the start of the race (T3). This basis for splitting the populations differs from the Asch et al. study, which was necessarily confined to consideration of betting within the show period, there being no opportunity for pre-show betting in a pari-mutuel system. The rationale for the approach followed here is to probe the effect of exposure to market-generated information on performance. Pre-show, there is no market-generated information; during the show period there is a turbulent and evolving information set; at the end of the show period, all market-generated information has emerged. Table 3.1 presents a number of indicators of comparative betting performance across the three time periods (T1, T2 and T3) discussed above. The percentage of Table 3.1 Indicators of bet performance in different time periods Time periods

Bets with a retuma Bets with a profitb Stakes with returnc Stakes with profitd

% % % %

T1

T2

T3

22.2 21.0 19.1 18.9(t3)

17.1(t1) 17.0 12.8(t1) 10.9(t1)

21.7 27.1(t2)+ 19.6(t2)+ 26.3(t2)+

Notes a Number of bets (irrespective of stake size) producing a positive return, which may be less than the amount staked, divided by the total number of bets placed. b Number of bets (irrespective of stake size) producing a return greater than the amount staked, divided by the total number of bets placed. c The total amount staked which produced a positive return, divided by the total amount staked. d The total amount staked which produced a return greater than the amount staked, divided by the total amount staked. e.g.

Bet 1 2 3

Stake (£) 10 4 6

Return (£) 20 0 2

Bets with a return % = 2/3 = 66.7%. Stakes with profit % = 10/20 = 50%. + = significant difference between the three statistics at the 0.05 level. ti (where i = 1, 2, 3) = significantly different from time period Ti at the 0.05 level. All ‘ti’s in parentheses indicate where (conservative) multiple comparison procedures also suggest significantly different from time period Ti at the 0.05 level.

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bets (irrespective of stake size) producing a return and the percentage of bets producing a profit are suggestive of some degree of inferior performance during T2. Consideration of the percentage of bets generating a profit yields a statistically significant difference between the three periods as a whole, and specifically between periods Tl and T2 and also periods T2 and T3. These results are confirmed and strengthened when the size of stake is included in the analysis. Thus, the percentage of stakes producing a positive return and those producing a profit indicate that stakes placed in T3 significantly outperform those placed in T2 and, to some extent, those placed in T1. Those bets placed in T3, in fact, produce a return/stake ratio of 0.91, compared with 0.5 in T2 and 0.78 in T1. Before considering further characteristics of betting across these periods, some tentative explanations for the performance differences are explored. A first proposition is that performance differences across groups may be related to the degree of market-generated information available to each group at the time of betting. This would appear to offer some explanation for the superior performance of T3 bettors over each of the other groups. Period T3 bettors’ decisions follow exposure to the full set of market-generated information. It is less obvious, in terms of access to exploitable information, why those betting in the absence of any market-generated information (Tl) should significantly outperform those in T2, who enjoy partial exposure to such information. One explanation for this may be that a bet placed during the evolution of the market may be vulnerable to the fact that prices in betting markets do not necessarily develop in a uniform or systematic fashion. For example, the horse which, due to its drifting price, appears to reflect lack of market confidence midway through the show period may be subject to late interest so that, by the end of the show period (in T3), its shortening price suggests that considerable market confidence has developed. The bettor placing his bet at the midway stage is basing his decision on an incomplete (and possibly misleading) set of information. In general terms, however, it may be difficult to accept that some information is worse than none as a basis for successful decision-making under uncertainty. Therefore, in enhancing our explanation of performance differences, we may need to consider factors, other than the completeness of the information set, which differ across the three periods in question. In developing this line of enquiry, the literature relating to the psychology of decision-making under uncertainty offers important insights. Two aspects of this literature are considered here: • •

The impact of environmental stimuli within the physical decision-making environment on the decision-maker’s behaviour and performance. The impact of complex, varied and dynamic information on the decisionmaker’s behaviour and performance.

On the first aspect, Dickerson (1979) pointed to the influence of environmental stimuli experienced by bettors in betting shops. He suggested that the

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typical sequence of pre-race announcements, e.g. ‘the horses are parading’, ‘they’re going down’, ‘they’re going behind’, ‘they’re being loaded up’, etc., raised levels of excitement and tension with potentially negative impacts on decision performance. He further suggested that the propensity to bet late might be attributable to the fact that this allowed maximum exposure to the excitement generated by the stimuli. He therefore discounted the notion of late betting as skilful, in terms of maximizing exposure to market-generated information. Clearly, in terms of our results, bets placed in T2 are made in an atmosphere charged with anticipation and excitement associated with sequential, race-specific announcements, so that Dickerson’s perspective may have a role in explaining that group’s poor performance. What is less immediately clear is why the T3 bettor, who has presumably also been exposed to these announcements, performs significantly better than the T2 bettor. It could be argued, however, that the rationality inherent in permitting oneself exposure to the full informational content of the market throughout the betting period is consistent with an individual who is less susceptible to the ‘excitement’ diversion and whose understanding of the need for careful and unemotional scrutiny of all available information is more sophisticated than the T2 bettor’s. A second aspect of the psychology of decision-making relates again to information. Rather than considering (as above) information from the economist’s perspective as a ‘commodity’ which assumes value in the presence of uncertainty, the psychological approach is to consider the effect of informational complexity, variety and dynamism on the individual’s ability to use that information in a way which assists effective decision-making. Eiser and van der Pligt (1988) provide a useful survey of the literature in this area. This includes reference to Abelson and Levi’s (1985) observation that there is a tendency for those exposed to large volumes of information to adopt simplifying decision procedures in situations of ‘information overload’ and to Janis and Mann’s (1977) observation that where a decision involves the weighing of positive and negative factors, the decision, once reached, tends to be held with more confidence and to be less sensitive to new information which might suggest grounds for amending the decision. The impact of these ‘cognitive constraints on effective decision-making’ are summarized as being important in two respects: Firstly, individuals tend to use simpler and less optimal choice rules as the information load increases. Usually accuracy declines considerably when the number of features or the number of alternatives increases. Secondly, the reliability with which choice rules are used tends to decrease as the decision-maker’s information load increases. Two further ‘non-cognitive’ constraints dealt with by Eiser and van der Pligt (1988) may have some explanatory power. First, what is described by Janis and Mann as hypervigilance, where excessive search for information and inability to discriminate between relevant and irrelevant information lead to ‘decision

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paralysis’. In countering this, the decision-maker’s behaviour may instead be characterized by: lack of vigilant search, distortion of the meaning of information, selective inattention and the construction of rationalizations. Janis and Mann argue that these avoiding tendencies are most likely to happen when stress is high. When stress is moderate interest in information is more likely to be open-minded. A second non-cognitive constraint, coined by Janis (1972, 1982) ‘groupthink’ may also have some bearing on the results reported above. ‘Groupthink’ describes ‘. . . a strong psychological drive for consensus within nuclear, selfcohesive groups, such that disagreement is suppressed’. Taken together, these psychological insights may go some of the way to explaining the results relating to comparative performance across subgroups and in particular the poor performance of those bettors who make their decisions during the active betting market (T2). Certainly, a number of the phenomena held responsible for distortion of the decision-making process would appear to be present in the betting office in the pre-race period. The bettor’s view of the outcome of a horse race is, for example, likely to be dependent on a whole range of qualitatively distinct characteristics. To name a few, there is the horse’s form, in absolute terms and relative to the other runners, the weight it carries, the distance of the race, the ‘going’ (condition of track), the jockey’s ability, the trainer’s form and perceived ability, the market’s evaluation of the horse’s prospects, the horse’s pre-race behaviour, etc. The list is large and varied. Additionally, certain elements of this information may be subject to rapid and continual change during the pre-race period. Most significantly, the price of the horse is subject to change, but bettors may also expect to hear news regarding pre-race behaviour, stable confidence, going or jockey changes, or ‘expert’ opinion. Naturally, some aspects of new information will be received as optimistic signs, others as pessimistic. In other words, in addition to its breadth and variety, the information set available to the bettor is also dynamic, requiring continual reappraisal. In these circumstances, it might not be surprising if the bettor chose to rely on one particular type of information, e.g. the jockey, or even simply on hunch. The notion that rational cognitive processes may be suppressed in this complex informational environment holds some appeal. As regards what Eiser and van der Pligt term the ‘non-cognitive constraints on effective decisionmaking’, it seems reasonable to acknowledge the presence of stress in the betting office, as manifested, for example, by the loud, enthusiastic and often frantic encouragement offered to jockeys and horses by bettors who are able to listen to or view their selections’ fortunes via the office’s audio or televised service. The concept of ‘groupthink’ may also be present to a degree, where established ‘clubs’ of bettors meet in a regular venue and opt to share both the successes and failures with their peers by suppressing individual evaluation and conforming to a consensus.

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In summarizing our explanation of performance differences between the three identified classes of bettor, two strands of literature are important – that relating to information and its use, and that which acknowledges the impact of environmental stimuli on decision-making. In terms of access to market-generated information, the T3 bettor enjoys the advantages of a full information set, the T2 bettor has some information but during the show period the information set at any particular time may provide misleading signals. The Tl bettor has no marketgenerated information, but equally does not face the hazards of partial information experienced by the T2 bettor. Incorporating the psychological dimension allows us to suggest that the T2 bettor’s partial information problem may be compounded by susceptibility to excitement from betting office stimuli, to information overload associated with the information-intensive pre-race period and to stress and group pressures. Each of these factors may be viewed as inhibiting the individual bettor’s ability to maximize his performance as a decision-maker and would therefore seem to enrich understanding of our results. The T3 bettor, aware of the importance of accessing and rationally evaluating all available market information (as evidenced by the timing of his bet), might be expected to be less susceptible to external disturbances and more capable of analysing complex and changing information sets. Again, the psychological dimension would appear to offer some reinforcement to the argument for superior performance based on access to information. The T3 bettor, though exposed to the environmental characteristics catalogued above, certainly in terms of excitement and informational complexity relating to the race on which he bets, appears relatively invulnerable to them. In terms of isolating opportunities for profitable betting strategies, this section suggests that there may be benefits associated with delaying bet placement until the market for the relevant event is fully developed, so long as the bettor is confident that his rational consideration of available information will not be adversely affected by his presence in the betting office. In developing this line of enquiry, the reasons for enhanced betting performance in T3 are explored. This involves a further disaggregation of the betting population by investigating the composition of each time-defined subgroup in terms of the board price and starting price bets in each time call. The performance and other characteristics of these different bet types are then considered. The significance of the decision on whether to take board price or accept starting price in bookmaker-based betting markets has been discussed. To reiterate briefly, in this type of market, the bettor is able to guarantee his return to a correct selection by ‘taking’ the board price. If he chooses, alternatively, to accept starting price, then his return is dependent ultimately on the betting behaviour of the whole market. It may be suggested therefore, that the taking of a board price implies that the bettor is confident that he possesses information which, should it become known and be generally regarded as credible, would drive the price down, below the board price taken.

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Board price taking may thus be viewed as a strategy associated with a bettor who is qualitatively well informed (with, for example, access to privileged information from a stable). This informational advantage may be seen as distinct from the late bettor discussed above, who is in a sense quantitatively well informed, in terms of his exposure to all market information at the time of his decision. It should be noted, however, that these two types of informational advantage are not mutually exclusive. Table 3.2 presents similar results to Table 3.1, but with additional disaggregation, of bets by board price (hereafter BP) and starting price (SP). Two aspects of these results merit particular attention. First, the splitting of bets between SP and BP clearly indicates a tendency for BP bets to perform better overall. This result offers tentative support to the notion that the taking of a BP may be indicative of some informational advantage. Much more striking, however, is the contrast between the performance of SP and BP bets in T3, where BP bets, on all three performance measures, are strongly superior to SP bets. This suggests, of course, that much of the overall performance superiority of the T3 bettor is accounted for by T3 BP bettors. Indeed, if we consider the comparative performance of SP bets across the three periods, the T3 superiority disappears. An immediate observation relating to the identification of this cell of exceptional betting performance is that it represents the coincidence of late betting and BP betting which we suggested might be indicative of quantitative and qualitative informational advantage, respectively. The magnitude of the differential between this cell and others suggests that the combination of these advantages may generate synergy effects in terms of resultant performance. Table 3.2 Indicators of bet performance in different time periods, disaggregated by BP and SP Time periods

Bets with return

%

Bets with profit

%

Stakes with return

%

Stakes with profit

%

SP BP SP BP SP BP SP BP

T1

T2

T3

All

19.1* 38.5 17.0* 30.2 21.4 20.4b3 18.8s2* 19.2b3

13.5* 24.1 10.8 16.8 15.0 18.7 8.0* 13.4

16.2* 50.0b2 14.9* 43.3b2 14.4s1* 52.4b2 14.2* 50.6b2

17.1* 32.3+ 14.9* 24.7+ 17.0+* 25.8+ 13.7+* 22.2+

Notes * = Significant difference between SP and BP bets in a given time period at the 0.01 level. + = Significant difference between T1, T2 and T3 at the 0.01 level. bi = Significantly different to time period Ti for BP bets at the 0.05 level (multiple comparison procedures). si = Significantly different to time period Ti for SP bets at the 0.05 level (multiple comparison procedures).

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J.E.V. Johnson and A.C. Bruce Table 3.3 Return/stake Time periods

SP BP

T1

T2

T3

0.84 0.67

0.44 0.57

0.63 1.47

Table 3.3 offers further evidence regarding the comparative performance across subgroups of bettors, in terms of rates of return to betting activity in the different cells. The pattern of comparative performance noted earlier is confirmed by these results. Significantly, for both SP and BP bets, the T2 bettors yield the lowest rates of return. The T1 bettor results demonstrate considerably better performance relating to SP bets. Clearly the most striking result concerns the performance of those bettors who place BP bets in T3. This is the only cell realizing a positive rate of return and the magnitude of the return confirms the cell as one of distinctly superior performance (significantly superior to SP bets in T3 and to both SP and BP bets in T2 at the 0.05 level). This result, therefore, offers strong corroboration for the earlier findings: the most successful bettors appear to be those who both possess superior quality information, returns to which are guaranteed by BP betting, and who use that information against a background of full exposure to market-generated information. An aspect of this cell’s behaviour which may require some additional explanation relates to the taking of BP at such a late stage in the betting market, as clearly the shorter the time span between bet placement and the start of the race, the smaller is the opportunity for the BP taken and the SP to differ. The incentive, under such circumstances, to take the BP may be explained in terms of the informed bettor’s awareness that any insider knowledge relating to his selection which exists at the racecourse is likely to be exploited by the placing of relatively large wagers immediately prior to the start of the race. This allows the informed bettor at the racecourse to monitor evidence of market developments and his horse’s behaviour prior to committing his money. Once the bet is placed, it is likely to affect the SP, which is established independently at the racecourse at the start of the race. Where such informed late betting occurs at the racecourse, it may well be the case that the declared SP is shorter than the last BP available to the betting office customer, due to the time lag between price changes on-course and their transmission to betting offices. Hence the informed betting office customer’s rational course of action is to take the last BP available, to insure against the erosion of returns by late on-course betting. Now that clear evidence for a cell of superior performance has been established, the final element in this analysis of cross-group betting characteristics is a comparison of average stake sizes. This allows the identification of any correlation

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Table 3.4 Average stake (£) Time periods

SP BP

T1

T2

T3

1.83 4.76

3.51 7.50

4.75 12.24

between performance and the degree of financial commitment. An a priori expectation is that if members of a subgroup are aware of their superior performance, then that might lead to increased average stakes for members of that group. Table 3.4 provides average stake sizes for groups of bettors, classified according to the time and the type (BP or SP) of bet. These results indicate (at the 0.05 level) that stakes on BP bets are significantly larger than those at SP and that there is a significant time dimension to the stake levels. This analysis demonstrates clearly that the cell associated with the best performance, T3 BP, is also that which bets the highest average stake. This invites the conclusion that the rationality inherent in the profitable use of information is confirmed by the strategy of placing larger bets where the chances of gain are highest. Similarly, if we consider those bettors in T2 to be less rational in the sense that they deny themselves exposure to all market information and permit themselves to be exposed to potentially damaging environmental stimuli, then this lack of rational behaviour is also confirmed by their propensity to stake relatively large amounts on bets where the opportunity for gain is lowest. Average stake for T2 SP betting is £3.51 compared with an average for all SP bets of £2.79; average stake for T2 BP betting is £7.50, compared with an average for all BP bets of £7.05. Summarizing, these results invite the view that more informed bettors are aware of their informational superiority and stake to reflect their greater confidence; less informed bettors appear less aware of their informational inferiority, however, so that their stakes remain relatively high in spite of their poor performance.

Conclusions The contributions of this chapter lie in three main areas. Methodological innovation Of central importance in this respect is the development of the dataset from which the results are derived. The distinctive feature of the dataset is its use of a large and geographically broad set of real betting decisions, details of which are individually recorded and reinforced by independent and precisely timed data relating to all developments in the betting market associated with each bet.

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This system offers clear advantages over those studies which have relied on data relating to one or a limited number of betting offices or racecourses, those which are based on laboratory simulation of betting behaviour and those which confine their attention to the identification of profitable betting opportunities, without being able to monitor whether opportunities are exploited. Results The novel and comprehensive nature of the database opens up new possibilities in the derivation of results. For the first time it is possible to examine, in detail, characteristics relating to the actual betting behaviour of variously defined subgroups of the aggregate betting population. Most importantly, the database permits accurate measurement of rates of return to betting activity in different groups. Additionally, it is possible to identify cross-group behavioural differences relating to types of bet, categories of horse selected and levels of stake. The detail relating to the development of betting markets through time allows a sensitive evaluation of the response of betting behaviour to market-generated information. Analysis The distinctive contribution of this chapter in the analysis of betting behaviour is its integration of economic analysis, relating to the use of information under uncertainty and psychological analysis, acknowledging the importance of environmental factors on decision-making. This integrated approach allows the development of richer insights and explanatory power in relation to betting behaviour.

Notes 1 A procedure was used to ensure a chronological spread of bets throughout the shop’s business hours. 2 During the period covered by this analysis, Extel plc provided an audio commentary to betting offices, indicating price changes at the course, other course information (e.g. jockey changes, going reports, when horses were parading, going to post, etc.) and a race commentary. 3 Tl extends from the opening of the betting shop (typically 10:15 am) until the first Extel announcement of course prices available in the betting shop on the race which is the subject of the bet. 4 T2 extends from the end of period Tl until 30 seconds prior to the start of the race which is the subject of the bet.

References Abelson, R.P. and Levi, A. (1985) ‘Decision-making and decision theory’, in G. Lindzey, and E. Aronson (eds), Handbook of Social Psychology, vol. 1, New York: Random House.

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Asch, P., Malkiel, B.G. and Quandt, R.E. (1982) ‘Racetrack betting and informed behavior’, Journal of Financial Economics, 1: 187–94. Asch, P., Malkiel, B.G. and Quandt, R.E. (1984) ‘Market efficiency in racetrack betting’, Journal of Business, 57: 165–75. Asch, P., Malkiel, B.G. and Quandt, R.E. (1986) ‘Market efficiency in racetrack betting: further evidence and correction’, Journal of Business, 59: 157–66. Bird, R. and McCrae, M. (1988a) ‘Racetrack betting in Australia: a study of risk preferences and market efficiency’, in W. Eadington (ed.), Gambling research: proceedings of the Seventh International Conference on Gambling and Risk-taking, vol. 4: 228–58. Reno: University of Nevada. Bird, R. and McCrae, M. (1988b) ‘The efficiency of gambling markets revisited’, in W. Eadington (ed.), Gambling research: proceedings of the Seventh International Conference on Gambling and Risk-taking, vol. 4: 2–25. Reno: University of Nevada. Crafts, N.F.R (1985) ‘Some evidence of insider knowledge in horse race betting in Britain’, Economica, 52: 295–304. Dickerson, M.G. (1979) ‘F.I. schedules and persistence at gambling in the U.K. bettingoffice’, Journal of Applied Behavioural Analysis, 12: 315–23. Dowie, J. (1976) ‘On the efficiency and equity of betting markets’, Economica, 43: 139–50. Eiser, J.R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Janis, I.L. (1972) Victims of Groupthink. Boston: Houghton Mifflin. Janis, I.L. (1982) Groupthink (2nd edn) Boston: Houghton Mifflin. Janis, I.L. and Mann, L. (1977) Decision Making: a Psychological Analysis of Conflict, Choice and Commitment, New York: Free Press. Shewan, D. and Brown, R.I.F. (1988) ‘Cognition, self esteem and fixed interval conditioning in off-course betting’. Presented to the Society for the Study of Gambling, London, May.

Part II

The impact of complexity on decision-making behaviour Introduction This part contains five chapters. These examine the impact which different types and degrees of complexity have on the choice of individuals to engage in risk taking and betting, the risk strategy they adopt and the level of performance they achieve. These chapters represent some of the first attempts to explore reactions to complexity in naturalistic environments. The chapters feature an innovative application of a framework distinguishing various types of complexity. A major contribution offered by these chapters lies in the clear distinction made between the effect of alternative- and attribute-defined complexity on decisions made in a real-world context. This part also provides important insights into the multifaceted nature of risk, the role played by risk-hedging mechanisms and the interactive nature of the relationships associated with risk strategy under task complexity. A complex decision-making environment may be characterised in a number of ways, but the chapters in this part focus on the effects associated with the number of alternatives open to the decision-maker (alternative-based complexity) and the ease with which alternatives can be discriminated using the attribute set associated with each alternative (attribute-based complexity). Decision-making under complexity involves, consciously or subconsciously, a decision sequence, including an initial choice of whether to engage in the activity, the application of decision processes to manage the complexity, the development of a decision strategy which embodies a particular degree of risk, and finally, an outcome from which an individual’s success or performance can be determined. Previous research largely focused on only one part of this sequence – the decision process employed. By examining the extent to which complexity affects the other stages, the chapters in this part complement and extend previous literature on decision-making in complex environments. The chapters all explore empirically decision-making in a naturalistic setting, and they all seek to determine the differential effects of increasing levels of alternative- and attribute-defined complexity on participation, risk strategy and

performance. A clear means of distinguishing between alternative- and attributebased complexity is provided, and the chapters employ some novel measures of risk and performance. Explanations for the research findings are offered in relation to previous decision process and ambiguity avoidance research, in terms of epistemic reasoning and in relation to the varying motivations for engaging in risk taking. Chapter 4 provides an overview of the factors influencing the voluntary participation of individuals in risk-taking activities, the risk strategy they employ and the decision performance they achieve when facing a complex decision environment. Cognitive limitations which appear to restrict their ability to handle complex data when making these decisions are outlined and the problems associated with laboratory investigations of factors affecting decisions made under complex conditions are identified. A case is made for further naturalistic investigation of the impact of complexity on decision-making behaviour and, in particular, the merits of exploring these issues using data drawn from betting markets are discussed. The research methodology adopted for all the chapters in Part II is explained and the manner in which the definitions of complexity used in these chapters is outlined. A summary of the results of the studies forming the basis of Part II is provided, in terms of the impact of complexity on voluntary participation in risk-taking activity, on the risk strategy employed and on the decision performance achieved. The implications of the complexity studies in this part for individuals and groups required to make decisions in complex contexts are discussed. One of the key findings which emerges is that there appear to be significant differences in the degree of risk individuals are willing to accept and the level of decision performance achieved in complex environments between laboratory and naturalistic settings. In addition, it is concluded that: different types of complexity impose different performance penalties, increasing complexity influences the degree of relative and absolute risk individuals are willing to accept and non-financial motivations appear to play an important role in individuals’ reactions to complexity. Chapter 5 explores the impact which varying levels of attribute- and alternative-defined complexity have on the first step in the decision sequence outlined above, the degree of voluntary participation of individuals in horserace betting. The chapter represents one of the first attempts to measure the extent to which varying degrees and forms of complexity impact on the choice to engage in decision-making in such environments. Surprisingly, in relation to previous decision process findings, individuals appear to prefer decision environments characterised by higher levels of alternative-defined complexity but show some aversion to attribute-defined complexity. The results are explained largely in relation to the variety of motivational influences on betting behaviour discussed in Part I and in terms of the epistemic reasoning employed by some bettors. Chapter 6 uses a probit model to explore the extent to which bettors defer to the market view when their own information-handling ability is challenged by a complex decision environment. This chapter argues that deferring to the market

in this way is a form of risk aversion. The multivariate technique employed permits a clear understanding of the relationship between complexity and risk strategy, since the technique controls for the effects of factors such as the presence of risk-hedging mechanisms. The results suggest that greater attribute- and alternative-defined complexity is associated with more risk-averse behaviour. These findings are explained in terms of the decision-process and decisionoutcome literatures. These literatures suggest that decision-makers associate complexity with a hostile environment. It is argued that the research reported in this chapter supports this view, since the tendency for more risk-averse strategies to be employed as complexity increases can be regarded as simply a means of coping with the perceived hostility of the decision environment. The greater influence of alternative-based complexity on risk strategy observed in this chapter is also supportive of the decision-process and decision-outcome literatures. This chapter represents the first attempt to explore risk strategy under task complexity using a probit model and employs a novel measure of risk propensity. Chapter 7 represents a significant development in the understanding of the impact of complexity on a multifaceted risk strategy. It specifically acknowledges that there is no universally accepted definition of risk. Consequently, the chapter explores the impact of increasing complexity on three specific forms of risk (i.e. size of risk, absolute risk and relative risk) associated with a betting decision strategy. Multivariate analysis of variance is employed to capture the full richness of the relationships and to ensure that the precise role played by risk-hedging mechanisms is clarified; as such it represents a further development of the research outlined in Chapter 5. The chapter concludes that alternative- and attribute-defined complexity exert an interactive influence on risk strategy; attribute-defined complexity and the existence of a risk-hedging mechanism also appear to exert interactive effects. It is observed that the size of risk accepted is not influenced by the degree of complexity and variations in risk strategy are confined to adjustments in absolute and relative risk propensity. The results generally corroborate the decision-process, decision-outcome and ambiguityavoidance literatures, and are supportive of a broadly defined bettor utility function (which offers support for findings on bettors’ motivation, outlined in Part I). However, the observed significant interactive influences of alternative- and attribute-based complexity run counter to most previous decision process and decision-outcome research. The principal contributions of the chapter lie in (1) the characterisation of a multifaceted risk strategy; (2) identification of interactive influences of alternative- and attribute-based complexity on risk strategy; (3) clear specification of the role played by risk-hedging mechanisms under conditions of complexity; and (4) the corroboration which the results offer for the ‘ease of justification’ argument for the well-documented ambiguity avoidance phenomenon. In addition, this chapter represents the first attempt to explore the relationship between risk strategy and task complexity using the multivariate analysis of variance technique. After examining upstream issues of participation and risk strategy associated with complexity in the preceding chapters in this part, Chapter 8 investigates the

downstream issue of the effect of different types and degrees of complexity on the performance of horse-race bettors. Only a very limited literature on decision performance exists and all previous research has examined performance under laboratory conditions. Chapter 8 makes a significant contribution by examining performance in a naturalistic environment. Unlike previous studies, it offers an unambiguous measure of performance, rather than assessing accuracy against a subjectively determined ideal. The research was amongst the first to offer measures of performance which adequately account for changes in accuracy relative to random selection. The results provide some evidence for improved performance as alternative-complexity increases but suggest little difference in performance under different attribute-complexity conditions. These findings are compared and contrasted with earlier decision-process studies, and in explaining these results, the important roles played by familiarity with the task and motivation are highlighted. In summary, the chapters in Part II provide an insight into a number of previously under-researched areas, in particular the degree of voluntary participation in complex decision-making, and the extent and manner to which the risk strategy employed and the performance of individuals varies with the level and type of complexity. This research also represents some of the first attempts to explore reactions to complexity in a naturalistic environment. One of the reasons for the lack of naturalistic studies in this area is the difficulty of developing a reliable and uniform scale by which to measure the diverse forms of complexity experienced in real-world settings. However, the chapters in this part feature an innovative application of a framework established in the literature for distinguishing between alternative- and attribute-defined complexity. Whereas the majority of previous laboratory-based decision-process studies have explored varying levels of attribute complexity in terms of the number of attributes, the studies reported in this part have employed the ease with which alternatives can be discriminated via their attributes. Consequently, the chapters contribute to an understanding of decision behaviour under a little-researched aspect of attribute complexity. The chapters in this section employ a number of novel measures of risk and performance. The application of these measures has facilitated the development of new insights into the manner in which different forms and degrees of complexity impact on the nature and extent of risk accepted and on the levels of individuals’ performance. In addition, the application of multivariate techniques in Chapters 6 and 7 provides important insights into the multifaceted nature of risk, the role played by risk-hedging mechanisms and the interactive nature of the relationships associated with risk strategy under task complexity. Finally, in terms of their general contribution, these chapters offer explanations for the research findings in relation to previous decision-process and ambiguity-avoidance research and in terms of epistemic reasoning and the varying motivations of bettors (explored further in Part I).

4

The complex decision Insights from naturalistic research A.C. Bruce and J.E.V. Johnson

Introduction It seems uncontroversial to suggest that the environment within which the contemporary business decision-maker must operate is characterised by unprecedented levels of complexity. In part this reflects the influence of factors such as the globalisation of markets and enterprises, the dismantling of traditional barriers between functional areas of operation, and the emergence of new institutional arrangements for managing productive and trading activities. In part, too, complexity is a function of the revolution in the capability of those industries and technologies associated with the assembly, computation and presentation of information. Ultimately, decisions made in such complex environments are invariably the responsibility of individuals or groups, who, whilst potentially benefiting from access to highly sophisticated decision-relevant information, remain vulnerable to human cognitive limitations in their ability to absorb and utilise complex sets of often diverse and turbulent data. Against this context, the principal aims of this chapter are twofold; first, to offer a synthesis of a body of recent naturalistic research into the impact of environmental complexity on various aspects of decision-making, such as participation in decisions, risk-taking behaviour and decision performance; second, and relatedly, to demonstrate the poverty of conclusions based solely on laboratorybased work and the consequent necessity for appropriately designed naturalistic inquiry in enhancing our understanding of the influence of phenomena such as complexity. The chapter is organised as follows. We begin by revisiting briefly a theme developed in an earlier paper (Bruce and Johnson, 1997), where some of the limitations of laboratory-based inquiry into decision-making were discussed. The naturalistic decision environment used in the investigations of complexity effects is then introduced and its ability to satisfy the prerequisites for effective naturalistic work is demonstrated, together with its particular suitability for the study of complexity effects. This prepares the ground for the results of the investigations, which are then related to the body of existing, laboratory-based work. The final section explores some of the implications of the results for decisionmaking in a business context.

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Decisions associated with project and business risk management are likely to benefit from insights into the nature of risk taking and individuals’ reactions to varying environmental conditions, which have emerged from previous research. However, much of this research has been conducted under controlled experimental conditions. An earlier paper (Bruce and Johnson, 1997) suggested that results derived from much of this laboratory-based inquiry should be treated with caution for a variety of reasons, including: • • • • • •

the artificiality of the decision environment, the overly simplistic representation of decisions, the subjectivity of the measuring instruments employed, the potential for modification of subjects’ behaviour due to researcher scrutiny, the subjects’ unfamiliarity with the decision task, the, at most, marginal impact which the decision has on the subjects’ welfare.

Notwithstanding these concerns, investigations in a laboratory setting do offer a number of benefits, including the ability to explore a limited set of important variables under a variety of controlled conditions. Consequently, it is argued that those involved in managing project and business risks could add to the insights generated by laboratory-based research by developing a body of complementary naturalistic inquiry. The following section introduces a naturalistic setting which has formed the basis for a range of investigations by the authors, and explains how concerns associated with laboratory-based inquiry are addressed.

Naturalistic inquiry in horse-race betting markets The off-course horse-race betting market in the United Kingdom is worth about £5 billion a year. As a decision-making setting, therefore, it is significant. More importantly for the purposes of research into risky decision-making, the offcourse betting environment meets, to a substantial degree, the requirements for effective naturalistic investigation. First, the betting office setting affords researchers the opportunity to examine the decisions of individuals via analysis of ‘betting slips’ completed by the decision-maker, which give comprehensive detail of the nature of the decision. Such detail includes the extent of financial commitment, various measures of the ‘riskiness’ of the decision as, for example, implied in the odds of the selection made or the type of bet selected, and the exact time at which the decision was made. This may be augmented by additional information, such as the gender of the bettor, detailed by betting office staff. A further important feature of this type of data is the ability to develop unequivocal measures of the quality of the decision. Each decision relates to a particular race; each race generates a result.

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The ability to fix the exact time of bet placement is an important feature in allowing an accurate picture of the prevailing decision environment. This is achieved by cross-referencing with details of the evolving betting market in relation to the relevant race to provide an accurate profile of the range of decision opportunities at various odds at all points through the market’s development. Access to a large sample of individual decisions also permits the analysis of decisions made under varying conditions of complexity, as measured by, for example, the number of runners in the race, or within competitive races where forecasting the winner is particularly difficult. A third suggested requirement for effective naturalistic study, the ability to observe decisions made voluntarily by individuals familiar with the form of decision task, is also satisfied by the off-course betting office. The decisions monitored are those of individuals freely engaging in a pastime in its natural setting, using their own resources within their chosen time frame. The decision task and its environment are familiar. It is, furthermore, straightforward to ensure that decision-makers are oblivious of the subsequent scrutiny of their activity. In relation to the results reported below, this is achieved by a systematic random selection of betting slips after close of business. Finally, it has been suggested (Bruce and Johnson, 1997) that the usefulness of naturalistic inquiry might in part depend on its ability to shed light on similar forms of activity in other settings. Betting on horse races shares many fundamental characteristics with decision-making, especially financial decisionmaking, in other contexts. For example, a bet involves processes such as the analysis of quantitative and qualitative information, the significance of precedent, the formation of expectations and consultation of expert opinion, each of which is present in wider financial markets. In addition, the bets are made within a complex, multi-event, multi-cue, informationally turbulent setting where each decision is essentially a speculative venture involving financial commitment, where the accuracy of the bettors’ judgements determine their future reward. As such, it seems reasonable to suggest that we may draw valid inferences from off-course betting behaviour to assist our understanding of behaviour in other settings. It should be stressed here, of course, that direct observation of decision behaviour in some of these other settings is elusive: decisions may be unidentifiable as discrete events or may be confidential to the decision-maker. In summary, it is argued that naturalistic studies which are focused on the UK off-course horse-race betting market provide the opportunity for developing a clearer understanding of decision-making under uncertainty in broader contexts. It is argued that those involved in project and business risk management can glean valuable insights from such empirical analyses when considered alongside existing laboratory-based investigation. The following section demonstrates the particular contribution which the naturalistic study of horse-race betting markets brings to our understanding of the effects of complexity.

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The impact of complexity on decision-making: insights from horse-race betting studies Most project and business risk management decisions are associated with complex environments. Decisions made under these conditions involve, consciously or subconsciously, a decision sequence, including an initial choice of whether to engage in the activity, the application of cognitive processes to manage the complexity, the development of a decision strategy which embodies a particular degree of risk, and finally, an outcome from which an individual’s success or performance can be determined. Previous laboratory-based research has focused largely on only one part of this sequence – the cognitive processes employed. The aim of this section is to introduce results from naturalistic studies conducted in horse-race betting markets which have explored ‘upstream’ issues, such as the degree to which complexity deters participation in decision-making and ‘downstream’ issues such as the analysis of the strategies which result from the cognitive processes or the implications of these strategies in terms, for example, of decision performance. These results will be compared with the findings of relevant laboratory-based studies. Research methodology The database The set of naturalistic horse-race betting studies conducted by the authors, which is discussed below, employs a database assembled from real betting decisions made under normal trading conditions operating in UK off-course betting offices. As indicated above, off-course bettors are required to record their decisions on ‘betting slips’, and these are retained by the betting operator. The slips can be used to access a variety of information concerning the betting decision, including inter alia, stake level, type of bet, the time the bet was made and the odds associated with the selection. The addition of supplementary information, such as the race result, details of the evolving betting market and the type of race involved, enables a comprehensive picture of the decision and its environmental context to be developed. The investigations discussed below employ a systematic random sampling system (based on a time-defined betting slip index number) to select for analysis betting slips from nearly 1,600 betting shops situated throughout the United Kingdom. Defining complexity Complex situations have been defined as those where decision-relevant information approaches the limits of the decision-maker’s cognitive capacity (Eiser and van der Pligt, 1988). An individual’s cognitive capacity may be challenged in various ways, but two of the most common concern the number of alternatives

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open to the decision-maker (alternative-based complexity) and the ease with which the alternatives can be discriminated using the set of attributes relevant to the decision (attribute-based complexity). It is relatively straightforward to classify betting events using the alternatives/ attributes framework. Any horse-race comprises a number of runners (alternatives) each of which embodies a set of characteristics which may influence its chance of success (e.g. previous performances, weight carried, jockey, etc.). The complexity of a decision, involving the selection of a likely winner, is likely to increase as the number of alternatives (runners) increases and where attributes are manipulated to make choices between alternatives difficult. Consequently, one means of classifying complexity is according to the numbers of runners. Races can also be classified as either ‘handicaps’ or ‘non-handicaps’. In handicap races, a key attribute, the weight to be carried by each horse, is adjusted in the light of the horse’s previous performances. The weight allocated to an individual horse is designed to offset apparent performance advantages elsewhere in its set of attributes. The aim is to generate a close contest between horses of differing ability. Handicaps are, therefore, races of deliberately manufactured attribute-complexity. This contrasts with non-handicap races, where the weights are not determined by past performances. These represent races of lower attribute-complexity. In the studies, discussed below, alternative-based complexity is defined by the number of runners in a race. Consequently, decisions associated with bets placed on races with larger numbers of runners are regarded as decisions made under conditions of greater alternative-based complexity. In addition, bets placed on handicap races are regarded as decisions made under conditions of high attribute-based complexity, and bets placed on non-handicap races are regarded as decisions made under low attribute-based complexity conditions. Results: complexity and participation A study conducted by the authors (Johnson and Bruce, 1997a) which explored the impact of complexity on the degree of voluntary participation of individuals in off-course horse-race betting represented one of the first attempts to measure the extent to which varying degrees and forms of complexity affect the choice to engage in decision-making. The results suggest that individuals show some aversion to attribute-based complexity, in that a significantly lower proportion of bets are placed on handicap races (high attribute-based complexity) than on nonhandicaps. However, unexpectedly, individuals appear to prefer decision environments characterised by higher levels of alternative-based complexity, in that a significantly higher proportion of bets are placed on races with greater than 12 runners than on races with fewer runners. The results relating to attribute-based complexity can be explained in terms of previous laboratory-based studies which suggest that individuals are generally inconvenienced by, and feel uncomfortable with, higher levels of complexity (Jacoby et al., 1974; Malhotra, 1982; Paquette and Kida, 1988;

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Sundstroem, 1989; Wright, 1975). The apparent preference for situations involving high levels of alternative-based complexity suggests that the bettors’ utility function is not dominated by financial return. Consequently, whereas the financial penalty associated with alternative-based complexity may act to deter some individuals from betting, or cause them to reduce their levels of stakes, other motivations, such as intellectual challenge or excitement (Brown, 1986; Griffiths, 1993), may stimulate others to bet or to increase their stakes in races with larger numbers of runners. Results: complexity and risk strategy There is no universal definition of risk, and as Fischoff (1985) observes: ‘people disagree more about what risk is than about how large it is’. Risk may be viewed as comprising various elements, including factors such as potential losses and the uncertainty of those losses. In the absence of an unequivocal definition of risk, two studies were conducted by the authors (Johnson and Bruce, 1997b, 1998). The first defined risk aversion in terms of the degree to which individuals defer to the market view of events. Greater risk aversion in this study was inferred in circumstances where more bets are placed on the market favourite – that is the horse with the lowest odds or, in the market’s view, the greatest probability of success, is selected. The second study examined risk as a composite of three measures: 1 2 3

Size of risk (level of stakes – the amount of a bettor’s money which is at risk on a wager). Absolute risk (the probability of loss implied by the horse’s odds – the greater the odds the higher is the implied probability of loss). Relative risk, defined as the probability of loss relative to the average probability of loss in the race under consideration, and calculated as the ratio of the odds of the selected horse and the mean odds of horses running in the same race. Consequently, the relative risk measure caters for the fact that in some races a horse with odds of 2/1 may be the horse with the lowest odds and therefore the greatest perceived (by the market) probability of success, whereas in another race a horse with odds of 2/1 may be the horse with the highest odds and, therefore, the least market-perceived probability of success.

In the former study (Johnson and Bruce, 1997b), a probit model was employed to explore the extent to which bettors defer to the market view when their own information-handling ability is challenged by a complex decision environment. The results suggest that greater attribute- and alternative-based complexity are associated with risk-averse behaviour since for races with larger numbers of runners (high alternative-based complexity) and in handicap races (high attribute-based complexity) bettors appear to be more inclined to defer to the market view, by backing horses with the lowest odds. This result was

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particularly significant in the former case (i.e. high alternative-based complexity). It is argued that the results are in line with previous laboratory-based, decision-process (Jacoby et al., 1974; Capon and Davis, 1984; Layman, 1985; Ford et al., 1989; Payne, 1976; Timmermans, 1993) and decision-outcome studies (Jacoby et al., 1974; Malhotra, 1982; Paquette and Kida, 1988; Jacoby et al., 1975) which suggest that decision-makers associate complexity with a threatening environment. It appears that individuals employ more risk-averse strategies as a means of coping with the perceived hostility of a complex environment. The greater influence of alternative-based complexity on risk strategy observed elsewhere (Johnson and Bruce, 1997b) is also supportive of the laboratory-generated, decision-process and decision-outcome literatures which identify greater modification to decision processes under alternative- as opposed to attribute-based complexity conditions (Payne, 1976). The second study (Johnson and Bruce, 1998) exploring risk strategy under task complexity employed a multivariate analysis of variance. This technique allows the full richness of the relationships between the attribute- and alternativebased complexity variables and the multifaceted risk strategy employed (i.e. defined by size of risk, absolute risk and relative risk) to be discerned. The paper concludes that alternative- and attribute-based complexity exert an interactive influence on risk strategy, where the extent of risk aversion is influenced simultaneously and interdependently by the number of runners in the race and whether the race is a handicap or non-handicap. Attribute-based complexity and the existence of a risk-hedging mechanism (the opportunity to back horses to either win or to be placed second or third) also appear to exert interactive effects. It is observed that the size of risk (level of stakes) is not influenced by the degree of complexity and variations in risk strategy are confined to adjustments in absolute and relative risk propensity. A particularly interesting finding is that where extreme levels of alternative and attribute complexity coincide (i.e. in handicaps where the number of runners exceeds 18) significant increases in voluntary risk exposure occur. The results are supportive of a broadly defined bettor utility function, where excitement and intellectual challenge, as well as financial gain, play a role. However, the observed significant interactive influences of alternative- and attribute-based complexity run counter to most previous laboratory-based decision-process (Payne, 1976; Olshavsky, 1979) and decision-outcome (Jacoby et al., 1974; Malhotra, 1982) research. In addition, the study, by observing a greater relationship between attribute-defined complexity and risk strategy, fails to corroborate earlier laboratory-based findings (Payne, 1976) and appears to contradict the results of the earlier naturalistic study discussed above. The contrast with laboratory-generated results may in part be explained by the observed interaction between risk-hedging mechanisms and attribute-based complexity, since subjects in laboratory studies have not generally been given the opportunity to employ such mechanisms. The apparent contradiction with the results of the earlier naturalistic paper (Johnson and Bruce, 1997b) may result from the different definitions of risk employed in the two pieces of work, with one study

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defining risk aversion in relation to the influence of market events (Johnson and Bruce, 1997b) and the other using a more complex threefold definition of risk (risk size, absolute risk, relative risk) (Johnson and Bruce, 1998). Results: complexity and performance Having examined upstream issues of participation and risk strategy, the authors have also examined the downstream issue of the effect of different types and degrees of complexity on performance (Bruce and Johnson, 1996). Prior to their performance study, only a very limited literature on decision performance under complex conditions existed and all previous research had examined performance under laboratory conditions. This study, in addition to being conducted in a naturalistic environment, also offered unambiguous measures of performance (i.e. ratio of return/stake and the proportion of bets yielding a return), in contrast to previous laboratory studies, which generally measured accuracy against a subjectively determined ideal. The results indicate that performance measured in absolute terms (e.g. the proportion of bets producing a profit) and relative to random selection (i.e. allowing for lower rates of ‘successful’ random choices in larger runner races) remains fairly constant as attribute-based complexity increases, since little difference in performance levels were detected for bets placed in handicaps and non-handicaps. However, there is some evidence that absolute performance falls but relative performance (over random selection) improves as alternative-based complexity increases (i.e. as the number of runners in a race increases). These findings contrast with earlier laboratorybased results (Jacoby et al., 1974; Paquette and Kida, 1988; Wright, 1975). In addition, whereas previous studies suggest that complexity induces the use of simplifying decision processes (Timmermans, 1993), such use does not appear to carry a significant performance penalty, relative to random selection, in the naturalistic setting of the betting office. As such, the subjects in this study appear to be relatively invulnerable to complexity-related errors previously identified (Doerner, 1980). There are a number of possible explanations for the contrast between the laboratory and the naturalistically generated results. The first is that the betting study involves individuals who choose to engage in risky decision-making as a pastime, and consequently they may be less sensitive to the influence of complexity. Second, decisions made by bettors in the naturalistic study have real welfare implications. It is possible, therefore, that this may stimulate bettors to exert greater effort under complex conditions, thereby reducing any performance penalties. Third, it might be argued that accuracy measures employed in previous laboratory studies, which involved comparison of a choice against a subjectively-determined ideal, are less useful than the unequivocal measures associated with the outcome of a horse race. Finally, the contrasting laboratory/naturalistic results may arise because the bettors are familiar with the betting task and with the environment in which it takes place, whereas most subjects in the laboratory are assigned tasks for which they have no expertise. The

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results of the betting study appear to confirm work of Ceci and Liker (1986) who noted the ability of horse-race bettors to act in a ‘cognitively sophisticated’ manner by incorporating data in a complex mental model that ‘contained multiple interaction effects and nonlinearity’. Implications of the complexity studies A number of implications emerge from the preceding discussion for those individuals and organisations required to take decisions in complex business contexts or who are subject to the results of such decisions. The clear impression is that there do appear to be a number of behavioural differences between laboratory and naturalistic settings. This would suggest that project and business risk managers should treat laboratory-based findings on complexity with caution unless they are confirmed by naturalistic studies. The latter studies do largely reinforce the views which emerge from laboratory studies regarding changes in cognitive processes. However, significant differences in the propensity to accept risk and decision performance under complex conditions exist between laboratory and naturalistic studies. In addition to the general conclusion that caution should be exercised in assessing laboratory-generated results, the naturalistic studies discussed above suggest a number of issues which should be considered by project and business risk managers when faced by complexity: 1

2

3

Differing forms of complexity (alternative- or attribute-based) appear to exert different performance penalties. Consequently, on those occasions where influence can be exerted over the type of complexity associated with a project, managers must be fully aware of the project objectives and the likely impact of alternative complexity forms. This is of particular importance at the project design phase. In addition, the naturalistic studies suggest that the degree of alternative- or attribute-based complexity associated with the project is likely to influence the decision-maker’s desire to participate in the project, the risk strategy they employ and their performance. Since one means of influencing the perceived complexity of the problem is the amount of data made available and the manner in which decision-relevant information is presented to the decision-makers, these issues need to be considered during the operational and design phase of the project. The naturalistic studies show that individuals who face a decision task within their domain of expertise appear to cope well with the demands of complexity, but that increasing complexity affects the degree of relative and absolute risk they are willing to accept. Decomposing complex decisions into a series of less complex problems is therefore unlikely to have significant performance implications (other than in the circumstances outlined in (3) below) but will influence the risk strategies employed. Where high levels of attribute- and alternative-based complexity coincide, individuals appear to seek/accept significant increases in risk exposure. This

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A.C. Bruce and J.E.V. Johnson would suggest that robust risk assessment and management systems are required under such extreme complexity conditions. The naturalistic studies discussed above suggest that non-financial motivations appear to play an important part in reactions to complexity. It is clearly important, therefore, that careful assessment is made of the motivations of those relied upon to make important business and project risk decisions under complex conditions and that a clear indication of performance measures is provided to focus attention on relevant variables. The horse-race betting studies suggest that complexity may impact differentially on different aspects of risk strategy. Project and business risk managers need to be aware of this and remain alert to the fact that the naturalistic studies suggest that the availability of risk-hedging mechanisms may also influence the strategy adopted.

Conclusion The aim of this chapter has been to demonstrate the contribution of naturalistic research in furthering understanding of decision-making behaviour in relation to complex tasks. It has shown how a set of prerequisites for effective naturalistic work, outlined in a previous paper (Bruce and Johnson, 1997), have been incorporated into a body of naturalistic work associated with betting decisions. The results of this work have been outlined and contrasted with laboratory-based findings. Reasons for suggesting that the naturalistically generated results apply to wider decision-making environments have also been discussed. Finally, a number of implications for project and business risk management are identified. The broad conclusion to emerge from this chapter is that the type and degree of complexity associated with a project is likely to have a significant impact on decisions taken by participants in terms of their reluctance to participate, the degree and type of risk they are prepared to accept and the performance that they are likely to achieve. It is argued here that relevant insights into these areas are unlikely to be obtained from laboratory research alone and that the most robust conclusions can only be drawn where results of well designed laboratory and naturalistic studies are mutually supportive.

References Brown, R.I.F. (1986) ‘Arousal and sensation-seeking components in the general explanation of gambling and gambling addictions’, The International Journal of Addictions, 21: 1001–16. Bruce, A.C. and Johnson, J.E.V. (1996) ‘Decision making under risk: effect of complexity on performance’, Psychological Reports, 79: 67–76. Bruce, A.C. and Johnson, J.E.V. (1997) ‘Analysis of risky decision-making; methodological issues and implications’, The International Journal of Project and Business Risk Management, 1: 287–97. Capon, N. and Davis, R. (1984) ‘Cognitive ability measures as predictors of consumer information processing strategies’, Journal of Marketing Research, 11: 551–63.

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Ceci S.J. and Liker, J.K. (1986) ‘A day at the races: a study of IQ, expertise and cognitive complexity’, Journal of Experimental Psychology: General, 115: 255–66. Doerner, D. (1980) ‘On the problems people have in dealing with complexity’, Simulation and Games, 11: 87–106. Eiser, J.R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Fischoff, B. (1985) ‘Managing risk perception’, Issues in Science and Technology, 2(1): 83–96. Ford, J.K., Schmitt, N., Schectman, S.L., Hills, B.M. and Doherty, M.L. (1989) ‘Process tracing methods: contributions, problems and neglected research questions’, Organisational Behavior and Human Decision Processes, 43: 75–117. Griffiths, M.D. (1993) ‘Tolerance in gambling: an objective measure using the psychophysiological analysis of fruit machine gamblers’, Addictive Behaviours, 18: 365–72. Jacoby, J., Speller, D.E. and Berning, C.K. (1975) ‘Brand choice behaviour as a function of information load: replication and extension’, Journal of Consumer Research, 21: 33–42. Jacoby, J., Speller, D.E. and Kohn, C.A. (1974) ‘Brand choice behaviour as a function of information load’, Journal of Marketing Research, 11: 62–9. Johnson, J.E.V. and Bruce, A.C. (1997a) ‘An empirical study of the impact of complexity on participation in horserace betting’, Journal of Gambling Studies, 13(2): 159–72. Johnson, J.E.V. and Bruce, A.C. (1997b) ‘A probit model for estimating the effect of complexity on risk taking’, Psychological Reports, 80: 763–72. Johnson, J.E.V. and Bruce, A.C. (1998) ‘Risk strategy under task complexity: a multivariate analysis of behaviour in a naturalistic setting’, Journal of Behavioural Decision Making, 11: 1–18. Layman, J. (1985) ‘Children’s decision strategies and their adaption to task characteristics’, Organisational Behaviour and Human Decision Processes, 35: 179–201. Malhotra, N.K. (1982) ‘Information load and consumer decision making’, Journal of Consumer Research, 8: 419–30. Olshavsky, R.W. (1979) ‘Task complexity and contingent processing in decision making: a replication and extension’, Organisational Behaviour and Human Performance, 24: 300–16. Paquette, L. and Kida, T. (1988) ‘The effect of decision strategy and task complexity on decision performance’, Organisation Behaviour and Human Performance, 41: 128–42. Payne, J.W. (1976) ‘Task complexity and contingent processing in decision making: an information search and protocol analysis’, Organizational Behavior and Human Performance, 16: 366–87. Sundstroem, G.A. (1989) ‘Information search and decision-making: The effects of information displays’, in H. Montgomery and O. Svenson (eds) Process and Structure in Human Decision-Making, London: John Wiley, 209–24. Timmermans, D. (1993) ‘The impact of task complexity on information use in multiattribute decision making’, Journal of Behavioural Decision Making, 6: 95–111. Wright, P. (1975) ‘Consumer choice strategies: simplifying vs optimising’, Journal of Marketing Research, 11: 60–7.

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An empirical study of the impact of complexity on participation in horse-race betting J.E.V. Johnson and A.C. Bruce

Introduction A number of factors have been shown to influence the decision to gamble or to persist in gambling. These ‘not only include the gambler’s biological and psychological constitution and the situational variables, but also the structural characteristics of the gambling activity’ (Griffiths, 1993a). A number of structural characteristics of gambling activity have been identified (Abt et al., 1985; Cornish, 1978; Weinstein and Deitch, 1974), but the impact which complexity of the gambling task has on voluntary participation in a particular gambling activity has received little attention. This chapter aims to address this issue by presenting the results of an empirical study into the impact of complexity in the horse-race betting market on levels of observed participation. In general terms, a complex decision-making environment has been characterised in the literature as one where the decision-relevant information approaches the limits of the decision-maker’s cognitive capacity, thereby exposing the bounded rationality of the individual. The cognitive capacity of the individual may be challenged in various ways, but the current chapter will focus on the effects associated with the number of alternatives open to the decision-maker (alternative-based complexity) and the ease with which each alternative can be discriminated using the attribute set (attribute-based complexity). Researchers have sought to understand how decision-makers respond to these types of complexity in terms of the cognitive processes they employ, the simplifying strategies they use and the types of error that are induced. Increasing the number of alternatives will, ceteris paribus, increase the volume of information which the decision-maker must process. In the face of complexity, measured in terms of information volume, decision-makers appear to resort to a variety of simplifying strategies (Onken et al., 1985; Sundstroem, 1989; Timmermans, 1993). These strategies are often based on heuristics, bias and irrational premises (Agnew and Brown, 1986; Kahneman et al., 1982; Keren and Wagenaar, 1985). In addition, as the number of alternatives increases, feelings of confusion increase (Wright, 1975) and both confidence in decisions and performance decrease (e.g. Jacoby et al., 1974; Malhotra, 1982; Paquette and Kida, 1988; Wright, 1975). Eiser and van der Pligt (1988), in summarising this

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literature, conclude (p. 100): ‘individuals tend to use simpler and less optimal choice rules as the information load increases. Usually accuracy declines considerably when the number of features or the number of alternatives increases’. Complexity may also be regarded as a function of discriminability between alternatives (Hogarth, 1975). The lesser the extent to which alternatives are distinct from each other in terms of utility, the greater will be the complexity of the choice task. The ability to discriminate between alternatives via the attribute set may be confounded in various ways, including attribute value ambiguity, heterogeneity of attributes and complicated attribute interactions. Each of these obstacles to discriminability is explored below. Attribute value ambiguity may relate either to problems of valuing the attribute set as a whole or to the placing of values on individual attributes within the set. These forms of ambiguity have been shown to lead to inaction on the part of decision-makers (e.g. Frisch and Baron, 1988; Ritov and Baron, 1990) or to selection of the least ambiguous option (e.g. Curley and Yates, 1985; Hogarth and Kunreuther, 1985). In addition, Meyer (1981) has shown that uncertainty regarding the value of a particular attribute significantly reduces the perceived desirability of that attribute. Heterogeneity of information, which can also reduce discriminability of alternatives, appears to induce decision-makers into making a number of errors (e.g. Doerner, 1980, Brehmer, 1992). Discriminability of alternatives may also be confounded by a complicated relationship between individual attributes (Klein and Yadav, 1989) and in summarising the literature relating to attribute interactions and heterogeneous information, Eiser and van der Pligt (1988) indicate that (p. 79): ‘when there are many cues or unusual relationships between the cues, people tend to violate (rational) decision rules’. A reduction in discriminability has also been shown to reduce choice accuracy (Keller and Staelin, 1987; Klein and Yadav, 1989) and to result in less accurate preference rankings (Malhotra, 1982). Since discriminability is primarily a function of the attribute set it is referred to as ‘attribute-based complexity’. Previous work on cognitive processes associated with complexity and decision-making, discussed above, suggests that individuals are generally inconvenienced by higher levels of both attribute- and alternative-based complexity. It might, therefore, be expected that gamblers would also be inconvenienced by higher levels of complexity and that this may deter them from engaging in those betting activities which are comparatively complex. Consequently, the formal hypothesis to be tested here is that decision complexity in the horserace betting market inhibits participation in horserace gambling.

Method The study employs a database of 1,161 randomly sampled betting decisions made during 1987 in 1,600 off-course betting offices, located throughout the UK. A key component of off-course betting in the UK is the betting slip, where details of the betting decision are recorded by the decision-maker, prior to submission of the slip to the betting office staff.

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The betting slip provides, most importantly, details of the selection made (the horse selected and the race in which it competes) and the amount of money committed to the bet (‘the stake’). The database was constructed by selecting, after the close of business, a systematic random sample of betting slips from a total of over 22 million slips. Only those slips with particular serial numbers were selected, to produce a sample of 1/10,000 of the total population of slips. This process resulted in a sample of 2,920 betting slips. In order to simplify the measurement of participation and the analysis of complexity only ‘single’ bets contained in this sample were analysed.1 This resulted in the sample of 1,161 ‘single’ bets which was used in the study. The bettors whose decisions were monitored were oblivious to the fact that their betting slips would be the subject of scrutiny and hence ‘observation effects’ were absent. It is important to acknowledge that the sampling procedure described above may be regarded as involving a greater proportion of bets by ‘heavy’ gamblers in the sense that there may be more bets placed by this group within the aggregate data. This is only true, however, if heavy gambling is defined in terms of frequency of betting, rather than the size of individual bets. In any case, if betting by heavy gamblers (defined by bet frequency) is an important component of total betting activity, then in a study of aggregate betting behaviour such as this, the density of ‘heavy bettor’ activity in the sample reflects appropriately that in the population as a whole. This is not to deny that there may be important differences in complexity impacts between subgroups of the betting population, but these are issues which this type of study could only address at the expense of the important benefits arising from the anonymity of subjects and the resulting absence of ‘observation effects’. A further important feature of the sample described above is that it captures decision-making behaviour in a naturalistic setting, with attendant advantages over laboratory-based simulations. Payne (1982), for example, questions the wisdom of relying on laboratory approaches, citing the sensitivity of decision behaviour to minor changes in task and context. Yates (1992) synthesises the concern with laboratory-based enquiry thus (p. 324): ‘There is reason to suspect that the actual risk-taking behaviour observed in comfortable, low stakes, laboratory settings differs in kind, not just degree, from that which occurs in the often stressful, high stakes, real world context’. This is of particular concern in studies relating to gambling behaviour since Anderson and Brown (1984) have clearly demonstrated that gambling behaviour differs to a significant degree in the laboratory situation and the natural environment. Procedures It is important to explain the particular potential for the investigation of complexity which characterises horserace betting data. In particular it will be seen that horseraces are especially suitable as a basis for employing the established alternatives/attributes basis for examining complexity and that the betting data

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employed in this study allow for the clear measurement of levels of participation. Typically, horseraces in the UK involve between about three and 30 runners, so that given a large sample of races, one means of classifying complexity, according to numbers of runners (in bands), becomes feasible. As regards each alternative’s attribute set, there are three types of attribute which may be distinguished in the horseracing context. First, there are attributes which carry the same value for all horses in the race. These would include, for example, the type of race, the ‘going’, the timing of the race within the season, the venue of the race and the distance of the race. There are then attributes which all horses possess, but which differ across horses. These would include the horse’s trainer, its jockey, its breeding details, its age, the weight carried and the ‘draw’ (starting position, for flat horses only). There is a final set of attributes, the number of which varies between horses. These attributes relate to horses’ ‘form’, that is their previous performances in horseraces. Taken together, these factors represent a substantial and qualitatively diverse set of attributes for each alternative. Evaluating and comparing the attributes of each alternative, individually and in terms of interdependencies, clearly constitutes a substantial and complex decision problem and is the essential task facing the bettor in making a selection. The qualitative diversity of attributes and the differing size of the attribute set between horses renders a continuous scale for the measurement of comparative complexities problematic. A grading which allows discrimination between more and less complex attribute sets is possible, however. This grading arises from the fact that horseraces are classified as either ‘handicaps’ or ‘non-handicaps’. The defining feature of the ‘handicap’ race is that a key attribute, the weight assigned to each horse, is determined by the official ‘handicapper’ in the light of the horse’s previous performances. The objective of the handicapping system is to generate a close contest between horses of differing abilities (as evidenced by previous form). As such, the weight assigned to an individual horse is designed to offset apparent performance advantages inherent elsewhere in its set of attributes. The result is a horserace of deliberately manufactured complexity, where manipulation of the weight attribute complicates analysis of the set of attributes and consequently inhibits discrimination between alternatives. This contrasts with ‘non-handicap’ horseraces, where the weights are not systematically determined by past performance. Ostensibly, with ‘non-handicaps’, the absence of this compensatory device renders the comparison of sets of attributes across alternatives less complex. The established perception within the racing and betting industries is certainly that ‘handicap’ races are generally more competitive events and this is evidenced by the frequent sponsorship of ‘handicaps’ by bookmaking organisations. Grading of horseraces according to their status as, alternatively, ‘handicaps’ or ‘non-handicaps’ therefore offers a basis for comparing decision-making in more and less (attribute-defined) complex settings. Participation patterns are measured straightforwardly by observing the distribution of betting activity, measured in terms of numbers of bets and the amount staked, across races, variously grouped. Thus, number of bets deals with the

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number of discrete decisions made, while the staking measure provides an additional indication of the magnitude of commitment to the decision or the extent of participation. Whilst it is acknowledged that any individual’s level of staking may in part reflect their financial circumstances, there is no obvious basis for suspecting systematic differences across the subgroups of the aggregate sample as defined below. With regard to complexity, two variables are employed to classify the bets in the sample. First, the distribution of the total sample of bets across races, grouped according to number of runners (alternatives), is computed. Specifically, bets are grouped according to whether they were placed on races of, respectively, ‘12 or fewer’ or ‘greater than 12’ runners. This allows comparison between decision problems of varying complexity in terms of the number of alternatives. A practical rationale for selecting 12 runners as the basis for splitting the sample lies in the fact that the highest number of runners for any race in the sample was 24, so that 12, in a sense, represents a ‘half way’ point, particularly as this classification gives a reasonably equal number of races (i.e. betting opportunities) in each category (92 v. 116, respectively). A further rationale for the division at 12 runners lies in the nature of alternative-defined complexity effects identified in the literature, where a degree of consensus focuses on ten alternatives as a threshold beyond which clear negative effects on decision performance are identified (Malhotra, 1982; Wright, 1975). If such effects are regarded as potentially influential in the participation decision, it is important to locate the division close to the point where such effects are likely to operate, whilst preserving sufficient observations in each subset. To ensure that the selection of the division at 12 runners did not generate unusual outcomes, however, the results were additionally derived using divisions at 11 and 13 runners. The results obtained generated substantially similar patterns to those reported below. A second measure of complexity divides the total sample between bets placed on ‘non-handicap’ and those placed on ‘handicap’ races. This allows a segregation of less and more complex decision settings in terms of the attribute set.

Results The results reported in Table 5.1 offer various measures of participation in betting and indicate no preference for placing bets on horses in races with relatively small numbers of runners. The raw numbers of bets and stakes are adjusted to reflect the opportunities for betting in each race-size class. Consequently, when the raw number of bets and the absolute amount of money staked in each race-size category (≤12 or >12 runners) is divided by the proportion of races in each size category there is no significantly greater tendency to place more bets and to stake more money on races with smaller numbers of runners. In terms of the comparative propensities to bet on horses in ‘handicaps’ and ‘non-handicaps’, the raw figures, reported in Table 5.2, are again adjusted to reflect the relative opportunities for betting in these two race types. When the smaller number of opportunities for ‘handicap’ betting is taken into account,

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Table 5.1 Participation in decision-making according to complexity, defined in terms of alternatives (numbers of runners) Races with ≤12 runners N races = 92 (SD) Raw numbers of bets placed Number of bets placed, adjusted by opportunities availablel Absolute £s placed £s placed, adjusted by opportunities availablel

Races with >12 runners N races = 116 (SD)

z

375 0.73

(0.024)

786 1.22

(0.017)

–7.972 NS

1,500.3 0.78

(0.025)

2,793.0 1.17

(0.017)

–6.202 NS

Notes NS: not significant at 0.05 level. 1 The adjustment modifies the raw number of bets or £s placed on races of different size (≤12 or >12) by dividing the proportion of bets or £s in a particular race-size class (i.e. ≤12 or >12) by the proportion of races which occurred during the sample period in that race-size class. The adjustment allows appropriate comparisons between the proportions of bets or £s placed on races of ≤12 runners with those on races of >12 runners, by adjusting for differential numbers of races (i.e. betting opportunities) throughout the sample period in each of these race-size classes. Where the adjusted index of preference takes a value of greater than 1 this indicates a preference (over random selection) for betting on races in the relevant size class. For example, the adjusted value for the number of bets placed on races of 12 or fewer runners is given by (n1/n)/(r1/r), where n1 = number of bets placed on races with ≤12 runners; n = total number of bets placed; r1 = number of races in the sample period with ≤12 runners; r = total number of races. Consequently, if, for example, 45 per cent of bets were on races of ≤12 runners, but races involving this number of runners accounted for only 10 per cent of all races in the sample period, then the adjusted index would yield a value of 45/10 = 4.5. This would indicate that 4.5 times as many bets were placed on races with ≤12 runners than a random distribution of bets would suggest. 2 The test statistic, for the adjusted number of bets, is calculated as a difference between two proportions, as follows:

z=

n1 / n n2 / n − r1 / r r2 / r 1

(r1 / r )

2

n1 / n(1 − n1 / n ) n2 / n(1 − n2 / n ) 1 + 2 n1 n2 (r2 / r )

where n, n1, r, and r1 are defined as above and n2 = number of bets on races with greater than 12 runners, and r2 = number of races in the sample period with greater than 12 runners. z is distributed approximately N(0,1) (Snedecor and Cochran, 1980). Values of z greater than +2.32 suggest that, at the 0.01 level, participation (number of bets) is greater in races with ≤12 runners. A similar statistic is calculated for the adjusted £s placed.

though ‘non-handicaps’ attract more bets in the sample, the difference in the number of bets placed on these two race types is not statistically significant. In terms of money staked, the adjusted results, which control for opportunities for betting on ‘handicaps’ and ‘non-handicaps’, illustrate a highly significant preference for the latter; a finding which is strongly supportive of the hypothesis.

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Table 5.2 Participation in decision-making according to complexity, defined in terms of alternatives (handicap/non-handicap status) Handicap races N races = 93 (SD) Raw numbers of bets placed Number of bets placed, adjusted by opportunities availablel Absolute £s placed £s placed, adjusted by opportunities availablel

Non-handicap z races N races = 115 (SD)

498 0.951

(0.022)

663 1.03

(0.019)

1.442 NS

1,698 0.891

(0.022)

2,595 1.09

(0.019)

3.482 **

Notes NS: not significant at 0.05 level. ** Significant at 0.01 level. 1 The adjustment (similar to that applied in Table 5.1) modifies the raw number of bets or £s placed on different race types (‘handicap’ or ‘non-handicap’) by dividing the proportion of bets or £s in a race type by the proportion of races of that race type which occurred during the sample period. This gives an adjusted index of preference, where a value of greater than than 1 indicates a preference (over random selection) for betting on races in the relevant category. For example, the adjusted value for bets placed on ‘handicap’ races is given by (n1 /n)/(r1 /r), where n1 = number of bets placed on handicap races, n = total number of bets placed, r1 = number of handicap races, and, r = total number of races. 2 The test statistic is calculated in a similar manner to that described in Table 5.1.

Discussion The first set of results suggests that the hypothesis, that participation in betting declines as complexity increases, can be rejected in respect of horserace betting when complexity is defined in terms of the number of alternatives. The reverse is observed in the sample: more bets and stakes are placed on the larger number of runners (more complex) races. This is somewhat surprising in that it appears to suggest that bettors are uninhibited by the presence of complexity in the decision environment when complexity is defined in terms of the number of alternatives (runners). However, the results are not inconsistent with figures for betting turnover recently published by Ladbrokes (1994). These indicate that of the 20 top betting turnover races in 1993, 19 had double figure fields. The figures appear to support the view that bettors enjoy competitive racing despite, or perhaps because of, its attendant decision-making complexity. The above results suggest that it may be important to acknowledge that the motivations underlying individual decisions to bet may themselves be complex. Certainly, it may be simplistic to assume that bettors are necessarily motivated by a utility function which is dominated by financial return. Other motivations to bet such as, for example, intellectual challenge or excitement may be important (see Brown 1986; Griffiths, 1993b) and previous research has associated higher levels of stakes with individuals who are primarily motivated by excitement (Bruce and Johnson, 1992). Whilst increasing complexity may be associated

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with financial penalties it might also serve to enhance these other aspects associated with the enjoyment of betting (e.g. excitement). Consequently, whereas the financial penalty associated with complexity may act to deter some individuals from betting or cause them to reduce their levels of stakes, the excitement associated with betting in large runner races may stimulate others to bet or to increase their stakes. The reported results suggest that these opposing effects operate in the case of increasing alternative-defined complexity. The results relating to ‘handicap/non-handicap’ betting are more in line with expectations than those relating to the number of runners in the race. Those races where discrimination between alternatives is likely to be confounded on the basis of the attribute set (‘handicaps’) attract significantly lower levels of stakes than races where the ranking of alternatives is likely to be easier (‘nonhandicaps’). These results are in line with the hypothesis that decision complexity inhibits voluntary participation in horse-race gambling. They can be explained in terms of the literature discussed above which suggests that individuals are generally inconvenienced by, and feel uncomfortable with, higher levels of complexity. However, the results relating to numbers of bets placed on ‘handicaps/non-handicaps’ indicated in Table 5.2 do not mirror the results associated with staking levels. Whilst fewer bets in the sample were placed on the more complex tasks in terms of the attribute set (‘handicaps’) the difference was not statistically significant. This suggests that the numbers of bets placed are unaffected by increases in attribute-based complexity. Taken together, the results relating to staking levels and number of bets suggest that the average bet size is lower for ‘handicaps’ than ‘non-handicaps’. Previous research has associated lower levels of stakes with bettors whose primary motivation is not financial gain or excitement but intellectual challenge (Bruce and Johnson, 1992). As such, the results presented here appear consistent with the notion of attribute-complex races (‘handicaps’) as events which attract bettors who primarily are seeking intellectual challenge. As well as reflecting the motivational factors discussed above, the relative absence of a complexity-related deterrent to participation associated with complex races (defined by the number of runners) compared with complex races defined by their ‘handicap’ status may, in part, be explained by the findings of earlier work in relation to the degree of inconvenience and performance penalties associated with differing forms of complexity. Specifically, previous studies suggest that attribute-defined complexity does not inconvenience decisionmakers as much as alternative-defined complexity. Payne (1982) and Timmermans (1993) observed that increasing the alternatives had a greater impact on the tendency to use simplification strategies than increasing attribute-defined complexity. These variations in decision process between the two forms of complexity are matched in a few studies by differences in the performance of subjects under the two complexity conditions. Jacoby et al. (1974), for example, whilst observing performance penalties associated with alternative-based complexity, failed to identify reduced performance as attribute-defined complexity increased. Similarly, Johnson and Bruce (1994) demonstrated that the bettor’s

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financial return to gambling (i.e. return/stake) in ‘handicaps’ was not significantly different to that in ‘non-handicaps’ (i.e. attribute-defined complexity did not affect performance), but that their return in races with larger numbers of runners was significantly lower than in races with smaller fields (i.e. alternativedefined complexity did affect performance). Given this observed differential in the inconvenience and performance penalties associated with, respectively, alternative- and attribute-defined complexity it is somewhat surprising to observe that participation is not inhibited by increasing alternative-defined complexity (the more problematic form), whilst it does appear to be inhibited, particularly in terms of (adjusted) stakes placed, as attribute-defined complexity increases. This tends to imply a greater positive influence for the motivational factor of excitement in the case of alternative-defined complexity, in the sense that it appears sufficiently strong to offset any of the negative (anti-participation) effects of this form of complexity discussed above. In other words, this suggests that ‘excitement’ motivations are playing a more significant role in larger runner races (high alternative-defined complexity) than in ‘handicaps’ (high attributedefined complexity). A final contributory factor in explaining why gamblers appear not to be deterred by complexity (particularly defined in terms of numbers of alternatives), despite the inconvenience, unease and performance penalties which this has been show to cause subjects, may be associated with the tendency of gamblers to employ epistemic reasoning (Wagenaar, 1988). If gamblers believe that the next race is a unique event where they will be ‘lucky’ or in which they ‘know’ which horse will win, then they will consequently fail to apply statistical considerations. Under such conditions, complexity per se may have little deterrent value. It could be argued that epistemic reasoning is more likely to feature in ‘handicap’ betting behaviour, where bettors may perceive themselves to be unlikely to improve on, via rational analysis, the judgement of expert handicappers embodied in the conditions of the race.

Conclusions This chapter has used data from the off-course horserace betting market as the basis for an empirical study of the effects of complexity on patterns of betting activity. Specifically, two definitions of complexity, relating respectively to numbers of alternatives and the discriminability of alternatives, have been used to test the hypothesis that more complex races are less attractive betting media. The results of the study invite rejection of this hypothesis, particularly in terms of alternative-defined complexity. Perhaps surprisingly, individual horserace bettors do not appear to be deterred by the prospect of engaging in gambling activities involving a large number of alternatives. There is evidence, however, that reducing the discriminability of alternatives via the attribute set (handicap races) does result in a reduction in stakes wagered. As well as adding to the debate regarding the significance of complexity in betting participation, this study has demonstrated the potential of horserace

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betting data as a vehicle for work in this area. Its ability to generate quantifiable measures of impacts observed in natural settings constitutes an important advantage over previous empirical investigations. The results of the current study, whilst providing an insight into the manner in which horserace bettors react to complexity, should be treated with caution in relation to other forms of gambling activity. Furnham (1985) has suggested that more intelligent people tend to prefer gambling games where the role of chance is minimised and he found that the (p. 500) ‘least educated appear to engage more in such gambling activities as bingo, dog racing and fruit machines, with the most educated gambling at horse racing’. Differing levels of intelligence or education amongst bettors engaged in different forms of gambling may influence the manner in which they react to complexity. In addition, a number of researchers have pointed to the differing motivations of bettors engaged in differing gambling activities (see, for example, Dickerson, 1993). The scope for further research, exploring the impact of complexity on participation in forms of gambling other than horseracing, is therefore considerable. Equally, though this study has focused on two simple measures of complexity, there would appear to be considerable scope for considering alternative measures. As Onken et al. (1985) observe (p. 15): ‘It is not clear to what extent task complexity is a function of the number of alternatives in a choice set, the number of attributes comprising those alternatives, or some multiplicative relationship between these variables’. In conclusion, the relative merits of the explanations offered here for the behaviour of bettors, when faced with complexity, and the differential influence of variously defined forms of complexity, clearly require further study. To this extent, the research reported in this chapter forms the basis for further potentially important investigations.

Note 1 ‘Single’ bets involve the selection of one horse in a particular race and the success of the bet depends solely on the performance of that horse.

References Abt, V., Smith, J.F. and Christiansen, E.M. (1985) The Business of Risk: Commercial Gambling in Mainstream America, Lawrence, Kansas: University of Kansas Press. Agnew, N. McK and Brown, J.L. (1986) ‘Bounded rationality: fallible decisions in unbounded decision space’, Behavioural Science, 31: 148–61. Anderson, G. and Brown, R.I.F. (1984) ‘Real and laboratory gambling, sensation seeking and arousal’, British Journal of Psychology, 75: 401–10. Brehmer, B. (1992) ‘Dynamic decision-making: human control of complex systems’, Acta Psychologica, 81: 211–41. Brown, R.I.F. (1986) ‘Arousal and sensation-seeking components in the general explanation of gambling and gambling addictions’, The International Journal of Addictions, 21: 1001–16.

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Bruce, A.C. and Johnson, J.E.V. (1992) ‘Toward an explanation of betting as a leisure Pursuit’, Leisure Studies, 11: 201–18. Cornish, D.B. (1978) Gambling: A review of the literature, London: HMSO. Curley, S.P. and Yates, J.F. (1985) ‘The center and range of the probability interval on factors affecting ambiguity preferences’, Organisational Behaviour and Human Decision Processes, 36: 273–87. Dickerson, M. (1993) ‘Fruit machine addiction in adolescence: a case study’, Journal of Gambling Studies, 9: 387–99. Doerner, D. (1980) ‘On the problems people have in dealing with complexity’, Simulation and Games, 11: 87–106. Eiser, J.R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Frisch, D. and Baron, J. (1988) ‘Ambiguity and rationality’, Journal of Behavioural Decision Making, 1: 149–57. Furnham (1985) ‘Attitudes to, and habits of, gambling in Britain’, Personality and Individual Differences, 6: 493–502. Griffiths, M.D. (1993a) ‘Fruit machine gambling: the importance of structural characteristics’, Journal of Gambling Studies, 9: 101–20. Griffiths, M.D. (1993b) ‘Tolerance in gambling: an objective measure using the psycho physiological analysis of fruit machine gamblers’, Addictive Behaviours, 18: 365–72. Hogarth, R.M. (1975) ‘Decision time as a function of task complexity’, in Wendt, D. and Vlek, C.A.J. (eds) Utility, Probability and Human Decision Making, Dordrecht: D. Reidel, 321–8. Hogarth, R.M. and Kunreuther, H. (1985) ‘Ambiguity and insurance decisions’, The American Economic Review. Papers and Proceedings of the 97th Annual Meeting of the American Economic Association, 75: 386–90. Jacoby, J., Speller, D.E. and Kohn, C.A. (1974) ‘Brand choice behaviour as a function of information load’, Journal of Marketing Research, 11: 62–9. Johnson, J.E.V. and Bruce, A.C. (1994) ‘Decision making in a risky environment: the impact of complexity on participation and performance’, University of Southampton: Accounting and Management Science Discussion Paper, 82: 1–22. Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgement under Uncertainty: Heuristics and Biases, New York: Cambridge University Press. Keller, K.L. and Staelin, R. (1987) ‘Effects of quality and quantity of information on decision effectiveness’, Journal of Consumer Research, 14: 200–13. Keren, G. and Wagenaar, W.A. (1985) ‘On the psychology of playing blackjack: normative and descriptive considerations with implications for decision theory’, Journal of Experimental Psychology: General, 114: 133–58. Klein, N.M. and Yadav, M.S. (1989) ‘Context effects on effort and accuracy in choice: an enquiry into adaptive decision making’, Journal of Consumer Research, 15: 411–21. Ladbrokes (1994) ‘Classics in bets slump’, The Sporting Life, 4 January, 1–2. Malhotra, N.K. (1982) ‘Information load and consumer decision making’, Journal of Consumer Research, 8: 419–30. Meyer, R.J. (1981) ‘A model of multi-attribute judgements under attribute uncertainty and informational constraint’, Journal of Marketing Research, 18: 428–41. Onken, J., Hastie, R. and Revelle, W. (1985) ‘Individual differences in the use of simplication strategies in a complex decision-making task’, Journal of Experimental Psychology: Human Perception and Performance, 11: 14–27. Paquette, L. and Kida, T. (1988) ‘The effect of decision strategy and task complexity on decision performance’, Organisational Behaviour and Human Performance, 41: 128–42.

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Payne, J.W. (1982) ‘Contingent decision behaviour’, Psychological Bulletin, 92: 382–402. Ritov, I. and Baron, J. (1990) ‘Reluctance to vaccinate: omission bias and ambiguity’, Journal of Behavioural Decision Making, 3: 263–77. Snedecor, G.W. and Cochran, W.G. (1980) Statistical Methods, 7th edn, Ames, Iowa: Iowa State University Press. Sundstroem, G.A. (1989) ‘Information search and decision-making: the effects of information displays’, in Montgomery, H. and Svenson, O. (eds) Process and Structure in Human Decision-Making, London: John Wiley, 209–24. Timmermans, D. (1993) ‘The impact of task complexity on information use in multiattribute decision making’, Journal of Behavioural Decision Making, 6: 95–111. Wagenaar, W.A. (1988). Paradoxes of Gambling Behaviour, Hove, Sussex: Lawrence Erlbaum Assoc. Weinstein, D. and Deitch, L. (1974) The Impact of Legalized Gambling: the socioeconomic consequences of lotteries and off-track betting, New York: Praeger. Wright, P. (1975) ‘Consumer choice strategies: simplifying vs. optimising’, Journal of Marketing Research, 11: 60–7. Yates, J.F. (1992) Risk Taking Behaviour, Chichester, UK: John Wiley.

6

A probit model for estimating the effect of complexity on risk taking J.E.V. Johnson and A.C. Bruce

Introduction The literature relating decision processes and strategies to the complexity of the decision environment is extensive and relates mainly to laboratory-based investigation. A principal focus is how much complexity modifies the decision process in terms of the extent of analysis of decision-relevant information by the decision-maker. A general finding is that increased complexity is consistent with proportionally less exhaustive analysis, a tendency to switch from compensatory to non-compensatory decision processes and a propensity to employ heuristics and biases in forming judgements (see, for example, Kahneman et al., 1982; Keren and Wagenaar, 1985; Onken et al., 1985; and, for an extensive review of earlier work, Ford et al., 1989). Unsurprisingly, these observed behavioural modifications may carry penalties in terms of decision performance (see, for example, Jacoby et al., 1974; Jacoby et al., 1975; Paquette and Kida, 1988). In terms of risky decision-making in particular, a number of studies (Meyer, 1981; Curley et al., 1986; Frisch and Baron, 1988; Ritov and Baron, 1990) contain discussions of the risk associated with complex decision settings. The notion of ‘ambiguity avoidance’ is significant here, in explaining both participation in risky decision-making and decision selection. On the issue of participation, Frisch and Baron (1988) focus on the notion of ambiguity as ‘missing information’; this allows them to develop a number of rationales for the avoidance of ambiguity, which reinforces the earlier work of Einhorn and Hogarth (1986). On decision choice, Curley et al. (1986) suggest that the ease of justifying the decision to others (‘other evaluation’) may be a dominant factor in rejecting ambiguous choices under conditions of risky decision-making. Although a variety of insights into the complexity of decision environments exists, an established framework for the analysis of complexity views it as broadly two-dimensional. Complexity is seen as increasing on the one hand with the number of alternatives between which the decision-maker may choose; this is referred to as alternative-based complexity. Equally, complexity may be defined in terms of the nature of the decision-relevant attributes associated with each alternative. For example, complexity increases with the number of attributes per alternative, where the individual or relative values of attributes are

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uncertain, and where the interaction between attributes is complex. In each case, discriminability between alternatives is confounded (for examples of studies using this framework, see Hogarth, 1975; Timmermans, 1993); this is referred to as attribute-based complexity. The research reported here focused on a key characteristic of any decision made under uncertainty – its inherent riskiness – and examined the sensitivity of risk to different levels and forms of task complexity, using a probit analysis of a dichotomous risk variable. The motivation for this focus in part reflects the fact that the relationship between complexity and risk has received little specific attention in the literature, although Reason (1990) observed modifications in individuals’ risk-taking behaviour induced by errors made in complex decision settings. The development of an understanding of this relationship offers the potential for augmenting the existing literature relating to decision processes (which lead to a risk strategy), whilst at the same time enriching the understanding of observed relationships between complexity and decision performance which result from a risk strategy (see Bruce and Johnson, 1996). Previous research suggests that increasing complexity results in greater use of simplification procedures by decision-makers and that these procedures are often associated with performance penalties. It might be expected, therefore, that increasing complexity will reduce a decision-maker’s confidence and thus result in a more risk-averse strategy being adopted. The research reported here addresses this question directly by testing the hypothesis that increasing either attribute- or alternative-based complexity will result in a more risk-averse strategy.

Method Empirical context This research study employs decisions made in the UK off-course horserace betting market, which accounts for over 90 per cent of all horserace betting activity (by value) in the UK. The off-course betting regime in the UK is such that bettors detail decisions (amount staked, selection, etc.) on betting ‘slips’. Two copies of each slip exist; one (which forms the raw data for this study) is validated and retained by the betting office staff, the other is retained as a receipt by the bettor. A systematic random sampling process, based on the code numbers of betting slips, was used to capture 1,212 individual betting decisions from betting offices throughout the UK owned by the UK’s largest bookmaking firm Ladbrokes. The method of data collection ensured that those making the decisions were oblivious to the fact that their decisions were to be the subject of scrutiny. All decisions in the sample are in the form of ‘single’ bets, the empirically dominant form of bet for which the success of the bet depends on the position of one horse in a single horserace. The ecological appeal of betting markets as a setting for empirical investigation of various aspects of decision-making is now well established (see, for example, Snyder, 1978; Hong and Chiu, 1988). An important

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factor is that it captures decision-making behaviour in a naturalistic setting, thereby permitting investigation which complements existing laboratory-based enquiry. The particular advantages of betting markets in facilitating investigation of complexity and risk in a naturalistic setting relate to the ease with which both more and less complex decision tasks and more and less risky decisions may be identified. The specification of dependent and independent variables which follows explains how these advantages were exploited in this study. Dependent variable In investigating the sensitivity of risk taking to complexity, a measurable basis for establishing the amount of risk associated with a decision is a clear prerequisite. A unique definition of the nature of risk is elusive, however, whether in a general sense or in the specific context of betting. Indeed, the variety of perspectives on risk available in the betting context is an issue explored by Bruce and Johnson (1996), wherein multivariate analysis of variance is employed to examine the relationship between non-dichotomous risk variables and complex settings. The results suggest that the nature of the relationship between risk and complexity may be sensitive to the form of risk measure used. For this study, a dichotomous dependent variable is employed, such that comparatively high- and low-risk decisions are represented by bets on ‘nonfavourites’ and ‘favourites’, respectively. The rationale for this approach requires an understanding of the concept of favouritism in betting markets. Favouritism emerges from the uneven distribution of betting support across horses in a particular race. The horse which attracts most support, in terms of weight of betting activity in the market, is known as the favourite. It represents an unambiguous indication of the consensus of opinion in the market as to the most likely winner of the race. The dominant form of betting market in the UK centres on the activity of bookmakers engaging in individual betting contracts with bettors. In such markets, the ‘odds’ of the favourite imply the greatest probability of success of all horses in the race (and least variance of returns). For example, odds of 2/1 for a horse imply that its probability of success is 0.33. The suitability of favouritism as a risk descriptor is based partly on the popular contention that a bet on the favourite represents a comparatively ‘safe’ (low-risk) bet. This, in turn, reflects the empirically greater statistical probability of success by favourites compared with any other identifiable subset of horses, defined in terms of related patterns of betting activity. For example, favourites were placed first in 34.8 per cent of all flat races run in the UK during the period 1991–5. A bet on the ‘favourite’ may reflect a genuine confidence in the accuracy of the signals generated by the pattern of activity in the market. Equally, it may represent a convenient default position for the bettor with limited time or confidence in his own capacity to engage in detailed analysis of the information set. Then again, it may reflect the fact that backing ‘favourites’ minimises the probability of loss and variance of returns, thereby

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minimising exposure to risk. Bruce and Johnson (1996) employed a number of measures of risk aversion in a betting context, but these all represented relative amounts of risk aversion, for example, odds, stake. The selection of a favourite, which is the horse with the lowest probability of loss and variance of returns in a given race, provides a distinct measure of absolute risk aversion. At the same time, it should be acknowledged that these risk-related considerations are unlikely to explain the decision fully whether or not to select the favourite in complex settings. For example, in terms of the concept of ambiguity, the ‘favourite’ may be regarded as the least ambiguous choice and as such a rational selection in Frisch and Baron’s (1988) terms, or it may be seen as the selection most easily defended to others, the importance of which was stressed by Curley et al. (1986). Nevertheless, whilst accepting the potential contribution of these influences, it seems reasonable to suggest that a major factor in the ‘favourite’ strategy is its perceived status as relatively low-risk, compared with an alternative strategy, such as selecting a ‘non-favourite’. Independent variables Utilising the definitions of complexity outlined above allows a horserace, which represents a decision task, i.e. to select the winner, relating to a particular bet (decision), to be identified as more or less complex in one of two ways. First, races may be placed within a complexity category, according to the number of runners (alternatives) in the race, with more runners signalling greater complexity. The second basis for defining complexity relates to the attribute set. Horseraces in the UK are classed as either ‘handicaps’ or ‘non-handicaps’. ‘Handicaps’ are races where, for each horse, a key attribute (the weight carried by the horse) is determined according to the horse’s previous performances in races. The objective of this procedure, where prior strong performance by a horse is penalised by additional weight, is to create a competitive horserace where theoretically each horse has a similar prospect of success. The result is a decision task of manufactured complexity on which the ability of the decisionmaker to discriminate between alternative horses is compromised by the pattern of weight allocations. This process may equally be seen as increasing the ambiguity of the ‘handicap’ race as a decision problem. Specifically, the weight adjustments, by increasing the uncertainty attaching to the probability of alternative outcomes, are suggestive of ambiguity as defined by Curley et al. (1986). ‘Non-handicaps’, by contrast, do not involve the process of weight adjustments to offset likely performance advantages. It seems reasonable, therefore, to characterise ‘handicaps’ and ‘non-handicaps’ as, respectively, more and less complex decision tasks. Clearly the empirical setting described above has the capacity to generate distinctions between more and less complex decision tasks and more and less risky decisions. The procedure employed to translate this potential into a testable model relating risk taking to decision complexity is now described.

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Procedure It has been suggested that bettors are motivated to engage in betting by a variety of factors, including the prospect of monetary gain, excitement, social interaction, intellectual stimulation and confirmation of judgement (Bruce and Johnson, 1992). In deciding between two courses of action a bettor, like other decision-makers, is likely to choose that action which provides the greater benefit or satisfaction (Baird, 1984). It was suggested, above, that minimising exposure to risk represents a significant factor in the decision to select a favourite. Consequently it might be expected that, if the hypothesis indicated above holds, i.e. increasing complexity induces a more risk-averse strategy, bettors will select favourites when amounts of attribute- or alternative-based complexity are high. To test the validity of the hypothesis a probit model is employed where for bet j, the act of selecting the ‘favourite’ in race i is denoted as Fij. Assuming that bettors seek to maximise potential satisfaction, a bettor will place bet j on a ‘favourite’ in race i if this action offers an advantage Fij* (derived from the risk implications indicated above) over backing ‘non-favourites’ in race i. Consequently, when Fij* > 0 the ex post probability of backing the favourite is unity [p(Fij ) = 1], whereas, when Fij* < 0 the bettor will not select the ‘favourite’. We assume that the perceived advantage (in placing bet j) of selecting the favourite in race i (Fij*) is a linear function of a constant term ao, a random error, ej, the number of runners in race i, (vl), (as a measure of alternative-based complexity), and whether the bet is placed in a handicap, v2 = 1, or a non-handicap race, v2 = 0 (as an indication of attribute-based complexity), and three other variables included as factors other than complexity that are likely to influence the propensity to select favourites: whether the bet is placed to ‘win’ (v3 = 1) or ‘each-way’ (v3 = 0), the amount of stake of bet j (v4) and the odds of the selected horse (v5). ‘Win’ bets generate a return only if the selection is placed first in its race, whereas for the same aggregate stake ‘each-way’ bets offer a reduced return, compared with the ‘win’ bet, if the selection wins, but in addition, a much reduced return if the selection is ‘placed’, normally second or third, in the race. The decision to place a bet to ‘win’, or ‘each-way’, v3, is expected to be correlated with the decision to select a ‘favourite’ or ‘non-favourite’, respectively. Because of the terms of an ‘each-way bet’, the insurance component inherent in the return to a ‘placed’ selection is unlikely to compensate the bettor fully for having not won in terms of returning his total stake, unless the odds of the selection are at least 5/1. Since the odds of ‘favourites’ are, generally, less than 5/1 it is therefore expected that the propensity to select ‘favourites’ will be correlated with the propensity to choose a ‘win’ bet. Stake, v4, is also included as a control variable, since it is expected that the larger the stake the greater will be the inclination to reduce the probability of loss. This probability is minimised if a ‘favourite’ is selected. Consequently, a positive relationship between stake size and the propensity to select a favourite is likely. The odds, v5, of horses selected might also be expected to be correlated with a propensity to select ‘favourites’

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since the favourite is by definition the horse with the lowest odds in a particular race. The inclusion of variables v3, v4 and v5 in the model ensures that any relationship which is found between the propensity to select favourites and the amount of complexity will not be confounded by the influence of the type of bet (‘win’ or ‘each-way’), stake or odds. The model employed in the analysis can be written as follows: Fij* =

5

Σ ak v k − e j k =0

If it is also assumed that ej follows a normal distribution and that its variance is standardised to unity, then the probability of selecting a ‘favourite’ is given by:

Prob ( Fij ) = 1 = Prob(Fij* > 0) = Prob[e j <

Φ

5

Σav k =0

k

5

k

= F( Σ ak v k )] = k =0

  ak v k Σ  k =0  5

This is the usual form of the probit model, and the coefficients ak are estimated by employing maximum likelihood facilities in LIMDEP.

Results and discussion The results of the model are displayed in Table 6.1. The test of the model hypothesis that the parameter vector is equal to zero is rejected at p = 0.1. It may therefore be concluded that the model is explaining a statistically significant amount of the variation in the propensity to select ‘favourites’. The model displayed in Table 6.1 was also used to develop estimates of Fij* for each bet in the sample; where Fij exceeded 0 the bettor was predicted to have selected a ‘favourite’. The predictions are compared with the actual outcome of the bet in Table 6.2. It is clear from this comparison that 88.53 per cent of bets in the sample are correctly predicted as having selected a ‘favourite’ or a Table 6.1 Results of probit estimation1 Variable

Coefficient

SE

t ratio

Constant (ao) Number of runners (vl) Handicap/non-handicap (v2) Win/each-way (v3) Stake (v4) Odds (v5)

–0.138 0.406 0.345 0.486 0.010 –0.352

0.239 0.012 0.112 0.154 0.004 0.024

–0.58 3.49+ 3.07+ 3.15+ 2.44* –14.45+

Note 1 The dependent variable takes the value of 1 if a ‘favourite’ is selected and takes the value 0 if a ‘non-favourite’ is selected. *p < 0.05. +p < 0.002.

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Table 6.2 Tests of goodness of fit of probit estimation Actual bets on:

‘Non-favourite’ ‘Favourite’ Total

Predicted bets on: ‘Non-favourite’

‘Favourite’

Total

885 91 976

48 188 236

933 279 1,212

Note The test statistic, L, is equal to 2 (Lu-Lr), where Lu and Lr are, respectively, the maxima of the logarithm of the likelihood under no constraint and when all the coefficients are constrained to equal zero. Asymptotically, the test statistic, L, follows the chi-squared distribution (with degrees of freedom equal to the number of constraints) under the null hypothesis that all coefficients equal zero. Unrestricted log-likelihood = −394.78; Restricted log-likelihood = −653.89; Likelihood ratio test (5 df); L = 518.24 [χ.0012 = 20.52].

‘non-favourite’. This further suggests that the model explains a significant amount of variation in ‘favourite’ selection behaviour. The probit model indicates that the control variables significantly influence the propensity to select ‘favourites’ in the direction predicted; consequently ‘favourites’ are more likely to be selected if the bet is placed to ‘win’ (cf. ‘eachway’), is at lower odds and involves higher stakes. The coefficients for number of runners, v1, and handicap or non-handicap, v2, are both positive and significant at p = 0.002 This implies that, when holding the control variables constant, the propensity to back ‘favourites’ increases significantly as the number of runners increases and when the race involved is a handicap. The findings appear to confirm the hypothesis that increasing either alternative- or attribute-based complexity results in a more risk-averse strategy. The results can be explained in terms of previous decision-process and decision-outcome research. A number of studies of decision process have found a decrease in depth of information search (Capon and Davis, 1984; Klayman, 1985) and the employment of a range of simplification procedures under complex conditions (Payne, 1976; Onken et al., 1985; Ford et al., 1989; Timmermans, 1993). The straightforward strategy of selecting a ‘favourite’ in preference to other strategies which might involve a complicated comparative analysis of the runners’ form could certainly be regarded as a simplification procedure. A related explanation draws on the literature relating to the concept of ambiguity (Curley et al., 1986; Frisch and Baron, 1988) for which the selection of the favourite under complex conditions appears consistent with ambiguity avoidance. In the particular context of the off-course betting office, wherein social interaction and exchanges of opinion and experience are features of the environment, Curley et al.’s (1986) identification of ‘other evaluation’ as a powerful factor in explaining avoidance of ambiguity seems particularly persuasive. Performance penalties have also been observed to be associated with complex conditions (Jacoby et al., 1974, 1975; Malhotra, 1982; Paquette and

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Kida, 1988). It appears, therefore, that complexity can induce information overload (Eiser and van der Pligt, 1988) which causes individuals to simplify their decision processes and that this in turn leads to performance penalties. The tendency, observed here, for more risk-averse strategies to be employed as complexity increases, may therefore simply be a means of coping with the perception of the decision environment as hostile, i.e. complex. Whilst the majority of previous studies have noted performance penalties associated with increasing complexity, a study of horserace bettors identified only limited reduction in performance as complexity increases (Bruce and Johnson, 1996). This suggests that the tendency for bettors to select ‘favourites’ increasingly as alternativeand attribute-based complexity increases is not only a simplification strategy but a rational strategy for maximising returns in such a hostile, complex environment. The results of the current study appear to contrast with those reported by Johnson and Bruce (1996), wherein the size of risk (stake) did not respond to increases in complexity and wherein larger amounts of risk were accepted (odds) as conditions become more complex. However, it should be noted that Bruce and Johnson (1996) define risk in relative terms, i.e. relative size of stake, relative odds, whereas this study defines risk in an absolute manner, i.e. propensity to select the horse with least probability of loss and lowest variance of returns. The fact that differences exist between riskcomplexity relationships, depending on the definition of risk employed, may not represent a contradiction; it might simply illustrate the multifaceted nature of risk. The decision-process and decision-outcome literatures suggest that increasing alternative-based complexity has a greater influence on decision processes than increasing attribute-based complexity (e.g. Payne, 1976; Malhotra, 1982; Billings and Marcus, 1983; Paquette and Kida, 1988). Whilst the results reported here suggest that increasing both forms of complexity leads to more risk-averse strategies, the result relating to the ‘number of runners’ (alternative-based complexity) is particularly significant, since the probability of randomly selecting the ‘favourite’ declines as the number of runners increases. This suggests that the differential effect of attribute- and alternative-based complexity on the decision process and outcome, observed in previous studies, is reflected in the risk strategy employed.

Conclusion This chapter has attempted to explore the influence of alternative- and attributebased complexity on the risk strategy employed by individual decision-makers, using an empirical analysis of decisions made in the off-course horserace betting market in the UK. A probit model was employed to test the hypothesis that increased complexity leads to the use of more risk-averse strategies. The results suggest that increases in complexity associated with both alternatives and attributes do reduce the risk propensity of decision strategies and that the impact

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of increasing alternative-based complexity is particularly marked. It is observed that these results appear to corroborate the results of earlier decision studies of process and outcome. Previous research has clearly shown that decision behaviour is contingent on characteristics of the decision environment, task and person (Ford et al., 1989). Consequently, further work is needed to confirm that the selection of relatively risk-averse strategies in the face of complexity also occurs in the other decision-making contexts.

References Baird, B. E. (1984) Managerial Decisions Under Uncertainty, New York: Wiley. Billings, R. S. and Marcus, S. (1983) ‘Measures of compensatory and non-compensatory models of decision behaviour: process tracing versus policy capturing’, Organisational Behaviour and Human Performance, 31: 331–52. Bruce, A. C. and Johnson, J. E. V. (1992) ‘Toward an explanation of betting as a leisure pursuit’, Leisure Studies, 11: 201–18. Bruce, A. C. and Johnson, J. E. V. (1996) ‘Decision-making under risk: effect of complexity on performance’, Psychological Reports, 79: 67–76. Capon, N. and Davis, R. (1984) ‘Cognitive ability measures as predictors of consumer information processing strategies’, Journal of Marketing Research, 11: 551–63. Curley, S. P., Yates, J. F. and Abrams, R. A. (1986) ‘Psychological sources of ambiguity avoidance’, Organizational Behavior and Human Decision Process, 38: 230–56. Einhorn, H. J. and Hogarth, R. M. (1986) ‘Decision making under ambiguity’, Journal of Business, 59: 225–50. Eiser J. R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Ford, J. K., Schmitt, N., Schechtman, S. L., Hults, B. M. and Doherty, M. L. (1989) ‘Process tracing methods: contributions, problems and neglected research questions’, Organisational Behavior and Human Decision Processes, 43: 75–117. Frisch, D. and Baron, R. (1988) ‘Ambiguity and rationality’, Journal of Behavioural Decision Making, 1: 149–57. Hogarth, R. M. (1975) ‘Decision time as a function of task complexity’, in D. Wendt & C. Vlek (eds), Utility, Probability and Human Decision Making. Dordrecht, Holland: Reidel, 321–8. Hong, Y. and Chiu, C. (1988) ‘Sex, locus of control and illusion of control in Hong Kong as correlates of gambling involvement’, The Journal of Social Psychology, 128: 667–73. Jacoby, J., Speller, D. E. and Berning, C. K. (1975) ‘Brand choice behaviour as a function of information load: replication and extension’, Journal of Consumer Research, 1: 33–42. Jacoby, J., Speller, D. E. and Kohn, C. A. (1974) ‘Brand choice behaviour as a function of information load’, Journal of Marketing Research, 11: 62–9. Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgement Under Uncertainty: Heuristics and Biases, New York: Cambridge University Press. Keren, G. and Wagenaar, W. A. (1985) ‘On the psychology of playing blackjack: normative and descriptive considerations with implications for decision theory’, Journal of Experimental Psychology: General, 114: 133–58. Klayman, J. (1985) ‘Children’s decision strategies and their adaption to task characteristics’, Organisational Behavior and Human Decision Processes, 35: 179–201.

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Malhotra, N. K. (1982) ‘Information load and consumer decision making’, Journal of Consumer Research, 8: 419–30. Meyer, R. J. (1981) ‘A model of multi-attribute judgements under attribute uncertainty and informational constraint’, Journal of Marketing Research, 18: 428–41. Onken, J., Hastie, R. and Revelle, W. (1985) ‘Individual differences in the use of simplification strategies in a complex decision-making task’, Journal of Experimental Psychology: Human Perception and Performance, 11: 14–27. Paquette, L. and Kida, T. (1988) ‘The effect of decision strategy and task complexity on decision performance’, Organizational Behaviour and Human Performance, 41: 128–42. Payne, J. W. (1976) ‘Task complexity and contingent processing in decision making: an information search and protocol analysis’, Organizational Behaviour and Human Performance, 16: 366–87. Reason, J. L. (1990) Human Error, Cambridge, UK: Cambridge University Press. Ritov, I. and Baron, J. (1990) ‘Reluctance to vaccinate: omission bias and ambiguity’, Journal of Behavioral Decision Making, 3: 263–77. Snyder, W. W. (1978) ‘Horse racing: testing the efficient markets model’, Journal of Finance, 33: 1109–18. Timmermans, D. (1993) ‘The impact of task complexity on information use in multiattribute decision making’, Journal of Behavioural Decision Making, 6: 95–111.

7

Risk strategy under task complexity A multivariate analysis of behaviour in a naturalistic setting J.E.V. Johnson and A.C. Bruce

Complexity and decision-making: existing literature The impact of task complexity on decision-making has attracted considerable attention in the literature, where enquiry has addressed, variously, the definition of complexity, the cognitive processes which individuals engage in when confronted by complex tasks and the implications of complexity for decision performance. The coverage of these themes is reviewed briefly here. Complexity is associated with decision-making environments where decisionrelevant information approaches the limits of the decision-maker’s cognitive capacity (Eiser and van der Pligt, 1988). The previous literature identifies a number of forms of complexity and two of these are explored in this chapter, namely alternative-based and attribute-based complexity. A widely employed framework (see, for example, Timmermans, 1993) relates complexity to the number of alternatives between which an individual must discriminate in making a decision. Since information load, the amount one needs to know in order to make effective decisions, and hence complexity are expected to increase with the number of alternatives, this is referred to as alternative-based complexity. Another perspective on complexity involves the nature of the attribute set. Of particular importance here is the concept of discriminability, that is, the ease with which alternatives can be distinguished by their attributes (see, for example, Hogarth, 1975). This may be affected by complicated relationships between attributes which confound analysis of a set of alternatives (Klein and Yadav, 1989). In addition, lack of knowledge on the part of the decision-maker or the nature of the problem may result in perceived ambiguity in the value of attributes or a lesser degree of relative attractiveness of alternatives; each of these may hinder discriminability since fewer alternatives can easily be eliminated (e.g. Malhotra, 1982; Ritov and Baron, 1990; Summers, 1974; Wilkie, 1974). Increasing ambiguity consequently reduces solvability of the task (Stein, 1981). Since discriminability is largely a function of the attribute set, the associated complexity is referred to as attribute-based complexity. The literature relating decision complexity to cognitive processes and resultant strategies is, in general, indicative of a preference for simpler, noncompensatory, rather than more sophisticated compensatory strategies as

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complexity increases (see, for example, Kahneman et al., 1982; Keren and Wagenaar, 1985; Onken et al. 1985). Klein and Yadav (1989) elucidate the motivation for the increased use of non-compensatory strategies by pointing to positive correlations between complexity, on the one hand, and effort, confusion, choice time and difficulty. A number of studies focus on the distinction between the decision processes employed under attribute-based and alternative-based complexity. The consensus from earlier work (e.g. Billings and Marcus, 1983; Jacoby et al., 1974; Olshavsky, 1979; Payne, 1976; Timmermans, 1993) suggests that increasing the number of alternatives has a greater influence on decision processes than does increasing the number of attributes, though Sundstroem (1989) finds that attribute variation exerts a greater influence. The relationship between complexity and decision performance has generated equivocal results. Performance penalties have been associated with alternative-defined complexity and with information overload (Jacoby et al., 1974, 1975). Malhotra (1982) draws attention to methodological concerns relating to these earlier contributions, but confirms the dysfunctional impact of increased information beyond specified numbers of attributes and alternatives. By contrast, Kerstholt (1992) observes constant accuracy under a variety of complexity conditions. Bruce and Johnson (1994) note varying relationships between attribute- and alternative-defined complexity, depending on the performance measure employed. While the above review indicates that the general area of decision-making under complex conditions has received considerable attention, particularly in terms of upstream issues such as decision process, certain downstream aspects, such as the resultant strategy employed, remain under-explored. In addition, most previous research has focused on decisions made in a risk-neutral environment. The majority of those studies which have explored risky decision-making in complex settings have investigated the rejection of ambiguous choices under risky conditions (e.g. Curley et al., 1986; Frisch and Baron, 1988; Ritov and Baron, 1990). However, Johnson and Bruce (1997a) explore the extent to which complexity inhibits risky decision-making and their results suggest that attribute-based complexity exerts a greater deterrent effect than alternativebased complexity. Reason (1990) illustrates the link between complexity and risk via the analysis of errors which, induced by task complexity, lead to a modification of risk-taking behaviour. The only study to explicitly address modification to risk propensity under complex conditions (Johnson and Bruce, 1997b) suggests that risk taking decreases as both alternative- and attribute-based complexity increases. The research reported in this chapter seeks to address the under-researched themes of risky decision-making in complex settings and the strategies employed under such conditions by exploring the degree of risk associated with the decisions made in complex settings. Specifically, drawing on the results of previous decision process and outcome studies and on the methodological approach which has dominated enquiry in the general field of complexity

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research, this contribution investigates the hypothesis that there exist significant differences between the risk characteristics of decisions made under varying degrees and types (attribute- and alternative-based) of complexity. It is well established that decisions made in betting markets offer insights into wider areas of decision-making (e.g. Hong and Chiu, 1988) since there are substantial similarities in the use of information, expectations, precedent and judgement in these decision environments (Snyder, 1978). Consequently, to test the hypothesis indicated above, decisions made in the UK off-course horserace betting market are analysed. In this study the number of runners in a race is used as a means of measuring alternative-based complexity. Attributes in a horseracing context relate to factors associated with each horse which might influence the betting decision (e.g. the horse’s previous record, ‘form’; the conditions of the racecourse, ‘going’; the weight carried, etc.). Decisions made under different attribute-complex conditions are explored by comparing bets on races which are deliberately designed to reduce discriminability between the runners’ attributes (i.e. handicap races) with bets on races where discriminability is easier (nonhandicap races). Similar definitions of alternative- and attribute-based complexity were employed by Johnson and Bruce (1997b). However, to investigate the impact of complexity on risk propensity they explored only one dichotomous measure of risk, employing a probit analysis. The current study measures various dimensions of risk propensity (the dependent variable), in particular the size of risk, embodied in the level of stake and the absolute and relative degree of risk, associated with the probability of loss and variability of returns. It is expected that the multidimensional character of risk captured within the current study is likely to reveal deeper insights into the nature of the risk/complexity relationship than the earlier studies. The detailed methodology employed, together with a more detailed description of the independent and dependent variables are outlined below.

Method Subjects The study employs a systematic random sample of 1,212 betting decisions made by members of the public in 1987 in off-course betting offices situated throughout the United Kingdom. Since 1,100 betting shops were involved in the survey it is highly unlikely that more than one bet in the sample was made by the same individual. Task The database was assembled from real betting decisions made under the normal trading conditions operating in off-course betting offices. Decisions of offcourse bettors are recorded on betting ‘slips’. These contain details of each bet placed, including, inter alia, stake level, type of bet and the odds associated with the selection. The decisions which constitute the database employed in this study

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are ‘single’ bets, where the decision relates solely to the performance of one horse in a single race. Though this is only one of many types of bet available to the bettor, it is significantly the most popular. Random selection of ‘single’ betting slips after the close of office business ensured the absence of potentially distortive ‘observation’ effects, thereby guaranteeing a data set of real betting decisions made in their natural setting. This is an important feature of the study in an area where investigation of decisionmaking behaviour has largely been conducted via laboratory-based simulations of the decision-making environment. The ecological limitations of laboratory simulation have, in general terms, been noted by Payne (1982), Reason (1990) and Orasanu and Connolly (1993). In the particular context of risk taking, Yates (1992) synthesizes the concern with laboratory-based enquiry thus: There is reason to suspect that the actual risk-taking behaviour observed in comfortable, low stakes, laboratory settings differs in kind, not just degree, from that which occurs in the often stressful, high stakes, real world contexts to which we would like to generalize. Concerns with laboratory-based studies should not, however, be taken as implying their inferiority. Certainly, in relation to the current empirical study it is accepted that the natural environment in which the research takes place also has its drawbacks. For example, in guaranteeing the absence of observation effects it was only possible to record the decisions made; the bettors’ motivations and decision processes could not be discerned. Previous laboratory studies, however, do provide a valuable guide in these areas and have therefore been called upon to provide a logic for the risk strategies observed. Consequently, it is the case that the naturalistically founded results reported below should be seen as complementing results from investigations in controlled environments. Independent variables: measuring complexity The basic nature of the decision task in relation to betting, in simple terms, involves the selection of one alternative (horse) from the set of alternatives in a particular race. Other things being equal, the greater the number of horses running in a race, the greater is the complexity of that race as a decision task. The view that larger fields complicate the decision faced by bettors is widely held by racing experts in the United Kingdom (Braddock, 1983; Coton, 1990) and results from the 1994 flat racing season confirm that fewer of those horses most backed by the racing public (i.e. horses with lower odds) do actually win in fields with larger numbers of runners.1 It seems reasonable to assume, therefore, that other things being equal, selecting the winner of a race involving a larger number of runners represents a more complex task. Previous research suggests that ten or more alternatives result in dysfunctional effects on decision-making (Malhotra, 1982; Wright, 1975). Consequently, races were categorized by number of runners to ensure that races with ten or more runners could be

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compared with races of fewer runners to provide a means of exploring the effects of alternative-based complexity on risk strategy. As noted, in the context of horse racing an obvious basis for differentiating according to complexity by attribute is to consider all handicap races as relatively complex (by design) and all non-handicap races as relatively non-complex. Handicap races in the UK involve horses of a wide range of racing ability and the weight which each horse carries is determined by its past performance in public horse races. The idea of the handicap is that the weight is used to counterbalance previous ‘form’ in order to create a race in which all participating horses have a similar chance of success. The ‘weight’ attribute is therefore designed to confound analysis of the attribute set as a whole, thereby complicating the task of distinguishing between individual runners’ chances of success (i.e. reducing the relative attractiveness of alternatives). Selecting winners of handicaps in the UK is regarded within the racing and betting industries as a particularly complex decision task because of this compensatory adjustment (see, for example, Braddock, 1983; Duncan, 1989; Hall, 1994). These views are confirmed by statistics from flat races run in the UK during the period 1991–5. During this time 42.2 per cent of non-handicaps were won by the ‘favourite’ and only 27.0 per cent of handicap races were won by the bettors’ most favoured choice. This would suggest that bettors, who create the market, find it harder to select winners of handicap races than non-handicap races. Bettors may decide to place their ‘single’ bets to ‘win’ or ‘each-way’. A win bet secures a return if the horse selected finishes first in its race whereas, additionally, some return results from an each-way bet if the selection is ‘placed’ (i.e. normally where it finishes first, second or third). However, selection of the ‘each-way’ option generates less of a return to a horse finishing in first place than the equivalent stake placed to win. Betting each-way might therefore be seen as a risk-hedging mechanism. It was observed (see Table 7.1) that there were large differences in each of the dependent variables between win and each-way bets. Consequently, in the model employed in this study a further Table 7.1 Observed data Bet or race type

No. of bets

Dependent variables: measures of risk propensity Mean stake (£)

Mean odds

Mean relative odds

Each-way Win

349 862

0.78 1.20

11.65/1 5.15/1

0.42 0.23

No. of runners ≤9 >9, ≤14 >14, ≤18 >18 Handicap Non-handicap

220 295 434 262 532 679

1.04 1.21 0.99 1.03 1.05 1.07

3.84/1 5.04/1 8.09/1 9.52/1 6.27/1 6.73/1

0.32 0.22 0.30 0.27 0.37 0.22

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independent categorical variable, WEW (which takes the value of 0 if the bet is placed each-way and 1 if the bet is placed to win), was used as a control factor to segment bets. It was expected that this would serve to reduce the withingroup variance for the numbers of runners’ variable and the handicap variable. The independent variables used in the procedures described below are, therefore, RUN, HCP and WEW which take the following values: RUN

0: runners in race ≤ 9 1: runners in race > 9, but ≤ 14 2: runners in race >14, but ≤ 18 3: runners in race > 18

HCP

0: non-handicap race 1: handicap race

WEW

0: each-way 1: win bet

Splitting the sample in this way provides an acceptable number of observations in each group (see Table 7.1). Dependent variables – risk measures It is important, initially, to acknowledge that there is no universal definition of risk. As Fischoff (1985, p. 89) observes: ‘People disagree more about what risk is than about how large it is. ‘Part of the problem resides in the fact that risk may be viewed as comprising various elements. Yates and Stone (1992), for example, while suggesting that risk, in broad terms, might be defined as ‘the possibility of loss’, argue that risk is a function of a number of factors such as potential losses and the uncertainty of those losses. In the absence of an unequivocal definition of risk, this study employs three measures, which reflect particular perspectives on risk in the context of betting. Specifically, we consider respectively, the size of risk, represented by the degree of financial commitment associated with decisions, the ‘odds’ and the ‘odds’ relative to the mean market odds (‘relative odds’); the latter two variables are referred to as the degree of risk since they are associated with the probability of loss and the variability of returns. The rationale for each of these measures, which act as dependent variables in the procedures outlined below, is now explained. The first measure employed views risk in terms of the potential for financial loss; that is, the amount staked. In the UK the choice of stake rests with the

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bettor. It seems reasonable to suggest, therefore, that the magnitude of risk accepted by off-course horse-race bettors increases as the stake increases. It should be acknowledged that the absolute size of stake may say less about risk propensity than the stake relative to the individual’s income or wealth. Nevertheless, with the large number of individual observations contained in the database and without reasons to suspect systematic bias in terms of the income or wealth distribution of the individuals included, raw stake size offers a valuable insight into risk propensity. Risk may also be associated with an outcome involving a higher probability of loss and a greater variability of returns. The remaining two measures of risk (odds and ‘relative odds’) seek to incorporate these aspects of the betting decision. It is important to emphasize that bets examined in this study are placed in off-course betting offices whereas the odds available to the bettors are determined by betting activity at the racecourse. It is not the case, therefore, that diffuse off-course activity must necessarily mirror betting activity on-course (see Johnson and Bruce, 1993). The current study explores the odds available in the market at the time a given bet is made where these odds represent the market’s ‘view’ of any individual horse’s probability of success. Thus, for example, odds of 2/1 imply that a horse has a one in three (33.3 per cent) chance of success (ignoring bookmaker’s profit). Since bets on horses with lower odds are associated with a lower probability of loss and a lower variance of returns, odds of the selection are used as a measure of risk in the procedures outlined below. Each horserace will have its own particular profile of odds and these odds include a ‘mark-up’ to provide the bookmakers with profit. However, in the UK, the bookmaker margin is extremely variable between different races (typically from 3 to 60 per cent) and consequently odds of, say, 2/1 may represent a different implied probability of success depending upon the particular race in which the horse runs. In certain betting markets, odds of 2/1 may invite the inference that the horse has the greatest chance of success of all horses in the race, whereas in another market context it might represent the horse with least chance of success. As a result, the second measure of risk associated with odds (relative odds), adjusts the raw odds observed in this study by dividing the odds of the selection by the mean market odds. Where the odds selected are ‘short’ relative to the market mean, this is taken to infer risk aversion since the bettor’s selection has a higher probability of success and a lower variance of return than the average market selection. Bettors are likely to be fully aware of these relative odds since the full profile of odds for a given race is readily available prior to placing a bet.

Procedures In order to explore differences in the dependent risk variables (stake, odds and relative odds) under different attribute-based and alternative-based complexity conditions a three-way multivariate analysis of variance (MANOVA) was

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employed. The MANOVA model facilitates an analysis of the dependence relationship, represented as the differences in the set of continuous risk measures (dependent variables) across the series of groups formed by the categorical (independent) complexity measures while taking into account the relationship between the three risk measures. MANOVA was confirmed to be an appropriate technique for exploring the dependent (risk) variables since they were significantly correlated, according to Bartlett’s Test for sphericity (1,814.3, p < 0.001). The dependent variable in the MANOVA model consequently provides a composite measure of risk, incorporating size of risk, probability of loss and variability of return. It was necessary to transform each of the dependent variables (using logarithms) to comply with the assumptions underlying MANOVA. Plots of the residuals for each of the models discussed, using the transformed variables, were approximately normal and the residuals were uncorrelated. The transformations helped to stabilize the variance/covariance matrices. The transformed variables are referred to as LSTK [log10 (stake)], LODS [log10 (odds)] and LREL [log10 (relative odds)]. The factorial model employed is of non-orthogonal design and consequently, as an added precaution, the significance of the models is tested using Pillai’s Criterion, which is particularly immune to violations of the MANOVA assumptions.

Results Means of the observed stake, odds and relative odds for each of the independent grouping variables are given in Table 7.1. There are apparent differences in respect of each of the dependent variables between win and each-way bets and between bets placed in races with differing numbers of runners. Differences in mean stake and mean odds for bets placed on handicaps and non-handicaps appear less marked, although the mean relative odds appear higher for bets placed on handicaps. A full factorial MANOVA model was applied to the data but the three-way interaction, HCP × RUN × WEW, was not significant (Pillai’s Criterion = 0.12, p > 0.13). The model was then rerun having removed this interaction effect. The interaction RUN × WEW remained insignificant (Pillai’s Criterion = 0.01, p > 0.20) and was removed before rerunning the model. For non-orthogonal designs (such as that used here) there is no test for the overall significance of the model (Morrison, 1976), but tests for each of the individual effects in the final parsimonious model are highly significant. In particular the results suggest that the interaction effects HCP × WEW and HCP × RUN are significant (Pillai’s Criterion = 0.03, p < 0.001; Pillai’s Criterion = 0.04, p < 0.001, respectively), indicating that the vectors of means of the risk measures differ, for bets placed on handicaps and non-handicaps and on races with differing numbers of runners, in an interactive manner. Consequently the effect of a handicap or non-handicap selection on the risk measures differs according to the number of runners, and according to whether bets are placed ‘each-way’ or to win. The effect size (partial

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eta squared) of HCP × WEW (0.030) is twice that of HCP × RUN (0.015), suggesting that, in practical terms, the former is the dominant effect. In order to assess which of the risk measures contributes most to the significant effect observed, separate univariate analyses of variance (ANOVA) were conducted for each of the dependent variables. Full factorial ANOVA models were applied to the data and non-significant interaction terms were systematically removed. The parsimonious models which resulted from these procedures are displayed in Table 7. 2. All three models are highly significant (p < 0.001). Turning to the model for risk measure LSTAK, the only significant effect is the main effect for WEW. This suggests that while there are differences in staking between win and each-way bets (confirming the results displayed in Table 7.1) there are no significant differences in staking between bets placed on handicaps and non-handicaps or between bets placed on races with differing numbers of runners. For each of the remaining dependent variables, LODS and LREL, the interaction effects HCP × WEW and HCP × RUN are significant. This suggests that the multivariate results are largely accounted for by the variables LODS and LREL. Table 7.2 ANOVA for dependent variables LODS, LREL and LSTAK (parsimonious models) Effect

SS

DF

MS

F

Significance of F

Eta square

Power (α = 0.05)

0.000 0.040 0.000 0.000 0.101 0.000

0.03 0.01 0.12 0.12 0.00

1.00 0.68 1.00 1.00 0.38

(b) Dependent variable: LREL (Log10 (relative odds)) Within + residual 147.31 1,201 0.12 HCP × WEW 2.38 1 2.38 19.39 0.000 HCP × RUN 1.61 3 0.54 4.39 0.004 WEW 12.15 1 12.15 99.09 0.000 RUN 3.27 3 1.09 8.88 0.000 HCP 7.27 1 7.26 59.23 0.000 Model 37.90 9 4.21 34.33 0.000 Total 185.21 1,210 0.15

0.02 0.01 0.08 0.02 0.05

0.99 0.87 1.00 1.00 1.00

(c) Dependent variable: LSTAK (log10 (stake)) Within + residual 555.08 6 0.46 WEW 8.21 1 8.21 17.83 RUN 0.83 3 0.28 0.60 HCP 0.02 1 0.02 0.04 Model 9.51 5 1.90 4.13 Total 564.59 1,211 0.47

0.02 0.00 0.00

0.99 0.23 0.10

(a) Dependent variable: LODS (Log10 (odds)) Within + residual 137.39 1,202 0.11 HCP × WEW 4.02 1 4.02 35.14 HCP × RUN 0.96 3 0.32 2.79 WEW 18.51 1 18.51 161.91 RUN 18.07 3 6.02 52.70 HCP 0.31 1 0.31 2.70 Model 52.84 9 5.87 51.37 Total 190.24 1,211 0.16

0.00 0.63 0.85 0.001

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1.2 Non-handicap 1.1

Log (odds)

1

Handicap

0.9 0.8 0.7 0.6 Each-way

Win

Figure 7.1 Dependence of mean LODS on HCP and WEW.

The interaction effects HCP × WEW and HCP × RUN for risk measures LODS and LREL are explored by graphing the relationships. In Figures 7.1 and 7.3, LODS and LREL, respectively, are plotted for HCP against WEW; Figures 7.2 and 7.4 include plots of LODS and LREL, respectively, for HCP against RUN. Figure 7.1 indicates that each-way bets are placed at higher odds on non-handicaps than on handicaps; an a priori contrast confirms that non-handicaps are associated with more, statistically significant, risk-propensive behaviour (F = 27.39, df = 1, 1210, p < 0.01). For win bets there is no significant difference in the odds for bets placed in handicaps and non-handicaps (F = 1.74, df = 1, 1210, p > 0.05).

1.1

Handicap

Log (odds)

1 Non-handicap

0.9 0.8 0.7 0.6 0.5 0<=9

>9<=14

>14<=18

Number of runners

Figure 7.2 Dependence of mean LODS on HCP and RUN.

>18

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Figure 7.2 indicates that the mean odds of bets placed on handicap and nonhandicap races are similar, other than when the number of runners exceeds 18. This impression is confirmed by conducting a priori contrasts. There is no significant difference between the mean odds of bets placed on handicaps and non-handicaps for races of fewer than 10 runners (F = 1.53, df = 1, 1210, p > 0.05), for races of between 10 and 14 runners (F = 0.30, df = 1, 1210, p > 0.05), or for races of between 15 and 18 runners (F = 1.04, df = 1, 1210, p > 0.05). However, for races of greater than 18 runners, bets on handicaps are placed at significantly higher odds than for bets placed on non-handicaps (i.e. more risk-propensive behaviour in handicaps; F = 9.52, df = 1, 1210, p < 0.01). Figure 7.2 also indicates that for bets on both handicaps and non-handicaps the mean odds of horses selected increase as the number of runners increases; suggesting that risk propensity increases as the number of runners increases. A priori contrasts indicate, for example, that the mean odds of horses selected in both handicaps and non-handicaps are significantly greater in races of over 18 runners than in races of fewer than 10 runners (F = 108.72, df = 1, 1210, p < 0.01 and F = 71.06, df = 1, 1210, p < 0.01, respectively). Turning to the results relating to ‘relative-odds’, the general picture to emerge from Figures 7.3 and 7.4 is of negative values for LREL for win and each-way bets on handicaps and non-handicaps and for bets in both types of race for all number of runner conditions. This suggests that, as might be expected, most bets are placed at odds less than the mean market odds. Figure 7.3 indicates that the relative-odds of win bets are lower (i.e. less riskpropensive behaviour) than for each-way bets on both handicaps and nonhandicaps. In addition, bets in the sample on non-handicap races are placed at lower relative odds than those on handicaps (i.e. less risk-propensive behaviour in non-handicaps), whether these are placed to win or each-way. These

Each-way

Win

−0.3

Log (relative-odds)

−0.4 −0.5

Handicap

−0.6 −0.7 Non-handicap −0.8

Figure 7.3 Dependence of mean LREL on HCP and WEW.

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Number of runners −0.3

<=9

>9<=14

>14<=18

Log (relative-odds)

−0.4

>18

Handicap

−0.5 −0.6 −0.7 Non-handicap −0.8

Figure 7.4 Dependence of mean LREL on HCP and RUN.

results contrast with those for odds displayed in Figure 7.1 and consequently offer support for the view that odds and relative odds represent distinct measures of risk propensity. A larger difference between the relative odds of bets placed on handicaps and non-handicaps appears to exist for win bets than each-way bets. These observations are confirmed by a priori contrasts which indicate a marginally significant difference in the mean relative odds of eachway bets placed on handicaps and non-handicaps (F = 6.55, df = 1, 1210, p < 0.05) but a highly significant difference for win bets (F = 140.18, df = 1, 1210, p < 0.01). Figure 7.4 clearly shows that bets in the sample on non-handicaps are placed at lower relative odds than those on handicaps (i.e. less risk-propensive behaviour in non-handicaps) irrespective of the number of runners in the race; this picture is confirmed by a priori contrasts (R = 0: F = 8.07, df = 1, 1210, p < 0.01; R = 1: F = 35.39, df = 1, 1210, p < 0.01; R = 2: F = 33.24, df = 1, 1210, p < 0.01; R = 3: F = 69.09, df = 1, 1210, p < 0.01). The results contrast with those for odds displayed in Figure 7.2 where no significant difference was found between the risk accepted in handicap and non-handicap races of less than 18 runners. However, Figure 7.4, in line with the result for odds, indicates a larger difference in relative odds between bets placed on handicaps and nonhandicaps for races involving greater than 18 runners, compared with races involving fewer than 10 runners.

Discussion The variety of results emerging from the procedures raises a number of important issues for discussion. This section addresses two main groups of themes; first, a discussion of the general risk/complexity relationship as revealed by the

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multivariate analysis; second, the patterns associated with the individual dependent risk variables are explored. It will be seen that the results offer, variously, support for and a challenge to existing work in the analysis of complexity.

Complexity and risk: interpreting the multivariate analysis The results of applying the MANOVA model clearly indicate that the risk strategy employed by bettors is significantly affected by the level of task complexity in general. In particular, it appears that the types of risk strategy adopted vary with the levels of attribute-based complexity (handicap versus non-handicap) and alternative-based complexity (number of runners) in an interactive manner. Additionally, there appears to be an interactive relationship between the existence of attribute-based complexity and the use of riskhedging mechanisms, on the one hand, and the risk strategy employed, on the other. The general risk/complexity relationship corroborates the findings of a number of earlier studies. Thus, studies which have focused on decision process have observed modification of that process under complexity (e.g. Capon and Davis, 1984; Ford et al., 1989; Klayman, 1985; Onken et al., 1985; Payne, 1976; Timmermans, 1993). Equally, work focusing on decision outcomes under complex conditions has noted performance penalties as complexity increases (Jacoby et al., 1974, 1975; Malhotra, 1982; Paquette and Kida, 1988). The interactive influence of attribute-defined and alternative-defined complexities on risk strategy runs contrary to the findings of earlier studies by Jacoby et al. (1974), Malhotra (1982), Payne (1976) and Olshavsky (1979), none of which identified interactive effects. However, the results of this study echo those of Biggs et al. (1985) and Timmermans (1993) who noted the significance of interaction in influencing information search and use, respectively, in decision making. The balance of evidence from previous studies relating to the comparative effects of alternative-defined and attribute-defined complexity on decision processes points to the more pronounced influence of the former (e.g. Billings and Marcus, 1983; Payne, 1976). However, the current study, by observing a greater relationship between attribute-defined complexity and risk strategy, is more supportive of the work of Sundstroem (1989). The failure to corroborate the earlier research may in part be explained by the observed interaction between risk-hedging mechanisms and attribute-defined complexity in this study. Subjects in the earlier studies were not generally given the opportunity to employ such mechanisms.

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Individual risk variables; interpreting the univariate analysis of variance procedures This section attempts to interpret the relationship between the risk strategy and complexity which emerged from the multivariate analysis in terms of the contributions of individual risk variables to the observed effects. Size of risk The results suggest that the size of risk, measured by stake, is not influenced by either attribute- or alternative-based complexity. In the light of observed negative correlations between complexity and decision accuracy (e.g. Jacoby et al., 1974; Paquette and Kida, 1988), this result may be regarded as surprising, in that a rational response to increasing complexity, at least for the returns-seeking bettor, would be to reduce stake. On the other hand, there is counter-evidence to suggest that accuracy remains constant as alternative- and attribute-based complexity increases (Malhotra, 1982) and as decision-makers switch from compensatory to non-compensatory approaches (Kerstholt, 1992). Equally, one might challenge the idea of such a narrowly returns-focused bettor utility function (Bruce and Johnson, 1992). The absence of a relationship between size of risk and complexity suggests that the risk/complexity link identified via the multivariate analysis is principally explained in terms of the degree of risk. That bettors control risk via the degree of risk rather than through the size of risk is confirmed by the data in Table 7.1, which indicates that win bets, in comparison to each-way bets, have higher stakes but lower odds and relative odds. The theory of risk homeostasis (Wilde, 1988) suggests that individuals have a ‘target level’ of risk; a level which represents the ideal balance of perceived benefits and costs associated with risky activity. Since win bets are more risky than each-way bets (higher probability of loss of stake) it might be expected that, in line with risk homeostasis, bettors having selected a win bet may attempt to reduce their risk exposure. The data in Table 7.1 suggest that they do this via the degree of risk rather than the size of risk. The two aspects which constitute degree of risk are absolute risk (risk implicit in the raw odds of the selection) and relative risk (risk implicit in the odds, controlled for mean odds in the relevant event) and the relationship between each of these risk concepts and complexity is addressed below. Absolute risk and relative risk The interpretation of the results in relation to absolute and relative risk under a variety of complexity conditions is presented as a discussion of four main themes. These themes are the significance for risk exposure of interactive effects between attribute- and alternative-based complexity; the comparative sensitivity of absolute and relative risk to complexity; the nature of risk taking where extreme forms of attribute- and alternative-defined complexity coexist and the

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role of hedging mechanisms in the modification of risk strategy under more and less complex conditions. Interactive effects The significance of the interaction between alternative- and attribute-defined complexity on the degree of absolute and relative risk exposure echoes similar interactive influences to those observed in the MANOVA procedure. In particular, modification in exposure to risk parallels the modified decision process under increasing complexity observed by Biggs et al. (1985) and Timmermans (1993). However, not all studies of the impact of varying forms of complexity identify the significance of interaction. For example, Billings and Marcus (1983), Malhotra (1982), Olshavsky (1979) and Sundstroem (1989) each argue that alternativeand attribute-defined complexity effects operate independently. Importantly, however, these studies employ the number of attributes, rather than the discriminability between attributes, as a measure of attribute-based complexity. Comparative sensitivities The comparative sensitivity of absolute and relative risk to complexity, variously defined, is not straightforward. For example, the relationship between absolute risk exposure (odds) and attribute-defined complexity appears highly sensitive, in terms of both sign and magnitude, to the use or otherwise of riskhedging mechanisms, a factor which receives detailed attention below. The relationship between relative risk exposure (relative odds) and attribute-defined complexity appears more consistent, indicating a propensity to take more relative risk under conditions of greater attribute-based complexity (i.e. in handicaps), though the degree of this sensitivity is damped when risk-hedging mechanisms are used. This increased relative risk in attribute complex settings (i.e. handicap races) is suggestive of the phenomenon of ambiguity avoidance (see for example, Meyer, 1981; Curley et al., 1986; Ritov and Baron, 1990) whereby individuals who dislike the risk inherent in an ambiguous problem choose not to participate in such problems. This would suggest that those who do engage in the more ambiguous forms of betting, in this instance handicaps, are less concerned by exposure to risk and are thus relatively risk propensive, compared with those who avoid ambiguity by betting on non-handicaps. To explain why more consistent differences exist between the implied risk propensity of bets on handicaps and non-handicaps when risk is defined in terms of relative odds rather than odds it is necessary to explore additional reasons for the avoidance of ambiguity. It has been suggested that individuals avoid ambiguous situations since the decision to do so is more readily justified to others (Curley et al., 1986). Backing horses with relatively low probabilities of failure is certainly an easier decision to justify to others, on the basis of ‘form’ and/or market signals. The size of odds themselves (absolute risk), without reference to the market for a particular race, would have less effect on the ease of justifying a

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decision to select a particular horse. The more constant relationship between relative risk exposure (cf. absolute risk exposure) and attribute-defined complexity may arise because those who engage in the less ambiguous forms of betting, in this instance betting in non-handicaps, are more concerned with the ease with which the decision can be justified. Consequently, they bet on horses with lower relative odds. In relation to varying degrees of alternative-defined complexity, absolute risk exposure increases significantly as alternatives increase, in both high and low attribute complexity cases. At first sight it might appear that this is an expected statistical phenomenon, i.e. average odds available on a race will naturally increase as the number of runners increases. However, there is no evidence to suggest that the range of odds available on races with different numbers of runners varies. Consequently, there is no statistical expectation that the odds of bettors’ selections will increase as the number of runners increase. This suggests that increasing alternative-defined complexity induces greater levels of absolute risk exposure. These results are in line with previous studies which have indicated significant changes in the decision processes employed (Payne, 1976; Timmermans, 1993) and feelings of confusion and confidence experienced (Wright, 1975; Jacoby et al., 1974). In general, however, it is not possible to discern a strong or consistent influence on relative risk as alternative-based complexity increases, for either attribute complex or attribute non-complex cases. This greater absolute risk sensitivity suggests that bettors are more influenced by the nominal rather than the ‘real’ (mean adjusted) odds in considering their risk strategies. Such effects have been commonly observed in other areas of economic behaviour, as for example, in the phenomenon of ‘money illusion’ (Shapiro, 1982). Overall, the results suggest that the levels of absolute and relative risk are differentially affected by complexity. However, in general terms they point to an increasing propensity to accept risk (in terms of the probability and relative probability of loss) as both alternative- and attribute-based complexity increases. As such the results are in line with the work of Streufert et al. (1983) and Streufert (1986). However, the results appear to contrast with those of Johnson and Bruce (1997b) who concluded that risk propensity decreased as attributeand alternative-based complexity increased. They employed a simple dichotomous measure of risk, whether or not the horse with least probability of loss was selected. The risk measures employed here are of a continuous nature and the fact that differences exists between the risk/complexity relationship, depending on the definition of risk employed, rather than representing a contradiction, may simply reflect the multifaceted nature of risk. ‘Extreme’ complexity effects In terms of absolute risk, it was noted that over the majority of complexities defined by number of alternatives, activity in low and high attribute complexity contexts showed very similar patterns of risk exposure, each increasing as

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alternative-defined complexity increased. The exception to this pattern lies in the extreme alternative complexity condition where number of runners exceeds 18. Here, bets in the high attribute complexity group displayed markedly greater absolute risk propensity than those in the low attribute complexity group, suggesting that under the most extreme complexity conditions observable within this study, there was a significantly increased absolute risk exposure. Similarly, in relation to relative risk exposure, the most marked risk sensitivity to the complexity occurs where alternative-defined complexity is at its greatest, with attribute complex activity displaying significantly greater risk propensity. One interpretation of this effect is that it implies that the nature of the interactive effects noted earlier is multiplicative in form, such that the combination of individually extreme complexities generates particularly high risk sensitivity. In terms of the existing literature, these extreme effects appear consistent with Malhotra’s (1982) study of performance and complexity, which concluded that: ‘after initial negative effects due to overload have set in, performance remains fairly constant until a second critical point is reached when breakdown occurs, followed by rapid deterioration in performance’ (p. 428). Malhotra (1982) found that this second critical point occurred at 25 alternatives. While the alternative categories used in the current study make precise confirmation of this critical point impossible, a significant change in risk behaviour, consistent with the notion of ‘breakdown’, does appear to occur at a level beyond 18 alternatives. Risk-hedging mechanisms It has been observed that the degree of sensitivity of risk exposure to complexity appears to be influenced by the use of risk hedging. In the particular context of this study, the relevant hedging mechanism is the opportunity to bet each-way rather than to win. The modifying effects of each-way betting are seen in Figures 7.1 and 7.3. The impact on absolute risk exposure is particularly marked, in that each-way betting is characterized by significantly greater levels of risk in both higher and lower attribute complexity cases. This behaviour is consistent with Wilde’s (1988) theory of risk homeostasis. It appears that betting each-way is perceived as a means of reducing the ‘cost’ of risk taking; as a result, bettors feel able to take more risk by selecting horses with higher odds. The results also indicate that win bets are associated with a marginally greater absolute risk propensity in cases of high attribute complexity, but each-way bets demonstrate a significantly greater degree of risk associated with low attribute complexity settings. The literature on ambiguity avoidance may offer a possible explanation for this phenomenon. As indicated above, those who wish to avoid ambiguity may bet in non-handicaps rather than handicaps. Previous research suggests that these individuals may be more risk averse (Curley et al., 1986). These risk-averse non-handicap bettors may then be liberated, in terms of their betting behaviour, by the hedging device, which causes them to accept markedly higher levels of absolute risk taking when each-way bets are employed. In the

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case of relative risk, the impact of the hedging element is again suggestive of risk homeostasis theory, since the use of the risk-hedging mechanism appears to induce higher levels of risk in both high and low attribute-defined cases. As with absolute risk, the more marked effect is on non-handicap (low attribute complexity) betting. Again, this suggests the relative appeal of hedging, essentially a risk control mechanism, to the comparatively risk-averse, non-handicap bettors. However, the results concerning the comparative sensitivity of absolute and relative risk to complexity, discussed above, suggest that ‘ease of justification to others’ is a more likely explanation of ambiguity avoidance (Curley et al., 1986) than risk aversion in the horse-race betting context. In this connection, those betting on non-handicaps (thus avoiding ambiguity) may more easily justify betting at higher absolute and relative odds where a hedging mechanism reduces the prospect of loss; particularly in view of the fact that the manner in which each-way returns are calculated suggests that this risk-hedging strategy is most sensibly employed where odds of the selection are comparatively high.

Conclusion This chapter has attempted to shed light on the impact of differentially defined complexity on risk propensity in individual decision strategies, using an empirical analysis of decisions made in the off-course horse-race betting market in the UK. The rationale for the study was explained in terms of previous neglect of research into the relationship between complexity and decision strategy, compared with other aspects of the decision, such as process and outcome. Procedures were developed which allowed testing of the hypothesis that there are significant differences between the risk propensity of individuals’ strategies according to whether complexity is defined in terms of alternatives or the attribute set. Generally the results support the notion of a propensity to accept greater degrees of risk as complexity increases. However, the results suggest that the size of risk accepted is not affected by complexity, but that attributeand alternative-based complexity influence the absolute and relative risk accepted in an interactive manner. In addition, the propensity to accept absolute or relative risk is affected jointly by the level of attribute-based complexity and whether a risk-hedging mechanism is employed. It has been observed that these results appear to corroborate some earlier process and outcome-related work. The significant influence of attribute-based complexity and the interactive nature of complexity influences on risk propensity observed here are less well documented in earlier studies. This may reflect the fact that previous studies generally focus on the number of attributes rather than discriminability as a measure of attribute-based complexity or because most previous studies were not conducted in real-world environments. However, since decision behaviour has been demonstrated in the past to be highly contingent on the task, decision environment and person characteristics, further work is needed to explore the extent to which the results of the current study apply in other decision-making contexts.

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Note 1 Horses with odds of 5/1 or less in 1994: 18.5 per cent of these won in races of more than 18 runners (average loss of £0.16 per £1 bet); 26.7 per cent won in races of fewer than 10 runners (average loss of £0.08).

References Biggs, F. D., Bedard, J. C., Gaber, B. G. and Linsmeier, T. J. (1985) ‘The effects of task size and similarity on the decision behaviour of bank loan officers’, Management Science, 31: 970–87. Billings, R. S. and Marcus, S. (1983) ‘Measures of compensatory and non-compensatory models of decision behaviour: process tracing versus policy capturing’, Organisational Behaviour and Human Performance, 31: 331–52. Braddock, P. (1983) Horserace Selection and Betting, London: Longman. Bruce, A. C. and Johnson, J. E. V. (1992) ‘Toward an explanation of betting as a leisure pursuit’, Leisure Studies, 11: 201–18. Bruce, A. C. and Johnson, J. E. V. (1994) ‘Decision making in a risky environment: the impact of complexity on participation and performance’, Discussion Papers in Accounting and Management Science, University of Southampton, 94–82, 2–22. Capon, N. and Davis, R. (1984) ‘Cognitive ability measures as predictors of consumer information processing strategies’, Journal of Marketing Research, 11: 551–63. Coton, M. (1990) Value Betting, London: Aesculus Press. Curley, S. P., Yates, J. F. and Abrams, R. A. (1986) ‘Psychological sources of ambiguity avoidance’, Organizational Behavior and Human Decision Process, 38: 230–56. Duncan, D. (1989) Betting for Profit, London: Foulsham. Eiser, J. R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Fischoff, B. (1985) ‘Managing risk perception’, Issues in Science and Technology, 2(1): 83–96. Ford, J. K., Schmitt, N., Schechtman, S. L., Hults, B. M. and Doherty, M. L. (1989) ‘Process tracing methods: contributions, problems and neglected research questions’, Organisational Behavior and Human Decision Processes, 43: 75–117. Frisch, D. and Baron, R. (1988) ‘Ambiguity and rationality’, Journal of Behavioral Decision Making, 1: 149–57. Hall, D. (1994) How to Win on the Horses, London: Headline Book Publishing. Hogarth, R. M. (1975) ‘Decision time as a function of task complexity’, in Wendt, D. and Vlek, C. (eds), Utility, Probability and Human Decision Making (pp. 321–8), Dordrecht: D. Reidel. Hong, Y. and Chiu, C. (1988) ‘Sex, locus of control and illusion of control in Hong Kong as correlates of gambling involvement’, The Journal of Social Psychology, 128(5): 667–73. Jacoby, J., Speller, D. E. and Berning, C. K. (1975) ‘Brand choice behaviour as a function of information load: replication and extension’, Journal of Consumer Research, 1: 33–42. Jacoby, J., Speller, D. E. and Kohn, C. A. (1974) ‘Brand choice behaviour as a function of information load’, Journal of Marketing Research, 11: 62–9. Johnson, J. E. V. and Bruce, A. C. (1993) ‘Gluck’s Second Law: an empirical investigation of horserace betting in early and late races’, Psychological Reports, 72: 1251–8.

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Johnson, J. E. V. and Bruce, A. C. (1997a) ‘An empirical study of the impact of complexity on participation in horserace betting’, Journal of Gambling Studies, 13: 159–72. Johnson, J. E. V. and Bruce, A. C. (1997b) ‘A probit model for estimating the effect of complexity on risk taking’, Psychological Reports, 80: 763–72. Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgement under Uncertainty: Heuristics and Biases, New York: Cambridge University Press. Keren, G. and Wagenaar, W. A. (1985) ‘On the psychology of playing blackjack: normative and descriptive considerations with implications for decision theory’, Journal of Experimental Psychology: General, 114: 133–58. Kerstholt, J. H. (1992) ‘Information search and choice accuracy as a function of task complexity and task structure’, Acta Psychologica, 80: 185–97. Klayman, J. (1985) ‘Children’s decision strategies and their adaption to task characteristics’, Organisational Behavior and Human Decision Processes, 35: 179–201. Klein, N. M. and Yadav, M. S. (1989) ‘Context effects on effort and accuracy in choice: an enquiry into adaptive decision making’, Journal of Consumer Research, 15: 411–21. Malhotra, N. K. (1982) ‘Information load and consumer decision making’, Journal of Consumer Research, 8: 419–30. Meyer, R. J. (1981) ‘A model of multiattribute judgements under attribute uncertainty and informational constraint’, Journal of Marketing Research, 18: 428–41. Morrison, D. F. (1976) Multivariate Statistical Methods, 2nd edn., New York: McGraw Hill. Olshavsky, R. W. (1979) ‘Task complexity and contingent processing in decision making: a replication and extension’, Organisational Behaviour and Human Performance, 24: 300–16. Onken, J., Hastie, R. and Revelle, W. (1985) ‘Individual differences in the use of simplification strategies in a complex decision-making task’, Journal of Experimental Psychology: Human Perception and Performance, 11: 14–27. Orasanu, J. and Connolly, T. (1993) ‘The reinvention of decision making’, in Klein, G. A., Orasanu, J., Calderwood, R. and Zsambok, C. E. (eds), Decision Making in Action: Models and Methods, Norwood, NJ: Ablex. Paquette, L. and Kida, T. (1988) ‘The effect of decision strategy and task complexity on decision performance’, Organizational Behaviour and Human Performance, 41: 128–42. Payne, J. W. (1976) ‘Task complexity and contingent processing in decision making: an information search and protocol analysis’, Organizational Behaviour and Human Performance, 16: 366–87. Payne, J. W. (1982) ‘Contingent decision behavior’, Psychological Bulletin, 92: 382–402. Reason, J. L. (1990) Human Error, Cambridge: Cambridge University Press. Ritov, I. and Baron, J. (1990) ‘Reluctance to vaccinate: omission bias and ambiguity’, Journal of Behavioral Decision Making, 3: 263–77. Shapiro, E. (1982) Macroeconomic Analysis, 5th edn., New York: Harcourt Brace Jovanovich International. Snyder, W. W. (1978) ‘Horse racing: testing the efficient markets model’, Journal of Finance, 33: 1109–18. Stein, J. (1981) ‘Contextual factors in the selection of strategic decision methods’, Human Relations, 34: 819–34. Streufert, S. (1986) ‘Individual differences in risk taking’, Journal of Applied Psychology, 16: 482–97.

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Streufert, S., Streufert, S. C. and Denson, A. L. (1983) ‘Information load stress, risk taking and psychological responsibility in a visual motor task’, Journal of Applied Psychology, 13: 145–63. Summers, J. O. (1974) ‘Less information is better?’ Journal of Marketing Research, 11: 467–8. Sundstroem, G. A. (1989) ‘Information search and decision making: The effects of information displays’, in Montgomery, H. and Svenson, O. (eds), Process and Structure in Human Decision-Making (pp. 209–24), Chichester: John Wiley. Timmermans, D. (1993) ‘The impact of task complexity on information use in multiattribute decision making’, Journal of Behavioral Decision Making, 6: 95–11. Wilde, G. J. S. (1988) ‘Risk homeostasis theory and traffic accidents: propositions, deductions and discussion of dissension in recent reactions’, Ergonomics, 31: 441–68. Wilkie, W. K. (1974) ‘Analysis of effects of information overload’, Journal of Marketing Research, 11: 462–6. Wright, P. (1975) ‘Consumer choice strategies: simplifying vs. optimising’, Journal of Marketing Research, 11: 60–7. Yates, J. F. (ed.) (1992) Risk Taking Behaviour, Chichester: John Wiley. Yates, J. F. and Stone, E. R. (1992) ‘The risk construct’, in Yates, J. F. (ed.), Risk Taking Behaviour, Chichester: John Wiley.

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Decision-making under risk Effect of complexity on performance A.C. Bruce and J.E.V. Johnson

Introduction This chapter presents the results of an empirical study into the effect of complexity on human decision-making, specifically the quality of decision-making. The empirical setting for these investigations is the off-course horse-race betting market in the UK, which holds particular advantages in terms of the grading of complexity, the measurement of decision-related variables and its naturalistic setting. The research complements earlier work on complexity where a recurring theme has been the understanding of the cognitive processes associated with solving complex problems, by measuring the extent to which task complexity affects performance. Several recent studies within the cognitive literature (discussed below) offer analyses of decision-making in complex environments, variously characterised. Generally, a complex decision-making environment may be regarded as one where the decision-relevant information approaches the limits of the decisionmaker’s cognitive capacity. There are various ways in which cognitive capacity may be challenged. The current study focused on two of these and specifically explored whether discrimination between alternatives is inhibited by the number of alternatives available to the decision-maker and by the nature of the set of attributes. Previous researchers in these areas have sought to understand how decision-makers respond to these differing forms of complexity in terms of the cognitive processes they employ, the simplifying strategies they use and the types of error that are induced. Task complexity is positively related to the number of alternatives from which the decision-maker must choose. The associated increase in information load induces a variety of simplifying decision strategies (see, for example, Kahneman et al., 1982; Keren and Wagenaar, 1985; Onken et al. 1985; Agnew and Brown, 1986; Sundstroem, 1989; Timmermans, 1993). The limited number of studies which have explored the accuracy of decisions as complexity (number of alternatives) increases suggest declining performance (Jacoby et al. 1974; Wright, 1975; Paquette and Kida, 1988). Hogarth (1975) viewed complexity as a function of the ease with which alternatives can be discriminated. The heterogeneity of attributes, complicated

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attribute interactions or attribute value ambiguity may all confound such discriminability. The relationship between heterogeneity of information and the incidence and type of decision error was discussed extensively by Doerner (1980), Eiser and van der Pligt (1988) and Brehmer (1992). The difficulty of discriminating between alternatives has also been observed to increase where complicated relationships exist between individual attributes or where the values of attributes associated with alternatives are ambiguous (Klein and Yadav, 1989). Ambiguity in the value of an attribute has been demonstrated to lead to a reduction in the perceived desirability of that attribute (Meyer, 1981), and Curley and Yates (1985), Hogarth and Kunreuther (1985) and Ritov and Baron (1990) have shown that this can lead to decision-makers’ inaction. Since problems of discriminability, described above, are a function of the attribute set, these are referred to as attribute-based complexity. Much work in complexity and decision-making has focused on the cognitive processes adopted under conditions of complexity in laboratory simulations. Few researchers have quantified the performance penalty associated with making decisions under complex conditions (for exceptions see Jacoby et al., 1974; Wright, 1975; Malhotra, 1982; Paquette and Kida, 1988), and even fewer have measured effects of complexity in natural settings. The emphasis of previous work and, in particular, the absence of field studies may in part reflect the difficulties associated with developing a reliable and uniform scale by which to measure the diverse forms of complexity experienced in real-world settings. However, the ecological limitations of laboratory simulation may constitute a concern. Reason (1990) and Payne (1982) pointed to numerous weaknesses in experimental design and the artificiality of laboratory approaches, which inhibits their explanatory capacity in relation to real-world contexts. There is scope, therefore, for a greater body of naturalistic empirical work. In addition, as Ford et al. (1989) highlighted, there is a need for research on quality of decisions under complex conditions, particularly the investigation of ‘decision problems with an identifiable high-quality alternative’ (p. 107). Accordingly, the following section describes assessment of the hypothesis that decision performance deteriorates as complexity increases, utilising the two definitions of complexity explained above and the quantifiable measures of performance indicated below. This offers the opportunity to explore, in a naturalistic setting, a theme which to date has been the focus of predominantly laboratory-based enquiry.

Method Analytical potential of horse-race betting markets The validity of using the analysis of decisions made in horse-race betting markets as an insight into wider decision-making contexts is well established. Apart from the quality of documentary detail associated with betting markets, betting decisions are acknowledged (see, for example, Snyder, 1978; Hong and Chiu, 1988) to share many characteristics with other decision-making contexts.

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A betting decision involves, for example, skills of information collection and processing, interpretation, consideration of precedent, formulation of expectations, ‘gut’ feelings and consultation of expert opinion. A key component of off-course betting in the UK is the betting slip, where details of the betting decision are recorded by the bettor, prior to submission of the slip to betting office staff. This study employs a systematic random sample of 1,161 betting slips, selected according to their serial numbers during 1987. They were collected, after the close of business, from off-course betting offices (the setting for over 90 per cent of all horse-race betting in the UK) throughout the UK owned by Ladbroke Racing, the UK’s largest bookmaking organisation. Bettors whose decisions were monitored were oblivious to the fact, thereby ensuring the absence of ‘observation effects’. The betting slips provide, most importantly, details of the selection made and the amount of money committed to the bet (‘the stake’). The incorporation of official information relating to the results of each race covered by the sample allows various unequivocal performance measures to be developed. All bets included in the sample are ‘singles’, the simplest form of bet, for which the stake is placed on an individual horse and a return is obtained if the horse is successful.1 The particular advantage of naturalistic analysis of betting was noted by Wagenaar (1988, p. 117) who observed that ‘psychologists can discover, in the millions of gamblers, a rich garden full of all those varieties of reasoning that are so cumbersome to study in the laboratory.’ Anderson and Brown (1984) and Yates (1992) reinforced the advantages of the current study, in observing the significant differences between behaviour in laboratory-based and naturalistic settings. Apart from the advantages of naturalistic setting and quantifiable performance, horse-race betting is easily accommodated within an established framework (see, for example, Timmermans, 1993) for the analysis of complexity. As any horse race comprises a number of runners, each of which embodies a set of characteristics which are held to influence its chance of success, it is relatively straightforward to characterise the horse race via an alternatives (runners) versus attributes (characteristics) matrix. Complexity can be seen as increasing with the number of alternatives (runners) and the number of attributes, and whether attributes are manipulated to make difficult choices between alternatives. Typically, horse races involve four to 30 runners so that, given a large sample of races, one means of classifying complexity is according to numbers of runners (in bands). As regards attributes, there are three types which may be distinguished in relation to each runner (alternative): first, attributes which carry the same value for all horses in the race, such as the type of race, the ‘going’ (ground conditions), the timing of the race within the season, the race venue and the distance of the race; second, attributes which all horses have, but which differ among horses, such as the horse’s trainer, its jockey, its breeding details, its age and the weight carried; third, attributes which vary in number among horses, such as horses’ ‘form’ (their previous performances in horse races). These

120 A.C. Bruce and J.E.V. Johnson factors represent a substantial and qualitatively diverse set of attributes for each alternative. Evaluating and comparing the attributes of each alternative individually and in terms of interdependencies clearly constitutes a complex decision problem. The qualitative diversity of attributes and the differing size of the attribute set across horses rules out a continuous scale for the measurement of complexity. A grading which allows discrimination between more and less complex attribute sets is possible, however. This arises from the fact that horse races are classified as either ‘handicaps’ or ‘non-handicaps’. In handicap races a key attribute, the weight to be carried by each horse, is determined by the official ‘handicapper’ in the light of the horse’s previous performances. The objective of this exercise is to generate a close contest between horses of differing abilities. The weight assigned to an individual horse is designed to offset apparent performance advantages inherent elsewhere in its set of attributes. The result is a horse race or problem in which manipulation of weight complicates analysis of the set of attributes. Handicaps are, therefore, races of deliberately manufactured attribute-based complexity. This contrasts with non-handicap horse races wherein weights are not systematically determined by past performance and wherein the absence of this compensatory device offers a less complex comparison of sets of attributes across alternatives. This distinction in type of race offers a further basis for comparing decision performance in more and less complex settings. Procedure There is considerable literature which suggests that financial gain is an important motivation amongst bettors (for example, Tuckwell, 1983; Wagenaar, 1988; Dickerson et al., 1990). Accordingly, the principal measures of performance used in this study are related to mean rates of return per bet and percentages of ‘correct’ decisions in terms of the proportions of bets or stakes generating either a simple ‘return’ where the sum returned is positive, but less than or equal to the stake, or a ‘profit’, i.e. the sum returned exceeds the stake. In measuring complexity, two variables are employed to classify the bets in the sample. First, the total sample of bets is split between bets on races of, respectively, ‘12 or fewer’ or ‘greater than 12 runners’, thereby allowing comparison across decision problems of varying complexity in terms of the number of alternatives. The second measure of complexity divides the total sample between bets placed on non-handicap and handicap races. This allows a segregation of less and more complex decision settings in terms of attributes. Whilst these bases for measuring performance and complexity allow an insight into the effects of complexity, simple comparison of performance between settings of high and low complexity neglects the fact that the possibility of randomly making a winning selection differs between sets of races with larger and smaller numbers of runners. It is, therefore, necessary to make adjustments to control for the random element. This involves dividing the actual rate of success of bets on races within a given set by the random success

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rate which is calculated from the distribution of races by number of runners within that set. This procedure2 generates results controlled for randomness wherein values in excess of 1 indicate performance superior to that expected from random selection.

Results and discussion Tables 8.1 and 8.2 detail both the raw and adjusted results relating to performance under complexity defined, respectively, by alternatives and attribute set. The results relating both to complexity by alternative and by attribute set invite rejection of the hypothesis since they do not give unequivocal evidence that decision performance deteriorates as complexity, using either definition, increases. The results suggest that performance, when measured relative to random success rates, may actually improve as alternative-defined complexity increases. This contrasts with earlier findings (for example, Wright, 1975; Paquette and Kida, 1988). To the extent that complexity in terms of additional alternatives induces the use of the simplifying decision processes noted above (see, for example, Timmermans, 1993), such use does not appear to carry a performance penalty in the betting context. As such, the subjects in this study appear relatively invulnerable to the complexity-related errors documented by Doerner (1980) and Brehmer (1992). Despite the superiority in performance relative to random selection for bets on races with larger numbers of runners, Table 8.1 indicates that betting on races with larger fields is substantially less profitable than betting on races with smaller fields. This disparity reflects the fact that the ‘odds’ range in races with large numbers of runners is greater and that longer odds tend to represent a greater overstatement of an individual Table 8.1 Comparative performance on races of different complexity, defined in terms of number of runners Performance measures

Races with ≤12 runners No. bets = 375

Races with >12 runners No. bets = 786

Proportion of bets generating a return Proportion of bets generating a profit Proportion of stakes generating a return Proportion of stakes generating a profit Average return/stake

0.28 0.24 0.29 0.28 0.92

0.18 0.13 0.16 0.10 0.52

4.09* 4.78* 5.51* 7.87* 2.04*

Improvement over random selection for: Bets generating a return Bets generating a profit Stakes generating a return Stakes generating a profit

2.34 1.95 2.43 2.30

3.06 2.15 2.66 1.67

–2.36 –0.75 –0.78 2.39*

Note *p < 0.05, one-tailed.

z

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horse’s actual chance of success than shorter odds. In other words, the ratio between the objective probability of a horse priced at 20/1 and the probability implied by its raw odds is considerably greater than the equivalent ratio for a horse priced at 2/1. Thus, longer-odds selections represent ‘bad value’. This phenomenon, the ‘favourite/longshot bias’, is empirically well-established (for example, Crafts, 1985; Bacon-Shone et al., 1992). Relatedly, an established feature of the bookmaking industry is that bookmakers’ profit margins on races with large numbers of runners tend to exceed margins on smaller races. The results in Table 8.1, therefore, suggest that bettors, although able to improve on random rates of return in large races, are unable to erode the bookmakers’ generally larger margins in such races. The results relating both to complexity by alternative and by attribute set may be influenced by the fact that the bets analysed in this study were made by individuals who chose to engage in risky decision-making as a pastime. These individuals may be less sensitive to the uncertainty associated with task complexity than those who choose not to engage in such activity. In addition, the increased motivation which stems from making decisions which directly affect the welfare of the subject in a naturalistic setting may prevent a deterioration in performance. Klein and Yadav (1989, p. 411) suggested that ‘the choice environment as well as the choice process may affect effort and accuracy and a sufficiently motivated decision-maker may be able to create strategies that simplify a choice without the loss of much utility’. Powerful environmental stimuli and a responsive decision-maker may overcome the problems associated with complexity via implementation of adaptive choice strategies. In the betting context there is certainly a case for believing that as complexity increases, i.e. for larger fields or handicaps, so does the intellectual challenge and possibly the excitement associated with competitive racing. This may stimulate greater effort which ensures that the penalties associated with complexity are minimised. This interpretation of the results echoes the findings of Klein and Yadav (1989) who demonstrated that decision-makers increase effort as they face more alternatives from which to make an active selection, i.e. fewer dominant alternatives. They concluded (p. 419) that decision-makers were not ‘completely confounded by adverse choice contexts. Respondents’ accuracy was far above chance levels even in the difficult . . . conditions, which suggests that choice strategies are adaptive’. The results also appear to confirm the work of Ceci and Liker (1986) who noted the ability of horse-race bettors to act in a (p. 255) ‘cognitively sophisticated’ manner by incorporating data in a complex mental model that ‘contained multiple interaction effects and nonlinearity’. The raw and adjusted performance results displayed in Table 8.2 suggest that bets on handicaps do not underperform those on non-handicaps, other than in terms of the proportion of stakes generating a return (raw and adjusted) and a profit (adjusted). The attribute-related results are, therefore, largely consistent with the findings of Jacoby et al. (1974) who observed no significant differences in performance as discriminability between alternatives decreased. However, it is important to note (see, for example, Onken et al., 1985) that the concepts of

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Table 8.2 Comparative performance on races of different complexity, defined in terms of handicap /‘non-handicap’ status Performance measures

Handicap races No. bets = 498

Non-handicap races No. bets = 663

z

Proportion of bets generating a return Proportion of bets generating a profit Proportion of stakes generating a return Proportion of stakes generating a profit Average return/stake

0.23 0.18 0.17 0.15 0.65

0.20 0.14 0.23 0.17 0.66

–1.53 –1.84 2.35* 0.69 0.04

Improvement over random selection for: Bets generating a return Bets generating a profit Stakes generating a return Stakes generating a profit

2.71 2.13 1.97 1.76

2.72 1.99 3.12 2.31

0.04 –0.51 3.89* 2.01*

Note *p < 0.05, one-tailed.

accuracy employed in earlier studies, relating similarity of a choice to a subjectively determined ideal, is arguably less useful than the unequivocal measure associated with the outcome of a horse race. The results reported here clearly add to the debate regarding the significance of complexity in decision-making and highlight the potential for using horserace betting data as a vehicle for further work in this area. The ability to generate quantifiable measures of effects observed in natural settings constitutes an important advantage over previous empirical investigations. Although this study has focused on two simple measures of complexity, there would appear to be considerable scope for considering alternative measures. As Onken et al. (1985) observe (p. 15): It is not clear to what extent task complexity is a function of the number of alternatives in a choice set, the number of attributes comprising those alternatives, or some multiplicative relationship between these variables. Apart from manipulation of the measures of complexity, it will also be necessary to explore whether the results are confirmed in naturalistic environments beyond the horse-racing context. To this extent, the research reported here forms the basis of, and highlights the need for, further potentially important empirical investigations.

Notes 1 For ‘win’ bets (which represent 80 per cent of all bets placed) the horse must be placed first for a return to be obtained. For most ‘each-way’ bets the horse must be placed first, second or third for a return to be obtained.

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2 An example to illustrate the adjustment used to control for success rates associated with random selection in a set of races of between three and six runners: Runners in race 3 5 6

Number of bets placed 4 12 4 ∑ = 20

In this case, the random rate would be the weighted average of the individual random rates of success for each bet. This would give (4 × 33) + (12 × 2) + (4 × 17) = 4.4, which, when divided by the total number of bets, 20, gives a figure of 0.22, a ‘random’ success rate over those bets of 22 per cent. If the actual success rate for races with fewer than six runners were 50 per cent, then the success rate, controlled for random selection, would be 50/22 = 2.27 for this set of races.

References Agnew, N. McK. and Brown, J. L. (1986) ‘Bounded rationality: fallible decisions in unbounded decision space’, Behavioral Science, 31: 148–61. Anderson, G. and Brown, R. I. F. (1984) ‘Real and laboratory gambling, sensation seeking and arousal’, British Journal of Psychology, 75: 401–10. Bacon-Shone, J. H., Lo, V. S. Y. and Busche, K. (1992) ‘Modelling winning probability’, University of Hong Kong: Research Report 10, Department of Statistics. Brehmer, B. (1992) ‘Dynamic decision-making: human control of complex systems’, Acta Psychologica, 81: 211–41. Ceci, S. J. and Liker, J. K. (1986) ‘A day at the races: a study of IQ, expertise, and cognitive complexity’, Journal of Experimental Psychology: General, 115: 255–66. Crafts, N. F. R. (1985) ‘Some evidence of insider knowledge in horse race betting in Britain’, Economica, 52: 295–304. Curley, S. P. and Yates, J. F. (1985) ‘The center and range of the probability interval on factors affecting ambiguity preferences’, Organizational Behavior and Human Decision Processes, 36: 273–87. Dickerson, M., Walker, M., England, S. L. and Hinchy, J. (1990) ‘Demographic, personality, cognitive and behavioural correlates of off-course betting involvement’, Journal of Gambling Studies, 6: 165–82. Doerner, D. (1980) ‘On the problems people have in dealing with complexity’, Simulation and Games, 11: 87–106. Eiser, J. R. and van der Pligt, J. (1988) Attitudes and Decisions, London: Routledge. Ford, J. K., Schmitt, N., Schechtman, S. L., Hum, B. M. and Doherty, M. L. (1989) ‘Process tracing methods: contributions, problems and neglected research questions’, Organizational Behavior and Human Decision Processes, 43: 75–117. Hogarth, R. M. (1975) ‘Decision time as a function of task complexity’, in D. Wendt and C. Vlek (eds), Utility, Probability and Human Decision Making, Dordrecht: Reidel, pp. 321–8. Hogarth, R. M. and Kunreuther, H. (1985) ‘Ambiguity and insurance decisions’, The American Economic Review, 75: 386–90. Hong, Y. and Chid, C. (1988) ‘Sex, locus of control and illusion of control in Hong Kong as correlates of gambling involvement’, The Journal of Social Psychology, 128: 667–73.

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Jacoby, J., Speller, D. E. and Kohn, C. A. (1974) ‘Brand choice behavior as a function of information load’, Journal of Marketing Research, 11: 62–9. Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgement under uncertainty: heuristics and biases, New York: Cambridge University Press. Keren, G. and Wagenaar, W. A. (1985) ‘On the psychology of playing blackjack: normative and descriptive considerations with implications for decision theory’, Journal of Experimental Psychology: General, 114: 133–58. Klein, N. M. and Yadav, M. S. (1989) ‘Context effects on effort and accuracy in choice: an enquiry into adaptive decision-making’, Journal of Consumer Research, 15: 411–21. Malhotra, N. K. (1982) ‘Information load and consumer decision making’, Journal of Consumer Research, 14: 200–13. Meyer, R. J. (1981) ‘A model of multi-attribute judgements under attribute uncertainty and informational constraint’, Journal of Marketing Research, 18: 428–41. Onken, J., Hastie, R. and Revelle, W. (1985) ‘Individual differences in the use of simplification strategies in a complex decision-making task’, Journal of Experimental Psychology: Human Perception and Performance, 11: 14–27. Paquette, L. and Kida, T (1988) ‘The effect of decision strategy and task complexity on decision performance’, Organizational Behavior and Human Decision Processes, 41: 128–42. Payne, J. W. (1982) ‘Contingent decision behavior’, Psychological Bulletin, 92: 382–402. Reason, J. L. (1990) Human Error, Cambridge, UK: Cambridge University Press. Ritov, I. and Baron, J. (1990) ‘Reluctance to vaccinate: omission bias and ambiguity’, Journal of Behavioural Decision Making, 3: 263–77. Snyder, W. W. (1978) ‘Horse racing: testing the efficient markets model’, Journal of Finance, 33: 1109–18. Sundstroem, G. A. (1989) ‘Information search and decision-making: the effects of information displays’, in H. Montgomery and O. Svenson (eds), Process and Structure in Human Decision-making, London: Wiley, pp. 209–24. Timmermans, D. (1993) ‘The impact of task complexity on information use in multiattribute decision-making’, Journal of Behavioural Decision Making, 6: 95–111. Tuckwell, R. H. (1983) ‘The thoroughbred gambling market: efficiency, equity and related issues’, Australian Economic Papers, 12: 106–18. Wagenaar, W. A. (1988) Paradoxes of Gambling Behaviour, Hove, Sussex: Erlbaum. Wright, P. (1975) ‘Consumer choice strategies: simplifying vs. optimizing. Journal of Marketing Research, 11: 60–7. Yates, J. E (1992) Risk Taking Behavior, Chichester, UK: Wiley.

Part III

Gender differences in decision-making behaviour Introduction This part provides a synthesis and analysis of research on gender differences in decision-making from a wide variety of sources. The difficulties of interpreting previous research (due to a number of methodological concerns) are highlighted. In addition, results of empirical research, exploring gender differences in decision performance, risk propensity and confidence, are presented. These demonstrate that the relationships between gender and decision quality, risk propensity and confidence are not as straightforward as previous research suggests. Established views, that males demonstrate greater confidence and superior performance in their decisions, are not supported and the results provide valuable evidence which may help explain why women have often been excluded from managerial positions. Part III consists of four chapters. Chapter 9 offers a categorisation of the purpose, strategy and methodology of previous research, and this is then used as a basis for a critical review of the literature on gender and decision-making. This literature review provides a basis for the research questions posed in the remaining three chapters. These present empirical explorations of the extent to which the decision quality, risk taking and confidence of males and females differ. Two of the chapters investigate gender-related decision characteristics of horserace bettors, whilst the third contrasts such differences with those observed in a population of managers and potential managers who have undertaken formal management education. These four chapters provide a critique of previous research, offer new insights into the nature of male and female decision-making in a naturalistic environment and suggest some implications for decisions made in broader organisational contexts. Chapter 9 provides a comprehensive and critical literature survey of the relationship between gender and the characteristics of individuals’ decisions. The discussion of gender differences in the character and quality of decisions is extended to an issue of direct concern to organisations: the design and use of decision support systems (DSS). The literature on cognitive aspects of DSS design and use is characterised by contradiction and inconclusion. The omission of significant moderator variables

has been highlighted in the literature as a possible explanation of these results, but the role of gender in decision-making has been neglected by DSS builders. The research presented in Chapter 10 is the first to identify gender as a possible moderator variable. The literature review explores gender differences in decision quality, motivation, ability, risk taking, confidence and decision style; the implications for DSS designers are explored. A distinctive feature of the literature survey is the categorisation of over 100 papers on the relationship between gender and decision-making by their research purpose, strategy, task, subjects and results. This serves to highlight some of the difficulties of interpreting previous research, which is characterised by varying research design, sampling procedures and measuring instruments. Consequently, it provides a basis for a critical evaluation of the literature. Chapter 9 also identifies a number of important implications for DSS designers of gender differences in decision-making characteristics and an agenda for further research is suggested. Chapter 10 examines empirically the relationship between gender and decision quality, risk propensity and confidence amongst horserace bettors. The research reported here offers a number of methodological advantages over previous studies which explore gender and decision-making. In particular, the study employs a sample of decisions made by males and females in a naturalistic environment, where subjects were unaware that their behaviour was being monitored – this contrasts with the majority of previous studies which have been conducted in the laboratory. The methodology employed also helped to overcome concerns associated with earlier work on gender and decision-making, connected with the following: (1) its failure to control for the differential behaviour of males and females in relation to the time pressure applied; (2) the gender of the experimenters; (3) the gender orientation of the task; (4) the amount of information available; and (5) the age of the subjects. An important contribution of the research relates to the results. They confirm previous findings that males exhibit greater confidence in their decisions. However, in terms of decision performance and risk propensity, they contradict the orthodox view established in the literature. A particularly important feature of the study was the employment of five separate measures of performance, which provide a broader, more comprehensive view of decision quality than that used in many previous studies. The measures employed also provide a clear reference point against which the quality of decisions can be judged. Superior decision performance by males (a common feature of previous research) was not observed in this study and females produced better results when employing some of the performance criteria. Various measures of risk propensity were used in the study to accommodate the multifaceted nature of risk. The results do not unequivocally support previous research which suggests that males are inclined to take more risk. A valuable conclusion of the study is that these results are indicative of gender differences in the definition and perception of risk. It is also suggested that the contradictions with previous findings may reflect the improved methodology employed in this study and the increasing role played by women as decisionmakers in political, commercial and industrial contexts.

The methodology employed in Chapter 10 represented an improvement over many previous studies, but it could not isolate all potential explanatory variables. Consequently, some ambiguities in the interpretation of the results remained. Chapter 11 explores, empirically, gender differences in performance, risk propensity and confidence amongst horserace bettors and seeks to overcome the difficulties of interpretation associated with the study reported in Chapter 10. In particular, the research benefits from all the methodological advantages associated with Chapter 10, but in addition, only ‘single’ bets were collected and analysed. These are bets placed on one horse in a given race. As a result, a clearer indication of the comparative betting behaviour of males and females is established. The results again represent an important contribution of this study, and they challenge the orthodox views of males as superior decision-makers and females as more risk averse. The findings relating to risk propensity are particularly valuable since they suggest gender differences in the perception of and approaches to the management of risk in horse-race betting. The results reinforce the findings indicated in Chapter 10. The chapter offers novel measures of decision-maker confidence and the results suggest that the established view, that males have greater confidence in their decisions, is open to doubt in the betting environment. Gender differences in betting motivation are postulated as one possible reason for the results obtained in this study. Since the 1980s there has been little empirical research exploring the female leisure experience. Consequently, the studies discussed in Chapters 10 and 11 represent timely investigations of certain aspects of the leisure betting experience of women, particularly since changes in legislation have served to create a more civilised environment in betting offices and have reduced the perception of betting as a male-orientated task. Chapter 12 extends the discussion of issues addressed in Chapters 10 and 11 beyond those engaged in horserace betting to the decision-making characteristics of male and female managers and potential managers who have undertaken formal management education. It is often argued that women are excluded from managerial positions owing to stereotypes of decision-making behaviour developed through observing non-managerial populations. In order to explore to what extent gender differences in the character and quality of decisions vary between ‘non-managerial’ and ‘managerial’ populations, two pieces of empirical work are reported. The first explores decision quality and risk propensity amongst male and female horse-race bettors and the second explores similar decision characteristics amongst a population of managers and potential managers who have undergone formal management education. The study identifies the horserace betting population as one which covers a broad cross-section of income and social groups. Consequently, comparing the decisions made in offcourse betting offices with those made by a managerial population provides a valuable means of exploring the proposition that gender differences in decision quality and risk propensity vary between non-managerial and managerial subpopulations. The results provide important evidence which suggests, particularly in regard to risk propensity, that differences between males and females do vary

between the non-managerial and managerial populations. This confirms the view that stereotypes derived from observing non-managerial populations should not be used for assessing a particular gender’s suitability for managerial positions. In addition to the empirical results, the study also offers a critical review of the gender/decision-making literature. Contradictions in previous research are highlighted and arguments are developed to reconcile these earlier findings. The main contributions offered by the chapters in Part III include: (1) the synthesis and analysis of research on gender differences from a wide variety of sources; (2) the highlighting of difficulties of interpretation of previous research due to a number of methodological concerns; and (3) the reporting of new empirical research conducted in a naturalistic environment (offering methodological advantages over previous studies). In addition, the empirical research includes novel measures of decision performance, risk propensity and confidence. These measures permit a more sophisticated analysis of the relationship between gender and decision characteristics than the criteria used in previous studies allow. The use of these measures leads to the important discovery that the relationship between gender and decision quality, risk propensity and confidence is not as straightforward as previous research suggests. The betting studies also represent some of the first attempts to explore empirically gender differences in decision performance, risk propensity and confidence among bettors. Additionally, the research reported here focuses on the betting leisure experience of women; this was particularly timely since changes in legislation served to create off-course betting office environments which are more conducive to female participation in betting. Two of the chapters offer insights into aspects of decisions made by males and females in an organisational context. The results provide valuable evidence to explain why women are often excluded from managerial positions. Finally, the chapters in Part III contribute to an understanding of why the literature on cognitive aspects of DSS is inconclusive and is characterised by contradiction, by suggesting that gender is an important moderator variable which has been neglected. A number of implications for DSS design and use of differences in the nature and quality of decisions made by males and females are also identified.

9

Gender and DSS design The research implications P.L. Powell and J.E.V. Johnson

Introduction Although decisions and decision-making lie at the heart of decision support system (DSS) research, certain aspects of human decision-making have been neglected by DSS builders. The editorial in the first issue of the Journal of Organizational Computing (Applegate et al., 1991) identifies many of these, but does not include the role of gender in decision-making. Currently, decision support systems are either constructed upon the assumption of an androgynous user or incorporate constructors’ implicit biases. But, clearly, if males and females take decisions in different ways or prefer different styles of information, then their use or construction of DSS may differ. For instance, the psychology literature suggests the existence of gender-based differences in areas such as problem-solving motivation, verbal, quantitative and visual-spatial ability, risk propensity, confidence, goals, preferred decision process and influenceability. These may have important organizational implications, especially as women ascend the corporate ladder and will affect the construction and use of decision aids. Within DSS research, decision-making has been tackled from two directions. The first, a form of knowledge engineering, seeks to produce a model based on expertise derived from an individual expert decision-maker, while the second, user modelling, considers the nature and skills of the user. Both of these approaches, but especially the latter, rely on aspects of cognitive style research, for instance, cognitive complexity, field independence/dependence and thinking mode. These have received much attention in the information systems and DSS literature (Zmud, 1978). Mann et al. (1989) echo many earlier researchers in maintaining that DSS which are in keeping with the users’ cognitive style will be more frequently used, more effective in decision-making and better accepted. They suggest that the impact of cognitive style research is most significant with regard to the design of dialogue between user and system. However, they caution that few operational guidelines for DSS design have emerged from current cognitive style research. Indeed Huber (1983) questions the worth of cognitive-based research as offering useful insights into information system construction arguing that there is no adequate theory of cognitive style, inadequate measuring instruments and faulty empirical research design. He goes on to

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suggest that the flexibility of DSS generators allows change at will and hence reduces the relevance of cognitive style. Huber, however, seems to have been over-optimistic in his projections for the technology. In consequence cognitive style research continues unabated. Cognitive style, however, is only one of a number of individual differences such as training, experience, intelligence and organizational factors which will affect DSS use. Each of these individual differences may be influenced by gender, but Mann et al. (1989), in discussing the implications of cognitive style on DSS use, fail to identify gender as an important factor. In fact there has been a marked decline in recent years in the number of studies examining differences between male and female abilities and judgement processes. This has not arisen because the previous results are conclusive, but may mark a growing reluctance to explore this sensitive area. The purpose of this chapter is to evaluate the literature on gender differences and to highlight explicitly the role of this literature in DSS design and use. It is hoped that, by raising dormant questions, the debate may be stimulated. The chapter concludes by identifying a number of guidelines to direct future research.

Current DSS design guidelines As a precursor to gender-based issues it is worth summarizing some of the current design guidelines for DSS. These will provide a reference point in the discussion which follows. Benbasat et al. (1991a) provide a comprehensive review of empirical research in management support systems (MSS). They draw out a number of recurring themes which have relevance here and this section briefly summarizes these. There are a variety of frameworks available by which to analyse the literature. Here, a simple dichotomy into design and use is followed. DSS design In terms of the design of DSS, user participation in DSS construction is important while evolutionary design may create a felt need and perceived usefulness is positively associated with involvement. Prototypes are recommended as a way to reduce apprehension and risk. There is evidence that DSS use tends to support the intelligence and design phases of decision-making, and that a knowledge engineer is vital in the efficient use of knowledge acquisition tools. However, Benbasat et al. comment that few normative guidelines for MSS design exist and design research is incomplete. In their criticisms of the literature, Dhaliwal and Benbasat (1990) identify problems with DSS design research including few direct comparisons of the techniques, a lack of experimental rigour and control and that most of the empirical studies have not accounted for the effects of moderator variables. This final point is of paramount interest. It is contended here that one of these may be gender-based effects and that these may have an impact on all the items identified above. As indicated in the introduction and discussed further below, gender plays a role in design since issues such as risk propensity (when embodied in the model base), a preference for problem-solving method

Gender and DSS design 133 rather than results and differences in verbal, quantitative and visual-spatial skills may manifest themselves during construction. DSS use Benbasat et al. suggest that previous research indicates that decision-makers perform better when provided with decision aids and that these have a moderating effect on different decision types. Contradiction exists as to the impact of DSS on decision quality and overall performance. While DSS use enables a greater understanding of underlying models, this is not reflected in perceived confidence and satisfaction or better decisions. There is also little evidence that DSS use increases the number of alternatives considered. In terms of DSS features, no presentation format is found to be consistently superior and the efficiency of these features are largely task dependent. In task terms, structured approaches and interactive aids lead to better performance, though DSS may be primarily used to reduce effort rather than enhance decisions. Again, the conclusion Benbasat et al. arrive at concerning prior research into DSS use is inconclusive. In group terms the role of a facilitator is paramount in effective group decision support systems (GDSS) use and, compared with face-to-face group meetings, GDSS give higher decision quality, more alternatives, longer decision times and more even participation from group members. Consensus and satisfaction are not necessarily enhanced but anonymity leads to more idea generation. Again the contradictions evident in the results of this research suggest the omission of significant moderating variables. Previous research in gender and decision-making suggests differences in use issues such as confidence and influenceability, problem content preferences and problem-solving motivations. Bearing this in mind, the literature on a potential missing moderating variable, gender, is assessed in the following sections.

Previous research in gender and decision taking Prescriptive models suggest that effective decision-making involves a series of steps including problem definition, objective setting, strategy determination, evaluation, selection and implementation. The eventual quality of a decision can be influenced by choices made at each of these stages. Previous research suggests that males and females differ in respect of their cognitive abilities, problem-solving motivation, risk attitudes, confidence and in their decision style. Each of these factors impinges on the various stages of the decision model suggested above and may, consequently, be responsible for gender differences in decision quality which have been observed in the literature. For example, an individual’s verbal, quantitative or visual-spatial abilities might influence the amount and type of information which they are able to gather and analyse prior to selecting a strategy; they might also determine the degree to which distracting stimuli influence their choice of strategy or the sophistication of the strategy selection device employed. An individual’s motivation may

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influence the amount of effort and commitment they are prepared to expend in satisfactorily completing any of the steps of the prescriptive decision model. Similarly an individual’s risk attitude and confidence might influence the degree of ambition reflected in the objectives which are set, or the amount of time spent gathering and analysing data, or the degree of risk involved in the selected strategy. Finally, decision style, which affects the manner in which decisions are taken, might determine the type of goals which are set (e.g. interpersonal versus financial), the type of information which is collected (e.g. qualitative versus quantitative), and the methods used to select strategies (e.g. autocratic versus participative). Whilst no single gender-difference in any of these areas is unanimously supported by the literature, certain distinctive differences in the nature and quality of male and female decision-making can be discerned. Those differences which have been established in the literature and which should be considered by DSS designers are examined below. The discussion is arranged as follows. A brief description of differences which have been observed in the quality of male and female decisions is followed by a discussion of the factors which have been highlighted in the literature as contributing to gender differences in the nature and quality of decisions, namely: • • •

abilities and motivation risk attitude and confidence decision style.

As has been suggested, the ignoring of gender may be a source of some of the inconsistency in previously published DSS and GDSS research. Consequently each of the following sections include a discussion of the implications for DSS and GDSS construction and use. In drawing conclusions from the following literature review two moderating factors must be considered: the research design and the cultural context in which the studies took place. The discussed research varies in terms of the research strategy employed, the task undertaken by subjects, the subjects involved and the decision-taking unit explored (i.e. individual versus group). These features are displayed in Appendix 9.1 for each research project discussed in order to allow a match between the topics explored below and differences in the research design of the various projects involved. Finally, it should be stressed that the research discussed in the following sections is drawn from work conducted in the UK and the USA. Hofstede (1980) classifies both countries as having an Anglo-culture and it would obviously be unwise to extend the conclusions reached to non-Anglo cultures.

Decision quality One of the most consistent findings in the personality and social psychology literature prior to the early 1980s was that of inferior problem solving by women

Gender and DSS design 135 (Carey, 1958; Maier and Hoffman, 1961; Hoffman and Maier, 1966; Milton, 1957; Priest and Hunsaker, 1969). These findings held even when differences such as intellectual aptitude and special abilities were controlled (Sweeney, 1953). Experiments examining gender-related differences in group decisions mirror, to some extent, earlier work on individuals. All-male groups were found to perform better on problem-solving tasks than all-female groups, but women in mixed-sex groups performed at least as well as males in all male groups (Maier and Hoffman, 1961). It has been suggested that females generally have a negative attitude to abstract problem solving and that this results in their apparent inferior performance in the majority of these exercises (Lynn, 1962). It was argued that problem solving is traditionally associated with the male role and that this is subconsciously reinforced by adults as children mature. Female sexrole socialization, however, reinforces a more negative attitude to this skill. Commonly held stereotypes that women lack decision-making abilities certainly appear to exist (see for instance, Kanter, 1977a; Nieva and Gutek, 1981; Terborg, 1977). Broverman et al. (1972) found that males were perceived to be more able to make decisions and such stereotypes clearly act to reinforce the sex-role socialization process indicated above. Post-1980 literature has tended to concentrate on business-orientated decisions among managers and entrepreneurs (see Appendix 9.1) and some of the recent studies have failed to identify any significant differences in the quality of decisions taken by men and women. Research by Hudgens and Fatkin (1985), for example, examining decisions taken on a computer-simulated task found no significant difference between the scores of males and females. Similarly Estes and Hosseini (1988) undertook a laboratory investigation of investment decisions, controlled for a range of variables including age, years of college work completed, years of business experience and the amount of the investment decision. They failed to identify any significant difference in the quality of male and female investment decisions. It could be argued that the inferior problem solving by women identified in earlier studies resulted from cultural norms existing at that time and that these gender differences have become blurred as the norms have changed (Eagly, 1978). It has been suggested that this blurring, to some extent, resulted from the women’s movement ‘which took shape in the 1960s and 1970s . . . [and] . . . has had a major influence on societal value systems’ (Masters and Meier, 1988, p. 32). However, a further and possibly more potent explanation for the contrasting findings on gender-related decision quality might be the manner in which the studies have been conducted. Eagly (1978, p. 87), reporting a critique of research examining differences in decisions taken by males and females carried out by Block (1976), observes that ‘studies examining sex differences have varied widely in the sensitivity of research designs, quality of sampling procedures, and reliability and validity of measuring instruments’. The studies discussed above (i.e. Hudgens and Fatkin, 1985; Estes and Hosseini, 1988), which showed no gender difference in decision quality, involved

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laboratory-based research (see Appendix 9.1). Recent research conducted by Johnson and Bruce (1993), however, specifically attempted to overcome the criticisms levelled at previous laboratory studies in this area and examined male/female decisions in a real-world context. This study revealed that there may be no simple answers concerning the differential quality of male and female decisions. The superiority of male or female decisions appears to be contingent on a variety of factors. This confirms previous research which demonstrated that certain conditions (i.e. degree of detail in instructions, extent of distracting stimuli, feminine/masculine content of problem, etc.) appear to affect males’ and females’ performance differentially (e.g. Priest and Hunsaker, 1969). It may be that the gender differences in motivation and cognitive abilities have resulted in certain research designs favouring one sex more than another. Certain types of problem may therefore produce better quality decisions by women than men and vice versa. This, consequently, may have caused the apparent discrepancy between results of earlier studies which explored gender differences in decision quality. Gender differences in motivation and abilities are therefore discussed below.

Motivation and abilities Research suggests that males and females differ in respect of motivation for problem solving and in three cognitive abilities: verbal, quantitative and visualspatial skills (e.g. Halpern, 1992; Hoffman and Maier, 1966; Varro, 1982). Each of these may influence decision quality. Motivation has been identified as a major factor influencing decision-quality differences between males and females. Hoffman and Maier (1966, p. 388) suggested that ‘women’s typically inferior performance . . . appears to be more a function of inappropriate motivation than lack of ability’. They reached this conclusion since, in their experiments, women’s problem-solving performance improved significantly when a change from a male to a female experimenter was made and when a prior motivational talk was provided by a male. They suggest that these changed conditions appeared (p. 387) ‘to arouse motives to stimulate effective performance, while the standard situation arouses motives which produce inferior performance’. A study by Kelly et al. (1982, p. 124) examining group decision-making explored the reasons for this lack of female motivation. They found that ‘females were less active than males during decision-making group interactions, and especially those involving more male-typed content areas’. This finding confirms the results of a study by Milton (1959) which showed that the problem-solving performance of women improved significantly when the given problem had a feminine rather than masculine content, even when the underlying logic was identical. Herschel et al. (1991) similarly argue that their experimental task ‘Lost at Sea’ is male-biased and that this results in males’ significantly superior performance in the task prior to any group work. Maier and Burke (1967) similarly concluded that the nature of the problem set had more impact on gender-induced

Gender and DSS design 137 differences in problem solving than cultural or ability differences. It may well be, therefore, that the masculine/feminine content of the problem has a significant effect on motivation, which in turn affects decision quality. Factors other than the gender content of the problem also appear to influence female motivation for problem solving. Some studies, for example, have demonstrated that women benefit to a greater extent than men if they are given brief instructions on how to solve problems, if they are given more time, if they are provided with more detailed information and if distracting stimuli are removed (e.g. Priest and Hunsaker, 1969). Whilst these factors may have a direct effect on motivation, their influence on decision quality is also likely to be affected by gender differences in verbal, quantitative and visual-spatial skills. There is clear evidence that males and females differ in respect of these three cognitive abilities (e.g. Halpern, 1992; Varro, 1982). Maccoby and Jacklin (1974), for example, examined over 1,000 research reports on sex differences and identified these three cognitive abilities as areas where sex differences have been established. Subsequent research has confirmed these findings. Verbal abilities embrace a range of concepts such as word fluency, grammar, spelling, reading, vocabulary and oral comprehension. Halpern (1992, p. 64) asserts that ‘evidence from a variety of sources supports the finding that, on the average, females have better verbal abilities than males’. Hyde and Linn (1988) undertook an extensive statistical analysis of the literature on sex differences in verbal ability and identified a significantly better performance by females for ‘all tests’ (as opposed to more specific vocabulary or reading comprehension tests) for adults over the age of 26 and for children less than five years. There were no significant differences for ages six to 25 years. These superior verbal abilities may help explain why women’s performance increases significantly more than men’s when they are given brief instructions or more detailed information (Priest and Hunsaker, 1969). Finally, superior word fluency and oral comprehension may also account for the finding that females are less influenced by the framing effect bias than males when undertaking a simulated risky decision-making task (Levin et al., 1988). All subjects in the experiment generally responded more favourably to gambles when the probability information was phrased in a positive manner (i.e. ‘chance of winning’) than when it was phrased in a negative manner (i.e. ‘chance of losing’), but females were less influenced by the manner in which the information was presented than males. Quantitative ability involves a number of different aspects, but there is clear evidence that males have a distinct advantage in some of these. Plake et al. (1981, p. 780), in summarizing sex-related differences in quantitative ability, conclude ‘there is little doubt that females score differently (lower) from males on mathematical tests’. Similarly Meece et al. (1982) reported significantly higher scores by males in quantitative tests even when the data were adjusted to take into account the number of mathematics courses the subjects had taken. Hyde et al. (1990), in analysing 100 previous studies, concluded that, overall, male adults were superior in quantitative ability. The

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nature of the task examined did influence the results and whereas there were no significant differences between the sexes in understanding mathematical concepts, there were very clearly significant advantages for males on mathematical problem solving – a result confirmed in a review of the literature carried out by Aiken (1987). The heterogeneous nature of the term quantitative ability is clearly demonstrated by a study carried out by Stones et al. (1982). Females scored significantly lower than males in measurement, geometry, probability and statistics, whereas they scored significantly higher than males in mathematical reasoning and on tests of mathematical sentences. Visual-spatial skills include the ability to detect the relationship among objects and shapes or the ability to imagine what an object would look like if it were rotated. Lohman (1988) has shown that visual-spatial skills are used extensively in engineering, chemistry, architecture, the building trades and aircrew selection. Whilst visual-spatial abilities have been shown to consist of several separate factors (Linn and Peterson, 1986), there is clear evidence that males perform significantly better in the majority of these (e.g. Linn and Peterson, 1986; Schiff and Oldak, 1990; Smith and McPhee, 1987). Whilst many of the studies examining visual-spatial skills have been conducted in the laboratory, those that have used the real-world environment have confirmed earlier findings (see Appendix 9.1). For example, a study by Holding and Holding (1989), examining judgements made about distances travelled, found that males were significantly more accurate than females. It can be argued that the most striking and consistent evidence for female disadvantage in tasks requiring cognitive abilities occurs on tasks testing visual-spatial abilities (McGee, 1976). The above discussion clearly demonstrates that the relationship between gender and decision quality is complex, but previous research indicates a range of gender issues associated with motivation and cognitive abilities which should be considered by the DSS designer. Implications for DSS It would be premature to propound firm conclusions for DSS based on the above literature review owing to the lack of specific DSS-related gender-based research. However, certain implications do suggest themselves. The first of these is simply that gender, as with many other factors, cannot necessarily be ignored by DSS builders – there is ample evidence that gender-based differences merit consideration. However, the caveat must be added that, although evidence suggests that in the population as a whole males and females differ in their decision-making habits, such a conclusion cannot necessarily be drawn about a trained managerial population (see Johnson and Powell, 1994). This may be a comfort for DSS builders. At least one might argue that within a trained population, decision-making behaviour may not differ significantly between males and females, though it may in the untrained. This conclusion, however, has only been reached in a single research study and clearly not all DSS users will be managerially trained. Those who are trained are more likely

Gender and DSS design 139 to be in senior positions within organizations and senior management are more likely to employ ad hoc DSS, whilst those at lower organizational levels use institutional ones (Keen and Scott Morton, 1978), though this is not necessarily the case for expert system use (Powell et al., 1992). Institutional DSS typically give less flexibility to their users and hence a difference in decision characteristics by users may be of less consequence, although an incompatible system may be rejected. Since higher level managers are often better trained, any inconsistency in actions may be mitigated. However, females forced to use a male-oriented system or vice versa might perform worse than when unaided. The general conclusions that aided users perform better and that decision aids have a moderating effect on different decision types will certainly be applicable to gender-based decision differences. The literature on gender differences in decision quality raises a number of important issues for DSS. DSS, for example, may help to overcome females’ poorer problem-solving performance, although Benbasat et al. (1991a) conclude that, while decision-makers generally perform better when aided by a DSS, the research is inconclusive. Similarly females’ problem solving improves when more time is allowed for the task. DSS may be an aid here, but the additional time needed may be a reflection of female preference for the method of solution, their desire to attempt to reach consensus on the solution or their greater preference for information gathering. Only in the latter case might a DSS assist. DSS designers must also be aware of the gender aspects of problem content since the nature of the problem set has been shown to influence outcomes. Thus DSS framed in a masculine manner (e.g. couched in a very aggressive way, perhaps emphasizing destructive competition) are likely to be off-putting to female users, and vice versa (Herschel et al., 1991). This may partially explain the mixed conclusions on the impact of DSS on decision quality and performance since the literature does not report any tests for sex biases in the studies carried out. This problem may apply in two distinct contexts, one in the framing of the DSS model and the other in the decision situation. One solution may be mixed gender construction teams. However, the move towards user-built models (Davis, 1982) may alleviate some of these difficulties by placing the onus of content upon the user, though this requires the user to have sufficient selfinsight. Yet, one step further removed, the producers of DSS generators may need to ensure that their products are equally useful to both sexes, since specific DSS will reflect the underlying characteristics of the generator used. DSS designers may need to take account of the negative socialization of females towards problem solving. Although DSS designers may not be able to alter this socialization process, they can make use of other research findings to counteract the adverse effect on decision quality. It has been shown, for example, that females benefit from, and make more use of, instructions. Although a feature of expert systems, the co-operative nature of problem solving with a DSS does not usually involve explicit instructions within the system. Dos Santos and Bariff (1988) do however recognize the superiority of structured model manipulation (which implies use of instructions) and maintain that systems designers should

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provide aids that guide users in structuring their use of a model while not constraining creativity. Females’ general lack of problem-solving motivation is difficult for the DSS designer to counter, though, of course, a DSS may replace part of the process of problem solving. The almost passive nature of DSS embodies them with very little motivational ability. Again, however, motivation may come from recognition of the system’s ability to aid decision-making. Simply, good systems provide motivation, poor ones do not. Motivation may also be increased by participation or involvement (Barki and Hardwick, 1989) in system construction since, as is demonstrated later, females are more concerned with aspects of the decision method, such as interpersonal factors and fairness than with results. Gender differences in cognitive abilities must also be considered by DSS designers. Males’ greater susceptibility to framing bias, for example, needs to be carefully handled. It is obviously more important for males than for females how the questions in the DSS are framed. This, when coupled with the increased risk propensity males exhibit (discussed in the next section), is a potent combination which may lead to incorrect inferences from DSS output. The use of DSS, however, may have a levelling effect on gender differences in verbal, quantitative and visual-spatial ability. Certainly this is the effect of DSS on different cognitive types (Benbasat et al., 1991). DSS typically require few visual-spatial skills and may mitigate inadequacies in quantitative and verbal skills. However, as the graphical capabilities of DSS increase, for instance in three-dimensional spreadsheet use, visual-spatial abilities may become more important. Equally, although males are better at tasks involving probability and statistics, females demonstrate superior mathematical reasoning and understanding of mathematical sentences, hence the nature of DSS construction is important. Indeed this poorer quantitative ability may be offset by females’ better comprehension, vocabulary and grammar. Similarly, female propensity for understanding and effectively utilising instructions may be a mitigating factor for quantitative deficiencies. The current literature on presentation formats for DSS is contradictory and again may demonstrate the lack of recognition of gender-based differences. One possible route to overcoming any of these problems may be the use of selfbuilt models. Yet self-built models may be inferior if poor verbal or quantitative models are reproduced. Mittman and Moore (1984) identify this as one of the negative characteristics of user-built models. In any case, account needs to be taken of females’ better verbal comprehension, communication, number reasoning and word fluency, particularly if they are building models for male use. Implications for GDSS Some of the cognitive and gender-based differences in problem solving may be alleviated by the use of groups. However, there are potential difficulties in group DSS use arising from the literature above. Though much research has been carried out on group decision support systems (GDSS), or computer-supported co-operative work (CSCW), there

Gender and DSS design 141 is only a single paper (Herschel et al., 1991) which specifically addresses the relative performance of single and mixed sex groups using computer-mediated support. Herschel et al. argue that most GDSS work has focused on the effectiveness of the technology and on group processes, dominance patterns and outcomes. Their literature review suggests that as the number of females in a group increases so stereotyping behaviour decreases and attitudes towards women improve. GDSS are seen as enabling parallel communication, giving the ability for individuals to decouple themselves from the group process, and enhanced anonymity (Dennis, 1990). GDSS may also provide motivation for problem solving by encouraging participation. King et al. (1990) find that gender has no effect on accuracy and capability of decision-making with or without computer support. Herschel et al. attempt to test the effect of group composition on task outcomes. Their results indicated that group gender composition does not affect brainstorming nor does it influence decision time. Yet in keeping with some of the literature reviewed earlier they found that uniform-female groups performed significantly less well than uniform-male or skewed-male groups. Their conclusions are that GDSS may help to overcome certain dysfunctional aspects of group activities such as providing anonymity and stereotype reduction. Benbasat et al. (1991b) concur that GDSS, by providing anonymity, reduce inhibitions and equalize status. Interestingly, Zigurs et al. (1988) find increased non-verbal communication in groups using DSS as opposed to unaided ones. It may be, therefore, that the nature of GDSS interaction removes the basis for many of the gender-related issues in group interactions. But it might be premature to suggest that GDSS are gender-neutral, especially if they reflect male-oriented tasks. Gallupe et al. (1986) find that the major effect on GDSS is the nature of the task. Here again GDSS are seen to enhance decision quality but not decision time. Significantly the level of participation by individuals is unaffected by GDSS use. None of Gallupe et al.’s work is, however, gender-related. No work has focused on the gender aspects of facilitators. While it has been shown that the presence and quality of the facilitator is a major factor in GDSS use, the foregoing literature might suggest that females’ decision quality will improve more than males when facilitated. A further important aspect of DSS and GDSS use concerns levels of risk, both those pertaining to the user and those inherent in the model, and the confidence with which models and outputs are used. Risk propensities and decision confidence are clearly important aspects of human decision taking since, as already discussed, they can influence the goals which are established, the time and thoroughness of the data search and the risk profile of the strategy selected. The next section, therefore, evaluates the literature relating to gender differences in risk taking and decision confidence.

Risk taking and confidence There is clear evidence that females are less inclined to take risks than males (Coombs and Pruit, 1960; Ginsburg and Miller, 1982; Hudgens and Fatkin,

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1985; Keinan et al., 1984; Kogan and Dorros, 1978; Levin et al., 1988; Roberts, 1975; Slovic, 1966; Thomas and Garvin, 1973). In a set of experiments conducted by Coet and McDermott (1979) risk taking was defined by the probability of ‘success’ which subjects considered acceptable before undertaking a particular course of action. In these experiments males, as individuals, were prepared to accept a lower probability of success before embarking on the course of action than females. Coet and McDermott (1979) also found that all-male groups took significantly greater risks than all-female or mixed-sex groups. They concluded (p. 1291) that in mixed-sex groups females may play ‘an influential role in “reducing” the reinforcing properties of risk-taking inherent in “male” roles’. In a further set of experiments Hudgens and Fatkin (1985) asked subjects to estimate the probability that a tank might successfully cross a number of minefields having first provided them with details of the pattern of mines in the fields. They discovered no significant sex differences in subjects’ ability to estimate these probabilities. Under most conditions, however, they discovered that males were prepared to send the tanks across minefields with lower estimated probabilities of a successful crossing, than were females. These results confirm earlier research which suggests that men are more inclined to take risks than women in a variety of situations. They also suggest that the inclination for males to take greater risks does not stem from differences in the perceived probability of success. An empirical study examining decisions in a natural environment by Saint-Germain (1989) confirmed these results. He investigated the actions of legislators in a state senate and found that, whilst women proposed fewer bills they were more successful in securing passage for them. Saint-Germain suggests that this provides evidence for risk aversion in females. The bulk of previous research has suggested that females are less willing to take extreme risks in gambling situations. Women appear to prefer gambles with a high probability of some, even low, return and men prefer gambles with a lower probability of some higher return (Coombs and Pruit, 1960; Kass, 1964; Johnson and Powell, 1994). In their review of the literature Hudgens and Fatkin (1980) and Fatkin and Hudgens (1982) reported 27 original investigations into gender differences in risk taking. In 20 of these males were reported to take greater risks, in three females took greater risks and in one no sex differences were found. Much of the empirical work in this field has focused on studying driving behaviour and pedestrian safety behaviour. In these ‘naturalistic’ studies men have been shown to consistently take greater risks. Lenney (1977) indicated that women tend to be more conservative than men when unsure of their decisions but are more extreme than men when very sure of their decisions. Hudgens and Fatkin’s (1985) research, discussed above, also identified one type of situation in which women take greater risks than men, but this was in circumstances characterized by a low probability of success. These findings suggest that the relationship between gender and risk taking is not straightforward. A few studies have not demonstrated any significant difference between the risk taking propensity of males and females (e.g. Arenson, 1978; Maurer, 1972; Noe and McDonald, 1983; Starr and Potashier, 1984). There are a number of

Gender and DSS design 143 possible explanations for this contradictory evidence. Coet and McDermott (1979) suggest that several studies showing no significant gender differences in risk taking used children as subjects (see Appendix 9.1). They argue that the significantly greater risk-taking propensity for males identified in most adult studies simply demonstrates that cultural pressure creates these gender differences. They point to evidence which suggests that risk taking in males is highly valued and consequently is reinforced at home and at school. Tuddenham (1952) demonstrated that risk taking among females is negatively valued and that females who take chances are unpopular. Cultural pressures, therefore, reinforce the ‘prescribed’ risk-taking behaviour of males and females. Slovic (1966) demonstrated that the expected differences in risk taking did occur, once children had adopted their ‘sex-role stereotype’. A further reason for some studies failing to confirm the more cautious risk taking of women may be the nature of the decision-making tasks involved in the experiments. Several of the studies which suggest female risk aversion have used ‘male-orientated’ tasks and Levin et al. (1988, p. 180) conclude that ‘before over-generalizing this result (females are less risk propensive) researchers should examine the interaction of gender and sex-relatedness of decision making tasks . . . Future studies of risk taking should include female-orientated as well as male-orientated tasks’. It is argued that experiments using tasks with which women are less familiar (e.g. military decision-making – Hudgens and Fatkin, 1985) may result in them exhibiting greater degrees of risk aversion. The literature review undertaken by Lenney (1977) appears to corroborate this view, as do the experiments carried out by Hudgens and Fatkin (1985). Their experiments involved subjects making risky decisions in repeated sessions. Whilst greater risk taking was exhibited by males during the initial session, the gender difference in risk taking was reduced or reversed on subsequent trials. This suggests, perhaps, that familiarity induces a change in risk propensity. Whilst the evidence of gender differences in risk taking is clearly not clear cut, the main body of past studies does suggest a tendency for males to be more risk propensive. An area related to risk taking which has produced clearer results concerns the degree of confidence which males and females express in their judgements. Definitions of confidence include ‘a feeling of consciousness of one’s powers or of reliance on one’s circumstances’ and ‘the quality or state of being certain’ (Webster, 1980). A review of the literature carried out by Lenney (1977) reported many studies in which women demonstrated significantly less confidence in their decisions than men. In one experiment, for example (Crandall, 1969), students were asked to predict how well they would perform on a given task. Males were generally optimistic, in that they predicted that they would do at least as well as they actually did, whereas women were more likely to be pessimistic, in that they predicted they would do worse than their performance indicated. In an extensive review of the confidence literature, covering a wide range of tasks from academic problem solving to manual dexterity, Maccoby and Jacklin (1974) reported that the overwhelming majority of studies indicated significantly greater confidence by males. In none of the studies did females

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exhibit greater confidence. More recent studies confirm these findings. Birley (1989) reported that when traditional personality tests are conducted the only significant difference which emerges between the sexes is that males exhibit a higher degree of self-confidence. A study by Estes and Hosseini (1988) examining investment decisions found that: Women were substantially less confident than men in their investment decisions even after statistically controlling for all the other variables. Thus if a man and a woman of the same age, equal business experience, same number of credit hours in accounting and finance and the same number of years of college, equal portfolio values and the same experience with and knowledge of common stocks and the stock market, and the same attitude about investing in common stocks, make the same investment decision, the woman can be expected to be significantly less confident in her decision. This result held, even though there was no evidence in the study to suggest that women made worse investment decisions than men. Women were clearly less confident than men in their choices, irrespective of the quality of the decision. The lower confidence of women in their choices has been confirmed by other recent studies (e.g. Nicholson and West, 1988). These latter authors suggest that this might be due, in part, to women’s often insecure positions within organizations. Implications for DSS Assessing the literature on risk preferences and confidence it is clear that there are two aspects of risk attitudes which are of particular concern to DSS builders. These concern the representation of risk within the model – which may be transparent to the user – and the reactions of users to output, possibly probabilistic, of the model. Male-built models may not reflect female risk preferences, which tend towards the risk averse. Similarly models incorporating female risk preferences will tend to overstate risk levels as perceived by male users. A further concern is that consistency is lost when individual managers react differently to the same pieces of output. This may be exacerbated if, as both Powell et al. (1992) and Berry and McLintock (1991) point out, there is evidence of decisionmakers using DSS output rather than the system itself, the system being operated by subordinates. In such an instance the data may have been twice filtered before decisions are taken. It might be argued that, where possible, objective rather than subjective risk estimates should form part of the DSS, thus avoiding the need to cater for different user preferences. Chervany and Dickson (1978) report that decision-makers, using summarized and filtered information, although making better decisions, were less confident in them than when making unaided decisions. This tendency, inherent in DSS output, may exacerbate females’ lower confidence in their decisions. Conversely DSS may add to males’ overconfidence in their abilities. The provision of

Gender and DSS design 145 summarized information by DSS may pander to males’ dislike of information or be off-putting to females who prefer greater amounts. Goslar et al. (1986), however, found that in an ill-structured environment, use of a DSS did not affect either performance or perceived confidence. Again, Aldag and Power (1986) discovered only limited support for the view that decision aids increased confidence and satisfaction. Neither of these studies was gender-based, however. Though DSS use may provide a greater understanding of the underlying decision models, this understanding is not reflected in greater confidence or satisfaction. A different component of risk comes into play during the building of a system. A method of reducing risk during construction may be via the use of prototypes giving users an opportunity to test and influence the final system. Alavi (1982) demonstrates how the use of prototypes can reduce adoption apprehension and risk. The notion that task familiarity increases with DSS use has not been tested. DSS use may insulate the user from any real interaction and identification with the problem. This loss of task familiarity is consistent with male disregard for the problem-solving method, but compatible with their interest in the decision result and this would be consistent with the majority of DSS having been built by males. Implications for GDSS The findings that all-male groups take more risks than all-female or mixedgender groups is important for GDSS construction (though a DSS may also be team built), but more so for use. All-male groups using GDSS will exhibit unwarranted confidence in their decisions and be prepared to take substantial risks while the reverse will be the case for all-female groups. As discussed above, the risk measures incorporated in the system will reflect the preferences of builders. The interplay here between the risk preferences of the group and that embodied in the DSS will be vital, given the potential cumulative effects of preferences of builders and users. The preferred manner in which decisions are made also has implications for DSS and GDSS construction and use. The literature relating to male and female decision style is therefore discussed in the following section.

Decision style Whilst research suggests that there are a number of similarities between the manner in which males and females take decisions, there is also much evidence to suggest that there are specific gender differences in decision style. This section therefore outlines the areas of similarity which have been identified in the literature before discussing the gender differences in decision style which have been observed. Ashburner (1991, p. 5), reporting a study carried out by Nicholson and West (1988) into male and female British managers, concludes that ‘differences ... found

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between men and women bore no relationship to the traditional stereotypes of male and female characteristics’. Welsch and Young (1984, p. 16) found that ‘no difference exists in personality characteristics between male and female entrepreneurs’. They identified no significant difference in self-esteem, locus of control, flexibility in thinking, ability to manipulate and persuade others and in their openness to innovation. These results confirm earlier work by Schwartz (1976). Welsch and Young (1984) also found that male and female entrepreneurs experienced similar numbers and types of problems under four categories – general management, operations, finance and marketing. This, they suggest, indicates that there is little difference in their perception of the nature and intensity of problems within organizations. Chaganti (1986) also found that female entrepreneurs manage their organizations in much the same way as male entrepreneurs. In particular the female entrepreneurs interviewed in the study employed strategies, structures, shared values, systems, staff and skills which were similar to those of successful male entrepreneurs. Gerritann et al. (1987) demonstrated that the motivations of male and female entrepreneurs were similar in terms of their need for money, independence and the identification of business opportunities. Birley (1989, p. 33) also reports that ‘when traditional personality tests are conducted, no significant differences emerge with regard to achievement motivation, autonomy, persistence, aggression, independence, non-conformity, goal-orientation, leadership and locus of control’. Despite these observed similarities between males and females which influence the manner in which they take decisions, a number of gender differences in decision style have been identified. In particular, males and females have been observed to hold different objectives, to emphasize different aspects of the decision process and to differ in the degree to which they are readily influenced or persuaded. Each of these aspects of decision style is addressed below. Objectives clearly play an important role in decision-making and women have been shown to establish goals which are influenced by their greater concern for interpersonal values (Hodgson and Watson, 1987; Kanter, 1977b). They consequently select strategies which support relationships, whereas men tend to follow absolute rules (Kohlberg and Kramer, 1969). Their greater emphasis on interpersonal goals may also explain why women perform better than men in group problem-solving tasks requiring discussion and consensus, whilst men prove better on problems requiring a number of separate solutions (Wood et al., 1985). It might similarly explain why female entrepreneurs have been observed (Chaganti, 1986) to employ a distinctive style of leadership which is more ‘people orientated’, less autocratic and more informal than that employed by male entrepreneurs. Eagly (1978) summarizing a range of coalition formation experiments suggests that the findings (p. 104): are generally compatible with the idea that females place greater stress on interpersonal goals: Women’s coalition behaviours have been described as more accommodative and orientated toward equity and maintenance of

Gender and DSS design 147 smooth interaction, whereas males are more exploitative and concerned with winning. In bargaining studies, such as those involving the Prisoners’ Dilemma, females have often been found to be less co-operative than males (e.g. Rapoport and Chammah, 1965). It is argued (e.g. Rubin and Brown, 1975) that female competitiveness in gaming situations results from their response to the social attributes of the other player. Males on the other hand simply attempt to maximize their winnings. Eagly (1978) argues that this interpretation is consistent with the view that females’ decision style is affected by their orientation towards interpersonal goals. She also suggests that this idea is compatible with empirical evidence on sex differences in the goals people have been found to hold in group settings. In these situations females appear to place greater emphasis on ensuring a smoothly functioning group by resolving interpersonal conflict. Several studies confirm that men and women have different goals in decisionmaking situations. Hong and Chiu (1988), for example, found that males and females took risks in a gambling situation for different reasons. They suggest their findings indicate that males gamble, in part, to regain illusory control, whereas females gamble to confirm their expectancy of external control. Studies by both Sargent (1981) and Barnett and Karson (1989) suggest that the selection and adoption of an appropriate method to accomplish a task forms an important part of the goals adopted by women, whereas the goals adopted by men focus more exclusively on the results of the decision. The decision processes employed by males and females, perhaps partly due to the gender differences in goals discussed above, have been shown to differ. Hudgens and Fatkin (1985) when examining sex differences in risk-taking decisions found that women, in low-probability-of-success situations, took longer to make their decisions, whereas under all other conditions men took longer. Subsequent interviews of the subjects involved in this experiment revealed that, under the majority of conditions, men spent more time analysing the situation before reaching, what they considered to be, an acceptable decision. Women appeared to make their decision having considered fewer variables in the problem. There is no evidence, however, that there are sex differences in analytic ability (Maccoby and Jacklin, 1974). Welsch and Young (1984), when examining the manner in which male and female entrepreneurs made decisions, found that women entrepreneurs valued written information sources significantly more highly than men and that they were more interested in attending seminars on business-related issues. Information is, clearly, highly regarded by women. Welsch and Young (1984, p. 17) conclude that women ‘take more time and trouble to gather information from written sources while utilizing other information sources as frequently as men’. These results are compatible with earlier work conducted by Priest and Hunsaker (1969), who found that women’s performance improved significantly more than men when they were given more detailed written instructions. This may arise from females’ superior verbal skills discussed above.

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The influenceability literature suggests that females are more easily persuaded or influenced in their decisions, irrespective of the risk involved (Baker, 1975; Hovland and Janis, 1959; Worchel and Cooper, 1976). An important social psychology text (Freedman et al., 1970, p. 239) summarizing this research suggests ‘women conform more than men. . . . This difference between men and women has been found in virtually every study in which both sexes participated’. One reason for this may be gender differences in levels of aggression. Research undertaken by Berkowitz (1962) indicated that women were less aggressive. A review of the literature by Maccoby and Jacklin (1974) confirms that males are more aggressive both physically and verbally. Several studies have suggested that females are more acquiescent in group pressure situations (e.g. Eagly, 1978; Maccoby and Jacklin, 1974). In an extensive review of much of this research, Freedman et al. (1970, p. 332) conclude that ‘there is a considerable amount of evidence that women are generally more persuasible than men’. Subsequent research has continued to reveal differences in influenceability, although the effect appears to depend on a number of factors. Ward et al. (1988, p. 247) summarizing the literature conclude that ‘the relationship is by no means consistent across all conditions . . . it . . . depends on the content of the influence topic (Sistruck and McDavid, 1971), the task to be performed and . . . the sex composition of the group-pressure situation (Crano, 1970)’. In relation to empirical studies it could be argued that women appear to be more conforming as they are often forced to acquiesce to male norms in organizations in order to gain promotion (Marshall, 1984). Many writers argue that the observed tendency for females to yield to group pressure results from socialization pressures applied in childhood. Middlebrook (1974, p. 190) summarizing this view suggests that ‘the feminine role in our society has traditionally emphasized passivity and yielding so that when little girls are socialized into their roles, they may be trained to yield’. Eagly (1978) in a major review of the influenceability literature found that whilst some of the studies showed no significant difference between males and females in the degree to which they were persuaded by others, the vast majority of studies suggested that females were more persuasible. Similarly in her review of the conformity literature, Eagly (1978) concluded that a significant number of studies found females to be more conforming to group pressure. She suggests that this tendency results from females’ desire to (p. 105) ‘preserve social harmony and to promote the positive feelings of group members toward one another’. Research by Kelly et al. (1982) confirms that males and females behave differently during decision-making group interactions. They found that (p. 123) ‘males performed in a more active manner than females in a variety of assessed social behaviours’ (e.g. in frequency of declarative statements, speech duration). Kelly et al. (1982) go on to argue that there is (p. 124) ‘the need for continued efforts to increase women’s social skills and assertiveness, and to decrease social inhibition, in such decision making roles’. This goal may be difficult to achieve, however, since research by Kelly et al. (1980) suggests that assertive behaviour

Gender and DSS design 149 by women (cf. men) is treated less favourably in group situations. This suggests women may encounter more resistance and less reinforcement in group decisionmaking situations. In summary, whilst there appear to be a number of similarities between males and females which influence the manner in which they take decisions, previous research suggests there are also important differences in decision style stemming from gender differences in goals, the decision processes employed and in influenceability. These factors require consideration by DSS and GDSS designers and users. Implications for DSS Perhaps the major concern for DSS builders in the extant decision style literature is the greater interest by females in the decision process, and by males in the decision results. Todd and Benbasat (1991) suggest that the DSS literature has focused almost exclusively on decision quality, whereas users may be more interested in effort reduction rather than accuracy maximization. Their empirical work supports this contention, but they do not test for differences between male and female subjects. The implication from the literature reviewed here is that such an effect will be more pronounced in males than females. DSS removes from the decision taker part of the decision process and most certainly lowers the human interaction element of problem solving (at which females excel). This and the females’ orientation towards interpersonal goals may induce lower satisfaction in females forced to use DSS. Similarly, female decision style, which is people-oriented and more informal, is less suited to a DSS environment. Benbasat et al. (1991b) propose that computer-mediated communication tends to be richer in task-oriented rather than social-emotional messages. This may be more efficient for short-run, specific tasks but reduces the process of group bonding. Clearly DSS, by facilitating option generation, provide a levelling in the quantity of alternatives and variables considered; though there is research (for instance Goslar et al., 1986) which suggests DSS use restricts alternative option generation. This could be a problem since it has been shown that females consider fewer variables when making decisions. The male dislike of written information is also a potential problem, particularly for complex DSS requiring guiding instructions or producing output which consists of multiple scenarios, for instance. This contrasts with females’ greater valuing of information and their superiority in the use of written information. Previous research has suggested that DSS are used primarily in the intelligence and design phases of decision taking, not in the choice phase. This is more suited to the female preference for method over results. However, it could be argued that what is evident is that systems have been constructed for those parts of the decision process which males dislike, and are therefore happier to delegate to a system. Little attention, however, has been paid to the choice phase of decision-making, which females are less motivated to perform. This may be a reflection of current DSS builders.

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The finding that in most situations men take longer to make decisions, but in low probability of success situations women take longer, may also have DSS implications. The source of the success probability is not well identified in the research. This may be subjective or it may be a given. If it is the latter, perhaps derived from DSS output, then females are likely to be coerced into swift decisions since they are less motivated to examine a variety of choices. As discussed, there is interestingly little evidence that DSS use increases the number of alternatives considered. This is in keeping with the male tendency to pay less attention to decision method. Finally, research is needed to establish the nature of influenceability or persuadability. This may derive solely from interpersonal interaction, in which case DSS models may not have the ability to persuade. Alternatively, the extent of influenceability may depend on the user’s confidence in the abilities of the system vis-à-vis the views they had of their own abilities. Again, males’ excessive confidence in their capabilities may provide an erroneous anchor point when using the DSS. The issues of influenceability and persuadability are more important in considering group DSS since both the system and the group will have the ability to influence or persuade. Implications for GDSS Hiltz et al. (1989) point to GDSS use encouraging a greater tendency of individuals to align themselves to group attitudes compared with non-computer-mediated situations. This is a general tendency – no reference is made to gender differences. This tendency may exacerbate females’ greater inclination to acquiesce to group pressure in mixed group circumstances, though women excel at tasks requiring discussion and consensus. Females have been shown to prefer strategies which support interpersonal goals and while this may be possible in a GDSS situation where others’ preferences are known, it is not possible in typical DSS-user interaction. The extent to which other group members’ preferences are revealed will depend on the facilitator and the mode of GDSS use. If the process moves too quickly towards solution (a male preference), then females may feel uncomfortable. Two further issues concern group influenceability (and within that influenceability by the system itself) and the degree of co-operation in bargaining. In bargaining situations females have been shown to display less co-operation than males, though this may stem from a greater desire to be ‘fair’ to other participants. However, such a tendency may prolong and disrupt GDSS sessions and is at odds with male preference for results. Yet the anonymity of electronic interaction of GDSS compared with face-to-face processes may inhibit the female search for equity.

Conclusion and agenda for future research The literature on cognitive aspects of DSS design and use may be characterized by contradiction and inconclusion. A number of authors point to additional variables

Gender and DSS design 151 which could account for this conflict. None, however, explicitly identifies gender as a moderating variable. The discussion presented here highlights that gender may play a significant part in certain cognitive activities, though, as Huber and others have pointed out, task variables may overwhelm these. The intention here is to provide a background for those researchers contemplating empirical research into DSS use and thus alert them to additional factors. This chapter points not just to gender as a differentiator, but to issues such as the gender-bias of tasks and presentation format as influencing choice. Several of the more recent studies discussed above attach conditions to what appeared to be clear-cut differences in decision attitudes and actions of men and women noted in earlier research (see Appendix 9.1). It has been suggested that this may have been brought about as a result of a change in cultural norms (Eagly, 1978). It could be argued that many of the stereotypes which have been shown to exist were developed and continue to be reinforced because women did behave in these ways in the past. The roles of men and women in Western society have been traditionally quite different and this served to create and reinforce many of the observed differences in behaviour. The nature of these roles is changing. For example, Birley (1989, p. 37) notes ‘the exploding number of small businesses owned by women reflects both social and economic transformations. Women have crossed a wider range of economic barriers than at any time since World War II.’ Differences in male and female decision-making are likely to become more fluid as society goes through this period of transition. A substantial amount of the psychological literature has historically been focused, as indicated above, towards an assessment of gender-related differences in the quality of decisions. More recently attention has shifted towards differences between decision quality of individuals with differing psychological sex roles. It is argued that, independent of a person’s gender, an individual’s personality can be essentially masculine (including forceful, dominant, assertive characteristics) or feminine (including sensitive, tender and expressive characteristics). Psychologists have developed means of assessing an individual’s sex role (Bem, 1974). Research has shown that sex roles are an important variable influencing gender-role-related decisions (Voelz, 1985). Milton (1957) demonstrated that men who identified with the masculine role were better problem solvers than those who identified with the female role and that women who identified with the male role were better problem solvers than women who identified with the female role. Similarly, research conducted by Kelly et al. (1982, p. 112) indicates that ‘females’ masculinity scores were substantially associated with ratings of effectiveness in the decision making groups’. Reviewing the sex-role literature, Kelly et al. (1982) conclude that individuals whose psychological make-up includes both feminine and masculine socially valued characteristics should demonstrate greater flexibility, adaptability and adjustment in their decision-making than individuals with only a single psychological sex role or individuals who are deficient in both femininity and masculinity. Therefore whilst the focus of this chapter has been towards examining the input of gender differences on DSS decision and use, a fruitful area for future research

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might well be the implications of different sex-role characteristics on the development and application of DSS. The concept that decision aids which match the cognitive style of users perform better (Benbasat and Dexter, 1982) and are used more (Snitkin and King, 1986) is well known in the DSS literature. These authors also point to the differing impacts of DSS on individuals and of individuals on DSS. The literature reviewed above supports the contention that males and females differ in certain aspects of their decision-making behaviour. If males and females are shown to build different decision models due to their preference for different decision styles, then the effects of male or female DSS builders in terms of type and form of model must be considered. Although the results from the cognitive style and human information processing literature have achieved wide acceptance in DSS construction, an additional, largely ignored, variable might be that of gender. If this is the case then perhaps user-built models will become of paramount importance. DSS may be able to equalize decision quality across the genders although, conversely, they may exacerbate differences. The output from a DSS may be the anchor point from which a decision is taken. Insufficient adjustment for data exogenous to the model may be applied. This additional adjustment may be from an unnatural starting point for any individual decision taker since the anchor point may not align with the individual’s preferences. Fjelsted and Konsynishi (1986) point to the greatest problem for DSS being the mismatch between the user’s mental representation of the problem and the task representation within the system. Similarly, Goodhue (1986) identifies user attitudes as not only important, but as a measure of the success of DSS. Male and female decision differences may be significant in both cases. One of the few ways to mitigate some of the problems identified is by allowing users to construct their own DSS. Further gender-related DSS research here would be beneficial, as would investigations into the degree of self-insight user-builders exhibit. Specifically, a research agenda might address the impact of DSS-aided decision taking on decision quality, decision style risk propensity and confidence. The possible moderating variable of gender must be considered. This will, hopefully, allow the design and construction of DSS which are more useful to a wider range of users. This chapter has pointed to the need to investigate gender issues in topics such as: the degree of training DSS users have at difference managerial levels both in the system and the problem content; the extent to which DSS mitigate poor problem-solving abilities; the content framing bias, the role of mixed gender construction teams; the problem-solving motivation of DSS; the effects of differences in quantitative, verbal and spatial skills, presentation formats and the role of instructions; actions of single and mixed-sex groups; effects of anonymity and stereotype reduction; risk preferences and incorporation; confidence: alternative generation and consideration; and finally, persuasibility and influenceability. This agenda is not meant to be definitive, but by highlighting this specific research agenda it is hoped that this chapter will not become the justification for ad hoc empirical investigation of the interplay between any aspect of DSS and gender. This chapter provides a starting point and a way forward.

Concept of DSS

Effects of DSS on performance

Explore age and sex differences in probability preferences Exploration of patterns of women’s employment Literature review

Alavi, M. (1982)

Aldag, R. and Power, D. (1986)

Arenson, S.J. (1978)

Barki, H. and Hardwick, J. (1989) Barnett, J.H. and Karson, M.J. (1989)

Baker, T. (1975)

–

Survey

Laboratory

Laboratory

Interviews

–

Research strategy

Theoretical/literature – review Assess role Questionnaire of gender and organizational variables in managerial decisionmaking

Literature review

Aiken, L. (1987)

Ashburner, L. (1991)

Research purpose

Authors (year)

Appendix 9.1: Summary of literature

– Choice dilemma

–

–

Gambling

Structured interviews Strategic management case study

–

Task

Insurance executives

–

Building society employees –

Children

Senior executives Students

–

Subjects

Individual

–

Individual

Individual

Individual

Individual

Individual

–

Individual/group

continued

Little change in pattern of women’s employment observed Females more easily influenced and lower achievement motivation Motivation from involvement Females more interested in method, males in results

Limited support that decision aids increase confidence of satisfaction No risk propensity differences

Superior male mathematical problem solving

Relevant results

Influence of attitude to problem solving on performance

Assess managerial styles of entrepreneurs

Carey, G.L. (1958)

Chaganti, R. (1986)

Case study

Laboratory

Laboratory

Measurement of sex-role perceptions

–

Literature review –

–

Literature review

Literature review

–

Literature review

Benbasat, I. et al. (1991a) Berkowitz, L. (1962) Birley, S. (1989)

Block, J.H. (1976) Broverman, I.K. et al. (1972)

Sex-role adaptability Laboratory

Bem, S.L. (1974)

Research strategy

Research purpose

Authors (year)

Appendix 9.1 continued

Questionnaire and problem solving written tests –

Questionnaire

–

–

–

–

Questionnaire /activity task

Task

Entrepreneurs

Students

College students

–

Entrepreneurs

–

–

Students

Subjects

Individual

Individual

Individual

–

Individual

Individual/group

–

Individual /group

Individual/group

Male and female entrepreneurs have same risk attitudes

Males more self-confident Previous literature of questionable quality Masculine characteristics more highly valued in society. Males perceived as better problem solvers, more self-confident and greater risk takers. Women perceived as more subjective, passive and non-competitive Inferior female problem solving

No gender differences in conformity or activity times Equalizing effect from DSS on cognitive types Females less aggressive

Relevant results

Estes, R. and Hosseini, J. (1988)

Dos Santos, B. and Bariff, M. (1988) Eagly, A. (1978)

Crano, W.S. (1970)

Coombs, C.H. and Pruit, D.G. (1960) Crandall, V.C. (1969)

Chervany, N. and Dickson, G. (1978) Coet, L.J. and McDermott, P.J. (1979)

Effects on user performance of software aids Explore gender differences in influenceability Identify personal characteristics that influence confidence in decisions

Explore gender differences in expectancy Factors influencing conformity

Questionnaire

Assess effects of sex, type of instruction and group composition on risk taking Probability and variance preference

Laboratory

Literature review

Laboratory

Laboratory

Laboratory

Laboratory

–

Literature review

Investment decisions

–

Questionnaire and physical and mental tests Conformity in a counting experiment Financial simulation

Gambling

Choice dilemma

–

Shareholders/ security analysts, institutional investors, general business persons

–

Students

Students

Students and children

Students

Students

–

Individuals

Individuals

Individuals

Individuals

Individuals

Individuals

Individual/group

–

continued

Females place greater stress on interpersonal goals Females exhibit lower confidence in their investment decisions. Other personal characteristics had no effect on decision confidence

Males optimistic, females pessimistic in performance predictions Influenceability is contingent on composition of group Structured DSS model manipulation superior

Females unwilling to take risks

Summarized information improves decisions but lowers confidence Individual males and all-male groups more risk preferring

–

Laboratory – Real world –

Decision quality

Explore motivations of entrepreneurs Explore sex differences in risk taking Literature review

Literature review

Gender and GDSS

Halpern, D.F. (1992)

Herschel, R. et al. (199l)

Laboratory

–

Laboratory

Risk taking at a zoo

–

Literature review

Effects of DSS on decision making

Marketing case –

–

Theoretical/ literature review

‘Lost at Sea’

–

Marketing case study

–

–

–

–

Literature review

Task

Fatkin, L.T. and Hudgens, G.A. (1982) Fjelstad, O. and Konsynishi, B. (1986) Freedman, J.L. et al. (1970) Gallupe, R. et al. (1986) Gerritann, J.C.M. et al. (1987) Ginsburg, H. and Miller, S. (1982) Goodhue, D. (1986) Goslar, M. et al. (1986)

Research strategy

Research purpose

Authors (year)

Appendix 9.1 continued

Students

–

Marketing Executives

–

Children

Entrepreneurs

Students

–

–

–

Subjects

Group

–

Group

–

Individuals

Individuals

Group

–

–

–

Individual/group

Importance of user attitude. DSS restrict alternative option generation Female verbal abilities superior. Male quantitative and visual-spatial skills superior Female group problem solving inferior, GDSS provide anonymity and stereotype reduction

GDSS enhance decision quality not decision time Motivation similar in males and females Females more risk averse

Mismatch between user’s mental representation and DSS task representation Females conform more

Males generally more risk preferring

Relevant results

–

Literature review

Explore gender differences in risk taking

Literature review

Hudgens, G.A. and Fatkin, LT. (1985)

Hudgens, G.A. and Fatkin, L.T. (1980)

–

Laboratory

–

Hovland, C.L and Janis, I.L. (eds) (1959) Huber (1983)

Real world

Laboratory

Effect of gender, locus of control and illusion of control on gambling behaviour Literature review

Hong, Y. and Chiu, C. (1988)

Holding, C.S. and Holding, D.H. (1989)

Explore national differences in work-related values Exploring sex differences in spatial ability

Hofstede, G. (1980)

Real world

Explore male/female Case history relationships in work place Exploration of Laboratory gender differences in problem-solving performance

Hodgson, R.C. and Watson, E.D. (1987) Hoffman, L.R. and Maier, N.R.F. (1966)

Computer simulation of minefield crossing –

–

–

Estimating distance and angle of roads from slides Questionnaire/ gambling

–

Military personnel

–

–

General population

Undergraduate students

Managers

Students

Problem solving

Questionnaire

Managers

–

–

Individual

–

–

Individual

Individual

Individual

Individual

Individual

continued

Majority of studies indicate female risk aversion

Cognitive style of less relevance to DSS No gender differences except in risk preferences

Females more easily influenced

Males gamble to regain illusory control, females to confirm expectancy of external control

Inferior female problem solving caused by lack of motivation. Mixed-sex groups perform as well as all-male ones National differences in culture impact on workrelated decisions Male superiority in judging distance and estimating angles

Females more concerned with relationships

Real world

Explore gender differences in decision quality, risk propensity and confidence Risk preferences

Kelly, J.A. et al. (1980)

Laboratory

Laboratory

Laboratory

Explore decision-making behaviour Measurement of risk-taker’s personality Examining differential reactions of assertive

Keinan, G. et al. (1984)

–

Literature review

Kanter, R.M. (1977b) Kass, N. (1964)

–

Literature review

Kanter, R.M. (1977a)

Field/laboratory

–

Literature review

Johnson, J.E.V. and Powell, P. (1994)

–

Literature review

Hyde, J.S. et al. (1990) Hyde, J.S. and Linn, M.C. (1988) Johnson, J.E.V. and Bruce, A.C. (1993)

Research strategy

Research purpose

Authors (year)

Appendix 9.1 continued

View video/ questionnaire

Questionnaire

Gambling

–

–

Betting/ risky decision

Gambling

–

–

Task

Undergraduate students

General population

Children

–

–

General population/ managers

General population

–

–

Subjects

Individual

Individual

Individual

Individual

Individual

Individual

Individual

–

–

Individual/group

Female assertiveness in groups treated less favourably than male

Female more risk averse

Trained populations do not differ in risk propensity, untrained males are more risk propensive Common stereotype: women lack decisionmaking skills Females more concerned with relationships Female risk aversion

Gender differences in decision quality and risk propensity contingent on a variety of factors

Superior male quantitative abilities Superior female verbal abilities

Relevant results

Linn, M.C. and Peterson, A.G. (1986) Lohman, D.F. (1988)

Levin, I.P. et al. (1988)

Kohlberg, L. and Kramer, R. (1969) Lenney, E. (1977)

Kogan, N. and Dorros, K. (1978)

King, W.R. et al. (1990)

Kelly, J.A. et al. (1982)

– –

Literature review

– –

Literature review

Laboratory

Influence of framing-effect on risky choice Literature review

Laboratory

Laboratory

Laboratory

behaviour in males and females Behaviour differences in complex social interactions DSS and accuracy and quality of decision-making Sex differences in risk taking and the attribution of risk taking to peers Literature review

–

–

Gambling

–

–

Choice dilemma questionnaire

Case study

Decisionmaking

–

–

Students

–

–

Undergraduate student

Students

Undergraduate students

Individual

Individual

Individual

–

Individual perceived by peers as more risk averse Individual

Individual

Group

continued

Visual spatial abilities extensively used

Females conservative when unsure, extreme when very sure of their decisions Females less influenced by framing bias, more risk averse Male superiority in visual spatial skills

Males follow absolute rules

Females more risk averse and females

Females less active especially in male-content problems. Performance related to sex role Gender has no effect on accuracy

Literature review

Effect of instructions/ suggestions on problemsolving ability

Maccoby, E. and Jacklin, C. (1974)

Maier, N.R.F. (1933)

Influence of response availability on gender differences in problem solving Maier, N.R.F. Gender and and Hoffman, L.R. group (1961) problem solving Mann, R. et al. Theoretical (1989)

Sex-role and parenting identification

Lynn, D.B. (1962)

Maier, N.R.F. and Burke, R.J. (1967)

Research purpose

Authors (year)

Appendix 9.1 continued

Problemsolving written tests Horse-trading problem –

Laboratory Example

Practical ‘lateral thinking’ problems

–

–

Task

Laboratory

Laboratory

–

Theoretical

Research strategy

–

Students

Students

Students

–

–

Subjects

–

Group

Individual

Individual

Individual

–

Individual/group

Dialogue style needs to make user’s cognitive style

Inferior female problem solving due to negative attitudes to abstract problems Differences in verbal, quantitative and visual spatial skills. Males exhibit greater confidence. No difference in analytical ability Inferior female problem solving. Instructions/suggestions improve female problemsolving ability more than men Inferior female problem solving. Females benefit more from instructions. Problem content significant Inferior female problem solving

Relevant results

Risk taking in groups Gender and cerebral hemisphere importance Gender and maths achievement/ theoretical Literature review

Maurer, R.J. (1972) McGee, M. (1976)

Nicholson, N. and West, M. (1988)

Milton, G.A. (1959)

Milton, G.A. (1957)

Middlebrook, P.N. (1974)

Assess effects of sex-role on problemsolving skill Explore effect of problem content on sex differences in problem solving Managerial role changes

Risk propensity

Masters, R. and Meier, R. (1988)

Meece, J.L. et al. (1982)

Literature review

Marshall, J. (1984)

Survey

Laboratory

Laboratory

–

Theoretical

Laboratory

Laboratory

Questionnaire

–

Questionnaire

Written problemsolving tests

Written tests

–

–

Choice dilemma Mental rotation test

Choice dilemma

–

Managers

Students

Students

–

–

Students

Children

Entrepreneurs/ managers

–

Individuals

Individual

Individual

Individual

–

Individual/ group Individuals

Individual

–

continued

Males more confident

Content of problem important

Female socialization emphasizes passivity (amongst others) Inferior female problem solving. Sex-role importance

Superior male quantitative abilities

Females forced to confirm to male norms in organizations Male and female entrepreneurs have similar risk attitudes No risk propensity difference Male superiority in visualspatial skills

Explore effects of age, sex and group composition on risk taking Explore sex differences in performance on mathematics tests

Noe, F.P. and McDonald, C.D. (1983)

Rapoport, A. and Chammah, A.M. (1965)

Priest, R.F. and Hunsaker, P.L. (1969)

Identify factors improving female problem solving Exploring sex differences in co-operative behaviour

Literature review

Nieva, V.F. and Gutek, B. (1981)

Plake, B.S. et al. (1981)

Research purpose

Authors (year)

Appendix 9.1 continued

Laboratory

Laboratory

Field study

Questionnaire

–

Research strategy

Mathematical problem solving and mathematical concepts tests Problemsolving written tests

Rank risktaking behaviour

–

Task

Students

Students

Children

General population of river users

–

Subjects

Individual

Individual

Individual superior female problem solving

Groups/ Individual

–

Individual/group

Females less co-operative

Inferior female problem solving. Females benefit more from instructions

Superior male quantitative abilities

Commonly held stereotype views that women are less capable than men. No consistent behaviour differences related to gender found among leaders. Subordinates react differently to similar behaviour exhibited by male and female leaders No risk propensity difference between males and females

Relevant results

Literature review

Gender and accuracy To assess the characteristics, motivation and attitudes of female entrepreneurs Exploring sex differences in conforming behaviour Exploring age and sex differences in risk-taking behaviour Examining male/ female visual-spatial skills

Sargent, A. (1981)

Schiff, W.C. and Oldak, R. (1990) Schwartz, E. (1976)

Smith, G.A. and McPhee, K.A. (1987)

Slovic, P. (1966)

Sistruck, F. and McDavid, J. (1971)

Effects of gender on public policy

Exploring sex differences in risk preferences Literature review

Rubin, J.Z. and Brown, B.R. (1975) Saint-Germain, M.A. (1989)

Roberts, G.C. (1975)

Laboratory

Real world

Laboratory

Field study

Laboratory

–

Real world

–

Laboratory

Physicaltarget test

Fairground game

Choice dilemma

Judging time to arrival Interviews

–

Longitudinal analysis of legislation

–

Children

Children

Students

Entrepreneurs

Students

Members of the Arizona State Legislature –

–

Students

Individual

Individual

Individual

Individual

Individual

Individual

Individual

–

Inidividual

continued

Male superiority in visual-spatial skills

Females more risk averse

Influenceability depends on topic

Females more interested in method, males in results Male superiority in visualspatial skills Male and female entrepreneurs share the same personality traits

Female competitiveness results from the social attributes of the opposition Females more risk averse

Females more risk averse

Laboratory

Gender and maths competence

Controlled for aptitude and ability Literature review

Sweeney, E.J. (1953) Terborg, J. (1977)

Tuddenham, R.D. (1952)

Exploration of sex differences in perception of peers

Thomas, G.P. and Explore gender Garvin, A.D. (1973) differences in choice of varying difficulty cognitive tasks Todd, P. and Impact of decision Benbasat, I. (1991) aids on strategies

Real world

Structure of preferences

Starr, M.W. and Potashier, M.R. (1984) Stones, I. et al. (1982)

Interviews

Laboratory

Evaluate peers

Choice amongst varying difficulty objective items in an examination paper Housing choice

–

–

Field study

–

Maths competence test

Ranking of features and functions Gambling

Task

Laboratory

Survey

Effectiveness of DSS

Snitkin, S. and King, W. (1986)

Research strategy

Research purpose

Authors (year)

Appendix 9.1 continued

Children

Students

Undergraduate Students

–

–

Students

General population

DSS users

Subjects

Individual

Individual

Individual

Individual

–

Individual

Individual

Individual

Individual/group

Need to consider effort reduction as well as decision quality Risk taking amongst females is negatively valued

Superior female mathematical reasoning, superior male measurement, geometry problems and statistics Inferior female problem solving Commonly held stereotypes that females lack decision-making abilities Females more risk averse

DSS matched to users’ cognitive style enhance performance No risk propensity difference

Relevant results

–

Zmud, R. (1978)

Literature review

Laboratory

–

Laboratory

Questionnaire

Laboratory

Laboratory

–

Zigurs, I. et al. (1988)

Worchel, S. and Cooper, J. (1976)

Welsch, H. and Young, E. (1984) Wood, W. et al. (1985)

Gender and group task performance Literature review

Explore gender role disparity on couples’ decision-making Effect of punishment risk on conforming behaviour Entrepreneurial characteristics

Voelz, C.J. (1985)

Ward, D.A. et al. (1988)

Literature review

Varro, B. (1982)

–

–

Small business cases Problem solving

Computersimulated game

Decisionmaking

–

–

–

Students

Entrepreneurs

Students

Undergraduate students

–

–

Group

Individual

Individual and group

Individual

Individual

Individual/pairs

–

Degree of influenceability is contingent and does not change with increasing punishment risk Risk attitudes of male and female entrepreneurs similar Female groups superior at discussion and consensus, males at separate solutions Females more easily influenced; less achievement motivation, less competitive Increased non-verbal communication when using DSS

Females superior verbal skills. Males superior quantitative and visualspatial bskills Importance of sex-role

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References Aiken, L. (1987) ‘Sex differences in mathematical ability: a review of the literature’, Educational Research Quarterly, 10: 25–35. Alavi, M. (1982) ‘An assessment of the concept of decision support systems as viewed by senior executives’, MIS Quarterly, 6(4): 1–9. Aldag, R. and Power, D. (1986) ‘An empirical assessment of computer-assisted decision analysis’, Decision Sciences, 17(4): 572–88. Applegate, L., Ellis, C., Holsapple, C., Radermacher, F. and Whinston, A. (1991) ‘Organisational computing: definitions and issues’, Journal of Organizational Computing, 1(1): 1–10. Arenson, S.J. (1978) ‘Age and sex differences in the probability preferences of children’, Psychological Reports, 43: 697–8. Ashburner, L. (1991) ‘Men managers and women workers: women employees as an under-used resource’, British Journal of Management, 2: 3–15. Baker, T. (1975) ‘Sex differences in social behavior’, in: L. Berkowitz, A Survey of Social Psychology, Hinsdale, Ill.: Dryden Press. Barki, H. and Hardwick, J. (1989) ‘Rethinking the concept of user involvement’, MIS Quarterly, March: 53–64. Barnett, J.H. and Karson, M.J. (1989) ‘Managers, values, and executive decisions: an exploration of the role of gender, career stage, organizational level, function, and the importance of ethics, relationships and results in managerial decision-making’, Journal of Business Ethics, 8: 747–71. Bem, S.L. (1974) ‘The measurement of psychological androgyny’, Journal of Consulting and Clinical Psychology, 42: 155–62. Benbasat, I. and Dexter, A.S. (1982) ‘Individual differences in the use of decision support aids’, Journal of Accounting Research, 20(1): 1–11. Benbasat, I., DeSanctis, G. and Nault, B. (1991a) ‘Empirical research in managerial support systems: A review and assessment’, Lucca, Italy: NATO Advanced Study Institute. Benbasat, I., Lim, F. and Todd, P. (1991b) ‘The user-computer interface in systems design’, in Jenkins, A. (ed.), Research Issues in Information Systems Analysis and Design, Dubuque, IA: Wm. C. Brown. Berkowitz, L. (1962) ‘Aggression: A Social Psychological Analysis’, New York: McGraw-Hill. Berry, B. and McLintock, A. (1991) ‘Accountants and financial modelling’, OR Insight, 4(4): 11–14. Birley, S. (1989) ‘Female entrepreneurs: are they really any different?’, Journal of Small Business Management, January: 32–7. Block, J.H. (1976) ‘Issues, problems and pitfalls in assessing sex differences: a critical review of the psychology of sex differences’, Merrill-Palmer Quarterly, 22: 283–308. Broverman, I.K., Vogel, S., Broverman, D.M., Clarkson, F.E. and Rosenkrantz, P.S. (1972) ‘Sex-role stereotypes: a current appraisal’, Journal of Social Issues, 28: 59–78. Carey, G.L. (1958) ‘Sex differences in problem-solving performance as a function of attitude differences’, Journal of Abnormal and Social Psychology, 56: 256–60. Chaganti, R. (1986) ‘Management in women-owned enterprises’, Journal of Small Business Management, October: 18–29. Chervany, N. and Dickson, G. (1978) ‘On the validity of the analytic-heuristic instrument utilized in the Minnesota experiments–a reply’, Management Science, 24: 1091–2.

Gender and DSS design 167 Coet, L.J. and McDermott, P.J. (1979) ‘Sex, instructional set, and group make up: organismic and situational factors influencing risk-taking’, Psychological Reports, 44: 1283–94. Coombs, C.H. and Pruit, D.G. (1960) ‘Components of risk in decision making: probability and variance preferences’, Journal of Experimental Psychology, 60: 265–77. Crandall, V.C. (1969) ‘Sex differences in expectancy of intellectual and academic reinforcement’, in Smith, C.P. (ed.), Achievement Related Motives in Children, New York: Russell Sage Foundation. Crano, W.S. (1970) ‘Effects of sex, response order, and expertise in conformity: a dispositional approach’, Sociometry, 33: 239–52. Davis, G.B. (1982) ‘Caution: user-developed decision support systems can be dangerous to your organisation’, Working Paper, University of Minnesota, Management Information Systems Research Centre. Dennis, A.R. (1990) ‘Effects of varying the level of electronic meeting support on the decision making performance of different sized groups’, IEEE Transactions on Systems, Man and Cybernetics, 20: 1110–28. Dhaliwal, J.S. and Benbasat, I. (1990) ‘A framework for the comparative evaluation of knowledge acquisition tools and techniques’, Knowledge Acquisition, 2(2): 145–66. Dos Santos, B. and Bariff, M. (1988) ‘A study of user interface aids for model-oriented DSS’, Management Science, 34(4): 461–8. Eagly, A. (1978) ‘Sex differences in influenceability’, Psychological Bulletin, 85: 86–116. Estes, R. and Hosseini, J. (1988) ‘The gender gap on Wall Street: an empirical analysis of confidence in investment decision making’, The Journal of Psychology, 122(6): 577–90. Fatkin, L.T. and Hudgens, G.A. (1982) ‘Human performance: more psychological and physiological sex differences (a selected bibliography)’, U.S. Army Human Engineering Laboratory, Aberdeen Proving Ground, MD. Fjelstad, O. and Konsynishi, B. (1986) ‘The role of cognitive apportionment in information systems’, San Diego: Proceedings of the 7th International Conference of Information Systems, pp. 81–3. Freedman, J.L., Carlsmith, J.M. and Sears, D.O. (1970) Social Psychology, Englewood Cliffs, NJ: Prentice-Hall. Gallupe, R., DeSanctis, G. and Dickson, G. (1986) ‘The impact of computer-based support on the process and outcomes of group decision making’, San Diego: Proceedings of the 7th International Conference of Information Systems, pp. 81–3. Gerritann, J.C.M., Beyes, C. and El Nannaki, M.S. (1987) ‘Female entrepreneurship revisited: the trait approach disputed’, R.V.B. Research Paper, March. Ginsburg, H. and Miller, S. (1982) ‘Sex differences in children’s risk taking locations at the zoo’, Child Development, 53: 426–8. Goodhue, D. (1986) ‘Attitudes: towards theoretical and definition clarity’, San Diego: Proceedings of the 7th International Conference on Information Systems, pp. 181–94. Goslar, M., Green, G. and Hughes, T. (1986) ‘Decision support systems: an empirical assessment of decision taking’, Decision Sciences, 17: 79–91. Halpern, D.F. (1992) Sex Differences in Cognitive Abilities, 2nd edn, Hillsdale, NJ: Lawrence Erlbaum Associates. Herschel, R., Wynne, B. and Noel, T. (1991) ‘The impact of group gender composition on group performance in an electronic meeting setting: a study of group gender composition’, Lucca, Italy: NATO Advanced Study Institute.

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Hiltz, S.R., Turoff, M. and Johnson, M. (1989) ‘Experiments in group decision making, 3: disinhibition, deindividuation, and group process in pen name and real name computer conferences’, Decision Support Systems, 5(2): 217–32. Hodgson, R.C. and Watson, E.D. (1987) ‘Gender-integrated management teams’, Business Quarterly, 52: 68–72. Hoffman, L.R. and Maier, N.R.F. (1966) ‘Social factors influencing problem solving in women’, Journal of Personality and Social Psychology, 4: 382–90. Hofstede G. (1980) Culture’s Consequences – International Differences in Work-Related Values, Beverley Hills, Calif.: Sage Publications. Holding, C.S. and Holding, D.H. (1989) ‘Acquisition of route network knowledge by males and females’, Journal of General Psychology, 116: 29–41. Hong, Y. and Chiu, C. (1988) ‘Sex, locus of control, and illusion of control in Hong Kong as correlates of gambling involvement’, The Journal of Social Psychology, 128(5): 667–73. Hovland, C.L. and Janis, I.L. (eds) (1959) Personality and Persuasibility, New Haven, Conn: Yale University Press. Huber, G. (1983) ‘Cognitive style as a basis of MIS and DSS design: much ado about nothing?’ Management Science, 29(5): 567–79. Hudgens, G.A. and Fatkin, L.T. (1980) ‘Human performance: psychological and physiological sex differences (a selected bibliography)’, U.S. Army Human Engineering Laboratory, Aberdeen Proving Ground, MD. Hudgens, G.A. and Fatkin, L.T. (1985) ‘Sex differences in risk taking: repeated sessions on a computer-simulated task’, The Journal of Psychology, 119(3): 197–206. Hyde, J.S. and Linn, M.C. (1988) ‘Gender differences in verbal ability: a meta-analysis’, Psychological Bulletin, 104: 53–69. Hyde, J.S., Fennema, E. and Lamon, S.J. (1990) ‘Gender differences in mathematics performance: a meta-analysis’, Psychological Bulletin, 107: 139–55. Johnson, J.E.V. and Bruce, A. (1993) ‘Gender and gambling: new perspectives’, Journal of Gambling Studies, 9: 183–98. Johnson, J.E.V. and Powell, P. (1994) ‘Decision-making, risk and gender: are managers different?’ British Journal of Management, 5: 123–38. Kanter, R.M. (1977a) ‘Men and women of the corporation revisited’, Management Review, 76: 14–16. Kanter, R.M. (1977b) Men and Women of the Corporation, New York: Basic Books. Kass, N. (1964) ‘Risk in decision making as a function of age, sex, and probability preferences’, Child Development, 35: 577–82. Keen, P. and Scott Morton, M. (1978) Decision Support Systems an Organisational Perspective, Reading, Mass: Addison-Wesley. Keinan, G., Meir, E. and Gome-Nemirovsky, T. (1984) ‘Measurement of risk takers’ personality’, Psychological Reports, 55: 163–7. Kelly, J.A., Kern, J.M., Kirkley, B.G., Patterson, J.N. and Keane, T.M. (1980) ‘Reactions to assertive versus unassertive behaviour: differential effects for males and females, and implications for assertiveness training’, Behaviour Therapy, 11: 670–82. Kelly, J.A., Wildman, H.E. and Uney, J.R. (1982) ‘Gender and sex-role differences in group decision making social interactions: a behavioural analysis’, Journal of Applied Social Psychology, 12(2): 112–27. King, W.R., Premkumar, G. and Ramamurthy, K. (1990) An evaluation of the role and performance of a decision support system in business education, Decision Sciences, 21(3): 642–59.

Gender and DSS design 169 Kogan, N. and Dorros, K. (1978) ‘Sex differences in risk taking and its attribution’, Sex Roles, 4: 755–65. Kohlberg, L. and Kramer, R. (1969) ‘Continuities and discontinuities in childhood and adult moral development’, Human Development, 12: 93–120. Lenney, E. (1977) ‘Women’s self-confidence in achievement settings’, Psychological Bulletin, 84: 1–13. Levin, I.P., Snyder, M.A. and Chapman, D.P. (1988) ‘The interaction of experiential and situational factors and gender in a simulated risky decision-making task’, The Journal of Psychology, 122(2): 173–81. Linn, M.C. and Peterson, A.G. (1986) ‘A meta-analysis of gender differences in spatial ability: implications for mathematics and science achievement’, in Hyde, J.S. and Linn, M.C. (eds), The Psychology of Gender: Advances Through Meta-analysis, Baltimore: The John Hopkins University Press. Lohman, D.F. (1988) ‘Spatial abilities as traits, processes, and knowledge’, in Steinberg, R.J. (ed.), Advances in the Psychology of Human Intelligence (Vol. 4), Hillsdale, N.J: Lawrence Erlbaum Associates. Lynn, D.B. (1962) ‘Sex-role and parental identification’, Child Development, 33: 555–64. Maccoby, E. and Jacklin, C. (1974) The Psychology of Sex Differences, Stanford, Calif.: Stanford University Press. Maier, N.R.F. (1933) ‘An aspect of human reasoning’, British Journal of Psychology, 24: 144–55. Maier, N.R.F. and Burke, R.J. (1967) ‘Response availability as a factor in the problemsolving performance of males and females’, Journal of Personality and Social Psychology, 5: 304–10. Maier, N.R.F. and Hoffman, L.R. (1961) ‘Sex differences, sex composition, and group problem solving’, Journal of Abnormal and Social Psychology, 63: 453–6. Mann, R., Watson, H., Cheney, P. and Gallagher, C. (1989) ‘Accommodating cognitive style through DSS hardware and software’, in Sprague, R. and Watson, H. (eds), Decision Support Systems: Putting Theory into Practice, Englewood Cliffs, NJ: Prentice Hall, pp. 118–30. Marshall, J. (1984) Women Managers: Travellers in a Male World, Chichester: John Wiley and Sons. Masters, R. and Meier, R. (1988) ‘Sex differences and risk taking propensity of entrepreneurs’, Journal of Small Business Management, January: 31–5. Maurer, R.J. (1972) ‘Risk taking and risky shift in children’, University of Houston: unpublished doctoral dissertation. McGee, M. (1976) ‘Laterality, hand preference, and human spatial ability’, Perceptual and Motor Skills, 42: 781–2. Meece, J.L., Eccles-Parsons, J., Kaczala, C.M., Goff, S.B. and Futterman, R. (1982) ‘Sex differences in math achievement: toward a model of academic choice’, Psychological Bulletin, 91: 324–48. Middlebrook, P.N. (1974) Social Psychology and Modern Life, New York: Knopf. Milton, G.A. (1957) ‘The effects of sex-role identification upon problem-solving skill’, Journal of Abnormal and Social Psychology, 55: 208–12. Milton, G.A. (1959) ‘Sex differences in problem solving as a function of role appropriateness of the problem content’, Psychological Reports, 5: 705–8. Mittman, B.S. and Moore, J.H. (1984) ‘Senior management computer use: implications for DSS designs and goals’, in: Sprague, R. and Watson, H. (eds), Decision Support Systems, Englewood Cliffs, NJ: Prentice Hall, pp. 93–103.

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Nicholson, N. and West, M. (1988) Managerial Job Changes: Men and Women in Transition, Cambridge: Cambridge University Press. Nieva, V.F. and Gutek, B. (1981) Women and Work: A Psychological Perspective, New York: Praeger. Noe, F.P. and McDonald, C.D. (1983) ‘Comparison of perceived risk taking in groups and implications drawn from the risky shift paradigm’, Perceptual and Motor Skills, 56: 199–206. Plake, B.S., Loyd, B.H. and Hoover, H.D. (1981) ‘Sex differences in mathematics components of the Iowa Test of Basic Skills’, Psychology of Women Quarterly, 5: 780–4. Powell, P.L., Connell, N.A.D. and Holt, J. (1992), The practical use of decision support and expert systems, in O’Leary, D. and Watkins, P. (eds), Expert Systems in Finance, Amsterdam: North-Holland, pp. 127–62. Priest, R.F. and Hunsaker, P.L. (1969) ‘Compensating for a female disadvantage in problem solving’, Journal of Experimental Research in Personality, 4: 57–64. Rapoport, A. and Chammah, A.M. (1965) ‘Sex differences in factors contributing to the level of cooperation in the Prisoner’s Dilemma game’, Journal of Personality and Social Psychology, 2: 831–8. Roberts, G.C. (1975) ‘Sex and achievement motivation effects on risk taking’, Research Quarterly, 46: 58–70. Rubin, J.Z. and Brown, B.R. (1975) The Social Psychology of Bargaining and Negotiation, New York: Academic Press. Saint-Germain, M.A. (1989) ‘Does their difference make a difference? The impact of women on public policy in the Arizona legislature’, Social Science Quarterly, 70(4): 956–68. Sargent, A. (1981) The Androgynous Manager, New York: AMACOM. Schiff, W.C. and Oldak, R. (1990) ‘Accuracy of judging time to arrival: effects of modality, trajectory and gender’, Journal of Experimental Psychology, Human Perception and Performance, 16: 303–16. Schwartz, E. (1976) ‘Entrepreneurship: a new female frontier’, Journal of Contemporary Business, Winter: 47–76. Sistruck, F. and McDavid, J. (1971) ‘Sex variables in conforming behavior’, Journal of Personality and Social Psychology, 17: 200–7. Slovic, P. (1966) ‘Risk taking in children’, Child Development, 37: 169–76. Smith, G.A. and McPhee, K.A. (1987) ‘Performance on a coincidence timing task correlates with intelligence’, Intelligence, 11: 161–7. Snitkin, S. and King, W. (1986) ‘Determinants of the effectiveness of personal decision support systems’, Information and Management, 10: 83–9. Starr, M.W. and Potashier, M.R. (1984) ‘The structure and preferences for gambling activities’, in Eadington, W. (ed.) Proceedings of the Sixth National Conference on Gambling and Risk Taking, Reno, NV: University of Nevada. Stones, I., Beckmann, M. and Stephens, L. (1982) ‘Sex-related differences in mathematical competencies of pre-calculus college students’, School Science and Mathematics, 82: 295–9. Sweeney, E.J. (1953) ‘Sex differences in problem solving’, Stanford University Department of Psychology Technical Report No. 1. Terborg, J. (1977) ‘Women in management: a research review’, Journal of Applied Psychology, 66: 647–64. Thomas, G.P. and Garvin, A.D. (1973) ‘Sex differences in risk taking on essay tests’, Journal of the Student Personnel Association for Teacher Education, 12: 32–6.

Gender and DSS design 171 Todd, P. and Benbasat, I. (1991) ‘Experimental investigation of the impact of computerbased decision aids on decision making strategies’, Information Systems Research, 1. Tuddenham, R.D. (1952), ‘Studies in reputation: I Sex and grade differences in school children’s evaluation of their peers: II The diagnosis of social adjustment’, Psychological Monographs, 66. Varro, B. (1982) ‘Men and women differences’, Chicago Sun Times, April 11. Voelz, C.J. (1985) ‘Effects of gender role disparity on couples’ decision-making processes’, Journal of Personality and Social Psychology, 49(6): 1532–40. Ward, D.A., Seccombe, K. and Bendel, R. (1988) ‘Influenceability of sex differences under conditions of risk taking’, The Journal of General Psychology, 115(3): 247–55. Webster’s New Collegiate Dictionary (1980) Springfield, Mass.: Merriam. Welsch, H. and Young, E. (1984) ‘Male and female entrepreneurial characteristics and behaviours: a profile of similarities and differences’, International Small Business Journal, Summer, 11–20. Wood, W., Polek, D. and Aiken, C. (1985) ‘Sex differences in group task performance’, Journal of Personality and Social Psychology, 48(1): 63–71. Worchel, S. and Cooper, J. (1976), Understanding Social Psychology, Homewood, Ill.: Dorsey. Zigurs, I., Poole, M. and DeSanctis, G. (1988) ‘A study of the influence in computermediated group decision making, MIS Quarterly, 12(4): 625–44. Zmud, R. (1978) ‘Individual differences and MIS success: a review of the empirical literature’, Management Science, 25(10): 966–79.

10 Male and female betting behaviour – new perspectives A.C. Bruce and J.E.V. Johnson

Introduction There exists a considerable literature relating to differences between the nature of male and female decision-making under uncertainty. Popular issues in the decision-making literature have included gender differences in performance, risk taking and degrees of confidence in decisions made under uncertainty. Betting involves decision-making under uncertainty and the aim of this chapter is to specifically compare the betting behaviour of men and women engaged in gambling on the outcomes of horse races in UK off-course betting offices. The following brief review of the literature on gender differences in decision-making forms the basis for the hypotheses addressed which relate specifically to comparative betting behaviour of males and females. Earlier work in the area generally supported the superior performance of men (e.g. Priest and Hunsaker, 1969). Recent studies, however (Hudgens and Fatkin, 1985; Estes and Hosseini, 1988), indicate no significant differences between male and female decision-makers. The decline of observed gender differences in decision quality (Masters and Meier, 1988) may partly reflect some adjustment in cultural norms resulting from the increased participation and status of women in political, commercial and industrial contexts and their consequent increased exposure to complex decision processes. Equally it may stem from methodological limitations of earlier work. For example Eagly (1978) observes: ‘studies examining sex differences have varied widely in the sensitivity of research designs, quality of sampling procedures, and reliability and validity of measuring instruments’. There is evidence to suggest that observed differences in decision performance may be attributable less to fundamental differences between the sexes than to other factors. These include the sex of the experimenter, the amount of time and information available to the decision-maker, the presence of distracting stimuli (Priest and Hunsacker, 1969) and whether the decision was essentially male- or female-orientated (e.g. Herschel et al., 1991). In addition, research has suggested that problem-solving ability is more closely associated with sex-role rather than gender (Kelly et al., 1982), an individual’s personality being essentially ‘masculine’ (i.e. forceful, dominant) or ‘feminine’ (e.g. sensitive, tender).

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In relation to the differential tendencies to take risk a general conclusion from the literature is that men have a higher propensity for risk taking (see, for example, Keinan et al., 1984; Hudgens and Fatkin, 1985; and Levin et al., 1988) than women. However, a few studies have indicated the absence of significant gender differences in risk taking (e.g. Arenson, 1978). Coet and McDermott (1979) suggest these results may relate to their propensity to test for differences between the behaviours of male and female children. The significance of this lies in the cultural stereotyping to which adults have necessarily been exposed, which assigns positive value to risk taking by males and negative value to risk taking by females (see Slovic, 1966). As such, the absence of observable differences among young subjects is unsurprising. Finally in relation to differential levels of confidence in making decisions there is strong evidence that women are less confident than men (e.g. Berry, 1980; Nicholson and West, 1988; Estes and Hosseini, 1988). A common explanation for observed confidence differences is that women’s behaviour is affected by their insecurity within male-dominated decision-making organisations (see, for example, Nicholson and West, 1988). This factor would not, of course, explain lower confidence levels outside the organisational context, though societal stereotypes of the male as decision-maker would remain influential. Much of the literature referred to above has explored gender differences in decision-making in a general context. This study, however, specifically investigates male and female betting decisions. Betting decisions share important common features with other decisions made in an uncertain environment including assessment of risk, analysis of qualitative and quantitative information from a variety of sources and prediction of future events. As such the general literature discussed above is valuable in the formulation of hypotheses in relation to gender differences in gambling behaviour. A number of studies have demonstrated that superior returns can be earned by horse-race bettors following particular betting strategies (e.g. Asch et al., 1984; Bolton and Chapman, 1986). In addition Ceci and Liker (1986) have shown that ‘expert handicapping was a cognitively sophisticated enterprise, with experts using a mental model that contained multiple interaction effects and nonlinearity’. These findings together suggest that off-course betting can involve a considerable element of skill. This skill is reflected in the methods used to assess each of the runners’ previous form, to analyse and sift journalist opinion, to interpret moves in the betting market, to choose an appropriate price at which to back a horse, etc. As indicated above the degree of skill exercised will be reflected in the betting strategy chosen and consequently in the degree of success achieved by a bettor. In view of the literature discussed above, the current study is designed to test the following hypotheses: 1 2 3

There is no difference between the performance of male and female bettors. Male bettors engage in more risk propensive behaviour than female bettors. Females demonstrate less confidence in their betting decisions than males.

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In testing these hypotheses the current study enjoys a number of methodological advantages over earlier work into male/female decision-making. Most importantly, these relate to its analysis of real decisions made in a natural setting and in the absence of observation effects. These methodological features are discussed further below.

Method Sample design A random sample of 50 betting offices throughout the UK, owned by Ladbroke Racing, the UK’s largest off-course bookmaking organisation, was selected. Staff in these offices were asked to mark all bets placed by females during a one-week period in 1991, without the knowledge of the bettor concerned. Each betting slip (see below) is uniquely identified by a code number and a random sampling procedure was devised to select a roughly similar size sample of male (N = 2,009) and female (N = 2,015) bets. The sampling system ensured that bets analysed were spread throughout each betting day of the seven-day period; this together with the wide geographical spread of the betting offices surveyed significantly reduces the possibility of any two bets selected having been placed by the same bettor. Dependent measure The basic dependent measures used in this study are obtained from the betting slips, which are submitted by bettors at the time of bet placement in a UK offcourse betting office. Betting slips provide detailed characteristics of each bet placed including the selection made, the stake wagered, the type of bet (single, accumulator, etc.) and the time the bet was placed. These are used to provide dependent measures of performance, risk taking and confidence. Procedure In testing hypothesis 1, that ‘there is no difference between the performance of male and female bettors’, a variety of measures of performance are used. Success is measured by the percentage of bets and stakes placed which yield either some return or a profit. Here a ‘return’ constitutes the amount collected following a ‘successful’ bet irrespective of whether this sum exceeds the stake wagered. Where the amount collected does exceed the original stake this is defined as a profitable bet. Success is also measured by the ratio of returns to stake. Profitable bets using this measure yield a value greater than one. In testing hypothesis 2, ‘male bettors engage in more risk propensive behaviour’, the comparative popularity of different bet types is examined. Bet types are categorised into high or low risk according to the likelihood, other factors remaining constant, of their producing a return or a profit.

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Single bets (‘singles’) generally involve the lowest risk, since a return depends on only one successful selection, whereas ‘accumulators’ require two or more successful selections and ‘forecasts’ require that the first and second horse in a particular race be correctly identified. ‘Any-to-come’ bets are ‘accumulators’ with built-in safeguards, whereby only part of the prior winnings is wagered on subsequent ‘legs’ of the bet. ‘Multiples’ involve a number of selections combined in ‘accumulators’ of varying complexity and/or where selections feature individually as ‘singles’; these bets often provide consolation dividends if only one selection is successful. Both ‘multiples’ and ‘any-to-come’ bets might be regarded as medium risk bets with a greater chance of obtaining at least some return, other things being equal, than either ‘accumulators’ or ‘forecasts’ but with less chance of producing a profit than ‘singles’. Tote bets may represent any of the above bet types settled at odds determined by the parimutuel pool operating at the racetrack. This bet type can represent varying degrees of risk. The bet types discussed above were also explored in greater detail to examine further the comparative risk propensity of males and females. The two most popular forms of ‘forecast’ bet involve the selection of the first and second horse to finish in a particular race, either in the correct order (‘straight forecast’) or in either order (‘reverse forecast’). The first bet type, other things being equal, involves more risk, in terms of the chances of losing the stake wagered. A tendency to select ‘straight forecasts’ (cf. ‘reverse forecasts’) is, therefore, taken as an indication of more risk propensive behaviour. Examination of alternative varieties of ‘accumulator’ bets is also used to explore gender-based risk preferences. ‘Doubles’ and ‘trebles +’ accumulator bets require the selection of the winners of two races or more than two races, respectively. Hence preference for ‘trebles +’ over ‘doubles’ is taken as an indication of greater risk preference. A further dimension of risk relates to the distinction between ‘win’ and ‘each-way’ wagers. Betting to win requires that the selection comes first in the chosen event in order to generate a return, whilst an each-way bet generates a return if the selection is placed first, second or third. It seems reasonable, therefore, to suggest that a win bet represents a riskier wager in terms of the prospect of producing some return. As such a tendency to win as opposed to each-way betting reflects a greater risk propensity. Hypothesis 3, ‘females demonstrate less confidence in their betting decisions than males’, is tested by comparing the staking levels of males and females. These are taken as an indicator of decision confidence in that they imply the degree of commitment that the subject is prepared to make to his/her decision.

Results Performance The first set of results indicated in Table 10.1 examines the comparative performance of male and female bettors, variously measured.

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Table 10.1 Comparison of male and female bet performance

Bets Stakes Return/stake

Performance criteria

Male (N = 2,009)

Female (N = 2,015)

with a returna (%) with a profitb (%) with a returnc (%) with a profitd (%) [SD]

11.7 ** 5.5 14.4 ** 9.3 0.453 [4.70]

14.6 6.1 19.7 9.2 0.427 [5.10]

Notes a number of bets (irrespective of stake size) producing a positive return (which may be less than the amount staked) divided by the total number of bets placed. b number of bets (irrespective of stake size) producing a return greater than the amount staked, divided by the total number of bets placed. c the total amount staked which produced a positive return, divided by the total amount staked d the total amount staked which produced a return greater than the amount staked, divided by the total amount staked. ** p < 0.01, two-tailed (large sample test for difference between proportions, independent t-test for return/stake statistic).

Taken together, these results offer some support for hypothesis 1 in that there is no strong or consistent case for performance differentials between males and females. The percentage of bets and stakes wagered producing a profit are very similar for males and females and there is no significant gender difference in the ratio of returns to stakes. However, the number of bets and stakes wagered yielding a return suggest that the aggregate performance of women in terms of generating some return (though not a profit) is significantly superior. Despite this apparent female superiority the return/stake ratio is higher for males (0.453) than females (0.427), though not significantly so. These results taken together suggest that men are placing bets which produce returns less often than women but which, on average, produce greater returns when they do win. This is supportive of hypothesis 2 since it suggests that men place riskier bets than females. Risk propensity Tables 10.2 and 10.3 examine the comparative risk propensity of males and females by exploring the popularity of different bet types. Table 10.2 indicates that males bet more on ‘singles’, but there is little difference between the propensity for males and females to use ‘forecasts’, ‘accumulators’ or ‘tote’ bets. Females, however, appear more likely to use ‘any-to-come’ bets and ‘multiples’. Table 10.3 offers clear evidence that males are more likely than females to choose ‘doubles’ rather than more complex ‘accumulators’, bet significantly more on ‘straight forecasts’ rather than on ‘reverse forecasts’ and are significantly more likely than females to place their bets to ‘win’ rather than ‘eachway’. Taken together, therefore, these results do not appear to offer clear support for hypothesis 2.

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Table 10.2 Comparison of bet type preferences of males and females Bet type ‘Single’ ‘Forecast’ ‘Accumulator’ ‘Any-to-come’ ‘Multiple’ ‘Tote’

Male N = 2,009 Bets (%)a Stakes (%)b Bets (%) Stakes (%) Bets (%) Stakes (%) Bets (%) Stakes (%) Bets (%) Stakes (%) Bets (%) Stakes (%)

42.8 63.8 8.4 5.8 12.6 7.6 5.5 2.8 25.8 18.1 4.9 1.9

Female N = 2,015 ++ **

33.7 47.8 6.9 4.8 12.4 8.3 9.9 5.7 33.0 31.5 4.2 1.8

++ ** ++ **

Notes a Represents the number of bets (irrespective of stake size) placed on singles divided by the total number of bets placed on all bet types. b Represents the total amount staked on singles divided by the total stakes placed on all bet types. Bets: (i) Testing for equality of multinomial proportions (male v females): X2 = 67.69, df = 5, p < 0.01 (ii) + + sources of significant difference between male and female proportions where standardised residuals exceed ± 2. Stakes: ** Proportions of male and female stakes significantly different (p < 0.01) using a special case of ratio estimation.

Table 10.3 Comparison of male and female propensity to select ‘straight’ or ‘reverse forecasts’, ‘doubles’ or ‘trebles +’, and ‘win’ or ‘each-way’ Bet type ‘Doubles’ (v ‘trebles +’) ‘Straight forecasts’ (v ‘Reverse forecasts’) ‘Win’ (v ‘each-way’)

Male Bets (%)a Stakes (%) Bets (%) Stakes (%)b Bets (%) Stakes (%)

64.0 73.1 58.6 80.3 60.2 68.2

Female ** ** ** ** ** **

53.4 46.0 21.4 56.5 53.8 61.8

Notes a Represents the number of bets (irrespective of stake size) placed on ‘doubles’ divided by the total number of bets placed on ‘doubles’and ‘trebles +’ combined. b Represents the total amount staked on ‘straight forecasts’ divided by the total stakes placed on ‘straight forecasts’ and ‘reverse forecasts’ combined. ** p < 0.01, two-tailed (large sample test for difference between proportions).

Confidence The third set of results, displayed in Table 10.4, indicates that males bet with significantly higher average stakes than women. In addition, whereas only 10 per cent of female bets involve staking levels of more than £4.40, 21.4 per cent

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Table 10.4 Comparison of male and female staking levels (£) Male Mean SD Kurtosis 25 percentile Median 75 percentile 90 percentile

4.06 9.00 146.60 1.00 1.65 3.85 10.00

Female **

2.27 4.91 303.80 0.61 1.10 2.20 4.40

Note ** p < 0.01, two-tailed (independent t-test).

of male bets exceed this stake level. These results offer some support for hypothesis 3. Additionally the statistics relating to standard deviation and kurtosis suggest a greater homogeneity in staking behaviour within the female population.

Discussion In interpreting the comparative results relating to male and female betting, it is important to acknowledge that the procedures used cannot claim to isolate all potentially explanatory variables. For example, the anonymity of the betters, an important advantage of the method employed, denies an insight into the motivational basis for individuals’ betting. Equally, potentially significant social organisational factors, such as the propensity for women to visit betting shops with male partners, cannot be isolated. As such the procedures and reported results should be seen primarily as offering an empirical insight into actual behaviour. The interpretation of the results which follows is intended to identify lines of enquiry which may contribute to an understanding of the observed patterns. Performance It is clear from Table 10.1 that in terms of the profitability of bets placed there is no evidence of gender-based differences in performance. These results are in marked contrast to investigations prior to the early 1980s, which generally supported superior decision performance of men over women. However, the conclusions of later studies (e.g. Hudgens and Fatkin, 1985; Estes and Hosseini, 1988) are confirmed by the results reported here. This may support the notion, discussed earlier, regarding the increasing role of women as decision-makers in organisational and social contexts. The findings that women are more likely to place bets which produce some return (not necessarily a profit) and that a greater proportion of their stakes generate a return may arise from females’ preference for low-risk bets. Earlier

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research has indicated that women prefer gambles with a high probability of some, even low, return and men prefer gambles with a lower probability of some higher return (e.g. Kass, 1964). The underlying reasons for this may relate to different motivational bases for betting. If, for example, female bettors are more motivated by intellectual challenge (Bruce and Johnson, 1992), some rather than no return may offer partial vindication of a betting decision. Equally, if male bettors focus on potential financial return, their satisfaction from betting may demand a return in excess of stake placed. Risk The results relating to the degree to which male and female bettors accept risk require careful interpretation. Whilst the consensus from earlier studies is for a greater propensity on the part of males to accept higher risk, the results in Tables 10.2 and 10.3 apparently fail to offer consistent support for this. The results relating to male preference for ‘straight forecasts’ over apparently ‘safer’ ‘reverse forecasts’ and for ‘win’ bets over apparently ‘safer’ ‘each-way’ bets is supportive of previous research. However, comparing the percentage of male and female bets and stakes on ‘doubles’ and ‘trebles +’ suggests a more riskpreferring profile for the female population. This is confirmed by the tendency for males to place more bets and to commit greater stakes on the low-risk bet type ‘singles’, whereas females commit greater stakes and place more bets on the medium-risk bet types ‘multiples’ and ‘any-to-come’. The above results are open to a number of interpretations. Previous research has found that women are more easily persuaded or influenced, irrespective of the risk involved (see, for instance, Baker, 1975; Worchel and Cooper, 1976). The results reported here may be seen as corroborating these observations in that females may be more readily induced than males by the considerable advertising in off-course betting offices for bet types which provide bookmakers with their highest profit margins (i.e. complex, multi-leg accumulators, ‘forecasts’ and ‘multiples’). Despite their apparent risk-averse nature, females may have been persuaded by advertising to use these higher-risk bet types. The extent to which females bet significantly less on the low-risk bet type ‘singles’ may simply be the corollary of their having been persuaded to bet proportionately more on the higher risk ‘multiples’ and ‘any-to-come’ bets. A second interpretation of these results may stem from gender-based differences in definitions of low- and high-risk bets. Females’ propensity to place more ‘each-way’ (v. ‘win’) and more ‘reverse forecasts’ (v. ‘straight forecasts’) than males may arise because these bet types are perceived as more likely to produce some return. This interpretation supports the earlier work of Kass (1964) and Lindgren et al. (1987). Further corroboration may relate to females’ preference for ‘multiples’ and ‘any-to-come’ bets, with their built-in consolation dividends and safeguards protecting prior winnings. For a given stake these bets are, other things being equal, more likely to produce some return (though not a profit) than the previously defined low-risk single bets.

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Low risk may be defined by males as ‘most likely to produce a profit’, but females may regard bets as low risk if they offer a ‘high probability of receiving some return’. A third interpretation of these results might be derived from the degree to which males and females differentially understand the true nature of the more complex ‘multi-leg accumulator’ and ‘multiple’ bets. A number of illusions may be created by these bets which may be differentially influential in modifying male and female betting behaviour. One multiple bet, for example, is termed a ‘Lucky 15’. This requires the bettor to select four horses in separate races and involves 15 separate single and accumulator bets. Bettors of a particular gender may be more influenced by the term ‘Lucky 15’ into believing that the bet is likely to produce a return. Problem-framing heuristics of this nature have been discussed by Wagenaar (1988) in the context of Blackjack betting. Clearly gambling illusions of this type, rather than differences in risk propensity, may explain female preference for ‘multiples’ and ‘trebles +’ accumulator bets. The results relating to risk preference could also be explained by females being motivated more by ‘intellectual challenge’ and males more by ‘financial gain’. Bets such as ‘multiples’ and ‘any-to-come’ and bets placed ‘each-way’ provide the likelihood of at least partial vindication of, or reward (i.e. some return) to, the bettor motivated by intellectual challenge. The only result relating to risk which cannot be explained in the above terms concerns females’ tendency to bet relatively more than males on ‘trebles +’ as opposed to ‘doubles’. There is generally less chance of obtaining some return from the former bet type. This result, however, supports the findings of Hudgens and Fatkin (1985), who demonstrated that whilst females are generally more cautious risk takers than males, in low probability events they take more extreme risks. ‘Accumulators’ generally can be regarded as high-risk bets (i.e. low probability of a return) and, clearly, having chosen this bet type women appear to then choose more extreme risk bet categories. In summary the results relating to risk preference in general terms offer some, though not consistent, support for previous research which suggests that females are more cautious risk takers. The results suggest, however, that there may exist gender differences in the definition and perception of what constitutes risk and may suggest that males and females are differentially influenced by various gambling illusions. Confidence Stake size might be regarded as a proxy for confidence in the bet selection and, consequently, the current results confirm earlier findings concerning the greater confidence exhibited by males in their choices. The decisions involved in the current study are not made within an organisational context and the results reported here would appear, therefore, to refute the suggestion by Nicholson and West (1988) that gender differences in confidence are caused simply by

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organisational pressures. The distribution of bet size for females implies that there is greater homogeneity in levels of confidence amongst female bettors than male bettors. It should, of course, be noted that gender differences in bet size may not relate simply to differential levels of confidence. The results may to some degree reflect the greater earning ability and/or access to capital of males. Additionally, if expected gain is the guiding principle in bet selection, then the higher average stake for males may simply demonstrate greater willingness on their part to risk their resources in the hope of some future gain. The results may, therefore, simply confirm the view that males are more risk propensive; demonstrating males’ greater willingness to risk their resources in the hope of some future gain. Methodological considerations It is important to expand briefly on the methodological advantages of the study reported here. As noted earlier, the exploration of real betting decisions compares favourably with samples derived from laboratory-based simulations. Anderson and Brown (1984) note: ‘it appears that gambling behaviour . . . differs to a significant degree in the real and the laboratory situations’ (p. 407). The fact that the sample in this study was selected after close of business removes any potentially distortive effects associated with studies featuring observable researcher presence in the betting office (e.g. Dickerson, 1979). Equally, distortion associated with the sex of the experimenter is not a concern when subjects are unaware that their decisions are being monitored, though betting office staff, in any case, comprised both males and females. Further methodological concerns associated with earlier work on gender and decision-making include the impacts of gender orientation of the decision task, time pressure, external stimuli, information availability and age of subjects. It seems reasonable to suggest that the results reported here are relatively invulnerable to such distortions. For example, though betting, as a predominantly male pursuit, may be viewed as a male-orientated decision task, this was presumably not regarded as an inhibiting factor by the females in this study, who voluntarily engaged in betting. To a large degree, the time available to make the decision, the access to information and exposure to external stimuli are under the control of the individual bettor in this study. This does not deny the possibility that in certain cases, bets might be placed by individuals accompanying friends of the opposite sex or spouses into the betting office. Under such circumstances, a bettor’s access to time and information could be influenced by the preferences of a partner. The fact that betting is illegal for those under 18 years of age renders irrelevant the criticism relating to the use of children as subjects in some earlier male/female comparative studies. Taken as a whole, therefore, it seems reasonable to suggest that as a basis for analysis this database offers a significant improvement over those employed in many of the earlier studies.

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Conclusion The relationships between gender and betting decision quality, risk propensity and levels of confidence, explored in the current study, are not straightforward. There appears to be some evidence of greater risk taking by males in their betting decisions, lower levels of females’ confidence in their choices and some degree of performance advantage for women. These conclusions, however, hinge on definitions of risk taking and successful performance which, as suggested above, may vary for males and females. Caution must also be exercised in extrapolating these results to the population at large since, as discussed above, the degree to which betting is a ‘male-orientated’ task might affect the current results. However, the current study does at least clearly demonstrate that significant gender differences in betting behaviour exist. Further research might fruitfully explore the odds of horses selected in the various bet types since this would provide further insights into the nature of gender differences in risk preference. Questionnaire and interview surveys might be addressed at exploring gender differences in motivation to bet and specifically address male and female definitions of risk taking and successful performance. In addition, the extent to which individuals of the opposite sex bet on behalf of, or influence the betting strategies of, their partners also requires investigation. Finally the degree to which gambling illusions created by complex bets differentially influence bettors of a particular gender requires explanation. This suggested research should go some way to extending the findings of the current study which indicate the existence of interesting gender differences in betting risk propensity, decision quality and confidence.

References Anderson, G. and Brown, R.I.F. (1984) ‘Real and laboratory gambling, sensation-seeking and arousal’, British Journal of Psychology, 75: 401–10. Arenson, S.J. (1978) ‘Age and sex differences in the probability preferences of children’, Psychological Reports, 43: 697–8. Asch, P., Malkiel, B.G. and Quandt, R.E. (1984) ‘Market efficiency in racetrack betting’, Journal of Business, 57: 165–74. Baker, T. (1975) ‘Sex differences in social behaviour’, in Berkowitz, L., A Survey of Social Psychology. Hinsdale, Illinois: Dryden Press. Berry, M.C. (1980) ‘Targeting more aid to women entrepreneurs’, Venture, May, 294–304. Bolton, R.N. and Chapman R.G. (1986) ‘Searching for positive returns at the track: A multinomial logit model for handicapping horse races’, Management Science, 32(8): 1040–60. Bruce, A.C. and Johnson, J.E.V. (1992) ‘Toward an explanation of betting as a leisure pursuit’, Leisure Studies, 11: 201–18. Ceci, S.J. and Liker, J.K. (1986) ‘A day at the races: a study of IQ, expertise and cognitive complexity’, Journal of Experimental Psychology, 115(3): 255–66. Coet, L.J. and McDermott, P.J. (1979) ‘Sex, instructional set, and group make up: organismic and situational factors influencing risk-taking’, Psychological Reports, 44: 1283–94.

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Dickerson, M.G. (1979) ‘F.I. schedules and persistence at gambling in the UK betting office. Journal of Applied Behavioural Analysis, 12: 315–23. Eagly, A. (1978) ‘Sex differences in influenceability’, Psychological Bulletin, 85: 86–116. Estes, R. and Hosseini, J. (1988) ‘The gender gap on Wall Street: An empirical analysis of confidence in investment decision making’, The Journal of Psychology, 122: 577–90. Herschel, R., Wynne, B. and Noel, T. (1991) The Impact of Group Gender Composition on Group performance in an Electronic Meeting Setting: A Study of Group Gender Composition, Lucca, Italy: NATO Advanced Study Institute. Hudgens, G.A. and Fatkin, L.T. (1985) ‘Sex differences in risk taking: repeated sessions on a computer-simulated task’, The Journal of Psychology, 119: 197–206. Kass, N. (1964) ‘Risk in decision making as a function of age, sex and probability preferences’, Child Development, 35: 577–82. Keinan, G., Meir, E. and Gome-Nemirovsky, T. (1984) ‘Measurement of risk takers’ personality’, Psychological Reports, 55: 163–7. Kelly, J.A., Wildman, H.E. and Uney, J.R. (1982) ‘Gender and sex-role differences in group decision making social interactions: A behavioural analysis’, Journal of Applied Social Psychology, 12(2): 112–27. Levin, I.P., Snyder, M.A. and Chapman, D.P. (1988) ‘The interaction of experiential and situational factors and gender in a simulated risky decision-making task’, The Jouna1 of Psychology, 122(2): 173–81. Lindgren, H.E., Youngs Jr, G.A., McDonald, T.D., Klenow, DJ. and Schriner, E.C. (1987) ‘The impact of gender on gambling attitudes and behavior’, Journal of Gambling Behavior, 3: 155–67. Masters, R. and Meier, R. (1988) ‘Sex differences and risk taking propensity of entrepreneurs’, Journal of Small Business Management, January: 31–35. Nicholson, N. and West, M. (1988) Managerial Job Changes: Men and Women in Transition, Cambridge: Cambridge University Press. Priest, R.F. and Hunsaker, P.L. (1969) ‘Compensating for a female disadvantage in problem solving’, Journal of Experimental Research in Personality, 4: 57–64. Slovic, P. (1966) ‘Risk taking in children’, Child Development, 37: 169–76. Wagenaar, W.A. (1988) Paradoxes of Gambling Behaviour, Hove, UK: Lawrence Erlbaum Associates. Worchel, S. and Cooper, J. (1976) Understanding Social Psychology, Homewood, Illinois: Dorsey.

11 Gender-based differences in leisure behaviour Performance, risk taking and confidence in off-course betting A.C. Bruce and J.E.V. Johnson

Introduction Betting represents an important leisure activity in the UK with a total turnover on all forms of betting of £14,700 million (HM Customs) during 1993/4. It is also a widespread phenomenon; a Mintel Survey, conducted during 1992, indicated that 74 per cent of the adult population participate in some form of gambling. A large proportion of this betting activity is conducted through off-course betting offices (43.5 per cent of total betting turnover during 1993: HM Customs/Gaming Board). However the nature and image of off-course betting offices in the UK has changed considerably in the last decade. Successive items of legislation have, over the last ten years, resulted in a significant relaxation of the controls which applied to the off-course betting office since the legalization of this form of betting in 1960. Legalization had been attended by a battery of restrictions on the off-course betting office, designed principally to ensure that betting should not be actively encouraged. Accordingly, restrictions applied to the physical fittings and furnishing of the betting office, the forms of broadcast media which could be transmitted to betting office customers and the times of opening. By 1993, many of these restrictions had disappeared. Betting offices could, for example, provide comfortable facilities for clients, sell non-alcoholic drink and food, and offer a wide range of audio and televisual transmissions, including live coverage of sporting events. Evening opening of betting offices was permitted for the first time in 1993. A further relaxation of restrictions on betting shop-front advertising occurred in April 1995. At the same time off-course bookmakers were permitted to allow the interior of their shops to be seen from the street. In short, bookmakers’ retail outlets underwent a wholesale transformation from the 1980s onwards. At the same time, innovation in the range of betting media beyond the traditional horse and greyhound racing orientation offers an increasing product portfolio to the leisure bettor. A strong impression to emerge from these developments is that betting as a leisure activity has developed a more civilized image. The more agreeable and less exclusive betting office environment means that betting has become a less clandestine activity which is moving from the margins of social acceptability towards a position as a mainstream leisure activity open to a wider public.

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Previous studies by the authors have explored the motivations of off-course bettors (Bruce and Johnson, 1992) and the role of excitement in leisure betting (Bruce and Johnson, 1995). These papers have addressed the off-course betting population as a whole, yet a potentially significant result of the developments discussed above is the likelihood that women will form an increasingly important group within the aggregate betting office clientele. It is, therefore, particularly appropriate at this time to explore differences in the betting behaviour of men and women. This chapter seeks to offer new insights in this area. To the bookmaking industry, such research offers potentially valuable insights into the female bettor, with attendant commercial applications in the strategic development of a traditionally underexploited area of the market. From an academic standpoint this study addresses, in a specific context, the need to consider explicitly the leisure experience of women. The past decade has seen a growing concern that the issues relating to women’s leisure have received insufficient or inappropriate attention. Henderson (1990) observed: ‘gender differences have not been a dominant theme in much of the leisure research. Many studies of leisure behaviour have tended to ignore possible gender differences’ (p. 233). Scraton (1994) noted: ‘It is significant that there has been little empirical research on women’s leisure since the main studies of the 1980s. There appears to be a gap in leisure research with research on women or gender relations having fallen from the agenda’ (p. 253). In terms of approaches to leisure and gender issues, it has been suggested that female perceptions and experience of leisure should be regarded as requiring distinct methodological and analytical treatment and that traditional approaches which are dominated by the application of a simplistic work/leisure construct shed little light on the leisure experience of females. The work/leisure dichotomy manifestly fails, for example, to take account of the significantly reduced ‘unobligated’ time available to women, which results from societal perspectives on their domestic and family-related roles and responsibilities. An early attempt to identify the origins and characteristics of these societal influences is outlined by Deem (1982). Henderson (1990) pointed to the need to acknowledge: ‘the constraints on women’s leisure that are imposed by dominant societal views regarding definitions of masculinity and feminity’ (p. 231). Henderson and Dialeschki (1991) highlighted how these societal norms lead to a pervasive sense of lack of entitlement to leisure among women, while Shaw (1991) and Firestone and Shelton (1994) offered corroborative empirical analyses of women’s leisure time. Accordingly, this chapter seeks to explore the leisure experience of women within off-course betting offices. It builds on earlier research by the authors (Bruce and Johnson, 1994) by presenting the results of a new set of empirical investigations, focusing on differences in male and female betting activity. In particular it explores the issues of comparative performance, risk propensity and confidence. A brief review follows of earlier findings relating to the comparative decisionmaking behaviours of men and women, both in the area of decision-making in

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general and of betting in particular. The database used by this study to address these areas is described and the superiority of the methodology employed over earlier approaches is explained. The results of the current study are then presented and analysed.

Gender, decision-making and betting Academic interest in the comparative characteristics of male and female decision-making is well established. Three areas of inquiry have dominated the literature in this area: the relative decision performance of men and women, their respective propensities to accept risks and their differential degrees of commitment or confidence in decisions. Each of these issues is addressed briefly here, before the results of earlier work in specific relation to comparative betting behaviour are discussed. A distinctive feature of the work relating to comparative decision-making is the lack of firm or enduring consensus in relation to the three main issues addressed. To some degree this may reflect the wide disparity in approaches to analysis of male/female distinctions; a factor noted by Eagly (1978). In relation to the comparative decision-making performance of men and women, a degree of consensus in favour of the ‘superior’ performance of men (e.g. Hoffman and Maier, 1966; Priest and Hunsaker, 1969) has given way to more recent suggestions that gender-based differences are negligible (Hudgens and Fatkin, 1985; Estes and Hosseini, 1988). A factor in this shift may have been an increasing awareness of and control for factors in earlier studies which owed less to the sex of the decision-maker per se than to other factors. For example, it has been suggested that the sex of the experimenter may influence results or that the nature of the decision, in terms of its essentially male or female orientation, may be important in determining results (Herschel et al., 1991). Diminishing evidence for significant gender-based differences may also reflect real changes as well as increased methodological sophistication. It may, for example, be argued that the enhanced status and expertise of women in professional decision-making contexts is mirrored increasingly in non-professional settings. Evidence of differential attitudes to risk taking points in general to some greater risk preference among males (e.g. Levin et al., 1988; Saint-Germain, 1989). Again, however, it should be acknowledged that factors other than gender, such as the nature of the decision task, cultural factors or age, may be important in contributing to the existence of observed differences between genders (Slovic, 1966; Levin et al., 1988). In terms of comparative confidence of males and females in decisionmaking, there is fairly consistent support for the greater confidence of male decision-makers (Estes and Hosseini, 1988; Nicholson and West, 1988; Birley, 1989). Where observed differences occur in organizational decision-making contexts, one explanation lies in the insecurity of females in male-dominated organizations (Nicholson and West, 1988).

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In moving from a general discussion of comparative decision-making characteristics to the specific area of betting, it is instructive to review the results of earlier work (Bruce and Johnson, 1994). This work was prompted by the issues in the general decision-making literature discussed above and tested for male/female differences in performance, risk taking and confidence in a betting context, using a sample of over 4,000 individual bets placed in UK betting offices. In terms of performance, measured by comparative returns across all bet types, women placed a greater proportion of bets and stakes yielding some return than men, but overall male bettors earned a greater rate of return over all bets placed. Taken together, these results suggested that when male bettors made a correct decision, the decision was inherently riskier (longer odds) on average, than the winning bets of women. A complicating factor here, however, relates to how one judges performance across different bet types. For example, it is not immediately clear how one should compare the performance of two bets, where one is an each-way single (the single selection must win or be placed) bet, which generates a return as a result of the selection being placed, and the other is an accumulator bet, where two out of the three selections win and the third is placed. In the latter case, the bet would generate no return, yet the decisions within the bet suggest a reasonably impressive level of decision performance. The results relating to comparative risk-taking propensity were based on the relative preferences of men and women for different types of bet, with differing degrees of inherent riskiness. Again, this produced somewhat ambiguous results, which suggested that common definitions for male and female bettors as to what constitutes risk may be inappropriate. For example, female bettors were observed to favour bets with built-in ‘insurance’ features. Such bets are unlikely to involve total loss, but are statistically less likely to produce profits than certain other bet types. The prospect of some return, albeit merely a consolation, might appeal to a bettor whose notion of risk focused on total loss. Such a bet might, however, be unattractive to a bettor whose focus is on the prospect of gain. Here, the ‘win’ bet on a ‘single’ selection (the simplest bet type with an ‘all or nothing’ characteristic) where success or failure depends on a single outcome, might be more appealing. This type of result prompts both a reconsideration of the differential risk perceptions of male and female bettors and suggests the need for greater control for such differentials in empirical work. Finally, results relating to confidence, measured in terms of comparative staking levels, were rather less ambiguous and suggested greater confidence by male bettors, whose stakes were significantly higher. It was recognized, however, that the comparative stringency of constraints imposed by disposable income might well have been an influence here. The research reported here seeks in its methodology to overcome the difficulties of interpretation associated with these earlier results. The chapter therefore aims to develop a set of procedures which allows a more confident indication of the comparative betting behaviour of males and females. Given the generally ambivalent or ambiguous nature of the study reported above, the

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specific hypotheses to be tested are that there are no significant differences in performance, risk taking or confidence between male and female bettors.

Database and procedures Database This section begins by describing the database used in this study, before explaining the procedures adopted to provide further insights into male/female differences in betting behaviour. The methodological refinements of the new approach are emphasized. The database employed in this study comprised a systematic random sample of 1,243 (728 male, 515 female) single bets made by men and women in betting offices throughout the UK. A random sampling procedure was devised, based on the serial number of the betting slip, to select a roughly similar size sample of male (n = 2,009) and female (n = 2,015) bets of all types. The ‘singles’ bets in this sample (n = 1,243) were then set aside for analysis. During the period of the sampling procedure in April 1991, all bets placed by women were marked by betting office staff, without the knowledge of the bettor. The ecological advantages of this form of direct empirical study over laboratory simulations of betting or limited empirical surveys in the presence of researchers have been discussed in detail in earlier work (see Bruce and Johnson, 1994). In simple terms these advantages relate to the use of real betting decisions, made in a natural setting and in the absence of potentially distortive observation effects. Equally, given that bettors were not aware that their behaviour was the subject of an empirical experiment, the potential problem of experimenter gender is absent. While the previous results reported above offered an interesting introduction to the empirical testing of gender effects, an important outcome of the authors’ earlier work was that some of the ambiguities in the results suggested scope for refinements in procedure. Principally, the fact that the earlier study involved taking a sample of all types of bet made by men and women meant that the interpretation of the results was at times prone to ambiguity. In seeking to address these ambiguities of interpretation, the procedures described below consider only ‘singles’ bets. This tighter focus controls for differential propensities to select different bet types and therefore offers a clearer insight into comparative performance, risk propensity and confidence. Procedures Performance ‘Singles’ bets involve the selection of one horse and the return depends solely on the performance of that horse. A comparison of male and female bets on singles only, therefore, offers the opportunity for less ambiguous judgement as

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to comparative performance. Five measures of comparative performance were employed: proportion of stakes (reflecting the number of bets placed) yielding, respectively, a return or a profit; proportion of stakes (reflecting the amount of money wagered) yielding, respectively, a return or a profit; average return to stake. These measures permitted a direct comparison with the earlier reported results across all bet types. Risk preference The possibility of differing cross-gender definitions or perceptions of risk complicated the interpretation of results which were based on bets of all types and inhibited the identification of clear patterns of risk preference. Confining investigation to single bets addressed this problem and allowed investigation of alternative measures of risk-taking propensity using a homogeneous sample of bet types. Specifically, risk preference was explored by examining the propensity to use ‘each-way’ as opposed to ‘win’ bets and by measuring the comparative propensities to select horses which the market suggested had greater or lesser chances of success (i.e. shorter odds versus longer odds horses). The latter measure of risk propensity required the addition of forecast odds and starting price odds to the original data set and, consequently, for this section of the analysis a randomly selected subsample of the original database was employed (684 bets; 343 male, 341 female). Forecast odds represent a prediction of the odds which will be available on each runner. The predictions used in this study were taken from The Sporting Life, a daily racing newspaper which is prominently displayed in all betting offices throughout the betting day. Starting price odds are the odds available on each horse at the start of the race (once betting activity has concluded) and these are the odds which were used to settle the majority of bets placed. Confidence To overcome the potential ambiguities associated with the interpretation of behaviour in relation to ‘exotic’ bets, perhaps involving several sub-bets or contingent bets, examination of staking patterns in this study was confined to single bets, which allow a straightforward comparison of male and female behaviour in an identical context. Additionally, confidence was considered in terms of comparative propensity to pay tax at the time of bet placement. The significance of this characteristic requires explanation. Bettors in UK off-course betting offices have the choice of meeting their betting tax liabilities by, alternatively, paying a 10 per cent tax on the stake wagered at the time of bet placement, or by paying no tax at time of bet placement but then incurring a 10 per cent tax on any returns generated, including the original stake. Clearly, for the confident bettor who expects success, tax liability is minimized by paying tax on the original wager. For the bettor who is less confident, non-payment of tax on the stake may be more attractive.

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Results and analysis Performance The results relating to comparative performance (see Table 11.1) suggest some evidence for the superior performance of female bettors across each of the five measures employed. Though the performance advantage is not, in any of the cases, statistically significant (at the 0.05 level), the figures offer a rather more consistent picture than the results of the previous study (Bruce and Johnson, 1994) where only three of the five measures indicated better performance by females. However, it should be noted in relation to the current study that the five performance measures were related to some degree and, consequently, less can be read into the consistent differences than if the measures were completely unrelated. Despite this reservation, the current results, in relation to betting, challenge earlier investigation which suggested that men outperform women (e.g. Priest and Hunsaker, 1969) and offer support for more recent studies (e.g. Estes and Hosseini, 1988; Masters and Meier, 1988) which find no evidence of male superiority in terms of performance. Whether the results presented here are indicative of methodological flaws in earlier investigations, or whether they reflect a genuine behavioural change is an interesting question. Herschel et al. (1991), for example, have suggested that the gender orientation of the decision task may have a significant effect on performance, with males likely to outperform females in male-orientated tasks. In this context the civilizing of the off-course betting office environment, which was described in the introduction, may partly explain the lack of gender differences in performance. It seems reasonable to suggest that whilst betting as an area of decision-making might at one time have been regarded as an overwhelmingly male-orientated task, the more civilized modern betting office setting has done much to erode that perception.

Table 11.1 Comparative male and female performance on single bets Male (n = 278) Proportion of bets with a returna Proportion of bets with a profitb Proportion of stakes with a returnc Proportion of stakes with a profitd Return/stake

0.10 0.09 0.13 0.12 0.44

Female (n = 515) + + + + +

0.12 0.10 0.16 0.15 0.48

Notes a Proportion of bets (irrespective of stake size) producing a positive return (which may be less than the amount staked). b Proportion of bets (irrespective of stake size) producing a return greater than the amount staked. c Proportion of total amount staked which produced a positive return. d Proportion of total amount staked which produced a return greater than the amount staked. + p > 0.05, two-tailed (large sample test for difference between proportions, independent t-test for return/stake statistic).

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It is interesting to note that single bets placed by females display a number of performance advantages over those placed by males in spite of evidence on participation patterns which suggests that females prefer more complex bet types (for example, Bruce and Johnson, 1994, noted that only 33.7 per cent of female bets and 47.8 per cent of female stakes were placed on singles, compared with equivalent figures for men of 42.8 and 63.8 per cent, respectively). This may suggest that females are either unaware of their performance advantage in single bets or may suggest that their motivation for betting includes factors other than financial gain. Risk preference The results relating to comparative propensity to accept risk in betting tend to confirm the view developed from earlier research (e.g. Saint-Germain, 1989) that male and female bettors’ attitudes to risk are different, whilst at the same time challenging, in relation to betting behaviour, the orthodox view of females as more risk averse. The two principal measures of risk employed involve consideration of the average odds of the horse selected and the type of single bet chosen (win versus each-way). A consideration of individual horses selected, in terms of the horse’s odds, either as forecast in the UK’s leading racing newspaper, The Sporting Life, or as represented by the starting price (SP), suggests there are marked differences between male and female behaviour (see Tables 11.2a and b). We consider, initially, the forecast odds as published in The Sporting Life. The rationale for using these odds as a measure of risk preference rests with the Table 11.2a and b Comparative patterns of male and female betting on horses nmale = 343 nfem = 341

Proportion of male bets

Proportion of female bets

Proportion of male stakes

Proportion of female stakes

(a) Different forecast odds Odds on 0.01 Evens – 5/1 0.41 + 11/2 – 10/1 0.34 11/1 – 20/1 0.22 >20/1 0.02

0.00 0.26 0.38 0.30 0.05

0.00 0.54 0.32 0.13 0.00

*

0.00 0.47 0.30 0.19 0.05

(b) Different starting prices (SPs) Odds on 0.02 Evens – 5/1 0.44 + 11/2 – 10/1 0.27 11/1 – 20/1 0.19 >20/1 0.08

0.00 0.29 0.30 0.27 0.14

0.03 0.57 0.19 0.18 0.04

*

0.00 0.49 0.25 0.17 0.09

Notes For Table 11.2a: χ2 = 28.84, df = 4, p < 0.01; for Table 11.2b: χ2 = 26.67, df = 4, p < 0.01. + Sources of significant difference between male and female proportions where standardized residuals exceed ± 2. * Proportions of male and female stakes significantly different (p < 0.05) using a special case of ratio estimation (Cochran, 1977).

192 A.C. Bruce and J.E.V. Johnson fact that for most off-course bettors The Sporting Life is one of the principal informational media. Invariably, pages of the newspaper are displayed in betting offices, indicating that day’s race details and offering comment, analysis, prediction and a forecast of the likely betting market for each race, with predicted odds for each horse. As such, data from The Sporting Life, including the forecast odds, may be expected to be an important factor in the individual bettor’s selection process. In terms of forecast odds, the results indicate marked and statistically significant differences between the selections made by men and women. Some caution should be exercised in drawing conclusions from the test for equality of multinomial proportions since the expected cell frequency for the ‘odds on’ category is small. However, since all expected cell frequencies are greater than one and the majority are greater than five, the χ2 test reported in Table 11.2(a) should not be invalidated. The results appear to indicate marked differences in male and female betting behaviour. For example, whilst 42 per cent of male bets and 54 per cent of male stakes are placed on horses with forecast odds of 5/1 or less, the equivalent figures for female bets are just 26 and 47 per cent. At the other end of the odds spectrum, only 24 per cent of male bets and 13 per cent of male stakes involve horses with forecast odds of greater than 10/1. By contrast 35 per cent of female bets and 24 per cent of female stakes fall within this category. These differences are reflected in differences in the average forecast odds of selections: for men these are 7.98/1, and for women, 11.30/1 (t = 3.89, p < 0.001, two tail). Taken together, these results suggest a marked preference by women for inherently ‘riskier’ bets, in terms of the probability of winning implied by the forecast odds. When actual SP rather than forecast odds is considered, a similar picture emerges. Here, 46 per cent of male bets and 60 per cent of stakes are placed on horses with SPs of 5/1 or less, compared with 29 and 49 per cent for women. Twenty-seven per cent of male bets and 22 per cent of stakes involve selections with starting price odds of greater than 10/1; the equivalent figures for female bets are 41 and 26 per cent, respectively. The average SP of male bets is 8.85/1, and that of female bets, 12.54/1 (t = 4.57, p < 0.001, two tail). Taken together, this set of results suggests that, in terms of horses selected, female bettors have a preference for inherently riskier wagers, a conclusion which runs contrary to the established literature on gender-based differences in decision-making behaviour in general. In isolation, however, these results offer only a partial picture of differential attitudes to risk. A further choice variable involved in the making of a single bet may offer an insight into risk preferences. This is the decision to bet on whether the selection will win the relevant race or whether it will either win or be placed. The second alternative (each-way betting) incorporates an element of insurance and is reasonably regarded, therefore, as inherently less risky. The results relating to male and female preferences for win or each-way betting indicate a clear comparative preference for each-way betting among women. Of all single bets placed by females, 39 per cent are each-way wagers compared with a figure of 25 per cent for male bets (t = 5.2, p < 0.001, two tail).

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In terms of stakes, the comparative figures are 27 and 18 per cent, respectively (t = 3.80, p < 0.001, two tail). In interpreting these and the earlier results, it is important to recognize the relationship between betting on short or long-priced horses and betting to win or each-way. The terms associated with each-way bets are such that, for a horse which is merely placed, the return is a fraction (normally 1/4 or 1/5) of the horse’s odds. Clearly, where the odds are short this renders a place return very small. There is, therefore, less incentive to engage in each-way betting on short-priced horses than on longer-priced horses. As such the observed combinations of short odds/win and long odds/each-way betting may in part reflect this factor. In order to control for differences in bet type the average SP and the forecast odds of horses selected by both males and females were determined for both win and each-way bets. The results displayed in Table 11.3 clearly indicate that, whatever the bet type (win or each-way), women select horses with higher average starting prices and higher average forecast odds than males. Taken together, the results relating to horse selection by odds and bet type (win/each-way) preference appear to invite conflicting conclusions as to the relative risk preference of male and female bettors. The horse (odds) selection results suggest female bettors are more risk preferring and the bet type results suggest male bettors are relatively risk preferring. One way of clarifying the issue may be to take a view as to which decision variable should be regarded as dominant, horse selection or bet type selection. It seems reasonable to suggest that the horse selection is dominant in that most bettors are presumably initially motivated to bet on a horse and, as a secondary issue, they decide whether to back the horse to win or each-way, in the light of other factors such as the profile of odds in the market. This is clearly more plausible than the bettor deciding that they wish to place, say, an each-way bet and then selecting a horse which, by virtue of its odds, represents good value for such a bet. Using this line of reasoning the results seem to challenge earlier work in the area fundamentally by suggesting that female bettors have a greater propensity to take risk than male bettors. The notion that bettors decompose what is a single decision into a series of component elements may be difficult to support, however, so that a safer line of interpretation may be to suggest that the results offer, in relation to betting activity, Table 11.3 Comparative patterns of male and female betting on horses Win bets

Each-way bets

Male Starting price Forecast odds

7.22/1 6.80/1

** *

Female

Male

9.49/1 8.00/1

14.58/1 12.11/1

Female *

Notes * p < 0.05. ** p < 0.01. Average odds significantly different using two-tailed, independent t-test.

17.94/1 17.13/1

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little support for the orthodox view of women as less prepared to accept risk than men (Hudgens and Fatkin, 1985; Levin et al., 1988; Saint-Germain, 1989). As such, the results presented here are in line with contributions of Noe and McDonald (1983) and Starr and Potashier (1984), each of whom found little basis for gender-based differentiation. One interesting feature to emerge from the results is that they suggest different perceptions of and approaches to the management of risk between male and female bettors. Specifically, the results suggest that males and females develop alternative strategies in seeking to attain their preferred exposure to risk. This exposure is composed of the risk implicit in the selection itself (odds) and in the medium for the selection (bet type). Males’ risk exposure relates chiefly to the chosen medium, whereas for females the selection appears to be the dominant factor in risk composition. This offers reinforcement for the results which emerged from earlier work (Bruce and Johnson, 1994) which suggested that there are gender differences in the definition of risk between male and female bettors. Confidence The final area of enquiry addresses the issue of gender-based differences in the confidence with which individuals make decisions. Two types of confidence measure, staking levels and the tax payment decision, are employed and the rationale for each is discussed above. The results relating to staking indicate a significant difference between males and females – their average stakes being £6.23 and £3.40, respectively. This difference is in large part accounted for by a differential propensity to place bets exceeding £5 (see Table 11.4). Whilst 32 per cent of male bets exceeded £5 and 80 per cent of stakes were accounted for by such bets, the comparable figures for women were 19 and 66 per cent, respectively. One potentially explanatory factor is the comparative ability to spend, which would Table 11.4 Comparative staking behaviour: males and females

50p or less 51p–£1 £1.01–£5 £5.01–£20 £20 or more

Proportion of male bets

Proportion of female bets

Proportion of male stakes

Proportion of female stakes

0.07 0.10 0.51 0.25 0.07

0.10 0.11 0.60 0.16 0.03

0.00 0.01 0.18 0.35 0.45

0.01 0.02 0.32 0.38 0.28

+ +

** *

Notes Testing for equality of multinominal proportions (male versus female): χ2 = 31.05, df = 4, p < 0.01. + Sources of significant difference between male and female proportions where standardized residuals exceed ± 2. *, ** Proportions of male and female stakes significantly different using a special case of ratio estimation (Cochran, 1977) [*: p < 0.05, * *: p < 0.01].

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be likely to favour male bettors. In order to control for differential income levels the mean stakes for male and female bettors were divided by the average income of male bettors (£16,256) and female bettors (£12,166), respectively.l When controlling for income levels in this manner the average stake per bet for men (£3.83) was still significantly different (t = 2.76, p < 0.01, two tail) than the average stake per bet for women (£2.79). Taken together, the results relating to staking suggest that male bettors exhibit greater confidence in their decisions. A second measure of decision confidence (tax payment decision) which does not rely on comparative access to financial resources was also employed. Here, the results indicate that women pay tax at the time of bet placement on 93 per cent of bets placed and 95 per cent of stakes placed, compared with equivalent male figures of 81 and 72 per cent (both differences are statistically significant at the 0.001 level). These figures appear to support the view that female bettors are significantly more confident in their decisions than male bettors, a result which runs contrary to the recent findings of Nicholson and West (1988) and Estes and Hosseini (1988). It should be acknowledged, however, that an alternative interpretation of female propensity to pay tax upon bet placement might be that it constitutes evidence of risk aversion, in that tax liability is determined immediately and with certainty. It seems reasonable to conclude that the results relating to confidence fail to offer a consistent case for clear differentials between male and female bettors. Whilst the staking results suggest greater male confidence, the tax payment results are suggestive of greater female confidence. However, it may be unrealistic to suggest a simple relationship between the tax decision and confidence. In the circumstances, the most appropriate conclusion may be that in relation to betting behaviour there is an absence of strong or consistent evidence to support the dominant view in the existing literature of greater male confidence. In interpreting the results from each of the three areas of comparative investigation, this section has concentrated on relating the findings of this study to earlier work in the field. As such, it has consciously not attempted to rationalize the observed gender-based differences in terms of the distinct and different female perceptions of leisure which spring from societal influences on gender roles, as discussed in the opening section. Extension of the analysis to incorporate the impact of these fundamental cultural and societal influences on behaviour is an obvious area for further research.

Conclusion This chapter represents a development and refinement of earlier work by the authors in this area. This earlier work was suggestive of identifiable differences in the betting behaviour of men and women, whose betting activity was monitored over a wide range of bet types. In order to address certain ambiguities introduced by the study of heterogeneous bet types, the results presented here focus on male and female ‘singles’ betting only.

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Three aspects of comparative behaviour were considered: performance, propensity to accept risk and confidence. These themes reflect areas of interest in the literature relating to gender-based differences in decision-making. The evidence emerging from the current study from these areas of enquiry challenges the orthodox view in the literature of better performance by males in relation to betting activity. In addition, it suggests that the dominant view in the existing literature of males as more risk preferring than females may be open to question where betting behaviour is concerned. In particular, it appears that there may be marked differences between the ways in which men and women bettors perceive and react to risk. On the issue of comparative confidence in betting decisions, there are conflicting messages from the procedures conducted, which at least suggest that the established idea of men as more confident may be open to some doubt in the betting environment. Beyond the specific contributions noted above, the significance of this chapter lies in part in its focus on the character of decisions made in a naturalistic setting. As such, it both develops and complements the earlier literature in the area, which focused on comparative behaviour under simulated, laboratory conditions. Additionally, during a period when the character of the UK betting office and its clientele has been subject to considerable change, this study contributes to the understanding of the betting behaviour of an increasingly important section of the active betting population. By examining explicitly the activity of women as a separate group of leisure participants, this research moves some way towards addressing the need for more work in the area of women’s leisure. It is acknowledged, however, that the generation of comparative empirical results represents just one element in the development of a comprehensive analysis of the determinants of female participation in leisure.

Acknowledgements The research reported here was made possible by grants from Ladbroke Racing. Special thanks to Caroline Beel for her help with data collection and to Philip Cooper for his invaluable statistical advice.

Note 1 Data to determine the average income of male and female bettors were obtained from Target Group Index, British Market Bureau (1992), and New Earnings Survey, Department of Employment (1992).

References Birley, S. (1989) ‘Female entrepreneurs: are they really any different?’, Journal of Small Business Management, January, 32–7. Bruce, A.C. and Johnson, J.E.V. (1992) ‘Towards an explanation of betting as a leisure pursuit’, Leisure Studies, 11: 201–18.

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Bruce, A.C. and Johnson, J.E.V. (1994) ‘Male and female betting behaviour: new perspectives’, Journal of Gambling Studies, 10: 183–98. Bruce, A.C. and Johnson, J.E.V. (1995) ‘Costing excitement in leisure betting’, Leisure Studies,14: 48–63. Cochran, W.G. (1977) Sampling Techniques, New York: John Wiley. Deem, R. (1982) ‘Women, leisure and inequality’, Leisure Studies, 1: 29–46. Eagly, A. (1978) ‘Sex differences in influenceability’, Psychological Bulletin, 85: 86–116. Estes, R. and Hosseini, J. (1988) ‘The gender gap on Wall Street: an empirical analysis of confidence in investment decision making’, The Journal of Psychology, 122(6): 577–90. Firestone, J. and Shelton, B.A. (1994) ‘A comparison of women’s and men’s leisure time: subtle effects of the double day’, Leisure Sciences, 16: 45–60. Henderson, K.A. (1990) ‘Anatomy is not destiny: a feminist analysis of the scholarship on women’s leisure’, Leisure Sciences, 12(2): 229–39. Henderson, K.A. and Dialeschki, M.D. (1991) ‘A sense of entitlement to leisure as constraint and empowerment for women’, Leisure Sciences, 13: 51–65. Herschel, R., Wynne, B. and Noel, T. (1991) The Impact of Group Gender Composition on Group Performance in an Electronic Meeting Setting: A Case Study of Group Gender Composition, Lucca, Italy: NATO Advanced Study Institute. Hoffman, L.R. and Maier, N.R.E (1996) ‘Social factors influencing problem solving in women’, Journal of Personality and Social Psychology, 4: 382–90. Hudgens, G.A. and Fatkin, L.T. (1985) ‘Sex differences in risk taking: repeated sessions on a computer-simulated task’, The Journal of Psychology, 119(3): 197–206. Levin, LP., Snyder, M.A. and Chapman, D.P. (1988) ‘The interaction of experiential and situational factors and gender in a simulated risky decision-making task’, The Journal of Psychology, 122(2): 173–81. Masters, R. and Meier, R. (1988) ‘Sex differences and risk taking propensity of entrepreneurs’, Journal of Small Business Management, January: 31–5. Nicholson, N. and West, M. (1988) Managerial Job Changes: Men and Women in Transition, Cambridge: Cambridge University Press, Noe, E.P. and McDonald, C.D. (1983) ‘Comparison of perceived risk taking in groups and implications drawn from the risky shift paradigm’, Perceptual and Motor Skills, 56: 199–206. Priest, R.E and Hunsaker, P.L. (1969) ‘Compensating for a female disadvantage in problem solving’, Journal of Experimental Research in Personality, 4: 57–64. Saint-Germain, M.A. (1989) ‘Does their difference make a difference? The impact of women on public policy in the Arizona legislature’, Social Science Quarterly, 70(4): 956–68. Scraton, S. (1994) ‘The changing world of women and leisure: feminism, ‘post-feminism’ and leisure’, Leisure Studies, 13(2): 249–61. Shaw, S.M. (1991) ‘Research note: women’s leisure time – using budget data to examine current trends and future predictions’, Leisure Studies, 10: 171–81. Slovic, P. (1966) ‘Risk taking in children’, Child Development, 37: 169–76. Starr, M.W. and Potashier, H.R. (1984) ‘The structure and preferences for gambling activities’, Proceedings of the Sixth National Conference on Gambling and Risk Taking, W. Eadington (ed.), Nevada: University of Nevada.

12 Decision-making, risk and gender Are managers different? J.E.V. Johnson and P.L. Powell

Introduction This chapter explores the nature of male and female decision-making and explicitly examines gender differences in decision quality and risk propensity. ‘Good managers, it is said, are those who make good decisions’ (Cooke and Slack, 1984, p. 3). Most management writers agree that effective decisionmaking lies at the heart of good management. Indeed, Drucker (1981, p. 374) argues that ‘The first managerial skill is . . . the making of effective decisions’. An organization’s success is to a greater or lesser extent, related to the decisionmaking ability of its managers. As most decisions taken by managers are made in environments characterized by uncertainty, judgements often involve subjective assessment of the uncertain opportunities and threats or costs associated with particular actions. Decision-making is therefore, at least in part, associated with risk taking; balancing the potential rewards against the possible negative consequences of a particular course of action. High potential rewards are often associated with large potential losses and consequently the propensity of a manager to seek or shy away from such high-risk options can have serious implications for an organization. Organizations, for example, suffering from stagnation due to overbureaucratic systems, may benefit from a manager who is prepared to risk trying new ideas such as reducing the levels of the hierarchy and empowering subordinates by providing them with greater degrees of autonomy and responsibility. Equally, however, a manager who is prepared to risk the solvency of an otherwise successful organization by persisting with an overambitious innovation project that has only a slim chance of producing what at best will be a mediocre product would not be regarded as an asset by many organizations. Whilst the ability of a manager to take effective decisions is invariably an asset to an organization, a manager’s inclination to take risks can, depending on the circumstances, be an asset or a liability. Any difference in the quality of decisions taken by male and female managers and any gender differences in risk propensity will clearly have important implications for organizations. In order to explore these issues, the chapter is arranged in four sections and proceeds as follows: the first section examines the

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changing role of women as decision-makers, especially in business management. The second section reviews the literature on gender and decision-making, categorizing it into three subsections to reflect three strands to the literature. The first, explored in subsection one, relates to the majority of research conducted pre-1980. This literature was instrumental in developing the accepted view of the period, that clear differences existed in the nature and quality of male and female decision-making. The second strand, discussed in subsection two, relates to a body of literature that questions the research methods employed in many studies conducted prior to 1980. This, together with often overlooked research evidence of the period, is examined. Subsection two concludes that the relationship between gender and decision-making was not as clear cut as the accepted view prevailing before 1980 would imply. Subsection three explores the post1980 literature which suggests that there is no uniform pattern of gender differences in decision quality or style but clearer gender differences in the degree of confidence in decision choices and in risk propensity. The third section reports two pieces of empirical work. These were undertaken to contrast gender differences in decision quality and risk propensity observed in two distinct populations. The first population (‘non-managerial’) consisted of a cross-section of individuals from a variety of occupational and social groups, the majority of whom had not undergone formal management education. The second population (‘managerial’) consisted exclusively of managers and potential managers who had undertaken formal management education. Whilst gender differences in decision quality and risk propensity are observed in the ‘non-managerial’ population, no such differences are observed in the ‘managerial’ population. The last section presents the conclusions and it is argued that some of the reasons given for excluding women from managerial positions may be based on false stereotypes derived from observations of ‘non-managerial’ populations.

The role of female decision-makers The role of women in the workplace is being reappraised, perhaps partially as a response to current demographic changes, and their economic value is being reassessed (Ashburner, 1991). In particular, the literature of the 1980s clearly demonstrates that entrepreneurial and risk-taking roles are being taken increasingly by women (Chaganti, 1986; Hisrich and Brush, 1984; Scott, 1986; Stevenson, 1986). For example, Birley (1989, p. 37) notes that ‘the exploding number of small businesses owned by women reflects both social and economic transformations. Women have crossed a wider range of economic barriers than at any time since World War II’. Despite these advances, research evidence suggests that women are often excluded from managerial positions of authority and leadership within organizations (Ashburner, 1991; Ashridge Management College, 1980; Collinson and Knights, 1985; Industrial Society, 1981). For example, one recent study (Collins et al., 1988) concluded that female managers must realize that ‘work is a game with rules and customs geared to reward traditional male behaviour’.

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Several reasons have been identified for the under-representation of females in managerial positions; amongst them a variety of commonly held stereotypes such as women’s lack of leadership and decision-making abilities (see, for instance, Kanter, 1977a, 1977b; Nieva and Gutek, 1981; Terborg, 1977). Research has supported the existence of these stereotypes. For example, Broverman et al. (1972) found that males were perceived to be more able to act as leaders, more dominant, more able to make decisions, less easily influenced, more aggressive and more independent than females. Barnett and Karson (1989) indicate that studies often emphasize the differences between male and female managers. The stereotypes are consequently reinforced. Despite these stereotypes, legislation and changing social values will ensure that female participation in organizational decisions is, and will continue to become, more equitable. Consequently, investigation of any real gender differences in the nature and quality of decision-making is clearly of value.

Gender and decision-making: a review of the literature The overwhelming majority of research into gender differences in risk propensity and in the nature of decision-making has been conducted in the USA and in the UK. Using his analysis of self-concept, Hofstede (1980) found that the UK and USA were grouped together as individualistic/masculine cultures and he classifies both countries as having an Anglo-culture. The following literature review is therefore restricted to exploring research conducted in the USA and the UK (Anglo-culture) and consequently it avoids ambiguities which may arise from comparing studies across a range of national cultures. Accepted view pre-1980s The dominant view in the personality and social psychology literature, from the 1950s through to the early 1980s, was that clear differences existed in the nature and quality of decisions taken by men and women. A consistent finding in studies during the period was the apparent inferior quality of problem solving by women, both individually and in groups – even when differences such as intellectual aptitude and special abilities were controlled (Carey, 1958; Maier and Hoffman, 1961; Hoffman and Maier, 1966; Maier, 1933; Milton, 1957; Priest and Hunsaker, 1969; Sweeney, 1953). It was argued (Lynn, 1962) that the female disadvantage in problem solving resulted from a negative attitude towards abstract problem solving acquired early in their sex-role socialization (i.e. problem solving is traditionally associated with the male role, and this is subconsciously reinforced as children grow up). There was also strong evidence that females were less inclined to take risks than males (Carlson and Cooper, 1974; Coet and McDermott, 1979; Cvetkovich, 1972; Ebbeson and Haney, 1973; Harper, 1970; Kogan and Dorros, 1978; Moon, 1973; Roberts, 1975; Slovic, 1966; Thomas and Garvin, 1973; Wallach et al., 1962). In particular, research suggested that females were less willing to take extreme risks in

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gambling situations – women preferring gambles with a high probability of some, even low, return and men preferring gambles with a lower probability of some higher return (Coombs and Pruitt, 1960; Kass, 1964). Several studies also identified a number of other behavioural differences between males and females, which may affect the nature of their decisions. Females were found to be more easily persuaded or influenced, irrespective of the risk involved (Baker, 1975; Hovland and Janis, 1959; Worchel and Cooper, 1976). One typical social psychology text of the period (Freedman et al., 1970, p. 332) indicates that ‘there is a considerable amount of evidence that women are generally more persuasible than men’. Research carried out in this period suggested that women were less aggressive (Berkowitz, 1962) and more acquiescent or conforming in group pressure situations (Cohen, 1964; Eagly, 1978; Kretch et al., 1962; Maccoby and Jacklin, 1974). Freedman et al. (1970, p. 239) concludes ‘women conform more than men . . . This difference between men and women has been found in virtually every study in which both sexes participated’. Research also suggested that women had less confidence in their decisions (see, for a review of the literature, Lenney, 1977) and were more conservative than men when unsure of their decisions. Women were, however, more extreme than men when very sure of their decisions (Brim, 1962; Wallach and Kogan, 1959) and they appeared to be better at verbal comprehension, communication, number reasoning and word fluency (Meyer and Bendig, 1961). The majority of research conducted pre-1980 and discussed above was instrumental in developing the accepted view of that period that clear gender differences existed in the nature and quality of decision-making. Pre-1980s research re-examined A closer inspection of the literature of this period reveals, however, that some of the observed differences arose because of the manner in which the research was conducted. Eagly (1978, p. 87) reporting a critique of this research by Block (1976) observes that ‘studies examining sex differences have varied widely in the sensitivity of research designs, quality of sampling procedures, and reliability and validity of measuring instruments’. Several studies have suggested that the relationship between gender and the nature and quality of decisions is more complicated than that indicated earlier. The problem-solving ability of women, for example, improved significantly when the problems set had a ‘feminine’ rather than ‘masculine’ content even when the underlying logic was identical. The feminine version of one problem in these experiments, for example, discussed dieting and the ability to get into a new dress, whereas the masculine version involved the time taken to climb a certain distance at a particular speed, with occasional slips (Milton, 1959). The ability of females to solve problems was also shown to improve when the experimenter was female and when the subjects were given a prior motivational talk by a male (Hoffman and Maier, 1966). Similarly, Priest and Hunsaker (1969)

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found that if women were given more time and/or more detailed instructions, and if distracting stimuli were removed, their problem-solving performance improved significantly more than men. In one set of experiments into group problem solving, women, in mixed-sex groups, performed at least as well as males in all male groups (Maier and Hoffman, 1961). The nature of the problem set has also been shown to have more impact on the results in problem-solving exercises than cultural, ability or motivation differences (Maier and Burke, 1967). Other research of this period has concluded that differences in problemsolving ability are related to identification with a sex role rather than the sex of the individual. Men who identified with the masculine role were better problem solvers than those who identified with the female role and women who identified with the male role were better problem solvers than women who identified with the female role (Milton, 1957). Research by Voelz (1985) has subsequently confirmed these results. In fact, Kelly et al. (1982) reviewing the sex-role literature of this period concluded that individuals whose psychological make-up includes both feminine and masculine socially valued characteristics demonstrate greater flexibility, adaptability and adjustment in their decision-making than individuals with only a single psychological sex role. In relation to influenceability, although there does appear to be some sexinduced difference, Ward et al. (1988, p. 247), reviewing the influenceability literature prior to 1980, conclude that: the relationship is by no means consistent across all conditions . . . it . . . depends on the content of the influence topic (Sistruck and McDavid, 1971), the task to be performed (Nakamura, 1958) and . . . the sex composition of the group-pressure situation (Crano, 1970). . . . The apparently conditional nature of the sex/influenceability relationship has led a number of scholars to question the traditional claim that females differ from males in psychological infiuenceability. A study by Eagly (1978) revealed that 82 per cent of all previously published papers on the topic found no significant difference between male and female influenceability. Contrary to the accepted view, prior to 1980, some studies during this period did not demonstrate that males take greater amounts of risk than females (e.g. Arenson, 1978; Jamieson, 1969; Maurer, 1972; Montgomery and Landers, 1974; Tajfel et al., 1964). The lack of a significant difference in these studies may be because the relationship between an individual’s gender and their risk-taking propensity is related to age. Coet and McDermott (1979), for example, point out that many of the studies showing no significant difference in risk taking were conducted on children before cultural pressure had created any sex-role differences. Research has suggested that risk taking in females is negatively valued and that females who take risks are unpopular – the reverse being true for males (Tuddenham, 1952). Cultural pressures consequently reinforce risk-taking behaviour in males and Slovic (1966) demonstrated that once children had

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adopted their ‘sex-role stereotype’ the expected differences in risk taking did occur. The above discussion suggests that the relationship between an individual’s gender and the quality and nature of his or her decision-making was not as clear cut as the accepted stereotypical view at that time, nor was it as unambiguous as the main thrust of research papers prior to the 1980s suggested. Post-1980 literature Recent research has cast further doubt on earlier conclusions. For instance, Birley (1989) questions whether female entrepreneurs really differ from their male counterparts. She concludes that although there seems to be a general supposition that male and female entrepreneurs differ in their personality traits, there is little empirical evidence to support this. Ashburner (1991, p. 5), reporting research by Nicholson and West (1988) into 2,300 British managers, concluded ‘they emphasised that differences . . . found between men and women bore no relationship to the traditional stereotypes of male and female characteristics’. Welsch and Young (1984, p. 17) in a study of entrepreneurs concluded that ‘the profiles of female and male entrepreneurs are relatively similar’. No significant differences were found in selfesteem, risk attitude, locus of control, flexibility in thinking, ability to manipulate and persuade others or in their openness to innovation. In similar vein, Chaganti (1986) found that women manage businesses in a similar manner to men in terms of the seven ‘S’s: shared values, strategies, structures, systems, staff, skills and styles. The motivation of female entrepreneurs has been shown to be similar to males in terms of their need for independence, money and the identification of business opportunities (Gerritann et al., 1987). Similarly Birley (1989, p. 33) reports that ‘when traditional personality tests are conducted, no significant differences emerge with regard to achievement motivation, autonomy, persistence, aggression, independence, non-conformity, goal-orientation, leadership and locus of control’. Self-confidence seems to be the only differentiator, as males exhibit a significantly higher degree than females. However, Smith et al. (1982) did find differences between male and female entrepreneurs. Females in their study tended towards opportunistic entrepreneurship, while the males were more craft orientated. Recent research appears to cast strong doubt on previous findings concerning the differential quality of decision-making of men and women. Hudgens and Fatkin (1985) reported no significant difference between the scores of males and females involved in a series of decisions taken under conditions of risk. A study by Estes and Hosseini (1988) examining investment decisions showed no significant difference between the quality of investment decisions of males and females. Research conducted since 1980, however, has confirmed earlier findings that males and females differ in terms of their verbal, quantitative and visual-spatial skills (Varro, 1982). A review of the literature undertaken by

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Halpern (1992) concludes that females are better, on average, than males in a variety of verbal skills including word fluency, grammar, spelling, oral comprehension, reading, etc. In terms of quantitative skills, however, Hyde et al. (1990) reported that in the vast majority of previous studies male adults were, on average, found to be superior to females. Lohman (1988) demonstrated that visual-spatial skills (i.e. ability to imagine what an object would look like if rotated or to detect the relationship among objects and shapes) are used extensively by professionals such as architects, chemists, engineers and pilots. Research evidence suggests that males generally perform significantly better on tasks requiring these skills (Linn and Peterson, 1986; Schiff and Oldak, 1990; Smith and McPhee, 1987). Similarly, recent research does appear to confirm earlier findings that women are less confident in their choices (Berry, 1980; Nicholson and West, 1988). Research by Estes and Hosseini (1988) found that women were less confident in their investment choices even though subsequent analysis showed no difference in the quality of male and female investment decisions. Nicholson and West (1988) indicated that this lack of confidence may simply be caused by women’s often insecure positions within organizations. Similarly, Marshall (1984) concluded that women are forced to acquiesce to male norms in order to gain promotion. The clear impression from recent research, therefore, is that differences in confidence and influenceability between males and females may be caused by organizational or social pressures. The majority of recent studies confirm earlier findings concerning the more cautious risk taking of women (Ginsburg and Miller, 1982; Hudgens and Fatkin, 1985; Levin et al., 1988). Some studies, however, demonstrated no significant difference between male and female risk taking (e.g. Noe and McDonald, 1983; Starr and Potashier, 1984). It could be argued that the results of experiments to examine differences in risk-taking propensity between the sexes are dependent on the nature of the decision-making tasks – several of the studies which indicate female risk aversion have used ‘male-orientated’ tasks (for instance, military decisions). Saint-Germain (1989), investigating the actions of legislators in a state senate, rejected the view that female legislators tend only to propose ‘female-oriented’ bills. However, he did find that women proposed fewer bills but were more successful in securing passage for them. He postulated that this may be evidence for risk aversion in females. Levin et al. (1988), however, concluded ‘before over-generalizing this result (females are less risk propensive), researchers should examine the interaction of gender and sex-relatedness of decision-making tasks. Future studies of risk should include female-orientated as well as male-orientated tasks.’ In fact, Chaganti (1986) found that males and females have the same motivations for starting their own businesses – independence, need for money and identification of business opportunities. These might imply the same attitudes to risk. Similarly, females’ access to capital did not differ from that of males, suggesting perhaps, that their business plans were of equal riskiness – or at least are perceived that way by lending institutions (Chaganti, 1986). Masters and Meier (1988) prefaced their study by

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suggesting that women are stereotyped as conservative and risk averse. They suggested that the increasing proportion of female entrepreneurs go against this stereotyping and their results showed no significant differences in the risk-taking attitudes of males and females. The evidence concerning the differences between male and female decision making is, contrary to the earlier literature, far from clear cut. For instance, in one set of experiments (Wood et al., 1985) women performed better than men in group problem-solving tasks which required discussion and consensus, whilst men proved better on problems requiring a number of solutions. This may be because women are more concerned with relationships than men (Hodgson and Watson, 1987; Kanter, 1977a) and select strategies which support relationships, whereas men follow absolute rules (Kohlberg and Kramer, 1969). It has been found (Chaganti, 1986, p. 18), for example, that female entrepreneurs ‘seem to prefer a more “people-orientated” and less autocratic management style, . . . their managerial styles in particular may be more feminine’. Various studies have suggested that men and women have different goals. Women appear to be primarily interested in the method used to accomplish a task, whereas men are more interested in the results (Barnett and Karson, 1989; Sargent, 1981). Eagly (1978) observes (p. 105) ‘males attempt to maximise their winnings, whereas females respond on the basis of the social attributes of the other player’. Perhaps because of this women ‘take more time and trouble to gather information from written sources while utilising other information sources as frequently as men’ (Welsch and Young, 1984, p. 17). It has also been suggested that the clear differences in decision actions and attitudes of men and women which were found in earlier studies have been blurred as a result of the change in cultural norms (Eagly, 1978). It is argued that this, in part, was brought about by the women’s movement ‘which took shape in the 1960’s and 1970’s . . . [and] . . . has had a major influence on societal value systems’ (Masters and Meier, 1988, p. 32). The stereotypes which had been shown to exist were developed and persist because women behaved in these ways in the past. The roles of men and women in Western society have traditionally been different. The nature of these roles is changing as, for example, more women enter full-time and part-time employment. It can be argued that it will take a considerable period in which a different behaviour is observed for more accurate stereotypes to be constructed.

Gender and decision-making: empirical tests The current picture, in terms of differences in the nature of male and female decision-making, appears more complex than earlier research suggested. This confusion may be caused by the current period of transition of Western (Anglo) society, resulting from the changing of cultural norms discussed above. No uniform pattern emerges, for example, in recent studies examining gender differences in decision quality. Some consistent gender differences in the nature of decision-making do emerge, however; adult females appear less risk propensive

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than males, females are often less confident in their choices and males, under certain conditions, are less readily influenced than females. Much of this research has, however, been conducted with subjects drawn from a general population. The results may, therefore, not be directly applicable to certain sub-populations such as actual or potential managers, who may possess characteristics which result in differences in the nature and quality of their decisions. This chapter sets out to contribute to the debate as to whether there are characteristic variations between men and women in the nature and quality of their decisions. Specifically, the research is designed to explore the extent to which gender differences in risk propensity and decision quality vary between a ‘managerial’ and a ‘non-managerial’ sub-population. The chapter aims to identify if formal management education and/or the personality types or behavioural characteristics of those selected as managers or potential managers may serve to eliminate any inferiority which may exist in a particular gender’s decision-making and any gender differences in risk propensity. To achieve this aim, the risk propensity and decision quality of males and females were observed amongst a sample of individuals drawn from a range of socio-economic groups, the majority of whom had not undergone formal management education. These are represented here by decisions taken by bettors within UK betting offices. These were contrasted with decisions taken by a sample of actual and potential managers who had undergone at least three years of formal management education. The role of formal management education in reducing gender differences in decision-making has received very little attention in the literature. Milton (1957), however, observed that differences in problem-solving skills between men and women might be the result of a set of learned behaviours that constitute a culturally defined sex role and (p. 211) ‘if major changes in problem solving performance are to be achieved, the relearning of sex-role would necessarily be accompanied by a period of relearning of problem solving skills’. The important role of formal training and education was confirmed in recent research examining male and female investment decisions (Estes and Hosseini, 1988, p. 577) where ‘familiarity with and present attitude about investing in the stock market, college credit hours in accounting and finance, experience in evaluating common stocks’ were all found to have a significant effect on the individual’s confidence in their investment decision. In addition, some previous research has demonstrated that decision-making, of women in particular, improves significantly as a result of focused education (e.g. Maier, 1933; Priest and Hunsaker, 1969). Empirical study 1: a non-managerial population Methodology The aim of the study was to examine gender differences in risk propensity and decision quality in a ‘non-managerial’ population; defined as a group of individuals who have not undergone formal management education. Laboratory

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experiments were avoided as they may well suffer from certain of the drawbacks of previous sex-difference studies (Block, 1976). To achieve the research objective, it was decided to examine a set of real decisions taken by men and women in a ‘natural’ environment. Hong and Chiu (1988, p. 667) have observed that ‘gambling behaviour is a prevalent social phenomenon across time and societies that provides fresh ground for testing social psychological theories’. Consequently, to satisfy the research aims, a sample of decisions taken in betting offices throughout the UK was analysed. This sample provides a number of distinct advantages (discussed more fully below) including: data relating to real decisions made in a ‘natural’ environment, decisions made by individuals who were unaware that their behaviour was being observed, clear reference points against which the quality of the decisions can be gauged, and the diversity of betting mediums and strategies available enables relative degrees of risk propensity inherent in a decision to be measured. The most important and distinctive feature of the data set is that it comprises real betting decisions, each selected randomly and without the knowledge of the person involved, thereby avoiding any ‘observation’ effects. This was achieved by the betting office staff discretely laying aside the selected betting slips for analysis following close of business. Betting slips form the basic raw material of the assembled database as they provide detailed characteristics of each bet placed, including the level of risk, evidenced by the type of bet, the quality of the decision, evidenced by success or failure of the horse(s) or dog(s) selected, and the level of commitment, evidenced by the size of the investment. The data collected have clear advantages over data derived from laboratory-based simulations and from studies which have involved the presence of researchers (Dickerson, 1979; Shewan and Brown, 1988). In relation to the former type of study, Anderson and Brown (1984, p. 407) note ‘It appears that gambling behaviour . . . differs to a significant degree in the real and the laboratory situations’. The database used in this study was drawn from a random sample of 50 betting offices owned by Ladbrokes. Staff in these shops were instructed to mark discretely all bets placed by females during the period 23–30 April, 1991. Each betting slip is uniquely identified by a time-dependent code number and a systematic random-sampling system was devised to select a sample of the marked female bets. This ensured a reasonable spread of bets in the sample throughout each betting day of the sample period. A similar system was employed to obtain an independent, roughly similar size, sample of male bets placed during this period. The data encompassed the main types of betting media (horse and dog). The data allow rates of return on each individual betting decision to be calculated by reference to the results of the relevant event. Comparison between male and female success rates – both in terms of percentage of correct decisions as well as rates of return – can therefore be made. Gender differences in the propensity to bet on certain types of high/low-risk bets and to bet with higher stakes can also be observed. The objective of this study was to observe the decision-making characteristics of a ‘non-managerial’ population. Research (Target Group Index, 1992) suggests that a large proportion of bettors are non-managers and non-professionals (89.2

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per cent, see Table 12.1). The vast majority of betting office customers are, therefore, unlikely to have received formal management education. Decisions taken in the betting office, therefore, provide a useful contrast to decisions taken by managers and potential managers who have undergone formal management education. Data provided by Target Group Index (see Table 12.1) suggest that bettors span a broad cross-section of income and social groups. The pattern of income received by, and the marital status of, bettors is similar to that for the population at large, but managerial and professional groups are under-represented in the betting population. In summary, the database allows an investigation of differences which might exist in the risk propensity and in the quality of decisions taken by male and female bettors. These individuals represent a subgroup of the ‘non-managerial’ population. It is not suggested that the results can be directly applied to the whole ‘non-managerial’ population. They do, however, at least provide a glimpse of differences in risk propensity and decision quality which exist in a sub-population covering a variety of socio-economic groups who have not undergone formal management education. Results The first set of results outlined in Table 12.2 examines the relative quality of male and female bettors’ decisions. The prevailing view in the pre-1980 literature was Table 12.1 Comparison of betting shop clientele with general population in the UK Betting shop customers (%)

General population (%)

Socioeconomic group Managerial and professional Non-manual Skilled manual Semi- and unskilled Other

10.8 19.8 28.8 24.4 16.2

18.0 24.2 27.0 17.7 13.1

Marital status Single Engaged Married Separated/divorced

21.2 2.1 65.9 10.8

20.8 1.7 64.1 13.4

Income (£’000) £35+ 25–34.99 20–24.99 15–19.99 11–14.99 5–10.99 < 4.99 Not stated

6.0 8.6 9.9 12.1 12.6 19.8 12.9 17.1

6.6 10.1 9.4 12.9 11.3 17.0 12.4 20.3

Source: Target Group Index, British Market Research Bureau, 1992.

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Table 12.2 Indicators of male/female decision quality (betting study)

Return/stake SD Bets with a profita Stakes with a profitb Bets with a returnc Stakes with a returnd

Male (N = 2801)

Female (N = 2894)

0.412 4.61 0.056 0.088 0.104 0.130

0.360 4.63 0.060 0.079 0.132 0.159

z 0.42 –0.67 1.22 –3.27 –3.14

Notes a Number of bets (irrespective of stake size) producing a return greater than the amount staked divided by the total number of bets placed. b Total amount staked which produced a return greater than the amount staked divided by the total amount staked. c Number of bets (irrespective of stake size) producing a positive return divided by the total amount staked. d Total amount staked which produced a positive return divided by the total amount staked.

that women make inferior decisions to men. In this research, quality of decisions was assessed in a number of ways. In general, however, decision quality was broadly defined as the demonstrated ability to use the available information to make the most appropriate choices, given the objectives or ‘rules’ of the exercise. In the betting context, financial gain and the vindication of one’s choices, evidenced by the return of at least some of the original stake, have both been demonstrated to be important objectives (Johnson and Bruce, 1992). In the current study, quality of decision-making is therefore measured by the proportion of bets producing a profit, by the percentage return earned for a given outlay (return/stake), and by the proportion of bets yielding some payout (not necessarily greater than the original stake). The percentage returns earned by males (41.2 per cent) and females (36.0 per cent) in the study are not significantly different (p > 0.33, one tail). Similarly the proportion of male and female bets producing a profit (5.6 per cent and 6.0 per cent, respectively, p > 0.74, one tail) and the proportion of male and female stakes producing a profit (8.8 per cent and 7.9 per cent, respectively, p > 0.11, one tail) do not support the prevailing view of the pre-1980 literature that women make inferior decisions. In fact, there is some evidence to suggest that the opposite may be the case. The proportion of female bets (and stakes) producing some return, even if this was less than the total amount staked (13.2 per cent bets, 15.9 per cent stakes), was greater than for male bets and stakes (10.4 per cent bets, 13.0 per cent stakes). These results are certainly not consistent with superior male decision quality (p > 0.99, one tail, for both comparisons). Consequently, the current study suggests no gender differences in decision quality when quality is measured by the propensity to win. Females, however, are identified as making more decisions which yield some payout. This payout can be less than the original stake, but the selection made is at least partially vindicated, as some of the original investment has been protected. This latter result

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may, of course, be related to differences in male and female bettors’ risk propensity. Table 12.3 summarizes a number of tests undertaken to examine whether such differences exist. The mean average stake per bet of males (£3.81) in the study was significantly greater than that of females (£2.10). Whilst these results may suggest that males are more willing to risk their resources in the hope of some future uncertain gain, the observed differences in mean staking levels may simply reflect the greater earning ability of males. In order to control for differential male and female income levels, the mean stakes for male and females bettors were divided by the average income of male bettors (£16,256) and female bettors (£12,166), respectively, to produce adjusted mean stakes. When controlling for income levels in this manner the mean stake per bet of males (£2.34) was still significantly greater (p < 0.001) than that of females (£1.67). These results are suggestive of more risk-propensive behaviour by males. Apart from deciding the level of stake to commit to a wager, bettors must also decide whether to place ‘win’ or ‘each-way’ bets.1 The betting strategy chosen provides additional insights into risk propensity as each-way bets involve an element of risk hedging. Each-way bets result in the bettor receiving money from the bookmaker (a payout) if the selection finishes first, second or third, whereas win bets only result in a payout if the selection wins. For a given outlay a win bet produces the highest return if the selection finishes first, but will result in no return if the selection does not win. The overall return earned on each-way bets in the study (42.0 per cent) was not significantly different (p > 0.25, two tail) to that earned on win bets (40.3 per cent). There is clearly no incentive for Table 12.3 Indicators of male/female risk propensity (betting study)

‘Win’ betsa ‘Win’stakesb ‘Multiple’ betsc ‘Multiple’ stakesd Mean stakes (£) SD Mean stake (£)/Mean incomee SD

Male (N = 2,801)

Female (N = 2,894)

0.524 0.640 0.199 0.150 3.81 8.60 2.34 5.29

0.459 0.528 0.265 0.252 2.10 3.49 1.67 2.77

z = 4.91* z = 8.62* z = 5.90* z = 9.87* t = 9.79* t = 5.96*

Notes a Number of ‘win’ bets (irrespective of stake size) divided by the total number of ‘win’ and ‘eachway’ bets. b Total amount staked on ‘win’ bets divided by the total amount staked on ‘win’ and ‘each-way’ bets. c Number of ‘multiple’ bets (irrespective of stake size) divided by the total number of bets. d Total amount staked on ‘multiple’ bets divided by the total amount staked on all bets. e Mean stakes of male and female bettors divided by the mean income (£’0000) of male and female bettors respectively (1.6256 and 1.2166). Source: Target Group Index, British Market Research Bureau, 1992, and New Earnings Survey, Department of Employment, 1992. * p < 0.001 (one tail).

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selecting each-way bets in terms of superior returns. This evidence, together with the issues discussed above, suggests that one of the important motivations for choosing to bet each-way is the protection of at least some of the original stake rather than the prospect of earning higher returns. The greater likelihood of each-way bets producing some payout is confirmed by the survey results which indicate that 16.4 per cent of stakes invested in each-way bets produce some payout (not necessarily greater than the original investment) compared with only 12.5 per cent for win bets. The willingness to risk losing the total stake wagered for the prospect of a higher return, evidenced by a win (cf. each-way) betting strategy, may therefore be indicative of a more risk-propensive nature. Results from the survey, outlined in Table 12.3, indicate that women chose to bet each-way significantly more often than men; women placing a significantly higher proportion of their bets each-way and committing a significantly higher proportion of their total stakes to each-way bets than men. These results are at least suggestive of a greater risk propensity for males. The greater willingness of males to take risks is further confirmed when ‘forecast’ betting is examined. This type of bet involves the selection of the winner and runner-up in a particular race. Forecast betting offers a further perspective on risk taking as, having decided to use this bet type, the bettor must choose between accepting a lower or higher level of risk – placing a ‘straight forecast’ (SF) or a ‘reverse forecast’ (RF) bet. In order to obtain a return on a SF bet, the bettor must correctly predict which horse or dog will finish first and which will finish second in a particular race. Returns on RF bets are obtained if the bettor correctly predicts the horses or dogs that will finish first and second, but without having to identify correctly the order in which they will finish. The potential return for a given outlay is higher on a SF bet, but RF bets clearly involve less risk of losing the original stake. Results from the survey indicate that of all male forecast bets (N = 354), 56.8 per cent are straight forecasts, whereas of all female forecast bets (N = 228), only 28.1 per cent are in this bet category. Similarly, whereas 70.3 per cent of the money males stake on forecasts is placed on straight forecasts, only 39.3 percent of the money females stake on forecasts is placed on this riskier bet category. These results confirm a greater willingness of males to risk losing their original stake for the prospect of a higher return (z = 6.79, p < 0.001, one tail; z = 7.52, p < 0.001, one tail; for bets and stakes, respectively). ‘Multiple’ bets require the selection of three or more horses or dogs in different races. In multiple bets, the selections are usually backed individually to win their respective races and in various combinations of ‘accumulators’ which provide a return if all the selected horses win (e.g. ‘doubles’ – where two selections must both win their respective races for a return to be obtained). Multiple bets also usually offer a number of consolation dividends. Consequently, some return is guaranteed for multiple bets if only one of the selections wins (or is placed in the case of ‘each-way multiple’ bets). Multiple bets offer, to some extent, a portfolio approach to betting as the stake is spread over a number of selections. The probability of receiving some return for a given outlay is

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consequently greater for this type of bet, ceteris paribus, than for any other type of bet. The selection of multiple bets may therefore be indicative of an attempt at risk spreading, reducing the chance of losing the whole stake. The survey results indicate a significantly greater proportion of women’s (cf. men’s) bets and stakes on multiple bets (see Table 12.3). These results, taken together with the tendency for males to commit higher stakes, to place more win bets and to select more straight forecast bets are, at least, suggestive of a greater degree of risk taking by males. In summary, the betting study, with the provisos indicated above, provides no evidence to confirm the inferior quality of decisions taken by women noted in much of the earlier literature. In fact, there is some evidence, depending on the definition of success, to suggest that the opposite may be the case. The betting study does, however, confirm much of the earlier research regarding risk propensity. In this subset of the ‘non-managerial’ population, made up of individuals from a variety of socio-economic groups, most of whom have not undergone formal management education, men appear to risk more of their resources for the prospect of a future uncertain gain than women, and are less inclined to choose risk-hedging strategies. These results, therefore, at least suggest that men in the study are more risk propensive than women. Empirical study 2: a managerial population The betting study results appear to suggest that, at least amongst the specific ‘non-managerial’ population sampled, there are differences in male and female decision-making, particularly in relation to their propensity to accept risk. Yet it may be argued that this difference reflects factors such as access to information, experience, education or personality types. Ladouceur et al. (1985) point to familiarity with a task giving the illusion of control. Thus, as individuals become more familiar with a situation, there is an expectation that their tolerance for risk taking will increase. The second empirical study therefore aims to explore the degree to which gender differences in risk propensity and decision quality exist amongst individuals destined to become managers who have undertaken formal management education. This group will have undergone some form of selection. They will also have chosen to become future business decision takers and they may therefore possess certain personality or behavioural characteristics. Methodology In order to explore the effects of management education, personality/behavioural traits and information availability on gender differences in risk attitudes and decision quality, a final year class of commerce undergraduates was given an assignment which, inter alia, required them to make a risky decision. The vehicle for this was a case study of a large civil engineering contract. Students were required to evaluate the project financially, test the sensitivity of their evaluation to a variety of identified risk sources and decide whether or not to

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recommend the undertaking of the project to the senior management of the contracting organization. The case was so designed that the original deterministic model and the riskadjusted model produced expected returns which were on the margin of acceptability and unacceptability. That is, the project gave a small positive expected net present value at the firm’s opportunity cost of capital when all the identified sources of risk were included. The students had all chosen and been selected for a management degree course and had undergone three years of formal management education, including specific training in financial analysis and the building of financial models. The students, who were generally equally skilled, were given exactly the same information set and were aware of the nature of the task and its mode of assessment. The students all came to financial conclusions of the same order and direction. As the expected net present value was small and positive when all risk sources were included (other than the student’s risk attitude) the student’s decision to accept or reject the project was used to provide an indication of their risk propensity. The more risk-averse students being inclined to recommend that resources not be committed to the project, which offers the prospect of uncertain gains (and losses) even though the expected net present value is positive; the more risk-preferring students being inclined to recommend that the project be accepted. This approach to assessing risk attitude is in keeping with that used in the betting study and is in line with Brochhaus’ (1980) definition of propensity for risk taking: ‘the perceived probability of receiving the rewards associated with success of a proposed situation which is required by an individual before he will subject himself to the consequences associated with failure’. The hypothesis tested was that there would be a significantly different choice made by males and females in accepting or rejecting the project as previous research suggests that females are more risk averse than their male counterparts. The student reports were assessed by three instructors, one male and two female, who were unaware of the students’ gender. All students were informed of the assessment method and were consequently aware of the ‘rules’ governing good and bad performance. The case study formed part of the overall course assessment and there was thus strong motivation to do well. The mark attained was therefore used as a measure of decision quality in this study in order to produce results that could be compared with the betting survey. The attainment of a high mark suggests that a student has demonstrated the ability to assess the information available and to make appropriate choices in the use of these data and in the presentation of their solution. This conforms with the definition of decision quality used in the betting study: the demonstrated ability to use available information to make the most appropriate choices given the objectives or ‘rules’ of the exercise. Apart from a measure of decision quality, the work of the students was graded so that it was possible to test whether students gaining higher marks made different accept/reject decisions from those performing poorly. Students were also given a locus of control questionnaire to test their degree of belief in self-determination. This was used to explore whether the degree of self-determination varied between those accepting or rejecting the project and between males and females. Complete

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data were obtained for 130 students, 84 male and 46 female, both full- and parttime students aged between 20 and 45 years; about 75 per cent were under 25 years of age. Approximately 40 per cent of the participants were practising managers undertaking the course part time, and of these about 40 per cent were female. Results The results provide a contrast with the betting shop study; no significant difference was found in any correlations (see Table 12.4). The first set of results in Table 12.4 indicate that there was no significant difference between the number of male and female students recommending that the project should be accepted (p > 0.50). As discussed earlier, rejection of the project was regarded as an indication of risk aversion and acceptance of the project as an indication of risk preference. The hypothesis that females who have undergone formal management education are less risk propensive than their male counterparts was therefore rejected. The results relating to decision quality indicated in Table 12.4 do not confirm pre-1980 research findings, which suggest a higher level of attainment by males in decision tasks. The mark awarded by instructors was used as a proxy for the student’s decision quality and the average mark awarded to male students (60.61 per cent) was not significantly greater (p > 0.10, one tail) than the average mark awarded to female students (59.12 per cent). There was also no significant difference between the mark awarded to those students who recommended that the project be accepted and those who recommended that it be rejected (p > 0.40, two tail). This suggests that attainment (measured by the mark awarded) is not a biasing factor in the students’ project recommendation decision. The final set of results in Table 12.4 suggests that there is no significant difference between males and females (p > 0.30, two tail) or between those students who recommended that the project be accepted or rejected (p > 0.30, two tail) in terms of their perceived level of self-determination (measured by a locus of control score). These results suggest that males and females who have undergone similar formal management education do not differ in their locus of control. In the current study, both males and females had received similar management education, similar levels of ability and access to information. Under these circumstances, the results suggest that males and females do not differ significantly in their risk propensity, locus of control or in the quality of their decisions. It is possible, of course, that the subjects may have responded differently in a real-life situation, but the results obtained suggest the conclusion that it may be differences in formal management education, knowledge of a subject (or perceived knowledge) or information availability which cause risk attitudes and decision quality to be different in males and females.

Conclusions This chapter has attempted to draw together the disparate literature on decisionmaking and gender. It has highlighted the contradictions in previous research

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Table 12.4 Indicators of risk propensity, decision quality and locus of control (managerial population) Risk propensity: recommendation/rejection of project according to gender – Males recommending the project Females recommending the project Males rejecting the project Females rejecting the project

40 21 44 25

Decision quality: mean (SD) percentage awarded by instructors according to gender – Male Female

60.61 (7.44) 59.13 (6.03)

t = 1.16

Decision quality: mean (SD) percentage awarded by instructors according to the students’ decision – Recommendation of project Rejection of project

59.54 (7.35) 60.57 (6.65)

t = 0.84

χ2 = 0.0087

Locus of control: mean (SD) score according to gender – Male Female

0.428 (0.158) 0.458 (0.192)

t = 0.96

Locus of control: mean (SD) score according to the students’ decision – Recommendation of project Rejection of project

0.422 (0.155) 0.453 (0.184)

t = 1.03

and tried to reconcile some of these. This chapter has then furthered the topic by providing two additional pieces of empirical evidence. An important conclusion of both studies is that males and females do not differ in the quality of their decision-making. This result is in contrast to much of the earlier literature. The betting shop study does, however, reinforce the findings of earlier research which suggests that males who have not undergone formal management education are more risk propensive than females. Of more importance in a management context, the financial modelling study suggests that these differences may be more related to experience, information access, formal management education and managerial personality types than to gender. No significant differences were found in this study in male and female decision quality or attitudes to risk. It should be pointed out, however, that in both studies the conclusions are drawn by simply examining the average performance of groups of male and female decision-makers. There is clearly no implication that an individual male or female can be assumed to be a qualitatively superior or more risk-averse decision-maker. There are a number of factors that could have caused the discrepancy between the decision-making behaviours identified in the two studies, such as average age

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of participants or intellectual ability. Further research will be needed to isolate the precise effect of formal management education and the personality types or behavioural characteristics of those selected to become managers. The current findings, however, suggest that no differences in risk propensity and decision quality exist between males and females in the ‘managerial’ sub-population. These results clearly contradict the commonly held stereotypes identified in previous research, which suggest that males and females differ in their managerial decision-making ability. This study suggests that these stereotypes may have been established by observation of the ‘non-managerial’ population in which formal management education is likely to be minimal. Previous research indicates that women are often excluded from managerial positions of authority and leadership within organizations because of such stereotypes. The current study suggests, however, that both male and female formally educated managers can contribute equally to the organizational decision process.

Acknowledgements The research reported here was made possible by grants from, and the cooperation of, Ladbroke Racing to whom the authors are most grateful.

Note 1 In the majority of races, ‘each-way’ bets produce a return if the selection finishes first, second or third. In races of six or seven runners, however, each-way bets only produce a return if the selection finishes first or second. In certain races of more than 15 runners, each-way bets produce a return if the selection finishes first, second, third or fourth.

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Part IV

The use of information by decision-makers and deviations from rational economic behaviour Introduction The ability of decision-makers to use available information in an appropriate manner when forming their judgements is a vital ingredient in successful decisionmaking. Many laboratory experiments suggest that individuals do not use information effectively; that they employ a range of heuristics when making decisions associated with uncertainty and that these often lead to systematic biases. However, there is significantly less documented evidence of their occurrence in real-life situations. Consequently, the chapters in part IV explore to what extent there is evidence for the existence of deviations from rational economic behaviour in decisions made in a naturalistic environment, in the horserace betting market. Clear examples of violations of rational economic behaviour in a naturalistic environment are provided, including a rarely observed violation of dominance. It is demonstrated that individuals appear to be more effective in using certain types of information (transparent information) more readily than others (opaque information) and that as a result markets which have long been regarded as efficient may in fact be associated with biased prices which can be exploited to make abnormal returns. It is shown that the suppliers to betting markets, bookmakers in particular, seem to be aware of the biased behaviour of bettors and their strategies capitalise on this behaviour. However, it is demonstrated that one of the most widely documented anomalies in betting markets, the favourite– longshot bias, may not stem from the biased behaviour of bettors, but rather from the deliberate pricing policy of bookmakers. An important theme underlying many of the chapters in this part is that the processes and protocols associated with a market, that is the market ecology, can have a significant effect on the behaviour of investors operating in that market. It appears that even small changes in the environment in which decisions are made can have a significant influence on the accuracy of individuals’ judgements. In particular, it is shown that under certain environmental conditions bettors in horserace betting markets can make remarkably accurate judgements.

The observations concerning market ecology and violations of rational economic behaviour are used to develop insights into various aspects of betting markets in general and individual betting behaviour in particular, and these are used to shed light on decision-making in broader contexts. The principle of dominance is an essential feature of decision theory and there is only a very limited literature exploring the violation of dominance; it has in fact rarely been observed outside the laboratory. Chapter 13, however, identifies and documents a widespread systematic violation of dominance in the horserace betting market. The nature and extent of this violation of dominance is discussed and an explanation for this phenomenon is postulated. It is demonstrated that the incidence of this violation varies systematically with the size of the wager and this is used to estimate the consumption value of gambling. This represents the first attempt to calculate the consumption value of gambling by employing bettors’ decisions made in a naturalistic setting. The study was also timely, following the launch and success of the National Lottery. Knowledge of the consumption value of gambling is likely to play an important role in strategic and operational decisions made by the government, betting industry regulators and suppliers of gambling services and products. Chapter 14 explores the extent to which bettors account for information contained in odds and odds movements. Previous research suggests that the combined judgements of investors in wider financial markets effectively discount historical price information in current prices, to the extent that profits cannot be made based on this information. Similar findings have been reported in betting market studies dispersed in time and geographical location. However, the research reported in this chapter demonstrates that by employing an appropriate technique, valuable information can be extracted from odds and odds movements and this can be used to make abnormal returns. The results clearly demonstrate that bettors are effective in using more transparent information, but they do not appear to discount more obscure information associated with closing odds and the movement of pre-closing odds, including their interactions. This is one of a very limited number of studies to demonstrate weak form inefficiency in betting markets and it is argued that this results from the use of an innovative technique for extracting predictor variables from price curves using orthogonal polynomials, which gleans more information from price information than has been achieved previously. The degree to which abnormal returns are achievable employing the approach introduced in this chapter is tested using a variety of techniques, including: (1) exploitation of a betting strategy which maximises the long run rate of growth of wealth, (2) cross-validation and jack-knifing, (3) parametric bootstrapping, and (4) an innovative test to ensure that the profits do not arise by chance or simply from information contained in final odds alone. All these tests point to a betting market where participants do not fully discount price information in final odds, despite numerous previous studies which have suggested the opposite. Chapter 15 reviews the literature on the atypical behaviour of bettors in horseraces which occur later in the betting day. This literature, which is

entirely based on pari-mutuel market or laboratory data, suggests that bettors continue to gamble despite persistent previous losses, as they evaluate outcome information in a biased manner. However, they appear to modify their behaviour in the face of these losses; becoming more risk preferring. Chapter 19 demonstrates that bettors in non-pari-mutuel betting markets also change their behaviour in later races but in a different and more complex manner than that suggested by the pari-mutuel studies. This chapter, by exploring the decisions of individual bettors, allows a more valuable insight into the nature of this phenomenon than can be obtained from pari-mutuel markets. Risk propensity, in terms of odds and stakes selected, is assessed together with two measures of performance, to test bettor rationality. The important contributions of the study include the evidence it provides of biases in behaviour in a naturalistic environment and the demonstration that significant differences exist between the behaviour of off-course horserace bettors and those who bet in pari-mutuel markets. The latter is a particularly important finding, since knowledge of reallife betting behaviour has largely derived from studies conducted in pari-mutuel markets. The origin of the favourite–longshot bias is a topic which has long exercised researchers. Chapter 16 examines whether the bias is caused by the actions of bettors or of bookmakers. A review of the favourite–longshot literature is provided and this demonstrates that the bias is widely reported in markets dispersed in time and place . . . many explanations for the bias focus on the behaviour of bettors, including attributing it to bettors’ propensity to take into account only a fraction of potential losses, or their risk-loving characteristics or to the important role played by their non-monetary motivations. A few papers explain the bias in terms of bookmakers’ pricing policy. They suggest that bookmakers deliberately reduce odds on longshots to minimise their exposure to the potential bets of those with access to privileged information, where a relatively small bet on a longshot could result in a large liability for the bookmaker. The limitations of previous papers in attempting to discover the origins of the bias are outlined; particularly important among these is the fact that they generally investigate the phenomenon in countries where only pari-mutuel markets operate. However, Chapter 16 examines odds in bookmaker and parimutuel markets which operate in parallel in the UK. A variety of procedures are employed to compare the odds in these markets and these clearly demonstrate a significantly greater favourite–longshot bias in the bookmaker market and an almost complete absence of the bias in the pari-mutuel market. The results are taken as important evidence that it is bookmakers’ behaviour which induces the majority of the bias in the UK and not the biased judgements of bettors and a number of behavioural factors associated with bookmakers, in addition to their desire to protect themselves from adverse selection, which might induce the bias. Chapter 17 examines the methodology employed in a study of betting market efficiency which sought to demonstrate that information efficiency is dependent upon a perceived element of information inefficiency in the market

(Vaughan Williams and Paton, 1997). Perceived information inefficiency is defined in this earlier paper as being associated with a ‘marked movement in bookmaker odds’. In this chapter a number of inappropriate methodologies and misleading interpretations associated with Vaughan Williams and Paton (1997) are identified, and it is suggested that these shortcomings are not uncommon in betting market studies. In particular, the use of significant odds movements as a signal of perceived market inefficiency and the difficulty of developing an appropriate means of defining a ‘marked price movement’ is questioned. Second, it is argued that the use of pari-mutuel data relating only to winners of races fails to examine the potential presence of inefficiency signals relating to non-winning horses. Third, it is suggested that shortening of odds and lengthening of odds should be regarded as very different price signals. In addition, Vaughan Williams and Paton (1997) assume that where arbitrage opportunities between the pari-mutuel and bookmaker markets are identified, they could necessarily be exploited by bettors. However, this ignores a number of distinct ecological features of these markets which can inhibit such behaviour. In summary, Chapter 17 highlights the need for studies exploring the manner in which individuals use information in markets to take full account of the unique characteristics of these markets. Without a full appreciation of the market ecology, both in terms of structure and process, the analysis of data drawn from these markets can be misinterpreted. A comparison is made in Chapter 18 of the degree to which the parallel bookmaker and pari-mutuel horserace betting markets are efficient. This was one of the first studies to explore this phenomenon using the set of odds relating to all runners in the UK pari-mutuel market, rather than relying, as many previous papers do, on the odds of winners. The chapter demonstrates that the method used in seminal papers by Gabriel and Marsden (1990, 1991) was flawed, since it failed to exclude horses with very high pari-mutuel odds, which could bias the results. This chapter demonstrates, in contrast to Gabriel and Marsden’s (1990, 1991) earlier analysis, that mean bookmaker odds significantly exceed mean parimutuel odds in low odds ranges, but the reverse is true in high odds ranges. These results demonstrate a clear arbitrage opportunity remains between pari-mutuel and bookmaker markets, which bettors do not exploit. However, it is argued that this sustained cross-market disparity may not result from the inadequate decisionmaking capability of bettors, but may be associated with the institutional features of these markets which limit the opportunities for arbitrage by on-course bettors. The results also appear to demonstrate bookmakers’ sensitivity to developing betting turnover, which they achieve by offering ‘good value’ odds on the more favoured horses. However, their fear of bets from individuals with access to privileged information on longshots, which could severely damage the bookmakers’ returns, appears to lead them to shorten the odds on longshots. This chapter offers an important insight into the market efficiency of UK horserace betting markets and demonstrates that a variety of features associated with the motivations of bookmakers and the processes and structures of the

market are at least as influential in determining patterns of market efficiency as those associated with the ability of bettors to use information appropriately. The results of a number of chapters in part IV suggest that the processes and structures associated with markets may influence the degree and manner with which individuals use information when making investment decisions. Chapter 19 sets out to explore the influence which market ecology (e.g. market form, the market’s processes and protocols, buyer/supplier power) exerts on the subjective judgements of participants in these markets. Specifically, the chapter investigates the role played by market ecology in explaining the differential incidence of the favourite–longshot bias, a well documented phenomenon whereby the odds of favourites tend to underestimate and the odds of longshots tend to overestimate their chances of success. The fundamental ecological differences between the bookmaker and parimutuel beting markets, which operate in parallel in the UK are identified, including the manner in which odds are determined, the buyer-supplier relationship, the supply-side structure, the ability to guarantee a given rate of return, the information environment and the learning opportunities afforded to bettors which help them improve their subjective probability judgements. In addition, a clear distinction is made, in ecological terms, between high and low class races, based largely on the degree to which event-specific information is publicly available on these race types. Data from over 2000 horseraces is used to compare the odds on favourites and longshots in the bookmaker and pari-mutuel markets as a whole and in the sub-markets for high and low class races. The results confirm the hypothesis that a lower incidence of the favourite–longshot bias exists in the pari-mutuel market. This is explained in terms of the ecological distinctions between these two markets. A significantly lower incidence of the bias is observed in high class races in both the pari-mutuel and the bookmaker markets, suggesting that markets with comparatively transparent information provide bettors with more opportunity for sophisticated analysis of each horse’s chance of success. However, differences in the incidence of the bias between high and low class races in the bookmaker and pari-mutuel markets are analysed and the results are taken to imply that the presence of demand-induced bias is largely influenced by the degree of information available to bettors. In addition, the bias observed in bookmaker markets is shown to derive from both demand-induced bias and from the pricing strategies of bookmakers. This chapter represents the first attempt to explain the favourite–longshot bias from a market ecology perspective and the results demonstrate that both market form and market type have a substantial influence on the nature of the bias. Equally, the chapter shows that the bias is influenced by both demand- and supply-side pressures. However, the key contribution of this chapter is that it clearly demonstrates the important role which market ecology can play in market behaviour. Chapter 20 explores the ability of individuals to make accurate probability judgements associated with future events. In particular, the chapter examines

the extent to which bettors accurately assess the probability of horses’ chances of success. The results of previous studies conducted in the laboratory consistently show that individuals’ subjective probability judgements are not well calibrated. However, those studies undertaken in naturalistic settings display a less uniform pattern; some studies demonstrating excellent calibration and others identifying inaccurate probability judgements. The results of these previous studies are used to develop a set of features associated with both decision-makers and their decision environments, which can lead to accurate probability judgements, including: (1) expertise, (2) training and feedback, (3) incentives for accurate judgements, (4) familiarity with the task domain, and (5) assessment of probabilities associated with future events, rather than associated with assessment of the accuracy of memory. It is argued that many of these factors are present in horserace betting markets, leading to the hypothesis that good calibration is likely in these markets, under appropriate ecological conditions. A large sample of bets placed in the UK pari-mutuel betting market is examined and almost perfect calibration is observed. This is attributed to the experience of many racetrack bettors, their incentives for making accurate judgements, their familiarity with the decision domain and the regular unequivocal feedback they receive. In addition a number of features associated with the pari-mutuel betting market are identified as contributing to the bettors’ decision accuracy, including: (1) the existence of a parallel bookmaker market where odds movements, often caused by the betting activity of those who hold privileged information, can be observed, and (2) the lack of alternative suppliers of pari-mutuel odds forces pari-mutuel bettors to focus on the task of accurately assessing the horses’ winning probabilities, rather than being distracted by comparing odds amongst numerous suppliers. In summary, Chapter 20 provides evidence that pari-mutuel bettors make excellent use of relevant information in forming their probability judgements and this is attributed not only to the bettors themselves but also to particular features of the pari-mutuel betting market. The main contributions of the chapters presented in part IV lie in the (1) identification of non-rational economic behaviour observed in a naturalistic environment, (2) demonstration of the importance of market ecology in influencing behaviour of market participants, (3) unearthing of the behavioural and marketbased origins of the favourite–longshot bias, (4) demonstration that the techniques employed in some earlier papers may have led to false conclusions regarding the behaviour of participants in betting markets, and (5) application of a new technique for extracting information from price curves which demonstrates that betting markets may be more inefficient than had previously been thought. Finally, and perhaps most importantly, the research clearly shows, in contrast to much of the evidence which emerges from laboratory experiments, that decision-makers with relevant experience and familiarity with their task domain, under appropriate ecological conditions, can make accurate judgements even in the face of uncertainty and a turbulent information environment.

References Gabriel, P.E. and Marsden, J.R. (1990) ‘An examination of market efficiency in British racetrack betting’, Journal of Political Economy, 98: 874–85. Gabriel, P.E. and Marsden, J.R. (1991) ‘An examination of market efficiency in British racetrack betting: Errata and corrections’, Journal of Political Economy, 99: 657–9. Vaughan Williams, L. and Paton, D. (1997) ‘Does information efficiency require a perception of information inefficiency?’ Applied Economics Letters, 4: 614–17.

13 A violation of dominance and the consumption value of gambling J.E.V. Johnson, R. O’Brien and H. S. Shin

Introduction The principle of dominance is a cornerstone of modern decision theory, both as a normative prescription for rational choice and as a basis for explaining behaviour. Although a few of the generalizations of the expected utility hypothesis allow for violations of dominance,1 the focus of this literature has not been on dominance itself. Even in otherwise comprehensive surveys of the literature (such as Machina, 1982), violations of dominance do not attract much more than a footnote. Moreover, even less is known concerning actual cases of violations of dominance away from the environment of experimental laboratories. In this chapter, we document evidence of a systematic violation of dominance in the horserace betting market in the UK. Our conclusion is made possible by an institutional feature of the tax system in the UK governing gambling. A tax rate of 10 per cent applies to the type of gambling examined in this chapter, but gamblers are given a choice as to when the tax is paid. The tax can either be paid at the time of placing the wager or the gambler can choose to pay the tax on the return from the gamble if it is successful. The terms ‘wager’ and ‘return’ refer, respectively, to the amount of money bet on the horse and the amount payable to the gambler by the bookmaker (before deduction of any tax which is due) as a result of a single bet on an individual horse. It can be shown that the choice to pay tax on the return is strictly dominated by another action in which tax is paid at the time of the wager. That is, whether the horse wins or not, the gambler ends up with a strictly higher level of wealth by following the latter action than with the former action. The difference in end-of-period wealth is of the order of t2, where t is the tax rate. In our sample of 25,000 individual bets placed (on which more later), more than 18 per cent of bets were placed by gamblers who chose to pay tax on the return. This apparent and widespread violation of dominance is in need of explanation. In attempting to explain this apparent anomaly in the behaviour of the gamblers in our sample, we explore the hypothesis that there is a consumption value of gambling which varies with the amount wagered, and that gamblers may countenance lower levels of wealth provided that they are compensated by a greater consumption value of gambling in the process. Furthermore, by utilizing

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the systematic variation in the behaviour of gamblers at different levels of the wager, we attempt to estimate the consumption value of gambling as a function of the size of the wager and show how this function may be approximated by means of the coefficients obtained in a probit analysis of the tax decision of the gambler. Our analysis reveals that the consumption value of gambling is increasing in the amount of the wager, but it varies in a complex and rather subtle way. We are also able to consider two alternative hypotheses for the observed violation of dominance, both of which appeal to irrationality of the gamblers in some form, and are able to reject both of them. The first of these is that some gamblers are simply irrational and that their bets figure randomly in the population of bets. We are able to reject this hypothesis by demonstrating that the incidence of the violation of dominance depends systematically on the size of the betting outlay. A second, more sophisticated alternative hypothesis is that irrational gamblers figure more prominently among gamblers who wager a smaller amount, and rests on the premise that smaller stakes are more likely to come from occasional and novice gamblers who do not understand the full consequences of the choices available. Thus, the hypothesis is that the incidence of the violation of dominance is decreasing with the size of the outlay. However, the data reveal a non-monotonic relationship between the violation of dominance and the size of the wager. Indeed, for the range of wagers which forms the vast majority of all observations (i.e. bets below £50), there is a strong positive relationship between the incidence of violation of dominance and the size of the outlay. Thus, at the very least, we are able to reject the two simplest alternative explanations of the violation of dominance. We regard our investigation as being timely, especially with the launch of the National Lottery game in the UK in 1994 and the unexpected success it has had in attracting players. This success seems particularly significant, given the low payout rate of the National Lottery game (currently 50 per cent). Spending on the lottery is estimated to be around £450 million per month, which is the equivalent of 3.4 per cent of all retail sales in the UK (The Economist, 1995). Given the importance of such games for the raising of revenue for the government, and the crowding out of other games and charitable giving, the estimation of the consumption value of gambling would seem to be of importance not only for intellectual curiosity but also for the formulation of government policy. The chapter is organized as follows. We start in the next section with a brief description of the institutional arrangements behind the UK horserace betting market and demonstrate that the decision to defer tax until the end of the race violates the dominance principle in terms of terminal wealth levels. We then postulate the existence of a component of utility which represents the consumption value of gambling, and show how this component may be constructed from observable variables. Having thus set the stage, we turn to our empirical task, and start by describing our dataset of 25,000 individual bets, and discuss some summary statistics. The probit analysis of the individual’s tax decision is then presented, from which we can offer our estimate of the consumption value of gambling. Let us begin with our demonstration of the violation of dominance.

A violation of dominance and gambling 231

A violation of dominance The market for bets in the UK on the outcome of horseraces is large and easily accessible. It is an important feature of the UK market that betting takes place not only at the race track, but also at nearly 10,000 of the so-called ‘off-course’ betting shops dotted throughout the country. The total amount wagered in a year at the off-course betting shops is in excess of £4 billion sterling,2 and over 90 per cent of all turnover on horserace betting is through the off-course betting shops. Gambling at betting shops is subject to a tax, but the gambler has a choice as to how this tax is paid. There are two options. Either the tax is paid at the time of placing the wager or it can be postponed until the result of the race is known. Then, if the gamble is successful and there is a positive return, the tax can be paid on this return. If the gambler loses, then no tax is paid under this second course of action. We will refer to the first action as paying tax on the wager, and refer to the second action as paying tax on the return. The term ‘return’ refers to the sum of the stake and the net winning from the successful gamble. However, there is a difference in the way in which the tax is calculated. When a gambler pays tax on the wager, the tax is calculated in gross terms. Thus, someone who bets £y incurs total expenditure of £(1 + t)y, where t is the tax rate. In contrast, when a gambler pays tax on the return, the tax rate is calculated in net terms. Thus, someone who stands to win £x in the absence of tax receives £(1 – t)x with the imposition of the tax. Crucially, the same tax rate of 10 per cent applies to both actions. Thus, if tax is paid on the wager, there is a tax of 10 per cent in gross terms, while, if tax is paid on the return, there is a tax of 10 per cent in net terms. To emphasize this distinction between gross and net tax rates, consider the case of 100 per cent taxation. Income tax is measured in net terms. Thus, if there is a 100 per cent income tax, every pound is taxed away, and I am left with zero income, and hence zero consumption. However, sales tax or VAT is measured in gross terms. When there is an expenditure tax of 100 per cent, this does not mean that my consumption is zero. Rather, it means that I can only consume half of what I used to before tax. So, for a fixed expenditure pattern, a 100 per cent expenditure tax is equivalent to a 50 per cent income tax. This point is worth emphasizing. Consider the budget constraint of a consumer who has income m and faces prices (p1, p2, . . ., pN). Denoting by xi the consumption of the ith good, the budget constraint in the absence of any tax is given by p1x1 + p2x2 + . . . + pNxN = m When income is taxed at the (net) rate of t, the budget constraint becomes p1x1 + p2x2 + . . . + pNxN = (1 – t)m

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However, if expenditure is taxed at the (gross) rate of t’, then the budget constraint becomes (1 + t')(p1x1 + p2x2 + . . . + pNxN ) = m Clearly, these two budget constraints are equivalent if and only if

1 + t′ =

1 1− t

In other words, a net tax rate of t is equivalent to a gross tax rate of t’ if and only if 1 + t’ = 1/(1 – t). In general, for a net tax rate of t to be equivalent to a gross tax rate of t’, we must have t' > t However, this is not the case for taxes on bets. The same tax rate of 10 per cent is applied. Thus, the gamblers are facing a lower effective tax when they pay tax on the wager than when they pay tax on the return. To spell this out, consider a gambler who wishes to wager £y on a horse whose odds of winning are k to m (normalized to b to 1, where b = k/m). The terminal payoffs resulting from the two alternative methods of paying tax are as follows. If the gambler chooses to pay tax on the wager, the initial outlay is (1 + t)y, of which ty is taxed away, and y is the size of the wager which is forwarded to the bookmaker. If the horse wins, the gambler receives a return of (b + 1)y

(1)

If the horse loses, then the gambler loses the initial outlay of (1 + t)y. In contrast, if the gambler wagers £x and chooses to pay tax on the return, then whereas the initial wager is not taxed, the return in the event that one’s horse wins is taxed at the same rate of tax t. Thus, the net return when the bet is successful is given by (1 – t)(b + 1)x

(2)

Exploiting the lower effective tax rate on paying tax on the wager, we can show that choosing to pay tax on the return is strictly dominated by an action in which tax is paid on the wager. Proposition 1.1 Suppose x > 0 is the stake of a gambler who chooses to pay tax on the return. Then, for any number y in the non-empty open interval x    (1 − t ) x,  1 + t 

(3)

A violation of dominance and gambling 233 If the gambler wagers y and chooses to pay tax on the wager, then irrespective of whether the horse wins or loses, the end-of-period wealth is strictly greater under the second action than under the first. In other words, choosing to pay tax on the return is strictly dominated by another action in which tax is paid on the wager. Let us prove this proposition. To see that the open interval is non-empty, it suffices to note that 1 – t2 < 1, from which it follows that 1 – t < 1/(1 + t). In considering the payoffs, it is helpful to use notation suggested by statecontingent claims and Arrow-Debreu securities. For a horse running in a race, let us denote π the price of a claim which pays £1 if this horse wins but which pays nothing otherwise. In this sense, π is the ‘price’ of this particular horse. This price corresponds to betting odds in the usual way. A horse with odds of b to 1 has the price 1/(1 + b). Denote by w the initial wealth of the gambler. Consider the act of wagering £x on a horse with a price π, and choosing to pay tax on the return. The end-of-period wealth then has two possible values, depending on whether the horse wins or not. They are: Win w − x + (1 − t ) x π Lose w – x Now, consider the act of wagering £y on the same horse, but choosing to pay tax on the wager. Again, the end-of-period wealth has two possible values, depending on whether the horse wins or loses. They are: Win w − (1 + t ) y +

y π

Lose w – (1 + t)y We show that if y lies between (1 – t)x and x/(1 + t), then the end-of-period wealth is strictly higher for the second action, whether the horse wins or loses. First, start with the fact that y > (1 – t)x.

(4)

Subtracting π(1 + t)y from both sides, and noting that y < x/(1 + t), y − π(1+t) y > (1− t)x − π(1+ t)y > (1 − t ) x − π x

Dividing by π and adding w to both sides gives:

w − (1 + t ) y +

y (1 − t ) x > w− x+ π π

(5)

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so that the end-of-period wealth when the horse wins is larger under the second action. Now, let us consider the case in which the horse loses. From y < x/(1 + t), multiplying both sides by – (1 + t) and adding w to both sides yields: w – (1 + t)y > w – x,

(6)

so that the end-of-period wealth is higher even when the horse loses when tax is paid on the wager.

Consumption value of gambling In attempting to explain the apparent anomaly in the behaviour of the gamblers in our sample, we will explore the hypothesis that the expected monetary payoff to the bet is only one component of the utility derived from gambling. In particular, we will suppose that there is a consumption value to gambling, where this value depends on the amount wagered. We will posit the existence of a function

ψ (.)

(7)

such that ψ (y) is the consumption value (measured in pounds) of wagering £y. The ‘ψ ’ stands for ‘psychological value’. The consumption value of gambling, as used here, is taken to include all aspects of utility derived from gambling which depend on the amount wagered, other than the expected monetary payoff to the bet. These might include, for example, the excitement associated with committing a larger stake, or the opportunity to increase one’s esteem among fellow gamblers, through association with larger stake betting. The aim of this chapter is not to identify the contribution of these individual components but to explore the overall consumption value of gambling. For any given outlay of x, if the gambler decides to pay tax on the return, all this amount can be wagered. However, if the gambler decides to pay tax on the wager itself, the size of the wager must be scaled down to x/(1 + t) in order that the total outlay is equal to x. Thus, although the choice to pay tax on the return is dominated in terms of final-period wealth, the consumption value of the gamble may well be larger if tax is not paid on the wager. If such an element is present in the decision of the gambler, we may hope to explain the gambler’s choice to pay tax on the return as a rational decision.3 We will conduct our analysis by defining two expressions for utility, depending on whether tax is paid on the return or the wager. First, we denote by U(x,t)

(8)

the utility of a gambler who wagers £x on a horse and chooses to pay the proportional tax of t on the return. U(x,t) is given by

~ ) + ψ (x) + u u(x,t) = E(w 1

(9)

A violation of dominance and gambling 235 ~ 1) is the expected end-of-period wealth given this act, ψ (x) is the where E(w consumption value of the wager, and u– is a constant, capturing any element of utility which follows from the act, but which does not depend on the size of the wager. Analogously, we denote by V(x,t) the utility of a gambler who incurs a total outlay of £x on a wager on the same horse but who chooses to pay tax on the wager. The actual size of the wager in this case for a total outlay of x is given by x/(1 + t). We define V(x,t) as the sum of three terms given by:

~ ) +ψ  x  + v V ( x, t ) = E ( w 2    1+ t 

(10)

~ 2) is the expected wealth from this act, ψ [x/(1 + t)] is the consumption value E(w - and of the wager x/(1 + t), and the constant v- is a dummy variable analogous to u, captures any element of the utility arising from the second act which does not depend on the size of the wager. Both equations (9) and (10) assume that the three components of utility are separable. While it is conceivable that this may not be the case, the model as specified retains intuitive appeal. It seems likely that u– and –v, which do not depend on the size of the wager, are considered distinct from those aspects of utility which do depend on wager size. Second, it is argued that considerations of end-of-period expected wealth are unlikely to impact on the consumption value of gambling, which includes elements such as peer esteem or excitement engendered by the act of risking larger stakes. If we denote by π the price on the horse, and by p the subjective probability that this horse will win, then the expected end-of-period wealth for the first act, ~ 1) is given by the weighted sum E(w (1 − t ) x   p w − x + + (1 − p )[ w − x] π  

(11)

Similarly,

 x  (12) E ( w% 2 ) = p  w − x + + (1 − p )[ w − x] (1 + t )π   Thus, taking the difference between the utility of the second act from the first, we have the following equation which expresses the utility advantage of paying tax on the wager for a given outlay x:

V ( x, t ) − U ( x, t ) =

x  p t2x  ⋅ − ψ ( x ) − ψ   + (v˜ − u˜ )   π 1+ t 1 + t 

(13)

This equation expresses the trade-off involved between the two actions. The first term (which is positive) represents the greater expected end-of-period wealth if the gambler pays tax on the wager. The second term is the difference in the consumption value of gambling between the two actions. If ψ is increasing, this second term will be negative, reflecting the larger effective

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wager of deferring tax until the end of the race. The last term is a constant, reflecting any difference in utility unaccounted for by expected wealth and the consumption value of gambling. Equation (13) implicitly assumes that the gambler is risk neutral as far as terminal wealth is concerned. It might be argued that subsequent estimates of the consumption value of gambling will necessarily be positive. This view might arise since odds available are almost always unfair to the gambler, and it may be assumed that this implies that the ‘rational’ gambler must love gambling for its own sake. However, there is considerable evidence to suggest that gamblers consistently overestimate their probability of winning, even in the face of clear objective evidence to the contrary (e.g. Gilovich, 1983). Research by Wagenaar (1988) clearly demonstrates that gamblers, while generally aware of the negative long-term effect of gambling on their wealth, fail to apply these statistical considerations to their ‘next bet’. He refers to this tendency for gamblers to isolate their next bet from the larger set of previous bets of which they have knowledge as ‘epistemic reasoning’. In the light of this evidence that a collective illusion persists, it appears that gamblers, when accounting for their subjective probability of success, may be risk neutral as far as terminal wealth is concerned. Consequently, the consumption value of gambling may contain no element derived from the gamblers’ risk preference. The case for constructing a more complex model involving a non-risk-neutrality assumption is certainly not clear-cut and, consequently, we proceed to construct the function ψ employing equation (13).

Constructing the function ψ The main objective of this chapter is to make inferences concerning the function ψ , and, if possible, to sketch its form from the data. In an ideal world in which we have information concerning the identity of the gambler as well as some of his or her personal circumstances, it would be possible to conduct a much more thoroughgoing empirical analysis, including the decision on how much expenditure should be incurred in betting. On the other hand, as we describe below, our data set does have the advantage that it pertains to actions of decision-makers in their own, everyday environment. This may be important in a study of gambling behaviour, as there is evidence that behaviour under laboratory conditions differs significantly from that outside the laboratory (Anderson and Brown, 1984). Nevertheless, it is a limitation of our data in that we do not have information concerning the identity of the gambler, or any of his or her personal characteristics. This limitation precludes the testing of a full optimizing model of the gamblers’ decisions, including the determination of the outlay x. The information provided by our data is the total outlay, the date and time of the wager and whether tax was paid on the wager.4 In the absence of an account of how the total outlay is determined, our approach is to take the total outlay as being exogenous to the model, and to investigate the (binary) tax decision conditional on the total outlay. Clearly, by leaving the determination of the outlay outside

A violation of dominance and gambling 237 the model, we cannot test the hypothesis that the observed associations in the data are due to underlying unobserved characteristics of the gamblers. While this is a possibility, we are able to consider two alternative hypotheses of the violation of dominance based on the incidence of irrational gamblers, and are able to reject both. Our own hypothesis is examined by means of a probit analysis of the tax decision, in which the dependent variable is the binary variable which takes the value 1 if the gambler pays tax on the wager, and 0 if the gambler does not (and instead pays tax on the return). On the right-hand side, we will include a constant term as our estimate of –v – –u, and will include a polynomial in the size of the outlay x as our approximation for the first two terms in equation (13). This will give us an estimate of the difference in utilities V(x,t) – U(x,t) as a polynomial in x for a given value of the ratio p/π That is, k

V ( x, t ) − U ( x, t ) = a0 + ∑ ai x i

(14)

i =1

By equating expressions (13) and (14), the constant terms a0 and –v – –u can be identified and eliminated, leaving us with the following equation, expressing the trade-off between expected wealth and the consumption value of gambling:

p t2x   x  k i ⋅ − ψ ( x) − ψ    = ∑ ai x π 1+ t   1 + t   i =1

(15)

Dividing both sides by tx/(1 + t) (which is equal to x – x/(1 + t)), and rearranging terms, we have

 x  ψ ( x) − ψ   pt 1+ t k  1+ t  ai xi −1 = − ∑ x t π i =1 x− 1+ t

(16)

This is the fundamental equation of this chapter, and is the focus of our empirical investigation. The left-hand side of the equation is an expression for the approximate slope of the function ψ at the point x, so that once we have our estimates of the coefficients {a1, a2, . . ., ak}, we can sketch the rate of change of the function ψ to changes in the size of the wager. We will plot equation (16) as a function of x and check whether this expression is positive for all values of x. If so, we may conclude that the consumption value of gambling is increasing in the size of the wager. This would seem to be a reasonable conjecture, and indeed, our results reported below bear this out. Finally, by treating equation (16) as an approximation for the derivative of ψ at x, we can integrate the expression on the right-hand side of equation (16) over the interval [0, x] to obtain an approximation of the value of ψ at x. Our estimate of

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the coefficients {a1, a2, . . ., ak} will allow us to plot this approximation of ψ , and thereby provide some concrete numerical estimates of the consumption value of gambling.

The data and summary statistics The data used for our empirical investigation draws on a survey commissioned by the bookmaking firm Ladbroke Racing Ltd, of 100,882 individual ‘betting slips’ issued at its off-course betting shops. Ladbrokes operates the largest chain of betting shops in the UK, and has around 25 per cent of the market share of bets placed off-course. Our sample of betting slips was collected by the employees of Ladbrokes at 1,690 of its betting offices spread throughout mainland UK, and any possible sampling bias was controlled for by using a sampling procedure operating on the serial numbers of betting slips. The sample was collected during the three-month period from 3 July 1991 to 1 October 1991. The gamblers were not aware that such sampling was taking place, and as such, our data could be regarded as being free from the possible effects of the subjects acting self-consciously. Anderson and Brown (1984) note that ‘gambling behaviour . . . differs to a significant degree in the real and laboratory situations’ (p. 407). Each of the 100,882 betting slips represents an individual wager, but not all these are bets on horseraces. The sample includes bets on a variety of sports (such as snooker or football). Bets on horseracing account for 77.3 per cent of the total bets, and 80.7 per cent of the total stake. Of the bets on horseraces, many are exotic bets which depend on the conjunction and/or disjunction of several events. However, ‘win-singles’ bets represent a substantial proportion of the bets, and this type of bet corresponds to the account presented above. These are the bets in which an amount is wagered on a single horse, and the gambler wins if and only if this horse wins the race. After eliminating bets with incomplete records, we ended up with a sample of 25,081 win-singles bets. This is the sample used in the probit analysis to be presented in the next section. Table 13.1 and Figure 13.1 present some summary statistics of our sample. The term ‘outlay’ refers to the initial expenditure of the gambler. If tax is paid on the wager, then the outlay includes the tax. If the tax is paid on the return, then the outlay is identical to the amount of the wager. Conditional on tax being paid on the wager, the average outlay was £6.61, while conditional on the tax being paid on the return, the average outlay was £8.78. Thus, the average outlay is greater for the payoff-dominated action. In our sample, 18.3 per cent were bets in which the tax was paid on the return (i.e. where a violation of dominance occurred). Table 13.1 and Figure 13.1 illustrate some apparently interesting variations in the incidence of the violation of dominance, particularly for bets of £50 or less (which represent about 98.6 per cent of the sample). For example, a violation of dominance occurred in 36.3 per cent of bets involving outlays of up to £1, in only

A violation of dominance and gambling 239 Table 13.1 Tax paid on the wager or the return by size of outlay Outlay (£)

Tax paid on return 0–0.50 0.51–1.00 1.01–3.00 3.01–5.00 5.01–10.00 10.01–15.00 15.01–20.00 20.01–50.00 50.01–100.00 100.01–200.00 200.01–300.00 300.01–400.00 400.01–500.00 500.01–600.00 600.01–700.00 700.01a+ Totals

%

Number of bets

487 646 1,051 985 708 91 314 244 51 9 1 4 1 1 1 0 4,594 18.83%

Tax paid on wager

All bets

605 1,391 9,150 1,837 3,670 2,024 170 1,304 221 92 15 3 1 1 2 1 20,487 81.7%

1,092 2,037 10,201 2,822 4,378 2,115 484 1,548 272 101 16 7 2 2 3 1 25,081

4.4 8.1 40.7 11.3 17.5 8.4 1.9 6.2 1.1 0.4 0.1 0.0 0.0 0.0 0.0 0.0

Note a Maximum outlay on an individual bet recorded in the sample: £770 (including tax paid on the wager).

10.3 per cent of bets with outlays between £1.01 and £3, in 23.5 per cent of bets between £3.01 and £10, in only 4.3 per cent of bets between £10.01 and £15, in 63.9 per cent of bets between £15.01 and £20, and in 25.8 per cent of bets between £20.01 and £50. While it is tempting to speculate on the reasons for these variations, caution must be exercised since the manner in which the categories are drawn is likely to affect the incidence of the violation of dominance. The data clearly show that wagers of a certain size are particularly popular (e.g. £1, £5, £10 and so on). Consequently, all wagers of, for example, £1, where tax is not paid on the wager, will appear in the outlay category of £0.50 to £1.00, where, partly as a consequence, the incidence of the violation of dominance is relatively high at 31.7 per cent. For wagers of £1, where tax is paid on the wager, these bets will appear in outlay category £1.01 to £3.00, where the incidence of the violation of dominance is, partly as a consequence, relatively low (10.3 per cent). In fact, if outlay categories are combined, the incidence of the violation of dominance appears to increase as the outlay size increases up to £50 (then £0.00–£3.00: 16.3 per cent, £3.01–£15.00: 19.2 per cent, £15.01–£50.00: 27.5 per cent). By modelling the binary tax decision in terms of the size of the total outlay via a probit analysis, difficulties of interpretation associated with outlay category boundaries can be avoided. We now turn to this probit analysis.

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100

Tax paid on wager (% bets)

90 80 70 60 50 40 30 20 10

100.01+

50.01−100

20.01−50

Outlay category (£)

15.01−20

10.01−15

5.01−10

3.01−5

1.01−3

0.51−1

0−0.5

0

Figure 13.1 Percentage of bets with tax paid on wager.

The probit estimation and alternative hypotheses The starting point of our probit analysis is the expression for the utility advantage of paying tax on the wager, given by V(x,t) – U(x,t). We shall represent this difference by means of a polynomial k

∑a x n =0

n

n

in the size of the outlay x, plus a random error term. In particular, this utility advantage of paying tax on the wager for a given outlay of xs is a random variable: k

Z s* = ∑ an xsn − ε s

(17)

n =0

where εs is a standard normal random variable. When the realization of Z*s is positive, the gambler pays tax on the wager, while if the realization of Z*s is negative, the gambler pays tax on the return. The probability of the former is given by the cumulative normal distribution evaluated at the point k

∑a x n =0

n n s

A violation of dominance and gambling 241 The probit estimates of the coefficients {an} are obtained as those values which maximize the likelihood function under the assumption of independence across bets. We report the results of our probit estimation in Table 13.2, obtained using the maximum likelihood facilities in LIMDEP. The sample size is 25,081, consisting of the simple win-singles bets described in the previous section. While the model is highly significant, the figures shown at the foot of Table 3.2 indicate that the model ‘predicts’ that very few bets will not include tax paid at the time of placing the wager. This does not suggest that the model is a poor one, since ‘predicts not paying tax on the wager’ means ‘assigns a probability of less than 0.5 of paying tax on the wager’. Consequently, given that the unconditional probability of not paying tax at the time of placing the wager is estimated directly from the data as 4594/25081 = 0.18, we would expect 18 non-tax-paying wagers in a sample of 100 wagers, but would unconditionally predict zero, as the probability of 0.18 is less than 0.5. Thus, with relatively improbable events, such as the probability of not paying tax at the time of placing the wager, the term ‘predict’ must be interpreted with caution. In the resulting model, indicated in Table 13.2, all the terms in the polynomial of degree five are significant at the 1 per cent level. Polynomials of degree greater than five were tried, but they introduced insignificant terms, and did not improve upon the 5th-degree polynomials in terms of explanatory power. However, in order to test the sensitivity of the estimates of the consumption value of gambling which are derived from this model, alternative polynomials in

Table 13.2 Results of probit estimationa Variable

Coefficient

Standard error

t-ratio

Constant Outlay Outlay2 Outlay3 Outlay4 Outlay5

1.0041 –0.20738E-1 0.28875E-3 –0.12538E-5 0.20417E-8 –0.11126E-11

0.1268E-1 0.1883E-2 0.3660E-4 0.1943E-6 0.3758E-9 0.2383E-12

79.19 –11.01 7.89 –6.45 5.43 –4.67

Notes a The dependent variable takes the value 1 if tax is paid on the wager and takes the value 0 if tax is paid on the return. Number of observations Zj = 0:4594 Zj = 1:20487. Log likelihood –11,869.89. Log likelihood ratio test (5 degrees of freedom) 145.43 [χ2 (0.01) = 15.09] Predicted Actual Zj 0 1 Total 0 6 4588 4594 1 2 20485 20487 Total 8 25073 25081

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degrees four and six were tried. The difference in subsequent estimates of the consumption value of gambling averaged only 6.5 per cent, with a maximum difference of 13 per cent. This suggests that estimates of the consumption value of gambling are relatively insensitive to varying the degree of the polynomial in the model. Figure 13.2 depicts the change in the probability of paying tax on the wager as the size of the wager varies. Figure 13.2(a) shows this for the whole sample, while 13.2(b) shows the probabilities for bets in the range from zero to £200. Figure 13.2(b) is the more interesting, since it focuses on smaller bets, which make up the majority of the sample. A particularly noteworthy feature is that for bets lower than £50, the probability of violation of dominance is actually increasing in the outlay. This result confirms our view that the apparent nonmonotonic variations in the incidence of the violation of dominance for bets up to £50, shown in Figure 13.1, may be more a feature of the outlay category boundaries than due to variations in behaviour. The increasing incidence of the violation of dominance as outlays increase (up to £50) is a significant finding in the light of our alternative hypothesis that observed violations of dominance can be attributed to occasional and novice gamblers, and that they are more likely to wager smaller amounts.5 If this alternative view were correct, we would expect the incidence of the violation of dominance to decrease with the outlay (and probability of paying tax on the wager to increase). This hypothesis is contradicted by the data. At the very least, this suggests that any alternative hypothesis for the violation of dominance must appeal to more subtle effects underlying the data. Figure 13.2(a) suggests that the incidence of the violation of dominance for bets in the range from £0 to £800 is non-monotonic. However, it should be borne in mind that we have very few observations of outlay larger than £200, so that the large fluctuations in the curve beyond £200 may be rather misleading. In addition, the analysis makes assumptions of normality and functional form to which Figure 13.2(a) will be sensitive. To investigate the degree of this sensitivity, we can estimate the probability of paying tax as a function of the wager non-parametrically. The probability that tax is paid (t = 1) at the time of the wager conditional on a particular outlay x is given by: p (t = 1| x ) = =

p (t = 1, x) p( x) p (x | t = 1) p (t = 1) p (x | t = 1) p (t = 1) + p (x | t = 0 ) p (t = 0)

We can estimate the marginal probabilities p(t = 1) and p(t = 0) directly from the data, and can use a variety of techniques for estimating density from frequencies to estimate p(xt = 1) and p(xt = 0). Silverman (1986) provides a review of these techniques and we employ the most popular, the kernel density estimator with Gaussian kernel, applied to the natural logarithm of

Probability of paying tax on wager

1 (a)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

100

200

300

400 500 Outlay (x)

600

100 Outlay (x)

150

700

800

0.95 Probability of paying tax on wager

(b) 0.9

0.85

0.8

0.75

Probability of paying tax on wager

0.7

0

50

200

0.9 (c)

0.8

0.7

0.6

0

100

200

300 400 500 Outlay (x)

600

700

800

Figure 13.2 Probability of paying tax on the wager for a given outlay (a)  £800; (b)  £200; (c)  £800 (derived using kernel estimators).

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wagers. The transformation is required to marry the kernel with the heavy skew in the wager distribution. The window width h which Silverman suggests in his equation (3.28) is too narrow for satisfactory estimates. The wager data is lumpy, with values such as £1, £2, £5 and £10 and their taxed equivalents providing a disproportionate fraction of the data, which contains only 224 distinct values in the 25,081 observations. To obtain reasonably smooth estimates of p(xt = 1) and p(xt = 0), we used a value of h four times larger than Silverman suggests. The resulting estimates of the probability that tax is paid at the time of placing a wager, given an outlay of a particular size are shown in Figure 13.2(c). Comparing the non-parametric estimates with the probit-based estimates displayed in Figure 13.2(a), we see in both a dip in the probability as outlays increase to around £50 (0.77 in Figure 13.2c and 0.72 in 13a), a similar maximum at an outlay of around £200 (0.89 in Figure 13.2a and 0.83 in 13.2c) and a subsequent decline as outlays increase to £500. However, the non-parametric estimates continue to decline beyond this point, while the probit-based estimates exhibit another local maximum. The difficulty in making further use of the non-parametric estimates is that an assumption of functional form is required to move from the probability of paying the tax to the difference in utilities in equation (14). Without some assumption linking utility and probability, we cannot proceed in the opposite direction. The non-parametric estimates clearly suggest that caution must be exercised in employing the probit-based estimates for outlays beyond £200. However, for outlays less than this, the probit-based results are broadly consistent with non-parametric results, and so we persist with the probit models. Consequently, we proceed to construct the function ψ. From our estimates of the coefficients {a1, a2, . . ., a5}, we have enough information to sketch the expression in equation (16) giving the approximate slope of the function ψ. Thus, we have: x  ψ ( x) − ψ   1 + x  pt 1 + t [ −0.0207 + 0.289 E − 3 * x − 0.125E − 5 * x 2 = − x π t x− 1+ t + 0.204 E − 8 * x 3 − 0.111E − 11 * x 4 ]

(18)

Figure 13.3 presents a sketch of this expression for the tax rate of 10 per cent when p/π is equal to 1. It can be seen that the estimated value of this expression is positive for the range of wagers in our sample. Thus, we conclude that the consumption value of gambling is increasing in the size of the wager in our case. By integrating the right-hand side of equation (18) we obtain an approximation of the function ψ itself. It is given by:

A violation of dominance and gambling 245 0.4 Slope of Ψ

0.2

0

0

100

200

300

400 500 Outlay (x)

600

700

800

Figure 13.3 Slope of ψ when t = 0.1 and p/π = 1.

ψ ( x) =

1+ t pt [−0.0207 * x + 0.144 E − 3* x 2 − 0.418 E − 6* x 3 x− π t + 0.510 E − 9* x 4 − 0.222 E − 12* x 5 ]

(19)

Figures 13.4(a) and 13.4(b) sketch this function when p/π is equal to 1. The latter magnifies the portion of ψ in the range from zero to £200. Alternative sketches of the function ψ(x) are presented in Figure 13.5 for different values of p/π. This exhibit should, however, be treated with caution. Our dataset did not contain information on p/π, so its influence on the consumption value of gambling must therefore be speculative. When conducting our probit estimation, we have assumed that p/π is a constant. Probit remains appropriate if p/π is a polynomial in x plus, possibly, a random, perhaps individual specific, component, independent of x. However, it becomes impossible to disentangle the dependence of p/π upon x from that of ψ. Further, a random component would in general make probit inefficient, and require restriction to avoid inconsistent estimation. We have no evidence for or against the assumption that p/π is a constant, and Figure 13.5 is constructed on that basis. This suggests that as the ratio p/π rises, the consumption value of gambling may also rise. This result seems plausible as it can be explained in the following terms. When p/π is high, the shortfall in the expected end-of-period wealth resulting from postponing tax is correspondingly high. Thus, in order to rationalize the fact that the gambler would forgo this amount of expected wealth, it can be postulated that the consumption value of the incremental wager by postponing tax is that much larger.

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Consumption value of gambling

(a) 100

80

60

40

20

0 0

100

200

300

400 500 Outlay (x)

600

700

800

35

Consumption value of gambling

(b) 30 25 20 15 10 5 0 0

100 Outlay (x)

200

Figure 13.4 Consumption value of gambling (a)  £800 when p/π  1 and (b)  £200 when p/π  1.

We can see that for small wagers, ψ shows decreasing marginal value of incremental wagers, but for larger wagers this ceases to be true. Again, it should be borne in mind that our sample contains very few observations of wagers greater than £200, so that the latter range of the curve should be treated with caution. The most surprising feature of our results (to us, anyway) is the large estimates we obtain for the consumption value of gambling. A wager of £100 leads to a utility valued in excess of £20. For smaller wagers, the proportional value is greater.

A violation of dominance and gambling 247

Consumption value of gambling

200 Ψ1 p/π=1.0 Ψ2 p/π=1.25 Ψ3 p/π=1.5 Ψ4 p/π=1.75 Ψ5 p/π=2.0

150

Ψ5 Ψ4 Ψ3 Ψ2 Ψ1

100

50

0 0

100

200

300

400 500 Outlay (x)

600

700

800

Figure 13.5 Consumption value of gambling as p/π varies.

Table 13.3 Consumption value of gambling as outlay and p/π varies Outlay (£)

10 50 100 150 200

p/π 1.00

1.25

1.5

1.75

2.00

3.13 12.98 20.99 26.34 30.68

3.38 14.23 23.49 30.09 35.68

3.63 15.48 25.99 33.84 40.68

3.88 16.73 28.49 37.59 45.68

4.13 17.98 30.99 41.34 50.68

Table 13.3 presents some indicative values of the consumption value of gambling for several sizes of outlay. Comparisons with the estimates obtained from alternative data sets would be valuable, and would be worth further research.

Conclusions Economists have traditionally been slightly uncomfortable in their explanation of why people engage in gambling (Rosett, 1965, is an early statement of the issues). The conventional explanations fall into two groups, where the first relies on differences of opinion (Morris, 1994; Shin, 1993), and the second on the risk loving preferences of the gamblers (Ali, 1977; Quandt, 1986). However, neither of these approaches can explain a failure of dominance. Indeed, even the

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numerous generalizations of the expected utility hypothesis would be inconsistent with the violation of dominance. In this chapter, we have taken a much more radical route in explaining this apparent anomaly. By postulating an explicit component of utility which derives from gambling, we have had some success in identifying a systematic relationship between the size of the wager and the consumption value of gambling associated with that wager. The numerical values thus obtained have been substantial, and should constitute food for thought for economists.

Acknowledgements We are grateful to Ladbroke Racing Ltd for the data used in this paper. We thank John Aldrich and three anonymous referees for insightful comments on an earlier version.

Notes 1 Kahneman and Tversky’s (1979) ‘prospect theory’ allows violations of dominance when the pay-offs resulting from a sequence of decisions are aggregated. Also, ‘regret theory’ of Loomes and Sugden (1982) allows limited violations of transitivity and dominance. 2 The turnover for the financial year 1993/4 for bets placed in off-course betting shops was £4,557 million (Racing Industry Statistical Bureau, 1995). For a description of the UK betting market, see Magee (1990). 3 Bruce and Johnson (1994) discuss, from a psychological perspective, the issue of the excitement generated by gambling. Thaler and Ziemba (1988) and Busche and Hall (1988) have explored the hypothesis that gambling is a consumption activity in explaining some empirical regularities in the US horseracing market. 4 Unfortunately, we do not have information on the odds at which the bets took place. This prevents us from exploring some of the consequences of well-documented biases in betting odds in reflecting true probabilities (Thaler and Ziemba, 1988; Shin, 1993). 5 Saunders and Turner (1987) present evidence in support of the premise that the outlays of occasional and novice gamblers are, indeed, smaller than those of regular, more experienced gamblers.

References Ali, M. M. (1977) ‘Probability and utility estimates for racetrack bettors’, Journal of Political Economy, 82: 803–15. Anderson, G. and Brown, R. I. F. (1984) ‘Real and laboratory gambling, sensationseeking and arousal’, British Journal of Psychology, 75: 401–10. Bruce, A. C. and Johnson, J. E. V. (1994) ‘Costing excitement in leisure betting’, Leisure Studies, 14: 48–63. Busche, K. and Hall, C. D. (1988) ‘An exception to the risk preference anomaly’, Journal of Business, 61: 337–46. The Economist (1995) ‘The National Lottery: whose lucky number?’ 10 June, p. 30. Gilovich, T. (1983) ‘Biased evaluation and persistence in gambling’, Journal of Personality and Social Psychology, 44: 1110–26.

A violation of dominance and gambling 249 Kahneman, D. and Tversky, A. (1979) ‘Prospect theory: an analysis of decision under risk’, Econometrica, 47: 263–91. Loomes, G. and Sugden, R. (1982) ‘Regret theory: an alternative theory of rational choice under uncertainty’, Economic Journal, 92: 805–24. Machina, M. (1982) ‘Dynamic consistency and non-expected utility models of choice under uncertainty’, Journal of Economic Literature, 28: 1622–94. Magee, S. (1990) The Channel Four Book of Racing, London: Sidgwick and Jackson. Morris, S. (1994) ‘Trade with heterogeneous prior beliefs and asymmetric information’, Econometrica, 62: 1327–48. Quandt, R. (1986) ‘Betting and equilibrium’, Quarterly Journal of Economics, 93: 66–83. The Racing Industry Statistical Bureau (1995) The Racing Industry Statistical Bureau Statistics, Wellingborough, Northants. Rosett, R. N. (1965) ‘Gambling and rationality’, Journal of Political Economy, 73: 595–607. Saunders, D. M. and Turner, D. E. (1987) ‘Gambling and leisure: the case of racing’, Leisure Studies, 6: 281–99. Shin, H. S. (1993) ‘Measuring the incidence of insider trading in a market for statecontingent claims’, Economic Journal, 103: 1141–53. Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis, London: Chapman and Hall. Thaler, R. and Ziemba, W. (1988) ‘Parimutual betting markets: racetracks and lotteries’, Journal of Economic Perspectives, 2: 161–74. Wagenaar, W. A. (1988) Paradoxes of Gambling Behaviour, Hove: Erlbaum.

14 Exploring decision-makers’ use of price information in a speculative market J.E.V. Johnson, O. Jones and L. Tang

Introduction There is a large body of evidence which suggests that the combined judgements of decision-makers within financial markets effectively incorporate information concerning historical prices into current prices, to the extent that abnormal returns cannot be made if buy and sell decisions are made on the basis of historical prices. The horserace betting market is one form of financial market that has received considerable scrutiny in this regard. An important reason for this focus is that ‘wagering markets are especially simple financial markets, in which the pricing problem is reduced. As a result, wagering markets can provide a clear view of pricing issues which are complicated elsewhere’ (Sauer, 1998, p. 2021). Previous studies which explore the extent to which horserace betting markets incorporate closing odds and the time-indexed movement of pre-closing odds fall into three broad categories. One set of studies explores the distribution of closing odds in horserace betting markets. These offer strong evidence for a consistent over- or underestimation of the probability of long shots or favourites winning (the favourite–long shot bias). These conclusions have been reached for studies widely dispersed in time and across a variety of countries (e.g. McGlothlin, 1956; Ali, 1977; Tuckwell, 1983; Ziemba and Hausch, 1986; Bird and McCrae, 1994; Bruce and Johnson, 2000). However, these studies do not generally detect opportunities for trading profitably on this information.1 A second set of studies explores the information content associated with changes in odds from the opening of the market to its close. Information held by those with privileged information may be transmitted to the market via their betting behaviour; this may be revealed as bookmakers adjust odds to account for their liabilities or pari-mutuel odds change to reflect relative volumes of bets. In general, previous studies suggest that betting activity reveals information that is not readily available prior to the formation of the market, but that betting strategies based on these odds adjustments do not yield positive expected returns (e.g. Asch et al., 1982; Bird and McCrae, 1987; Crafts, 1985; Schnytzer and Shilony, 2002; Tuckwell, 1983). Sauer (1998, pp. 2048–9), reviewing these studies, concludes that ‘the evidence suggests that an informed class of bettors is responsible for altering prices in these markets (but) the opinions of “experts” appear to be fully discounted in market prices’. A

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third set of studies attempt to construct arbitrage betting strategies which employ information revealed within one market in a parallel market. Some of these studies have demonstrated that positive returns are possible by exploiting differences in pre-closing odds in independent win pools (e.g. Hausch and Ziemba, 1990; Schnytzer and Shilony, 1995) or between win and place or show pools (e.g. Hausch et al., 1981).2 However, opportunities for profitable betting employing the above strategies are limited and the degree of inefficiency is often small. Consequently, this third set of studies offers little more than a ‘crease in what is predominantly a smooth pattern of efficiency in the racetrack betting market’ (Sauer, 1998, p. 2048). It is clear from the preceding discussion that various aspects of closing odds and odds movements from the opening of the market to its close, taken alone (e.g. under-betting of favourites – Vaughan Williams and Paton, 1997; odds assessed by different handicappers – Figlewski, 1979; differences between morning line and closing odds – Crafts, 1985; odds at different time points – Lo, 1994) do contain information, but that this is discounted in closing odds, to the extent that profitable wagering strategies based on this information cannot be constructed. However, Ceci and Liker (1986) demonstrate that expert horse handicapping requires bettors to combine different types of information in complex, interactive models. We set out, therefore, to develop such a comprehensive model. This model combines closing odds and variables derived from the movement of preclosing odds to closing odds, which capture information that (1) may not be closely associated in the public’s mind with a horse’s success (e.g. the volatility of odds changes) and (2) are less readily discernable by bettors (e.g. odds changes scaled by closing odds). In addition, we include interaction terms between the variables. Our view is that bettors may not readily discount the combined effect of such variables and their interactions. Consequently, it may be possible to construct profitable wagering strategies based on such a model, and hence demonstrate that the horse-race betting market is not weak-form efficient. This chapter proceeds as follows. In the next section we outline the data employed, provide a rationale for the model which is used to test for market efficiency, and discuss the significant components of the fitted model. Then the model is tested, to explore the extent to which it demonstrates that information on changes in pre-closing odds is discounted in closing odds. Finally, we summarise our conclusions.

Description of the data and the model There are two distinct forms of horserace betting market that operate in parallel at racetracks in the United Kingdom; the pari-mutuel and the bookmaker markets. The latter forms the setting for this study. The odds on offer in the bookmaker market are determined by the decisions of both bettors and bookmakers and bets are settled at the odds available in the market at the time the bet is struck. The more serious bettors and those with access to privileged information are most likely to bet in the bookmaker market (Crafts, 1985; Sauer, 1998; Schnytzer and Shilony, 1995) because they can secure their return without

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the possibility of a bandwagon effect eroding their gains (which can happen in the pari-mutuel market). Consequently, because we seek to exploit as much information as possible contained in closing odds and pre-closing odds and their changes over time, it seems appropriate to use bookmakers’ odds. Independent bookmakers (generally 10 to 50) operate at each racetrack and post odds at the commencement of the market before each race. These odds change according to the relative weight of demand, reflecting bettors’ opinions, as a result of each bookmaker’s desire to balance their books and, to some extent, to reflect bookmakers’ subjective views of the horses’ relative prospects. Bettors in the United Kingdom are also permitted to bet in off-track betting offices at the preclosing odds (or the closing odds) prevailing in the on-course market at any given time. An independent organisation, Satellite Information Services (SIS), transmits the evolving racetrack bookmakers’ odds to off-course betting offices. SIS employs assessors who use their judgement to determine a unique value for the odds available on each horse at each moment in time; these are the maximum bookmaker odds available to a ‘substantial wager’ at the track. Accordingly, we collected pre-closing and closing bookmaker odds data supplied by SIS from 1,200 races run at 41 different racetracks in the United Kingdom over the period April–June 1998. Only ‘flat’ races of less than two miles were included. The number of horses in each race varies from 2 to 20, with a mode of 11. The betting period for each race lasts from 2.5 to 30 minutes, and averages 12.5 minutes (σ = 4.5 minutes). The odds for a given horse in the sample can change from 0 to 10 times, with a mode of 2 and an average of 2.7 changes. The information employed consists of, for each race i and each horse j = 1, . . ., k(i) in race i, a sequence of times and odds {(ti,j(1), ui,j(1)), . . ., (ti,j (n), ui,j (n))}. This sequence is unique for horse j in race i, being the odds transmitted by SIS. The final pair (ti,j (n), ui,j (n)) is always the ‘off time’ and ‘closing odds’. The length of the sequence n = n(i, j) varies from horse to horse, and the number of horses k = k(i) varies from race to race. When we are in the context of a single race we will drop the index i; and when in the context of a single horse we will drop the indices i and j. We scale the times so that t(1) = 0 and t(n) = 1. We regard the odds as a function of time, piecewise constant with jumps where the odds change, and call this function a price curve. The left-hand diagram of Figure 14.1 displays a typical example of a price curve: the points * are the points (t(1), u(1)), . . ., (t(n), u(n)). Note that the final pair (t(n), u(n)) are generated by the start of the race and not by a change in odds, so u(n) = u(n – 1). Taking the price curves as its input, we wish to build a model for pi = (pi(1), . . ., pi(k)), the vector of winning probabilities for race i, where pi(j) = Pr(horse j wins race i). Suppose that for horse j in race i we have extracted from the price curve, predictors xi,j = (xi,j(1), . . ., xi,j(m)), where m is fixed over all i and j. We use a conditional logit model for the pi. That is, for a fixed vector of coefficients  = (β(1), . . ., β(m)), we suppose that pi ( j ) =

exp(< β, xi , j >)

∑

k (i ) l =1

exp(< β, xi ,l >)

,

(1)

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Orthogonal polynomial components 4

6.5 6.0

3

5.5

4.5

2

Odds

Odds

5.0

4.0

1

3.5 3.0

0

2.5 −1

2.0 0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

Time

Time

Figure 14.1 Orthogonal polynominal decomposition of a price curve. Notes The left diagram shows the price curve and its constant, linear, quadratic and cubic approximations. The right diagram shows the separate constant, linear, quadratic and cubic components, which are added to give the approximations in the first diagram.

Where < , xi,j > = ∑mh=1β(h)xi,j (h). We justify this choice of model by noting that it allows the exponent < , xi,j > to be interpreted directly as the ability of horse j, independent of the race i. To see this, suppose that εi( j), j = 1,..., k(i) are independent identically distributed random variables with the double exponential distribution. That is εi(j) has cumulative distribution function Fε(v) = exp(–exp(–v)), for –∞ < v < ∞. If we put Wi( j) = < , xi,j > + εi(j) then it can be shown that pr(Wi( j)  Wi(l),l = 1, ..., k(i)) = pi( j) (Maddala, 1983). We can interpret Wi(j) as a ‘winningness’ index. That is, the winner of race i is the horse with maximal Wi(j), and we can interpret the deterministic component < , xi,j > of Wi(j) as a direct measure of horse j’s ability. If we observe N races, and the winner of race i is horse j*, then the joint likelihood L = L() is the probability of observing this set of results, assuming the pi are as above. That is N

N

i =1

i =1

L(β) = ∏ pi ( j*) = ∏

exp(< β, xi , j* >)

∑

k (i ) l =1

exp(< β, xi ,l >)

.

(2)

We employ maximum likelihood estimation to choose  that maximizes L(). Extracting predictors from the price curve To construct a model for pi(j) we require a consistent set of predictors, drawn from the price curve for each horse. In doing so we have two aims: (1) to provide a general summary of the shape and other physical characteristics of the price curve, and (2) to pick out particular features that have been identified in the literature or by active gamblers as having an effect on the horse’s winning probability. For all

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the predictors we consider, there is an implicit dependence on the race i and horse j, however, to simplify, we will not make this explicit in the notation. We are interested to include predictors that reflect the general shape of the price curve that, amongst other things, will reflect the timing of bets by those with privileged information. However, the precise shape of a price curve that is likely to signal a potential winner (or loser) is unclear. We therefore provide a general summary of the shape of a price curve {(t(1),u(1)),..., (t(n),u(n))} by using an orthogonal polynomial expansion of order three. This allows us to measure the height of the curve (closing odds), the linear trend, the curvature (quadratic component) and change in curvature (cubic component). By using an orthogonal polynomial expansion, we can measure the size of each component (constant, linear, quadratic and cubic) independently of the others. Orthogonal polynomials are a classical statistical tool; details of their construction can be found for example in Wetherill (1981). We summarise the procedure here and it is illustrated in Figure 14.1. Given a set of points {(t(1),u(1)), . . ., (t(n),u(n))}, an orthogonal polynomial basis is a sequence of polynomials f0, f1, f2, . . . such that fi is of order i and n

∑ f (t (l )) f l =1

i

j

(t (l )) = 0 for all i ≠ j.

(3)

It can be shown that an orthogonal polynomial basis always exists and that there is a unique set of coefficients a0, a1, a2, . . . such that ∞

u (l ) = ∑ ai f i (t (l )) for all

l = 1,K, n.

(4)

i =0

The ai can be found by least squares. By restricting ourselves to an order three expansion we get an approximation to u. As the fi are orthogonal, we can interpret ai as the size of the order i component in the price curve. In fact, Equation (3) does not specify a unique basis, and we can impose further constraints without compromising orthogonality. In our case, because of the importance of the closing odds u(n), we take f0(t(n)) = f0(1) = 1 and fi(1) = 0 for all i 1. The effect of this is to make the constant component a0 equal to u(n). We also norm each fi so that its leading term is simply ti. In particular, this implies that a1 is the slope of the least squares regression line constrained to pass through (t(n),u(n)). We interpret a2 as a measure of the curvature of the price curve and a3 as a measure of the change in curvature. A potential problem with polynomial expansions is that they are unstable when only a small number of points are used. That is, if n is small, then a small change in one of the (t(i),u(i)) can produce a large change in a2 and a3. To mitigate this, we regularise the procedure by introducing a roughness penalty when fitting ai. Let F(t) = ∑3i=0ai fi (t), then we choose the ai to minimise n

∑ (u (l )) − F (t (l )) l =1

2

+ λG ( F )

(5)

where G(F) is the roughness penalty and λ is some constant of proportionality. Typically G(F) is some measure of curvature such as a Sobelov norm (that is, a norm based on first-, second-, and sometimes higher-order derivatives of F).

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However, the slope of F at t(n) is of particular interest to us as a measure of late price movement; so we do not want to depress this unnecessarily. So, instead of a Sobelov norm, we put G(F) equal to the area of F above umax = max u(i) and below umin = min u(i). That is, 1

1

0

0

G ( F ) = ∫ max( F (t ) − umax , 0)dt + ∫ max(umin − F (t ), 0) dt.

(6)

In addition to a general summary of the shape of the price curve we also included two predictors to measure the volatility or roughness of the price curve; the number of price changes and the absolute variation. That is, for price curve {(t(1),u(1)), . . ., (t(n),u(n))}, we put b1 = n − 2

and

b2=

n −1

∑ | u(l ) − u(l − 1)|.

(7)

l =2

Clearly there will be some degree of correlation between b1 and b2. The remaining three predictors in the model were included since previous literature suggests that they may have some influence on a horse’s probability of success. First, a number of studies have demonstrated a close correspondence between probabilities implied by closing odds and winning probabilities (e.g. Bruce and Johnson, 2000). The closing odds for horse j in race i imply a ‘track probability’ of winning qi(j), via the relationship

ui , j (n) =

1 − qi ( j ) 1 , qi ( j ) = . qi ( j ) 1 + ui , j (n)

(8)

Taken together the ‘track probabilities’ are not true probabilities because typically ∑nj=1 qi ( j) > 1. This arises because bookmakers overestimate each horse’s prospect of success so that on average they secure a profit. We already include the closing odds in the model as a0 = ui,j, which gives pi(j) ∝ exp(β(a0) . (1 − qi(j)) / qi(j)). However, it is plausible that a more direct relationship between pi(j) and qi(j) would result in a better fit. Accordingly, we include the predictor c1 = ln qi(j) = –ln(1 + ui,j(n)), which gives pi( j) ∝ exp(β(c1) . c1) = qi(j)β(c ). In fact, Chapman (1994) even found that c1 added significant explanatory power in a sophisticated fundamental handicapping model that included 20 variables associated with the horse and its jockey. Rather than using ln qi( j) we could use q−i( j), where q−i( j) = qi( j)/∑lq (l). However, given the form of our model in Equation (1), this scaling actually has no effect on pi(j), so we prefer to use the simpler ln qi(j) terms. Crafts (1985), Tuckwell (1983) and Bird and McCrae (1987), amongst others, have demonstrated that a horse’s enhanced prospects of success are revealed by a large reduction in odds from the start to the completion of the market. Consequently, we include in our model c2 = closing odds – initial odds = ui,j(n) – ui,j(1), although this will be highly correlated with the slope a1. 1

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Those with access to privileged information have an incentive to bet late in the market (Asch et al., 1982; Schnytzer, et al., 2003). Consequently we use a predictor to capture late changes in the betting. Let U(t) be the odds at time t, that is for t(i)  t  t(i +1), U(t) = u(i). Let [a, b] be a small subinterval of [0, 1], close to 1. We take as our measure of late change the most extreme slope (U(1) – U(t))/(1 – t) for t ∈[a,b], that is, the slope with the largest absolute value. We let the latechange predictor be c3, and provide two illustrations in Figure 14.2,where c3 is the slope of the line plotted though (1,U(1)). Values of a and b were chosen to make c3 reasonably robust, so that small changes in U(t) do not produce large changes in c3, while minimising correlation with the overall trend a1. Taking [a, b] = [0.9, 0.95] gave reasonable results. If the price curve were smooth, then c3 would simply be an approximation to the derivative at t = 1. Consider again our orthogonal polynomial expansion of the price curve, F(t) = ∑3i=0 ai fi(t). F(t) is a smooth approximation of the price curve, so we expect c3 to be highly correlated with F′(1) = a1 + 2a2 +3a3. Finally, two refinements of the predictor set were incorporated, based on our understanding of how prices behave in practice. First, it is known that on longodds horses (those with high closing odds), the odds change by larger amounts than for short-odds horses, and we believe that the relative size is more important than the absolute size of any change. Consequently, before calculating predictors a1, a2, a3, b2, c2 and c3, the price curve {(t(1),u(1)), . . ., (t(n),u(n))} was rescaled by dividing u(i) by u(n) for i = 1, . . ., n. Predictors a0 and c1, which are based on the closing odds, were not rescaled, and b1 is unaffected by this rescaling. Second, practising gamblers interpret the price curve differently when the odds are coming in (decreasing) or going out (increasing). This suggests that we should interpret price changes differently when there are changes down rather than up. Accordingly predictors a1, c2 and c3 were split into pairs xi+ and xi–, where xi+ = xi if xi > 0 or 0 otherwise, and xi– = xi if xi < 0 or 0 otherwise. Similarly, predictors b1 and b2 were split into two parts, depending on whether or not a1 > 0. Model fitting To fit and test the model given in Equation (1), the data set was split into two parts. The first 800 races were used to fit the model, and the remaining 400 used to test it. A stepwise fitting procedure was used to select a set of predictors significant at the 5 per cent level. Pairwise interactions of all the predictors were also Odds U(t)

0

Odds U(t)

a

b 1 Time t

Figure 14.2 Late-change predictor.

0

a

b 1 Time t

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considered. In the final model the predictors a1+, b2–, c1 and c3– and the interaction a1+b1 were all significant at the 5 per cent level. The estimated coefficients  are given in Table 14.1. The log-likelihood ratio of the model over the constant alternative is 857.05, which gives us that the model is significant with a p-value of 0.0000. First we note that, as a1, b2 and c1 are in the model, it is not surprising that c2, b1 and a0 are not, as we knew these predictors were correlated. We interpret this as saying that a1, b2 and c1, respectively, capture more relevant information concerning overall change in odds, volatility and closing odds than c2, b1 and a0. Second, some degree of correlation between c3 and a1 + 2a2 + 3a3 was expected, so the presence of c3 in the model in part explains why a2 and a3 do not appear. The predictor c1 = ln qi(j), has a large influence. Considering just the effect of c1 on the model probability we have pi(j) ∝ exp(1.1678 ln qi(j)) = qi(j)1.1678, which is similar to the utility function derived in Ali (1977). We interpret this relationship as a reflection of the so-called favourite–long shot bias. That is, the shorter a horse’s closing odds, the nearer the true probability of winning is to the implied track probability. A plot of ln ui,j(n) = ln (1-qi(j))/qi(j) against ln qi(j)1.1678 gives a very close match to the analogous plot given in Bruce and Johnson (2000), which was obtained by modelling the favourite–longshot bias directly in the UK bookmaker market in 1996. The significance of the predictor a1+ suggests that, when odds lengthen (i.e. the least squares regression line constrained to pass through t(n), u(n) has a positive slope), the horse has a significantly lower chance of winning. The effect of the a1+b1 interaction is to reduce this effect when the odds worsen in a large number of small steps, as opposed to small number of large steps. The late change down predictor, c3– acts as expected. c3– is always negative in sign, so when there is a late change down the effect is to increase the probability of winning. The coefficient of b2– is negative, indicating that high volatility in the price curve makes a horse less likely to win, but only when the odds have come in. Each of the predictors with significant coefficients might be described as relatively difficult to discern (relatively opaque) compared with an equivalent, but more transparent predictor excluded from the model; for example, a1 versus Table 14.1 Estimated coefficients of the model Predictor

Description

Coefficient

Standard error

p-value

a1+ b2– c1 c3– a1+b1

Slope up Absolute variation down ln(track probability) Late change down Slope up and number of changes interaction

–2.0493 –0.4227 1.1678 –0.0666

0.8110 0.1907 0.0648 0.0331

0.0115 0.0266 0.0000 0.0440

0.4371

0.1937

0.0240

Note a1+, b2–, and a1+b1 ≥ 0; and c3– ≤ 0.

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c2, slope of the least squares regression line through t(n), u(n) versus closing – initial odds; b2 versus b1, the absolute value of (scaled) odds changes versus number of odds changes; c1 versus a0, natural log of the probability implied by closing track odds versus closing track odds. Whilst the late-change predictor c3, which appears in the model, has no directly comparable transparent alternative, we found that the coefficient for the scaled version of c3 is significant, whereas that for the non-scaled (more transparent) version of c3 is not. Taken together, the results suggest that more readily discernable (or relatively transparent) information is more efficiently discounted in betting markets than more opaque information.

Model testing To test the model we (1) explore, using log-likelihood ratio tests, whether the model contains more information than a model based solely on closing odds; (2) test whether the additional information contained in the model can be exploited to make profits; (3) use cross-validation and jack-knifing to check that the observed profits do not arise by fortunate selection of the training and validation sets; (4) use parametric bootstrapping (on the training set employed in 2) to test whether the profits we observe arise because our model incorporates more information than that available from closing odds alone or whether the profits arise by chance; and (5) explore the features of winning bets suggested by the model to identify any systematic features of such bets. Log likelihood tests To explore the joint importance of the predictors in the model we conduct loglikelihood ratio tests. We compare the log-likelihood (LL) of the full model given in Table 14.1 (LL = –2,243.9) with that of a model simply using normed final track probabilities (LL = –2,262.7). An LL ratio test comparing the two models has a p-value < 0.0001. This test confirms that there is significant sample evidence to suggest that the full model incorporates more information than final track probabilities alone. In the following section we explore the extent to which this extra information is substantive, to the extent that we are able to employ it profitably. Kelly betting To assess whether the observed inefficiency can be exploited sufficiently to make profits, races 801 to 1200, run during May and June 1998, were used to test the predictive ability of the model. As we do not have repeated observations (each race is only run once), we must use indirect methods. We consider a betting strategy which maximises the long-run rate of growth of wealth (the Kelly strategy). We use the model probabilities and closing odds as inputs, and analyse the returns produced. Let ri(j) = 1 + ui, j(n) be the return on a bet of a pound if horse j wins race i. Let vi(j) be the fraction of our current wealth we wager on horse j in race i.

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Let vi = (vi(1), . . ., vi(k)). As usual, we will drop the subscript i when the context makes it unnecessary. Betting fraction v, if horse x wins then our current wealth will increase by a factor of 1 – ∑kj=0 v(j) + v(x)r(x). The Kelly strategy consists of choosing v to maximise the expected log payoff, F(v) where k

(

)

F ( v ) = ∑ p ( x) ln v( x)r ( x) + 1 − ∑ j =1 v( j ) . x =1

k

(9)

This betting strategy was introduced by Kelly (1956). It was later shown to be asymptotically optimal by Breiman (1961), in the sense that it maximises the asymptotic rate of growth for wealth, with zero probability of ruin. Using the Kelly criterion, the total wealth grows at an exponential rate, although the standard deviation remains proportional to total wealth and, thus, also grows exponentially. We also note that this strategy only gives zero probability of ruin if arbitrarily small bets are allowed. In practice this caveat has led some authors to consider modified Kelly strategies (e.g. Benter, 1994; Ziemba and Hausch, 1986), whereby some fixed fraction of v is bet. As we are interested in the theoretical rather than practical performance of our model, we restrict ourselves to the usual form. The Kelly strategy tells us which races to bet on, as well as how much to bet on each horse. We can bet on more than one horse in a race, although our bets are usually restricted to horses that give a positive expected return (a Kelly strategy occasionally includes wagers on horses with a negative expected return, provided there are sufficient diversification benefits in the wager). By betting on a number of horses in a race the risk of losing is reduced at the expense of reducing the expected return. Nonetheless, bet sizes suggested by the Kelly strategy will be larger when the probability of winning is greater (for the same expected return) and when the expected return is greater (for the same winning probability). In this manner, a Kelly strategy makes full use of the information provided by the model. Given correct probabilities as inputs (as opposed to estimated probabilities), the Kelly strategy gives non-negative expected returns. Thus, if it gives non-negative returns using our model probabilities pi(j) as inputs, we take this as evidence that the pi(j) are reasonably accurate. Moreover, a positive return indicates that abnormal returns can be made by simply employing historical price information. Figure 14.3 plots the natural logarithm of the cumulative wealth, applying the Kelly strategy to the test set, starting with initial wealth 1. Over the out-ofsample test period, total wealth increased by a factor of 2.4597. In testing the significance of returns from bets it is common to consider the profit per pound bet Bi. However, if we let Xn be the wealth after n races, then we obtain Xi+1 = Xi + biXiBi = (1 + biBi)Xi , where bi is the amount bet per pound of initial wealth on race i. That is, we cannot express the increase in wealth solely in terms of the Bi. Let wi be the profit made per pound of initial wealth on race i, so that Bi = wi/bi (defining Bi = 0 when bi = 0). In the context of Kelly betting, a more natural object to consider than Bi is Wi = 1 + wi, which is the factor by which wealth has increased after race i. That is Xi+1 = WiXi. Taking logs, we turn the multiplicative form of the cumulative wealth into an additive form, to obtain ln(Xn) = ln(X0) +

J.E.V. Johnson et al. 4.0

1.2

3.5

1.0

Log (cumulative wealth)

Log (cumulative wealth)

260

3.0 2.5 2.0 1.5 1.0 0.5 0

0

200

400 Race

600

800

0.8 0.6 0.4 0.2 0 −0.2

0

100

200 Race

300

400

Figure 14.3 Natural logarithm of cumulative wealth using the Kelly strategy. Notes The wealth for races 1 to 800 (those used to fit the model) is shown on the left; the wealth for races 801 to 1,200 (the test data set) is shown on the right; wealth is given as a multiple of original wealth.

∑ni=1 ln(1 + wi). Let Ai = ln(1 + wi). Then Ai is a natural object to average, and Xn exhibits long-term growth if and only if E(Ai) > 0. Note that it is not the case that Xn exhibits long-term growth if and only if E(Bi) > 0, because there is (typically) positive correlation between bi and Bi, in which case E(1 + biBi) > 1 + E(bi)E(Bi). From the testing set we estimate µ = E(Ai) = 0.00226 and σ2 = Var(Ai) = 0.04772. When using Kelly betting, µ is the asymptotic growth rate for wealth (per race). From the Central limit theorem, our estimators are approximately normally distributed, which allows us to calculate that a test of the hypothesis µ = 0 against the alternative µ > 0 is significant at the 17 per cent level. Using our estimates for µ and σ2, we can estimate the number of races that we would need to consider to ensure that we are 95 per cent certain of making profit (noting that not all races are bet on). This corresponds to the smallest value of n such that Pr(∑ni=1 Ai > 0)  0.95. Using the central limit theorem to approximate the sum by a normal random variable, we find that n = 1,653. We conclude from these results that when using the full model with the Kelly betting strategy there is some evidence of making profit if betting in a sufficiently large number of races. This, in turn, suggests that closing odds do not fully incorporate active market odds information; that is, the market is not weak-form efficient. An important operational issue is the effect on closing odds of wagers based on the model predictions. With the pari-mutuel system, large wagers automatically reduce the odds at which a bet is settled. However, our model is developed for a bookmaker market and requires that bets are placed close to the start of a race. Although there may be some feedback to closing odds if a large bet is made, this would not affect returns because these are fixed in a bookmaker market at the time the wager is made. It is possible that an individual bookmaker may refuse a bet or offer reduced odds on a very large bet. However, the odds employed in this study

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(provided by SIS as indicated in the previous section) are the odds available to a ‘substantial wager’ at the track. In addition, in the United Kingdom there are upwards of 20 independent bookmakers at any racetrack as well as thousands of independent off-track bookmakers who accept bets at the odds on offer at racetracks at any given time. Consequently, a well organised group of individuals could split a very large wager into smaller amounts and place these simultaneously at several outlets without affecting the odds at which the bet would be settled. We note that to make a profit in the racetrack betting market, it is necessary to overcome the bookmakers’ margin, which is typically between 15 per cent and 20 per cent. That is, betting at random, we would expect to see E(Wi)  0.85. For our full model, using the test data set, we get a 95 per cent confidence interval (CI) for E(Wi) of (0.9993, ∞), significantly higher than the 0.85 we would expect from random betting. Cross-validation and jack-knifing We use cross-validation and jack-knifing to explore whether the profits we observe from application of the model arise by fortunate selection of the training and validation sets. In particular, we use them to reinforce our estimate of µ. For the cross-validation we split the data into 12 blocks of size 100. We then consider all possible choices of eight blocks for the training set and four blocks for the testing set. For each of the 12C8 = 495 possible choices, we fit the model to the training set and then estimate µ from the testing set. Let µˆj be the estimate obtained from the jth trial, then the cross-validation estimate of µ is 1 495  ˆj = 0.00218. 495 ∑ j=1 µ We also obtain that 80 per cent of the cross-validation estimates are positive, which is again in close agreement with the analysis above. As the µˆj are all highly correlated, it is not possible to obtain a confidence interval for µ directly from the cross-validation estimates. We also applied a particular variant of cross-validation known as the jack-knife: race i is set aside for testing, and the remaining races are used for model fitting. This is repeated for each of the 1,200 races. Let AiJ be the observed wealth growth rate obtained by using the fitted model to bet on race i. Note that the model will change marginally each time as the training set changes slightly. Let µij be the mean of Aij. We can view µijas a continuous non-linear function of the estimated model parameters , which now also depend on i. Thus, in general, µiJ ≠ µ, where µ is the asymptotic growth rate of wealth (per race) for the parameters  fitted using the original training set (races 1 to 800). However, maximum likelihood estimation produces consistent estimators, so our estimates of  will converge to some limit as the size of the training set increases. Thus it is reasonable to assume that µiJ ≈ µ. Because the models used to produce A iJ are highly dependent, A iJ is also dependent. Nonetheless, most of the variation in AiJ comes from the race i on which the model was tested and not the model itself. Thus AiJ will be approximately independent, which allows us to give a confidence interval for µ. The jack-knife sample had mean = 0.00309 and standard deviation = 0.07055, giving

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an approximate 95 per cent CI for µ of 0.00309 ± 0.00399 = (–0.00090, 0.00708). A test of the hypothesis µ = 0 against the alternative µ > 0 is significant at the 6.5 per cent level. We note that the mean of AiJ is higher than the mean of AiJ , as above, possibly due to a better estimate of  resulting from a larger training sample. However, the variance of AiJ is higher than the variance of the Ai , which is probably due to the variation in the models used to calculate each AiJ. That is we are getting variance from the model and the test sample point. Overall, the results of the jackknife procedure provide further evidence that the model can be exploited to earn positive returns; indicating that the market is weak-form inefficient. Parametric bootstrapping The likelihood ratio test shows that our full model captures significantly more of the information in the price curve than that available from the closing odds alone, and the application of the Kelly betting strategy suggests that there may be enough actionable information in the model to make a profit. However, there is still a question as to whether the ability to make a profit depends only on closing odds (plus some good fortune) or can be attributed to the extra information included in the model. We explore this using a parametric bootstrapping approach, which involves re-sampling from a model fitted to the observed data. Note that if we apply the Kelly betting strategy using a model based on final track probabilities, then we never actually place any bets as the model never overcomes the bookmakers’ margin. Consequently, in this section, we consider a model based on normed final track probabilities, which does allow us to apply the Kelly betting strategy and, thus, provides a comparison with the full model on the basis of profit earned rather than likelihood. We norm the track probabilities qi = (qi(1), . . ., qi(k)) so that they sum to one – = (q– (1), . . ., q– (k)), where (q– (j) = and call the normed track probabilities q i i i i (qi(j)/∑ιqi(l). Under the hypothesis H0 that the model pi(j) depends only on closing odds, we have (pi(j) = (q–i(j) + εi(j) where the εi(j) are independent errors, conditional on ∑j(pi(j) = 1, that is ∑j(εi(j) = 0. We note that log q–i(j) is just a scaled version of the predictor c1. To mimic the form of the conditional logit model, we rewrite pi( j) as exp(log q–i( j) + ε~i( j)) = q–i( j) exp(ε~i(j)) where ε~i( j)) = log(1 + εi( j) / – qi(j) are again independent errors, conditional on ∑jpi(j) = 1. pi( j) are estimated using the full model as given in the previous section and ε~i(j) is a measure of the discrepancy between pi( j) and q–i( j). The aim of this analysis is to judge whether or not pi( j) provides more actionable information than q–i( j); that is, whether the additional information captured by the full model over closing odds alone is needed to generate a profit. If profitability depends only on the closing odds, then ε~i(j) is effectively a random adjustment to q–i( j), which we can simulate. Consequently, to test whether pi( j) tells us more than just q–i( j),we test whether or not using the real ε~i(j) is any better than using a randomly generated ε~i(j). We estimate the distribution of ε~i(j) directly from the training data set. Figure 14.4 gives a histogram of ε~i(j)) = log(pi(j) / –qi(j) for all horses in races 1 to 800.

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The sample mean and standard deviation are –0.1012 and 1.1865, respectively. The Kolmogorov-Smirnov test for normality gives a p-value of 0.1492, indicating that there is no significant cause not to accept this as a normal distribution (this justifies the error form used). Thus, under the hypothesis H0 that pi(j) depends only on closing odds, we obtain

pi ( j ) =

qi ( j ) Zi ( j )

∑ q (l ) Z (l ) l i

i

for Zi ( j ) i.i.d. ln normal( −0.1012,1.1865) (10)

We use Equation (10) to test the hypothesis that the ability of the model to make profit depends only on closing odds. Under H0, our full model is just as effective as that given by Equation (10). We proceeded as follows. For each race in the test data set (races 801 to 1,200) we randomly generated sample pi(j) using Equation (10). These were then used to calculate the asymptotic growth rate for wealth µ, as above. We then repeated this 500 times to obtain an empirical distribution for µ under H0. From the testing set (above) we estimated µ = 0.00226, and we now estimate that under H0, P(µ > 0.00226) = 0.006. That is, under H0, the probability of observing a value of 0.00226 or higher (the value achieved by the full model) is less than 0.006. This suggests that the profit we observed in the previous section is likely to be attributable to factors in the model other than closing odds. Features of winning bets We explore under what circumstances the model produces successful bets in order to identify any systematic features of such bets and, in particular, to identify what variables or combination of variables are needed to distinguish the Histogram of log error 1,200 1,000 800 600 400 200 0

−5

−4

−3

−2

−1

0

1

2

3

4

5

Figure 14.4 Histogram of log error. ε~j(j), under the hypothesis that pj(j) depends only on closed odds.

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horses we should bet on. To achieve this, for each race in the holdout sample, we determine, for the winning horse, its probability of winning given by the model, the normed track probabilities, and whether we successfully backed the horse. We plot the results in Figure 14.5; to spread the points, we plot ln (model probability) against ln (normed track probability). Winning horses which we backed are depicted by triangles, and horses we failed to back because we backed another horse in the race (thereby losing money) by crosses; in races where no horse was backed, the winner is depicted by a dot. We see from Figure 14.5 that we only backed horses when the model probability was greater then the normed track probability. The favourite–longshot bias means that this happens more frequently for short-odds horses, and the model is better at picking short-odds winners than long-odds winners. In fact, the results suggest that by restricting our bets to horses where ln (model probability) > –2.5 (i.e. model probability > 0.08), profits would improve. We also note that for winning horses the differences between the normed track probabilities and the model probabilities were generally not very large, although there are a few exceptions. The relative importance to overall profit can be gauged by plotting the profit made on the z-axis. To visualise this rather than produce a threedimensional plot, we projected the above points onto the main diagonal, and then plotted these against the profit made per pound of wealth (Figure 14.6). From this we see that profit does not depend on occasional very large profits on long-odds horses or on bets in a particular odds range (other than suggesting that bets be restricted to where the model probability > 0.08). Comparative probabilities for winning horses 0

Log normed track probability

−0.5 −1.0 −1.5 −2.0 −2.5 −3.0 −3.5 −4.0 −4.5 −4.5 −4.0 −3.5 −3.0 −2.5 −2.0 −1.5 −1.0 −0.5 Log model probability

Figure 14.5 Analysis of bets on winning horses.

0

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Profit for winning horses 0.6

Profit per pound of initial wealth

0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −4.5 −4.0 −3.5 −3.0 −2.5 −2.0 −1.5 −1.0 −0.5

0

Log probability

Figure 14.6 Profit obtained from winning horses.

To gain further insight into how the model works, we consider the effects of our predictor variables for all winning horses in the holdout sample (Set A = 400 horses) and for winning horses we successfully bet on (Set B = 61 horses). For each set we give box plots of –2.0493*a1+ + 0.4371*a1+b1, –0.4227*b2–, 1.1678*c1 and –0.0666*c3–. The sum of these four gives the ‘winningness index’ < , xi,j > for horse j in race i. Box plots provide a graphical representation of the distributions of each factor, including the interquartile range (boundaries of the larger box) and the more extreme values of the distribution. From Figure 14.7, we see that there is little difference between the factors from Set A to Set B, other than that winning horses that were wagered on in the sample start at slightly lower odds than winning horses in general and that there is a preference for selecting lower odds variance horses. However, the differences are not large enough to conclude that there is any significant difference between the four factors from Set A to Set B, indicating that in general the model requires a combination of the factors for it to distinguish which horses to bet on. If we look at winning horses for which the model probability is much larger than the track probability (by a factor of 1.1 or more), then there are some common characteristics. There were 14 such horses; for 13 of them the odds increased and for seven there was a late change down. A late change down increases < , xi,j > and thus the model probability pi(j). However, increasing odds decrease < , xi,j >, and have a larger impact than a late change (resulting

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Predictors for winning horses when bet

0

0

−1

−1

−2

−2

−3

−3

−4

−4 1

2

3

4

1

2

3

4

Figure 14.7 Influences of predictor variables for winning horses. Note Column 1: 2.0493 · a1  0.4371 · a1b1; Column 2: 0.4227 · b2 ; Column 3: 1.1678 · c1; Column 4: 0.0666 · c3

from the sizes of the coefficient and the variables). We conclude that in these 13 cases the model probability has only improved because of the relative change in < , xi,j > for the winning horse compared with the other horses in the race. Again this indicates that information from many sources must be carefully weighed to be able to model successfully the probability of winning. In summary, this analysis suggests that the profits derived from the model are not dependent on a few long-odds winners and no one predictor can be used to decide when to bet; the model achieves its success by combining a variety of factors. Overall, the results of model testing suggest that the model predictors contain significantly more information than that contained in closing odds. In addition, there is something in excess of an 80 per cent chance that a betting strategy based on the model will produce a long-term increase in wealth. Although this is not conclusive proof that the horserace betting market is weak-form inefficient to the extent that it can be exploited by an expert to his or her advantage, the results suggest that this may be the case.

Conclusions In this chapter, we set out to explore whether the horserace betting market fully incorporates a variety of historical bookmaker price information variables, including interaction effects. We conclude that there is valuable information contained in odds and pre-closing odds movements that is not fully discounted in closing odds, which suggests that the market is weak-form inefficient. Our attempts to use a betting strategy to exploit this inefficiency are also suggestive, if not conclusive, that our model could be employed to make profits. We believe this is because, as Ceci and Liker (1986) observe, expert handicapping

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requires the ability to combine different types of information in complex, interactive models. Our results suggest that betting market participants as a whole do not achieve this to the extent of our model, which incorporates a range of variables covering different aspects of information associated with closing odds and the movement of pre-closing odds to the closing odds, including their interactions. The results also suggest that market participants are largely effective in discounting readily discernable (more transparent) information concerning a horse’s enhanced prospects in their decisions, but they do not appear to incorporate less readily discernable (more obscure) information. We conclude that closing odds and the manner in which pre-closing odds move, are rich but subtle information sources, which bettors do not fully utilize. The model has served our purpose in exploring the weak-form efficiency of horserace betting markets. However, we have not been tempted to undertake a real-life test of the model because this would involve considerable effort in terms of real-time data capture and operation of the model and moreover, the estimated growth rate for wealth, although positive, is small and may not warrant the potential risks. In summary, this chapter adds to our knowledge of the degree to which different types of information are discounted in decisions made in betting markets. It also introduces a technique for extracting predictor variables from price curves using orthogonal polynomials and a variety of approaches for testing a model that produces probabilities. Future work exploring other financial markets, using the techniques introduced here, may yield interesting conclusions regarding market efficiency and the manner in which information is employed by market participants.

Notes 1 The one exception, a study conducted by Ziemba and Hausch (1986) in the USA, identifies a small expected profit from betting on a very small number of extreme favourites (odds < 3/10). 2 In the pari-mutuel market, separate pools are created for win bets (those which attempt to select the winner), place bets (those which attempt to select the horse to finish first or second) and for show bets (those which attempt to select horses to finish first, second or third). Odds are determined separately in each pool by the relative amount of money on each horse.

References Ali, M.M. (1977) ‘Probability and utility estimates for racetrack bettors’, Journal of Political Economy 82: 803–15. Asch, P., B.G. Malkiel and R.E. Quandt (1982) ‘Racetrack betting and informed behavior’, Journal of Financial Economics 10: 187–94. Benter, W. (1994) ‘Computer based horse race handicapping and wagering systems: A report’, in D.B. Hausch, V.S.Y. Lo and W.T. Ziemba (eds), Efficiency of Racetrack Betting, London: Academic Press, 183–98. Bird, R. and M. McCrae (1987) ‘Tests of the efficiency of racetrack betting using bookmaker odds’, Management Science 33: 1552–62.

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Bird, R. and M. McCrae (1994) ‘Racetrack betting in Australia: a study of risk preferences and market efficiency’, in W.A. Eadington and J.A. Cornelius (eds), Proceedings of the 7th International. Conference on Gambling and Risk Taking, Institute for the Study of Gambling and Commercial Gaming: Reno, 228–58. Breiman, L. (1961) ‘Optimal gambling systems for favourable games’, Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, 63–68. Bruce A.C. and J.E.V. Johnson (2000) ‘Investigating the roots of the favourite–longshot bias: an analysis of supply and demand side agents in parallel betting markets’, Journal of Behavioral Decision Making 13: 413–30. Ceci, S.R. and J.K. Liker (1986) ‘A day at the races: a study of IQ, expertise, and cognitive complexity’, Journal of Experimental Psychology: General 115: 255–66. Chapman R.G. (1994) ‘Still searching for positive returns at the track: empirical results for 2000 Hong Kong races’, in D.B. Hausch, V.S.Y. Lo and W.T. Ziemba (eds), Efficiency of Racetrack Betting, London: Academic Press, 173–81. Crafts, N.F.R. (1985) ‘Some evidence of insider knowledge in horse race betting in Britain’, Economica 52: 295–304. Figlewski, S. (1979) ‘Subjective information and market efficiency in a betting market’, Journal of Political Economy 87: 75–88. Hausch, D.B. and W.T. Ziemba (1990) ‘Arbitrage strategies for cross-track betting on major horseraces’, Journal of Business 63: 61–78. Hausch, D.B., W.T. Ziemba and M. Rubinstein (1981) ‘Efficiency of the market for racetrack betting’, Management Science 27: 1435–52. Kelly, J.L. (1956) ‘A new interpretation of information rate’, Bell System Technical Journal 35: 917–26. Lo, V.S.Y. (1994) ‘Application of logit models in racetrack data’, in D.B. Hausch, V.S.Y. Lo and W.T. Ziemba (eds), Efficiency of Racetrack Betting, London: Academic Press, 173–81. Maddala, G.S. (1983) Limited Dependent and Qualitative Variables in Econometrics, New York: CUP. McGlothlin, W.H. (1956) ‘Stability of choices among uncertain alternatives’, American Journal of Psychology 69: 604–15. Sauer, R.D. (1998) ‘The economics of wagering markets’, Journal of Economic Literature 36: 2021–64. Schnytzer, A. and Y. Shilony (1995) ‘Inside information in a betting market’, Economic Journal 105: 963–71. Schnytzer, A. and Y. Shilony (2002) ‘On the timing of inside trades in a betting market’, The European Journal of Finance 8: 176–86. Schnytzer, A., Y. Shilony and R. Thorne (2003) ‘On the marginal impact of information and arbitrage’, in L. Vaughan Williams (ed.), The Economics of Gambling, London: Routledge, 80–94. Tuckwell, R.H. (1983) ‘The thoroughbred gambling market: efficiency, equity and related issues’, Australian Economic Papers 22: 106–18. Vaughan Williams, L. and D. Paton (1997) ‘Why is there a favourite–longshot bias in British racetrack betting markets?’, Economic Journal 107: 150–8. Wetherill, G. B. (1981) Intermediate Statistical Methods, London: Chapman and Hall. Ziemba, W.T. and D.B. Hausch (1986) Betting at the Racetrack, L.A.: Dr. Z Investments Inc.

15 Gluck’s Second Law An empirical investigation of horserace betting in early and late races J.E.V. Johnson and A.C. Bruce

Introduction Gluck’s Second Law, ‘The Best Time to Bet the Favourite is in the Last Race’, is based on the assumption that bettors select relatively long-odds horses in the final race(s) of the betting day. The principal objective of this chapter is to test this premise in relation to bettors in off-course bookmaker-based betting markets. Two further features of betting on later races are also considered, the behaviour of bettors in terms of staking levels and betting performance, variously defined. This involves an empirical study of horse-race betting decisions made by individuals in UK off-course betting offices. The chapter proceeds as follows. The first section briefly reviews the existing literature relating to the atypical behaviour of bettors on later races. The second section explains the methodology used together with the nature of the database. The third section outlines the procedures employed to investigate the nature of betting behaviour in early and late races and reports analyses of the data. A discussion of the results in relation to existing literature is provided in the last section.

Existing literature It is well documented that gamblers persevere in the face of previous failure. Gilovich (1983), for example, argued that (p. 1111) ‘gamblers continue to gamble despite persistent previous losses . . . because gamblers evaluate outcome information in a biased manner’. It is argued that they explain away unsuccessful outcomes and readily accept successes as a justification of the selection procedures they use. Despite bettors’ persistence, their behaviour in the face of losses may be modified, perhaps becoming more risk-preferring or risk-averse. Such changes in behaviour may be exploited by knowledgeable bettors. Kopelman and Minkin (1991) tested two hypotheses (‘Gluck’s Laws’) relating to patterns of horse-race betting and odds, using pari-mutuel betting markets, in the United States. According to Kopelman and Minkin, ‘Gluck’s Second Law’ holds that ‘The Best Time to Bet the Favourite is in the Last Race’ (p. 701). This is based on the

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premise that since on average bettors lose, their total capital will decline throughout the racing day and that they ‘seek to recoup their losses by betting on long shots in the last race’ (p. 701). Under a pari-mutuel betting system, such support for comparative ‘outsiders’ tends to increase the odds against the favourite, thus rendering its odds ‘good value’. The aim of this chapter is to explore whether bettors, in off-course bookmaker-based betting markets in the UK, behave in a manner consistent with ‘Gluck’s Second Law’. Kopelman and Minkin’s findings confirm earlier empirical studies by McGlothlin (1956), Ali (1977), Asch et al. (1982) and Metzger (1985) who found a stronger tendency to ‘under-bet’ favourites and to ‘over-bet’ long-shots in later races. It has been argued (Asch et al., 1982) that the general tendency to ‘under-bet’ favourites in later races stems from a change in the bettor’s risk attitude, the reduction in capital experienced by the representative bettor throughout the betting day being responsible for a change toward more risk-preferring betting behaviour in later races. The main supporting evidence for ‘Gluck’s Second Law’ comes from the behaviour of bettors frequenting racetracks operating pari-mutuel betting systems. In the UK, however, bookmaker betting markets prevail. Approximately £4,000 million is wagered annually in off-course betting shops on horse races, and less than 10 per cent of this sum is wagered at the racetracks with bookmakers themselves. The odds at which most bets are settled are determined solely by the odds on offer by bookmakers at the racetracks immediately prior to the start of the race. The large off-course bookmakers transmit some of the money wagered on horses, for which they face significant liabilities, to the racetracks (via agents who place bets with on-course bookmakers in order to shorten the odds available). The effect of sustained support for ‘outsiders’ could be expected to generate adjustments of the favourite’s odds in a similar manner to that observed in pari-mutuel markets. A significant proportion of the money wagered in off-course betting shops, however, is not relayed to the racetrack by off-course bookmakers and, consequently, betting patterns off-course may not mirror betting patterns on-course. The environment in which bets are placed in off-course betting offices is obviously different to that experienced by bettors at racetracks. Bets in betting offices, for example, can be placed on races at a variety of racetracks, and bettors, whilst removed from the live action, are provided with audio and televisual information from a variety of sources: odds movements, and pre-, during and post-race action are relayed from a variety of racetracks. In addition, the wide distribution of betting shops in the UK ensures that most bettors can frequent betting shops close to their homes. This affords them the relatively costless opportunity, compared with racetrack bettors, of returning home during the afternoon racing period, either to replenish their finances or to abandon their betting activity for the day. The main objective of this chapter is to investigate whether bettors in offcourse, bookmaker-based, betting markets select relatively long-odds horses in

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later races, as appears to be the case in pari-mutuel markets. The methodology employed in this study is indicated below.

Method The basic raw material of the database used in this study is the betting slip submitted by a bettor at the time of bet placement. Betting slips record detailed characteristics of each bet placed in a UK betting office, including the selected horse, the stake wagered, the type of bet (single, accumulator, forecast, etc.) and the exact time and location at which the bet was placed. A systematic random sample of 1,212 bets was drawn from betting offices throughout the UK, owned by Ladbroke Racing, the UK’s largest bookmaking organization. All bets included in the sample are ‘win-singles’, the simplest form of bet, where the stake is placed on an individual horse and a profit is obtained if that horse is placed first. ‘Win-singles’ were chosen since they constitute the most common type of bet placed. In addition, the selection relates to an individual race, providing an unambiguous picture of early and late race betting patterns. An important feature of this database is that it comprises real betting decisions made by bettors who were unaware that their selections were being monitored. A systematic random sample was selected by betting office staff according to the serial numbers of betting slips (which are chronologically arranged), following close of business. For each betting slip selected in this manner a further set of relevant information was compiled. Most significantly, by using precisely timed transcripts of the betting information transmitted to betting offices, an accurate picture of the odds relating to the selection at the time the bet was made was obtained. The sample was selected from bets placed on horses in the period 12 March to 18 April 1987 and includes data from 88 separate races involving 13 different racetracks. No single race accounts for a large proportion of the data; the two most popular betting races account for 4 per cent and 33 per cent but none of the remainder accounts for more than 2.0 per cent of the total bets in the sample. In the results which follow, attention is confined to bets placed during the ‘show’ period of each race, that is, the ten to 15 minutes prior to the start of the race when odds from the racetrack are transmitted to the betting shop. Consequently the results relate to a sub-sample of 490 bets placed on the first and last three races.

Results The first set of results, summarized in Table 15.1, compares bets placed on races at different stages of the afternoon racing programme. Specifically, attention focuses on the average odds of horses selected in different races, at the time the bet was placed. It is clear from the results shown in Table 15.1 that there is a strong tendency for bets relating to the later races of the betting day to be placed on horses at

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Table 15.1 Mean odds of bets placed during the show period on races at different stages of the racing day Early races

First First two First three

Late races

M

SD

n

9.7/1ad 9.0/1bc 10.1/1cf

10.3 9.3 15.5

91 159 244

Last Last two Last three

M

SD

n

5.8/1abc 6.1/1def 7.8/1

3.9 4.6 19.5

81 161 246

Notes abcdef p < 0.05.

shorter odds. The most striking distinction may be seen by comparing the last race with the first three races. The mean odds for bets placed on the last race are 5.8/1 compared with mean odds for bets placed on the first three races of 10.1/1. Similar results were obtained when final racetrack odds were computed, as opposed to the odds prevailing at the time the bet was struck. For example, the mean of the final racetrack odds for bets placed on the last race was 6.3/1, compared with mean odds for bets placed on the first race of 12.5/1 (p < 0.05, twotailed) and on the first three races of 12.0/1 (p < 0.05, two-tailed). One interpretation of the apparent tendency to back shorter-odds horses in later races might simply be that these races have a smaller number of runners which would cause the average odds of each runner to be lower. Consequently, to control for the size of the field the odds of each horse were divided by the number of horses in the race and the resulting means of the adjusted odds were calculated. The results are reported in Table 15.2 and these suggest that even when the number of runners is controlled for in this manner the mean adjusted odds for bets placed in later races are lower than those in earlier races. As such the patterns of betting identified in Table 15.1 are confirmed. These results show a pattern of behaviour which clearly refutes the premise that last race bettors tend to favour longer-priced selections. Last race bettors in off-course betting offices appear to back shorter-priced horses. To confirm this view the percentages of bets placed on first favourites in early and late races were contrasted, where the favourite was determined at the time the bet was placed. The results summarized in Table 15.3 indicate that generally more bets are placed on favourites in later races. No significant differences are found, however, between the extent of favourite-backing in the last race compared with earlier races. The relative propensity to back favourites in later races could simply reflect smaller later-race fields. During the study period, however, the mean numbers of runners in the first and last races were almost identical (14.83 and 15.17, respectively) as were the mean numbers of runners in the second and third races combined and in the third from last and penultimate races combined (11.71 and 11.72, respectively). It would appear, therefore, that betting losses (which are the general rule) may tend to generate a more rather than less risk-averse attitude to later betting

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Table 15.2 Mean ‘odds of bets placed/number of runners’, during the show period, on races at different stages of the racing day Early races

First First two First three

Late races

M

SD

n

0.602a 0.600bc 0.655d

0.633 0.583 0.887

91 159 244

Last Last two Last three

M

SD

n

0.400abd 0.484cd 0.598

0.276 0.419 1.41

81 161 246

Notes abcd p < 0.05 (two-tailed).

Table 15.3 Percentage of bets placed on favourites, during the show period, on races at different stages of the racing day Early races

Late races 17.6ad 20.8be 20.1cf

First First two First three

Last Last two Last three

22.2 30.4def 30.9abc

Notes abcdef p < 0.05 (one-tailed).

Table 15.4 Mean staking levels (£) of bets placed on races at different stages of the racing day Early races

First First two First three

Late races

M

SD

4.73a 4.13b 4.34c

12.91 10.04 10.54

Last Last two Last three

M

SD

6.56 6.07 6.51abc

13.72 12.33 13.36

Notes abc p < 0.05 (two-tailed).

events in terms of the odds or degree of ‘favouritism’ of the horse selected. To explore later-race betting in more detail two further aspects are considered in the results which follow, staking behaviour and performance. Table 15.4 summarizes comparative staking levels. The means of stakes for bets on later races in the sample are in excess of £6, whereas the means of stakes for bets on earlier races in the sample are less than £5. The results clearly indicate that stakes do not decrease throughout the betting day. There is, in fact, some evidence to suggest a tendency for staking levels to increase for later races, the mean stake for bets on the last three races (£6.51)

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Table 15.5 Performance of bets placed, during the show period, on races at different stages of the betting day Early races

Late races

Return/stake

First First two First three

Return/stake

M

SD

Winning bets, %

0.637 0.627 0.604

2.69 2.61 2.82

12.1 12.6 10.2a

Last Last two Last three

M

SD

Winning bets, %

0.820 0.703 0.578

3.19 2.95 2.41

18.5a 15.5 15.0

Notes a p < 0.05 (two-tailed).

being significantly different from the mean stake for bets on the first two races (£4.13; t = 2.04, p < 0.05) and on the first three races (£4.34; t = 2.0, p < 0.05). At first sight, this seems to be at odds with the increasingly risk-averse behaviour implied by the results in Table 15.1 in that bettors appear, to some extent, to be prepared to risk more in terms of stake as the day progresses. On the other hand, it could be argued that committing higher stakes to selections on which the odds imply a higher probability of success constitutes a rational attitude to risk taking. The final set of results offers a simple test of the ‘rationality’ of such behaviour by considering the comparative performance of bets on races at different stages of the day. Table 15.5 presents results on comparative performance. The proportion of bets in the sample producing a return greater than the initial outlay (‘winning bets’) is greater for later race bettors than earlier race bettors across all categories of race examined. Winning bets, for example, account for 18.5 per cent of all bets placed on the last race compared with only 10.2 per cent for bets placed on the first three races. Similarly, bets on both the last race and the last two races produce mean returns (return/stake) in excess of those earned on bets in either the first, the first two or the first three races, last race bettors in the sample receiving on average 82.0 per cent of their stake in ‘winnings’ compared with only 60.4 per cent for bettors on the first three races. Despite these observations, only one of the early/late race performance comparisons is statistically significant (p < 0.05). It is clear, however, from these results that late race bettors perform at least as well as earlier race bettors.

Discussion The results reported in this chapter do not support the central premise of Gluck’s Second Law, that favourites are under-bet in the last race, but do suggest evidence of atypical betting behaviour associated with later races. The results indicate a tendency to bet on ‘favourites’ in the last race of the betting day and contrast with the majority of previous studies exploring pari-mutuel markets. The results are, however, in line with the work of Thaler and Johnson (1990) who suggested

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that ‘prior losses can decrease the willingness to take risks’ (p. 644). In their experiments, ‘subjects reported that the loss of $9 would hurt more after an initial loss of $30 than if it had occurred by itself. This increase in loss aversion would tend to produce risk aversion for gambles that risk additional losses’ (p. 657). The tendency for off-course bettors in later races to back horses with shorter odds may result from such an increase in loss aversion. It is possible that losses resulting from earlier races may create a negative affect which, as Isen et al. (1982) have demonstrated, can strongly influence risk-taking behaviour. The results reported in this chapter, whilst not supporting the tendency to bet on ‘long-shots’ in later races do, in terms of comparative staking levels and performance, suggest differences in betting behaviour between earlier and later betting events. In particular, bettors on the last three races have a propensity to place higher stakes on short-priced horses, with at least as much success as earlier race bettors. It may be, as reported by Thaler and Johnson (1990), that bettors have a strong motivation to ‘break-even’ and that the bettor who is behind by say £10, having through negative affect been induced to risk aversion, prefers the prospect of betting a further £10 on an even-money favourite with a ‘high’ probability of success than risking a further £1 on a 10/1 shot with only minimal chance of success. Exotic and multi-race bets (e.g. correctly predicting the first and second horse in a particular race; correctly combining the winners of two or more races in one bet) typically involve high composite odds. The larger stakes placed on ‘winsingles’ in later races may to some extent reflect the limited availability of exotic and multi-race bets at this time. The tendency to back horses with shorter odds as single bets in the last race suggests, however, that bettors are not seeking higher odds bets in these later races. The limited availability of relatively high odds exotic and multi-race bets in the later period is therefore probably not the main cause of larger staking on win-singles. Further research in this area might, however, usefully address staking patterns for exotic and multi-race bets, since higher staking on these relatively high-odds bets could reflect a desire to recoup earlier losses. The current study does show significant differences between betting patterns in earlier and later races in general. Differences between betting patterns in the first and last races in particular are, however, less clear. Bettors in the last race are shown to prefer horses at shorter odds than bettors on the first race, but no significant difference is found between these races in terms of the proportion of bets on favourites, the average stakes or the bettors’ success rates. These results are, in some aspects, similar to those reported by Metzger (1985) who examined 11,000 horseraces run in the US in 1978 and found no significant difference between betting patterns in the first and last races. She suggested that the field size might influence patterns of betting more than the experience of unsuccessful bets, but as indicated earlier, field size did not appear to influence results of the current study. The results reported here, particularly in relation to the propensity of bettors to select shorter-priced horses in later races, are in marked contrast to most

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earlier work conducted in pari-mutuel betting markets. It may be that off-course bettors in the UK are now aware of ‘Gluck’s Second Law’ and are attempting to exploit it or to exploit a variant of it, such as ‘The Best Time to Bet the Favourite is in the Last Three Races’. The current results may in part arise because of the different environment encountered by bettors in an off-course betting office compared with that experienced in betting at the racetrack. The conveniently located off-course betting office may, for example, provide bettors with a relatively simple opportunity of returning home and consequently they may stay for fewer races than would occur at the racetrack. Off-course bettors may, therefore, suffer less decline in capital prior to the last race and they may consequently have less incentive to back outsiders in later races than those bettors at the racetrack. Clearly, the precise reasons for the atypical later race betting patterns noted in this study require further investigation, but these results certainly shed doubt on the central premise of Gluck’s Second Law in relation to off-course betting markets.

Acknowledgements The authors acknowledge their grateful thanks to Ladbroke Racing and Colin Walker for their co-operation. Thanks are also due the anonymous referees for their insightful comments on an earlier draft.

References Ali, M. M. (1977) ‘Probability and utility estimates for racetrack bettors’, Journal of Political Economy, 85: 803–15. Asch, P., Malkiel, B. G. and Quandt, R. E. (1982) ‘Racetrack betting and informed behaviour’, Journal of Financial Economics, 10: 187–94. Gilovich, T. (1983) ‘Biased evaluation and persistence in gambling’, Journal of Personality and Social Psychology, 44: 1110–26. Isen, A. M., Means, B., Patrick, R. and Nowicki G. P. (1982) ‘Positive affect and decision making’, in M. S. Clark and S. Fiske (eds), Affect and Cognition. Hillsdale, NJ: Erlbaum, pp. 243–61. Kopelman, R. E. and Minkin, B. L. (1991) ‘Toward a psychology of pari-mutuel behaviour: test of Gluck’s Laws’, Psychological Reports, 68: 701–2. McGlothlin, W. H. (1956) ‘Stability of choices among uncertain alternatives’, American Journal of Psychology, 69: 604–15. Metzger, M. A. (1985) ‘Biases in betting: an application of laboratory findings’, Psychological Reports, 56: 883–8. Thaler, R. H., and Johnson, E. J. (1990) ‘Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice’, Management Science, 36: 643–60.

16 Investigating the roots of the favourite–longshot bias An analysis of decision-making by supply- and demand-side agents in parallel betting markets A.C. Bruce and J.E.V. Johnson

Introduction The aim of this chapter is to further the understanding of a behavioural phenomenon which has become an empirically well-established feature of betting markets. This is where the odds which reflect the decisions of individuals in such markets deviate in a systematic way, in terms of implicit probability, from the realized or objective probabilities which are determined by event outcomes. Specifically, this phenomenon, the ‘favourite-longshot bias’ may be summed up thus (Thaler and Ziemba, 1988): ‘Favourites win more often than the subjective probabilities imply, and longshots less often’. Given that the existence of the bias is essentially the product of human decision-making behaviour, it is perhaps surprising that much of the debate surrounding this phenomenon has, to date, been conducted within the economics literature. This reflects its significance to the study of market efficiency issues, where the existence of favourite-longshot bias enables the identification of inefficiency in terms of profitable subsets of aggregate betting activity. More recently debate within the economics literature has turned away from efficiency issues per se, that is, the implications of bias, and towards identification of the origins of the bias. This has shifted the emphasis of enquiry squarely into the domain of behavioural decision-making. A central question here is whether the existence of favourite-longshot bias owes more to the motivations and behaviour of agents on, respectively, the demand side or the supply side of betting markets. Against this background, this chapter has two specific objectives. First, it aims to exploit the opportunities presented by a hitherto unavailable data source to shed light on the relative contributions of supply and demand influences. Second, it develops the debate relating to the specific form of those influences by integrating explanations offered by the narrower, context-specific studies with perspectives suggested by the more general behavioural decision-making literature.

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The chapter is organized as follows. The next section offers a brief review of the economics literature relating to the favourite-longshot bias and some observations on the methodologies employed. The third section presents the rationale behind the analysis presented in this chapter and explains the nature of the dataset. The fourth section outlines the procedures employed to analyse the data. The fifth section presents the results of these procedures and the sixth section interprets the implications of these results in relation to the existing body of work. Some concluding remarks follow.

The favourite-longshot bias: the literature With few exceptions (e.g. Busche and Hall, 1988; Busche, 1994), analyses of the distribution of prices (or odds) within betting markets have provided consistent evidence for the favourite-longshot bias. Dowie’s (1976) study represents an early and extensive empirical confirmation using a large sample of UK bookmaker-based markets. This study noted a steady decline in cumulative returns to level staking as successively ‘longer’ priced horses were incorporated into the calculation. Thus, level staking on all horses with prices of ‘evens’ or shorter (i.e. an implied 50/50 or better chance of success) generated a return of minus 0.4 per cent. This loss grew to minus 10.1 per cent for all horses up to and including 2/1, minus 16.2 per cent for all horses up to and including 14/1 and minus 39.4 per cent for the whole sample. For the 3,739 horses with odds of 20/1, the objective odds of success were, in fact, 90/1. Thaler and Ziemba (1988) observed a similar phenomenon using Californian pari-mutuel data. Here a steep fall in return was reported at odds in excess of 18/1 and the objective odds of a 100/1 chance were 730/1. Further evidence of the effect is found, inter alia, in Henery (1985) and Bird and McRae (1994). Various theories have been advanced as to the origins of the favourite-longshot bias. In general, the emphasis has been on identifying origins in the decision behaviour of, alternatively, bettors or bookmakers. Thus, for example, Henery (1985) models the bias in terms of the bettor’s propensity to take into account only a (fixed) fraction, f, of potential losses. In this model, bettors explain away or discount losses as atypical or unrelated to their skill: such behaviour has been observed by Gilovich and Douglas (1986). Henery argues that if the objective probability of a horse losing a race is q, the bettor will judge the probability of losing as fq. He demonstrates that such behaviour leads to the favourite-longshot bias. Other demand-side rationales relate to the alleged risk-loving characteristics of bettors as decision-makers (Quandt, 1986) or to the potential importance of elements in the set of bettor motivations which are not related to financial return (Thaler and Ziemba, 1988). Bruce and Johnson (1992) are supportive of this view of a wider and non-homogeneous bettor utility function, as are Gabriel and Marsden (1990) in seeking to explain differential returns to winning selections across parimutuel and bookmaker-based markets. More recent attention has focused on attempts to explain the bias as a behavioural response by bookmakers to an ‘adverse selection’ problem. Here, the

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argument is that bookmakers take the decision to adjust odds on offer so as to minimize their exposure to the activity of informationally privileged bettors. It is argued that those with privileged information will generally be motivated to place bets with bookmakers, since the return is determined by the odds available at the time the bet is placed. Subsequent ‘followship’ behaviour by bettors who are not informationally privileged will therefore not erode the returns of the ‘insiders’ (this contrasts with the situation in pari-mutuel markets). Consequently, it is suggested that bookmakers will significantly reduce the odds available on longshots. This has the effect of reducing the potentially substantial gains which those with inside information might make from betting on horses with long odds. The work of Shin (1991, 1992, 1993) develops this line of reasoning, using a methodology developed from financial markets analysis. He explains the correlation between number of runners and the sum of prices in terms of the suppliers’ response to the presence of insider trading. Vaughan Williams and Paton (1997) offer some support for the view that the bias originates in the decisions of bookmakers, using UK bookmaker-based data for a set of events segmented according to the expected prevalence of insider activity. Before discussing the limitations of the existing body of work, it is important to clarify the distinctions between the two main forms of horse-race betting market, the pari-mutuel and the bookmaker-based market. In pari-mutuel markets, winning bettors simply share, pro rata, an ex ante and exogenously fixed proportion of betting turnover. The operator of the market (invariably a state monopoly) receives the fixed deduction from turnover to cover costs and normal profit. Thus, to illustrate via a simple example: where there are two winning bettors, with stakes of £5 and £10 respectively, in a pari-mutuel market with an aggregate betting turnover of £180 and with a deduction of 16 per cent, the winners would receive, respectively, £50.40 and £100.80. These sums represent pro rata shares of the post-deduction pool of £151.20 at odds of 9.08/1 in each case. Had the £10 bettor been the sole winner, the whole post-deduction pool would have been returned to him at odds of 14.12/1. Thus it is clear that in such markets, in the absence of an active supply side, returns are uniquely determined by the pattern of relative demand. By contrast, bookmaker-based markets involve an active dialogue between bookmakers and bettors. The pattern of odds in the market emerges and evolves as a result of the interaction between buyer and supplier behaviours. These are revealed via their betting and pricing decisions, respectively. From the bettor’s perspective, these decisions reflect, inter alia, subjective evaluation of outcome, attitude to risk and the perception of value implicit in horses’ odds. Equally, the bookmaker’s pricing decision will be influenced by factors such as subjective evaluation and the desire to manage exposure to liabilities. This market interaction takes place, typically, over a period of some 20 minutes prior to the relevant race. It culminates in a set of starting prices (SPs), those odds which obtain at the end of the active market period and which are co-determined by the decisions of bookmakers and bettors (i.e. supply- and demand-side agent behaviour).

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A major limitation of the existing body of investigations into the origins of favourite-longshot bias is that it is dominated by analyses of pari-mutuel markets. As such, any bias-inducing effects associated with the behaviour of supply-side agents are necessarily unobservable. In addition, the analysis of pari-mutuel markets is frequently compromised by the restrictions relating to the public reporting of odds in such markets. In the UK, for example, pari-mutuel odds are declared in relation to winning horses only. This has limited the scope for comparison of activity between bookmaker and pari-mutuel markets in one of the rare settings where the market forms co-exist. In bookmaker markets, a further problem is that it is not straightforward to assign the origin of causal factors when the decisions of bookmakers and bettors are, as detailed above, essentially interdependent. For example, if low odds are offered on a particular horse, this may have arisen from the bookmaker’s assessment of the horse’s prospects, or from substantial financial support by members of the public or a combination of the two. There are further difficulties associated with attempts to model formally the processes at work within bookmaker-based markets. The requirements of a formal characterization of the market dialogue do not sit easily with the complex idiosyncrasies of horse-race betting markets. Consequently the formal modelling which characterizes many of the economic approaches struggles to capture the richness of the setting. This is arguably an important shortcoming. The effects for which an explanation is sought may in part be a function of the particular framework of institutions and practices which shape the market environment. Relatedly, the specification of the utility function which is held to drive the behaviour of bettors’ decisions in the market is invariably rather vague. Finally, in terms of its ability to interpret and to rationalize evidence relating to the origin of the bias, existing work has made little attempt to embrace the more mainstream behavioural decision-making literature. Thus, for example, the potentially illuminating contributions offered by Kahneman and Tversky’s (1979) Prospect Theory, Poulton’s (1977) insights into the weakness of quantitative subjective assessments, Thaler’s (1988) work on cognitive illusion and Thaler and Johnson’s (1990) mental accounting model are neglected in the explanation of observed effects. This represents a considerable shortcoming for an area of enquiry which has become increasingly located within the behavioural decision-making domain. The methodology described in the following section seeks to address the principal concerns outlined above.

Data and methodology It was observed above that the profile of prices which emerges from pari-mutuel markets is exclusively determined by the decision behaviour of bettors on the demand side, given the absence of an active supply side in such markets. However, in bookmaker-based markets, it is the process of active exchange between bookmakers and bettors which generates the distribution of prices in the market. As such, in both markets, the odds on offer at the end of the betting

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period represent the combined subjective beliefs concerning the horses’ relative chances of success of those individuals operating in the respective markets. Clearly, a set of procedures which is able to compare the profiles of prices which emerge from these parallel markets for a given set of events offers an important methodological opportunity. Specifically, it enables the isolation of the respective influences of bookmaker and bettor decisions on the pattern of prices and, thereby, on the degree of favourite-longshot bias. This type of comparative study is limited to a very few settings where pari-mutuel and bookmaker-based markets co-exist, the most significant of which is the UK horse-race betting market. Even in such settings, however, investigation is generally constrained by the incomplete nature of price information in relation to pari-mutuel markets. The key constraint is that the odds or returns are made public only in respect of horses which win or are placed. The method employed in this study addresses this problem by utilizing a new data source which offers detailed information on all pari-mutuel betting activity on all horses in a large sample of recent UK horse-races. This allows the compilation of a complete profile of decision-making behaviour within each individual pari-mutuel horse-race betting market. The evidence from the set of pari-mutuel markets is then compared with evidence from the parallel bookmaker-based markets for the same set of events. Access to data relating to these markets was made possible via the co-operation of the sole UK pari-mutuel market operator, the Tote, and the largest UK non-pari-mutuel bookmaking organization, Ladbroke plc. The precise nature of the price data which comprise the database requires some discussion. First, the pari-mutuel data were assembled from computerized records of betting turnover on each of 19,396 horses which ran in 2,109 races in the UK between 1 June and 31 August 1996. These data were supplied by the Tote. This resource enabled the computation of accurate Tote odds for each horse (see below). Consequently, a complete profile of pari-mutuel odds for each race was determined, thereby offering a uniquely detailed insight into a betting market in the UK where odds are determined purely by the pattern of bettors’ decisions. The starting price odds in the parallel bookmaker-based market for the same set of events were then added to the dataset. This represented a more straightforward task in that ‘starting price’ odds relating to each horse in a race are published in this type of market. Within the UK, bettors at the racetrack have the choice of placing their bets with bookmakers or with the pari-mutuel system (the Tote). In placing a bet with a bookmaker, the odds offered at the time of bet placement are secured by the bettor. However, the odds on offer vary, depending upon a variety of factors such as the bookmaker’s subjective judgement as to the outcome of the race, competition between bookmakers and demand by bettors. Whilst bettors with the Tote are made aware of the odds available on each horse at any moment in time (via computerized display screens at the racetrack) they cannot secure a particular set of odds for their selection. The odds which they will receive are those determined by the relative amounts of money placed on each horse (see below for a more detailed discussion). To reiterate, the data described above

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Table 16.1 Comparison of mean Tote odds and mean bookmaker odds Bookmaker odds

N

Tote odds (mean: x/1)

Bookmaker odds (mean: y/1)

ta

Significance

<1/1 ≥1/1, <5/2 ≥5/2, <5/1 ≥5/1, <10/1 ≥10/1, <20/1 ≥20/1

305 1,292 3,029 4,895 4,815 5,060 19,396

0.60 1.66 3.58 7.63 20.86 54.80

0.63 1.75 3.54 6.83 12.95 35.94

2.75 5.72 –0.56 –3.27 –2.61 –7.98

p < 0.006 p < 0.001 p > 0.577 p < 0.001 p < 0.005 p < 0.001

Note a Paired samples t-test.

allow a direct comparison between the purely bettor-determined pari-mutuel odds, on the one hand, and the bookmaker-based odds, which result from a combination of bookmaker and bettor decisions, on the other. The main additional data component relates to the success (or otherwise) of each horse in the sample. This element was drawn from publicly available statistical records. Preliminary analysis of the dataset indicates that for horses in the sample, the average starting price was 15/1 (σ = 18.22), the minimum starting price being 0.04/1 and the maximum 500/1. The corresponding average Tote odds were 22.1/1 (σ = 135.33) with a minimum of 0.1/1 and a maximum of 4,311.3/1.1 The average Tote odds were significantly higher than the average starting price (t = 7.24, p < 0.01). In order to undertake a preliminary investigation of cross-market differences, the average Tote odds and the average starting prices (SP) were calculated for all horses whose starting prices fell into particular categories. The results are summarized in Table 16.1. It appears from these results that for shorter odds horses (SP  5/2), starting prices are significantly higher than Tote odds. For midrange odds (5/2  SP < 5/1) there is no significant difference between the two sets of odds and for higher odds horses (SP  5/1) Tote odds are significantly greater than starting prices. These preliminary investigations suggest that the favouritelongshot bias may be more pronounced in bookmaker-based markets than in parimutuel markets. We now turn to outlining the procedures employed to establish if this is the case and, if so, to determine the precise nature of the differences in patterns of betting behaviour between the two markets.

Procedures The chapter aims to assess whether the behaviour of demand- or supply-side agents causes the favourite-longshot bias. To achieve this aim, logistic regression was employed. This enables an exploration of the extent to which odds derived from individuals’ betting behaviour (Tote market) and odds determined by a combination of bookmakers’ and their clients’ decisions (bookmaker market)

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differ in the degree to which they contribute to the favourite-longshot bias. If the traditional favourite-longshot bias is discerned employing Tote odds, this would imply that features associated with bettors’ decisions are causing the phenomenon. This can be implied since Tote odds for a given horse mechanistically reflect the relative amount of money wagered on that horse in a particular race. The supplier has no effect on these odds, given that the level of deduction from the betting pool is exogenously determined. The Tote odds for horse i(Qit can therefore be represented as Qit =

T (1 − d ) −1 hi

(1)

where: T = total amount bet on the Tote for race i, d = Tote deduction (0.16 for the period in which the sample was collected), and hi = amount bet on horse i. Since the Tote odds represent the combined judgements of all those who bet with the Tote, we assume that these can be used to assess the Tote bettors’ degree of belief concerning a horse’s relative chance of success. Given the Tote bettors’ awareness of the level of Tote pool deductions and the odds available, it is expected that, as rational agents, they will continue to place money on horse i, up to the amount hi, such that their subjective probability of horse i winning is given by: Pit =

hi 1 or O +1 T (1 − d ) t i

(2)

If the observed probability of winning for horses with high/low Tote odds is found to be consistently under/over the bettors’ implied subjective probability, this would suggest that the traditional favourite-longshot bias operates in Tote markets. If, in addition, the relationship between observed probabilities and the probabilities inherent in bookmakers’ odds suggests a similar pattern, we can confirm favouritelongshot bias in this type of market also. Furthermore, if observed bias is greater in bookmaker markets than in pari-mutuel markets, this suggests that, in addition to demand factors, the decisions of those on the supply side (bookmakers) also contribute to the favourite-longshot bias. Starting prices represent the bookmakers’ odds which are available at the racetrack immediately prior to the start of a race. The odds offered at the racetrack at the commencement of betting represent the bookmakers’ initial subjective opinions of the likely outcome of the race. These may, according to Shin (1992), involve some element of protection against the actions of informationally privileged bettors. As a result of money wagered at the racetrack and competition between bookmakers, horses’ odds rise or fall in line with demand. Whilst only 10 per cent of total money wagered on races in the UK is placed at the racetrack, off-course bookmaking organizations also balance their liabilities by betting at the racetrack through their agents. Consequently, it is assumed that bookmaker odds offered on horse i immediately prior to the start of

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the race (O bi) can be used to represent a combination of the bettors’ and bookmakers’ subjective probabilities of horse i’s chance of winning (P bi) in the following manner: Pib =

1 O +1 b i

(3)

Irrespective of the race in which it is running, it is assumed that odds on horse i (Tote or starting price) of Oi would imply that the relevant set of bettors’ subjective probability of the horse’s success, is 1/(Oi + 1). Consequently, data from the whole sample, which indicate for each horse the starting price, the Tote odds and whether or not the horse won its race, were used to develop two separate logit models. A full description of these models and the assumptions on which they are based is given in the Appendix and a summary of the models’ main characteristics appears below. The first, model 1, employed the starting price, and the second, model 2, used the Tote odds to predict the winning probability of horses, associated with particular odds. To develop these models an index (Y *i for model 1, X *i ) for model 2) is derived for each horse i in the sample. Asch et al. (1984) suggest that such an index may be ‘thought to measure the “winningness” of a horse and to depend on a systematic part and a stochastic part’. The index can be regarded as ‘nature’s or fate’s views’ concerning a particular horse’s chance of winning. It is assumed that ‘nature’ will choose horse i as a winner if its index of winningness is greater than 0 and select the horse as a loser if its index is less than or equal to 0. Odds have been demonstrated to be reasonable predictors of a horse’s winning chance (e.g. Asch et al. 1982; Dowie, 1976). Consequently, it is tempting to test particular functional forms to relate the underlying odds, via the ‘index of winningness’, to the probability of success. However, there is no unanimity in the literature concerning the form of the relationship between odds and the ‘winningness index’ (Asch et al., 1984; Bacon-Shone et al. 1992; Figlewski, 1979). In addition, whilst many studies identify a favourite-longshot bias (e.g. Tuckwell, 1983; Thaler and Ziemba, 1988) some do not (e.g. Busche, 1994; Busche and Hall, 1988). A further complicating factor exists since there is no previous evidence available concerning the existence of favourite-longshot bias in parallel pari-mutuel and bookmaker markets. As indicated above, there is considerable debate concerning the main sources and strength of the bias. The above discussion suggests that there are no a priori reasons for assuming a particular functional form for the relationship between odds and the probability of success (via the winningness index). In an exploratory study such as this, any hypothesized relationship based on little or spurious evidence might be regarded as restrictive at best. Consequently, the relationship between odds and probability was investigated for model 1 by defining the winningness index Y *i as a polynomial of the natural logarithm of the starting price together with a random error term, ei. For model 2, X *i was defined as a

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polynomial of the natural logarithm of the Tote odds together with a random term, ui, as follows: k

Yi * = ∑ ar ln (Oib ) − ei r

Model 1

(4)

Model 2

(5)

r =0 1

X i* = ∑ br ln (Oit ) − ui r

r =0

Yi* and Xi* are determined such that if horse i is identified as a winner in the sample, Yi* > 0 and Xi* > 0, and if horse i was not a winner, then Yi*  0 and Xi*  0. If horse i is a winner, this implies that k

ei <

l

∑ a [ln(O )] r

b i

r

and ui <

r =0

∑ b [ln(O )] r

t i

r

r =0

The variable we observe in the sample is Wi, which takes the value of unity if horse i wins and is 0 if it does not win. Consequently, for model 1:  p(Wi = 1) = p(Yi* > 0) = p ei < 

r

∑ a [ln(O )]  = ∫ r

r

b i

z

−∞

f (e)de

(6)

where

z = ∑ ar ln (Oib )

r

r

Assuming that ei follows a logistic distribution implies that:

p (Wi = 1) =

ez 1 + ez

(7)

In a similar manner, for model 2:

p (Wi = 1) =

eq 1 + eq

(8)

where

q = ∑ br ln (Oit )

r

r

The coefficients ar and br are estimated by developing a joint probability or likelihood function for the sample. Assuming that the observations are independent leads to the following likelihood functions for model 1:

 ez   ez  p (W1 = w1 ,W2 = w2 ,L ,WN = wN ) = ∏ 1 − ∏   1 + e z  wi =1  1 + e z  w=0 

(9)

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Taking the natural logarithm of this joint probability produces a log-likelihood function. The coefficients ar are those which serve to maximize the loglikelihood function. Since the equations are non-linear they require an iterative solution. The log-likelihood function for model 2 is derived and solved in a similar manner. Having determined the coefficients ar and br equations (7) and (8) were employed to determine, respectively, the predicted probabilities of success for horses with various starting prices (model 1) and Tote odds (model 2). These predicted probabilities are termed pre-b and pre-t respectively. The predicted probabilities based on starting price were then constrained to sum to unity within each race. This produced proportionately ‘normalized’ predicted probabilities, npre-b. Consequently, for a race with m runners, the ‘normalized’ probability of success, for horse i, npre-bi, with a predicted probability of success of pre-bi, was calculated as follows: npre − bi =

pre − bi

(10)

m

∑ pre − b i =1

i

A similar calculation was employed to determine the predicted probability of success for each horse in the sample, based on its Tote odds (npre-t). Since m

∑ pre − b i =1

i

m

and

∑ pre − t i =1

i

were not constant between races, a given pre-b or pre-t resulted in a range of values for npre-b and npre-t. Curve-fitting facilities within SPSSX were employed to determine the appropriate functions for determining the most likely realized probability of winning for a horse associated with a particular value of Tote odds or bookmaker odds. The resulting functions were graphed. A number of methods could have been employed to normalize the predicted probabilities pre-b and pre-t (Lindley et al., 1979). However, in studies of bookmaker betting markets a proportional adjustment, similar to that shown in equation (10) is extensively employed (Bird and McCrae, 1987; Dowie, 1976; Tuckwell, 1983). It has been demonstrated that the probabilities inherent within bookmaker odds sum, within a race, to a larger amount the greater the number of runners (Ayton, 1997; Shin, 1993). This is not the case in the pari-mutuel market since the level of the operator’s deduction from the pool is constant across all races. Longer-odds horses are more likely to feature in races with a larger number of runners. Consequently, it might be argued that a proportionate deduction would amplify or even create any differences in the favourite-longshot bias observable between the bookmaker and Tote markets. In order to avoid potential bias of this nature the results obtained via the proportionate normalization procedure were validated by developing functions relating starting prices and Tote odds directly to the non-normalized predicted probabilities, pre-b and pre-t,

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respectively. Close similarity between the graphs constructed from the normalized and non-normalized predicted probabilities would confirm that the normalization procedure does not contribute significantly to the effects observed. In turn, graphs relating the Tote and bookmaker odds to the proportionately normalized probabilities of success (npre-ti and npre-bi, respectively) can then be used with confidence to identify any differences which exist between the favourite-longshot bias in the parallel betting markets.

Results We report the results of the logit estimations in Table 16.2, obtained using maximum likelihood facilities in SPSSX. The sample size is 19,396 and the models involving bookmaker odds (model 1) and Tote odds (model 2) are both highly significant. Polynomials of degree greater than 2 in the case of model 1 and greater than 1 in the case of model 2 were tried, but they introduced insignificant terms, and did not improve upon the explanatory power of the models outlined in Table 16.2. Employing equations (7) and (8), separate estimates, pre-b and pre-t, were developed for the unique probability of success of horse i with particular bookmaker odds, O bi and Tote odds, Oit, respectively. The sum of the estimated probabilities derived from bookmaker odds in each race was then constrained to equal one, as were the estimated probabilities derived from the Tote odds. Consequently, for a given starting price or a particular value of Tote odds, a range of ‘normalized’ predicted probabilities, npre-b and npre-t, was obtained. Curve-fitting facilities within SPSSX were employed to estimate unique values of ln(pre-b) and ln(pre-t) for each category of bookmaker odds and

Table 16.2 Results of logit estimations for model 1 and model 2 Variable

Coefficient

Standard error

Model 1: Independent variable = Loge (bookmaker odds)a Constant –0.0419 0.0563 Ln(bookmaker odds) –0.9957 0.0676 [Ln(bookmaker odds)]2 –0.0596 0.0214 Model χ2 = 2,213.8 (2 degrees of freedom) Log likelihood = –5,571.0 Number of observations Wi = 0: 17,283; Wi = 1: 2,113 Model 2: Independent variable = Loge (Tote odds)a Constant –0.2370 0.0445 Ln(Tote odds) –1.0041 0.0248 Model χ2 = 2,095.6 (1 degrees of freedom) Log likelihood = –5,630.1 Number of observations Wi = 0: 17,283; Wi = 1: 2,113

Wald

Significance

0.55 0.4572 216.78 0.0000 7.74 0.0054 [χ2(0.001) = 13.82]

28.43 0.0000 1,638.62 0.0000 [χ2(0.001) = 10.83]

Note a The dependent variable takes the value 1 if the horse wins and takes the value 0 if the horse loses.

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Tote odds. As a result of these procedures the following equations were derived: ln(npre − b) = −0.7012 − 0.5910 ln(O b ) − 0.1211[ln(O b )]

2

[ R2 = 0.996, degrees of freedom = 19393, F = 2373962( p < 0.0001)]

(11)

ln(npre − t ) = −0.8450 − 0.5721 ln(Ot ) − 0.0996[ln(Ot )] + 0.0073[ln(Ot )] 2

3

[ R2 = 0.999, degrees of freedom = 19392, F = 6724139( p < 0.0001)]

(12)

Polynomials of degrees greater than 2 for the model derived for bookmaker odds and greater than 3 for the model derived for Tote odds were tried. However, they introduced insignificant terms and did not improve upon the explanatory power of the polynomials indicated in equations (11) and (12). Employing equations (11) and (12), Figure 16.1 depicts differences in the change in the natural logarithm of the predicted probability of success for horses with particular Tote odds and bookmaker odds. In order to explore the effect of the normalization procedure indicated above, curve-fitting facilities within SPSSX were employed to determine appropriate functions relating bookmaker odds and Tote odds to their respective nonnormalized predicted probabilities of success pre-b and pre-t. Employing a similar method to that indicated above the following equations were derived: ln( pre − b) = −0.6814 − 0.6117 ln(O b ) − 0.1172[ln(O b )]

2

[ R2 = 0.999, degrees of freedom = 19393, F = 1.8E + 7( p < 0.0001)]

0

Ln (win probability)

−2 −4 −6 Bookmaker −8 Tote −10 Reference line: −12 −14 −2.00

win prob=1/(1+odds) 0.00

2.00

4.00

6.00

8.00

Ln (odds)

Figure 16.1 Predicted win probabilities (post-normalization).

(13)

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ln( pre − t ) = −0.8207 − 0.6021 ln(Ot ) − 0.0931[ln(Ot )] + 0.0069[ln(Ot )] 2

3

[ R2 = 1.00, degrees of freedom = 19392, F = 3.4 E + 7( p < 0.0001)]

(14)

Figure 16.2 depicts changes in the natural logarithm of the predicted probability of success as Tote and bookmaker odds vary. As indicated above, this figure is constructed without reliance on any normalization procedure. A comparison of Figures 16.1 and 16.2 clearly indicates a close correspondence. This suggests that the proportionate adjustment to the predicted probabilities did not have a significant effect on the favourite-longshot bias observed. The implication is that Figure 16.1 can be used with confidence to compare the degrees of favourite-longshot bias in the Tote and bookmaker markets. It is apparent from Figure 16.1 that for the longshots, Tote odds do not overstate the horses’ chance of success as much as the equivalent starting prices. For example, a horse with Tote odds of 200/1 (implied subjective probability = 0.00498) has a predicted probability of success of 0.0037, whereas a horse with bookmaker odds of 200/1 has a predicted probability of success of only 0.0007. However, for horses with low odds, starting prices appear to understate the horses’ chances of success, whereas Tote odds overstate the probability. For example, a horse with bookmaker odds of 0.2/1 (implied subjective probability = 0.833) has a predicted probability of success of 0.94, whereas a horse with Tote odds of 0.2/1 has a predicted probability of success of 0.81. Further comparisons of predicted probabilities of success arising from bookmaker and Tote odds are displayed in Table 16.3.

Table 16.3 Predicted probabilities of success arising from bookmaker and Tote odds Odds

0.2/1 0.5/1 0.8/1 1.0/1 1.5/1 2/1 5/1 10/1 20/1 50/1 100/1 200/1 500/1

Bookmaker odds

Tote odds

Predicted probability of success

Implied objective odds

Predicted probability of success

Implied objective odds

0.94 0.70 0.56 0.50 0.38 0.31 0.14 0.07 0.03 0.008 0.003 0.0007 0.0001

0.06/1 0.42/1 0.78/1 1.02/1 1.60/1 2.20/1 6.10/1 14/1 34/1 128/1 395/1 1,364/1 8,351/1

0.81 0.61 0.49 0.43 0.34 0.28 0.14 0.07 0.04 0.015 0.008 0.0037 0.0015

0.24/1 0.61/1 1.06/1 1.30/1 2.0/1 2.6/1 6.3/1 12.5/1 25/1 64/1 131/1 269/1 673/1

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A.C. Bruce and J.E.V. Johnson 0

Ln (win probability)

−2 −4 −6 Bookmaker −8 Tote −10 Reference line: −12 −14 −2.00

win prob=1/(1+odds) 0.00

2.00

4.00

6.00

8.00

Ln (odds)

Figure 16.2 Predicted win probabilities (prior to normalization).

Interpretation of results The graph displayed in Figure 16.1 plots equations (11) and (12) and this provides a rich insight into the nature and origin of the favourite-longshot bias. In interpreting the significance of the graph, it is instructive to consider the significance of the reference line which provides a benchmark against which to assess the data relating to SP and pari-mutuel returns. On a log scale, this line is a locus of points whereby the subjective probabilities implicit in the range of odds are equal to the objective probability of success. Deviation from this benchmark by the sp or pari-mutuel functions indicates the degree to which odds in each form of market fail to reflect the objective probability of success. Two features of the relationship between these functions suggest significant differences between the decision-making behaviour in bookmaker-based and parimutuel markets. First, in considering the SP function, it is clear that at odds of less than 0.92/1, the predicted objective probability of success exceeds that implicit in the odds. For all odds in excess of 0.92/1, the reverse is true. By contrast, the relationship between the subjective probability implicit in pari-mutuel odds and the predicted objective probability derived from the data is uniform in terms of the direction of relative magnitude. The subjective probability consistently exceeds predicted objective probability. The second striking difference concerns the degree to which the subjective probability functions deviate from the objective function. Here, using SP data, there is a tendency for the subjective and objective functions to deviate to an increasing degree as odds increase. However, with pari-mutuel data, the subjective/objective probability ratio is much more stable in magnitude, as well as being uniform in sign. There is some tendency for subjective and objective

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values to converge at low extreme odds values. In colloquial terms, these results suggest that bookmaker-based markets offer better ‘value’ in the short odds range, compared with pari-mutuel markets, but considerably inferior ‘value’ at higher odds. More formally, the results offer strong evidence for the existence of the favourite-longshot bias in bookmaker-based markets, with a corresponding absence of such an effect in the pari-mutuel case. These are powerful results, especially as they relate to the full range of betting opportunities in each of the institutionally distinct forms of betting market, across a large and identical set of events. The association of the strong favourite-longshot bias with the bookmakerbased market and its absence from the pari-mutuel market invites the conclusion that its origins lie principally in the decision behaviour of bookmakers. As such, the results presented here offer substantial corroboration for the work of Shin (1991), who assigned a supply-side origin to the bias. In developing the discussion relating to the origin of the bias, it may be instructive to consider further the specific nature of the influence associated with bookmaker behaviour. In particular, we consider the tendency of bookmakers to offer odds in the higher range which considerably overstate objective probability. Shin’s (1991) argument was firmly couched in terms of a rational bookmaker response to the possible existence of informationally privileged bettors. Shin (1991) argues that by offering lower odds on the longshots, bookmakers reduce the degree to which those with inside information can capitalize on the information. The plausibility of this explanation is not questioned here. However, the veracity of this explanation could be tested in markets where longshots exist but where the scope for inside information is more limited (e.g. soccer tournaments). The absence of or a reduction in the favourite-longshot bias in these markets would suggest that bookmakers in horse-race betting markets do insure themselves against insider information for long-odds horses. Further explorations of this nature are beyond the scope of this chapter, but previous research (e.g. Shin, 1991; Vaughan Williams and Paton, 1997) is consistent with the existence of such bookmaker behaviour. In addition to insuring against insider information, the bookmakers’ behaviour may also be explained by their attempt to induce greater expenditure by bettors on horses whose objective probability of success is actually very small. Thus, whilst the odds of a horse in terms of weight of money wagered might realistically be 200/1, bookmakers are aware that such a price, if advertised, would be likely to carry a strong negative message to the betting public. Under such circumstances, bookmakers may be inclined to advertise such a horse at, say, 50/1 in order to induce support from bettors for what appears now to be a genuine ‘outsider’ but not a ‘no-hoper’. Such activity, as well as indicating the essentially interactive nature of bookmakers’ and bettors’ decisions, would contribute to an explanation of the increasing divergence between odds and objective probability in the higher-odds range. There is a narrowing of the (bookmaker-based) subjective/objective probability differential in the lower-odds range, and indeed subjective probabilities exceed objective probabilities at odds of less than 0.92/1. This appears unusual

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if one extends the line of reasoning used above to further the explanation for wider disparity at longer odds. Such reasoning might suggest that bookmakers would be inclined to deter bettor activity in the lower-odds range, due to the greater objective probability of bettor success. Instead, what is observed is that bookmakers offer relatively ‘better value’ at lower odds. The explanation for this may lie partly in the nature of the bookmakers’ objective function. It could be argued, for example, that bookmakers may be prepared to sacrifice some element of profitability in return for higher revenue generation opportunities, an idea supported by Tuckwell (1983). In this context it should be noted that mean staking levels are invariably much higher in the lower odds zone (see, for example, Bruce and Johnson, 1992). The identified patterns of relative ‘value’ between the parallel markets raise the possibility that bettors may select the market in which they place their bet according to the odds range within which their selection falls. However, the durability of the distinction between the markets rules out such a pattern of behaviour, which in itself would serve to erode any cross-market returns disparity. It was observed in reviewing the existing literature that little attempt had been made to integrate perspectives offered by the more mainstream behavioural decision-making literature in informing understanding of the specific nature of the favourite-longshot bias. As such, it is important to acknowledge the contribution of the wider field in adding to our perspective on this particular phenomenon. Thus, for example, the substantial body of work by Kahneman and Tversky (1979) in the area of Prospect Theory sees decision makers as employing a probability-weighting function. Specifically, the observed tendency for individuals to underweight large probabilities and overweight small probabilities appears entirely consistent with the favourite-longshot bias. Similarly, though from a somewhat different perspective, the work of Poulton (1977) may contribute to our understanding of the phenomenon. Poulton (1977) draws attention to the unreliability of quantitative subjective assessments. In particular, he notes their vulnerability to ‘response range effects’, whereby a range of stimuli is interpreted by the subject as located within a ‘squeezed’ scale. In the context of betting behaviour, this is again consistent with over- and underestimation, respectively, of low and high objective probabilities and a marked centralizing tendency. The work off Thaler (1988) demonstrates how the existence of a cognitive illusion may induce systematically non-rational behaviour, via the example of the ‘winner’s curse’. Here, individuals’ bids in an auction for an asset of unknown value invariably generate a mean bid considerably below, but a winning bid in excess of, actual asset value. Various laboratory and field variants of this type of phenomenon are cited as evidence of the robustness of this effect. The parallel with the type of behaviour observed in this study resides in the systematic and consistent form of behavioural response which leads to the favourite-longshot bias and which may result from a particular perception of a set of implied probabilities. It has also been argued that bettors employing a mental accounting model (Thaler, 1985; Thaler and Johnson, 1990) are more likely to bet longshots at the end of a day, in an effort to break even for that day.

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This behaviour was also observed by Kopelman and Minkin (1991) in a parimutuel market in the USA. It is possible that bookmakers may take advantage of this behaviour by inducing bettors, via their pricing policy, to significantly overbet longshots at the end of a day. This, in turn, may contribute to the favouritelongshot bias. However, it is argued that this effect is unlikely to have played a significant role in creating the results observed here since studies in the UK have failed to observe the phenomenon of bettors preferring longshots in late races (Johnson and Bruce, 1992). In addition, the data analysed here cover betting activity across the betting day, so that the effects of the type identified by Thaler and Johnson (1990) and Kopelman and Minkin (1991) will, at best, appear muted in our results. It is important to remember that whilst the effects discussed above are perhaps more easily associated with the behaviour of demand-side agents (bettors) in this study, the results of the analysis suggest that the observed bias has its origins in supply-side agents (bookmaker) behaviour. Consequently, the relevance of the wider literature needs to be re-evaluated. For example, bookmakers may be able to influence bettor behaviour by the range of prices they offer. A natural assumption might be that bettors, responding to such a decision environment (essentially controlled by bookmakers), might be vulnerable to the type of cognitive illusion which induces bias-forming behaviour. However, it may be the case that bookmakers are themselves susceptible to this type of illusion in devising a set of prices. Perhaps a more plausible explanation is that bookmakers are aware of the susceptibility of bettors to bias-inducing behaviour and this influences the set of prices which bookmakers offer. Bookmakers are likely to increase their profits if they succeed in encouraging bettor behaviour in this direction. This point is essentially an extension of the effect postulated earlier in relation to price-setting behaviour and the manipulation of bettor expectations. In summary, it might be argued that bookmakers who are aware of the susceptibility of bettors to the cognitive illusions which induce bias may manipulate prices to encourage such behaviour. Where no such manipulation occurs (i.e. in the pari-mutuel market) results suggest that bettor behaviour remains unbiased. Clearly, the results presented above run contrary to the majority of earlier studies in the area which have generally, though not exclusively (see Busche, 1994; Busche and Hall, 1988), identified favourite-longshot bias within parimutuel markets. This requires some comment. One possible explanation lies in the fact that most earlier studies of pari-mutuel activity have related to betting at a particular racetrack, using relatively small samples. These studies may be susceptible to location-specific effects. For example, certain tracks may incorporate well-publicized track biases (e.g. horses drawn on the inside rail being particularly advantaged). At these tracks, horses which are perceived by the betting public to occupy a favourable position have been shown to be over-bet and those occupying less favourable positions to be under-bet (Quirin, 1979). This phenomenon could exaggerate the favourite-longshot bias at these tracks.

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By contrast, this larger-scale study covers a large range of racetracks and is therefore less susceptible to location-specific effects. However, perhaps the most important potential explanation resides in the important contextual difference between the markets under consideration in this study and those in earlier studies. Specifically, the body of earlier work in this area relates exclusively to monopoly pari-mutuel markets. Distinctively, this study analyses parimutuel activity given the existence of a competitor bookmaker market. As such, it should not be regarded as unusual for dissimilar patterns of behaviour to emerge between the two pari-mutuel markets. A possible explanation for the absence of bias in this study is that bettors who are simultaneously exposed to a competing bookmaker market are more sensitive to notions of ‘value’ at various odds. This sensitivity may be reflected in their decision-making behaviour in the pari-mutuel market, whereby horses which are available at longer odds than those available in the bookmaker market are the subject of support. Such behaviour is suggested by the close congruence between the subjective probabilities inherent in their decisions and objective probability.

Conclusion This chapter has sought to exploit the unique opportunities offered by access to hitherto unavailable data relating to parallel pari-mutuel and bookmaker-based UK horse-race betting markets. The focus of the investigation has been an inquiry into the behavioural origins of a well-established empirical phenomenon, the favourite-longshot bias. Employing logit models to generate the predicted objective probabilities across the range of odds in each market provides a comparison, over a common set of betting events, between markets with, respectively, active demand- and supply-side agents, and active demand-side agents only. This allows the isolation of the supply effect on the favourite-longshot bias. The results are strongly supportive of a significant role for the influence of bookmakers’ decisions in explaining the existence of the favourite-longshot bias in UK horserace betting markets, thereby corroborating the earlier theoretical conclusions of Shin (1993).

Acknowledgements We are grateful to Peter Dow of the Tote and to Michael Vanning of Ladbrokes for the data used in this chapter, to Raymond O’Brien and Raymond Chambers for their invaluable statistical guidance and to the anonymous referees for their insightful comments on an earlier draft of this chapter.

Notes 1 In computing the pari-mutuel odds, an institutional practice of the Tote is explicitly recognized; the Tote pays a minimum of £1.10 to a £1.00 stake, even where the proportion of stakes placed on a selection would warrant a lower return. Consequently, this minimum Tote return is employed in such cases to produce Tote odds of 0.1/1. At the

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other extreme, there were only four cases where no money was placed on a particular horse to win its race. In these cases, where in reality no dividend would have been paid, the Tote odds are set to 10,000/1. 2 A non-parametric approach could be employed, such as kernal estimation, however, the results would be difficult to interpret.

Appendix: derivation and assumptions associated with the model to predict win probabilities Models 1 and 2 predict a horse’s win probability from its associated bookmaker and Tote odds, respectively. In all other respects the models are derived in a similar fashion and the discussion which follows applies to both models. Throughout this discussion the generic term of ‘odds’ is used in place of bookmaker or Tote odds. We could have developed a relationship directly between odds and the probability of success, using a linear probability model. In this model the probability of success of horse i may have been modelled as a function of odds together with a random error term. However, this would not have been appropriate, since the approach would lead to estimates which (Aldrich and Nelson, 1984, p. 30): (1) have no known distributional properties, (2) are sensitive to the range of data, (3) may grossly understate the magnitude of the true effects, (4) systematically yield probability predictions outside the range of 0 to 1 and (5) get worse as standard statistical practices for improving the estimates are employed. In searching for alternative distributional assumptions we wish to avoid such problems whilst ensuring that decreases in odds are associated with increases in the probability of success (i.e. a monotonic transformation). The desired properties suggest the use of a cumulative probability function. The model we develop incorporates such a transformation. In this model we develop an index, Z i* (referred to as Yi* for model 1 and X *i for model 2), for each horse i in the sample. Odds have been demonstrated to be good predictors of a horse’s winning chance. However, for the reasons indicated above, there are no a priori grounds for assuming a particular functional form for the relationship between odds and the ‘winningness index’, Z i*. Consequently, to explore the form of this relationship, Z i* is defined as a polynomial of the natural logarithm of the odds together with a random error term ζi. The transformation of odds to ln(odds) was deemed appropriate as this served to normalize the underlying data. In addition, the natural logarithm of odds lies in the range –∞ to ∞ (whereas odds lie in the range {0, ∞}) and as one of the independent variables this served to create an index Z i* in the desired range (i.e. {–∞, +∞}), with a random error term which is also unrestricted. Consequently, for horse i, the index of ‘winningness’ was defined as follows:

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A.C. Bruce and J.E.V. Johnson m

Zi* =

∑ c [ln O ] r

m

i

− ζi

(A1)

r =0

Z *i cannot be directly observed. However, we can observe Zi such that if horse i wins Zi = 1 and if horse i loses Zi = 0. This implies:  P( Zi = 1) = P( Zi* > 0) = Pζ i < 

m

∑ c [ln O ] r

r =0

i

m

 

(A2)

Equation (A2) suggests that in order to estimate the probability of horse i winning we must be able to calculate the probability that m

ζi <

∑ c [ln O ] r

m

i

r =0

If we assume, as seems likely, that ζi is a continuous random variable, then: p( Zi = 1) =

∫

Di

−∞

m

f (ζ )dζ

where Di = ζ i <

∑ c [ln O ] r

i

m

(A3)

r =0

In order to produce estimates for the probability of horse i winning it is necessary to specify the probability distribution of ζi. Since it might reasonably be assumed that there are many independent factors which might combine additionally to this random error term, the central limit theorem can be used to justify the assumption that ζi is normally distributed.2 This leads to a probit model. However, due to its computational advantages and since the differences between the models are slight, we assume ζi follows the logistic distribution. As Greene (1996) argues, other distributions have been suggested, but in econometric applications the probit and logit models have been used almost exclusively . . . it is difficult to justify the choice of one distribution or another on theoretical grounds . . . in most applications it seems not to make much difference. Assuming that the disturbances ζi follow the logistic distribution implies that the probability of horse i winning, Pi, is given by:

Pi = P (Z i = 1) =

e Di 1 = Di 1+ e 1 + e − Di

(A4)

Equation (A4) demonstrates a further advantage of employing a natural logarithm of odds, since it creates a model which contains the special case where the odds perfectly determine the true winning probability,  1   i.e. Pi = 1 + O   i

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This special case can be demonstrated as follows: From equation (A4), Pi =

1 −(c0 + c1 ln Oi + c2 (ln Oi ) +L) 2

1+ e

(A5)

When odds perfectly reflect the underlying probability values then c1 = 1 and cj = 0, ∀j ≠ 1. Consequently: Pi =

1 e

ln Oi

1 + 1 1 + Oi =

(A6)

It might be suspected that the natural logarithm transformation of odds employed in equation (A1) implies that the random error structure is multiplicative at the level of the data. In an ordinary regression this would be the case since a transformed model of the form ln Yi = a ln Xi+ui would produce a multiplicative error in the basic model (i.e. Yi = X ui e ui). However, the log transformation employed in the logistic model produces an error term which is additive in the index function:

Pi =

e Di +ζ i 1 + e Di +ζ i

(A7)

As indicated above, this seems appropriate. The model described in equation (A4) assumes that Z1, Z2, . . ., ZN (where N denotes the sample size) are statistically independent. These conditions are not strictly met here since there will be some correlation between the disturbances for horses running in the same race. However, the sample size is large (19,396 horses running in 2,109 races) and whilst the estimators may be marginally less efficient, the results indicate that this causes few problems here. The approach adopted above also assumes that the same model applies to all observations. This could have caused problems if the data had been collected over a considerable time period, since the competitive nature of the betting industry may have changed over this period, which in turn may have altered the relationship between horses’ odds and their probability of success. However, races contained in the database covered a short period of three months and it is unlikely that competitive conditions would have changed significantly during this time.

References Aldrich J.H. and Nelson F.D. (1984) Linear Probability, Logit and Probit Models, London: Sage Publications. Asch P., Malkiel B. and Quandt R.E. (1984) ‘Market efficiency in racetrack betting’, Journal of Business, 57: 165–74. Ash P., Malkiel B. and Quandt R.E. (1982) ‘Racetrack betting and informed behavior’, Journal of Financial Economics, 10(1): 187–94.

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Ayton P. (1997) ‘How to be incoherent and seductive: bookmakers’ odds and support theory’, Organizational Behavior and Human Decision Processes, 72: 99–115. Bacon-Shone J.H., Lo V.S.Y. and Busche K. (1992) ‘Modelling winning probability’, Research Report 10, University of Hong Kong: Department of Statistics. Bird R. and McCrae M. (1987) ‘Tests of the efficiency of racetrack betting using bookmaker odds’, Management Science, 33: 1552–62. Bird R. and McCrae M. (1994) ‘Racetrack betting in Australia: a study of risk preferences and market efficiency’, in Proceedings of the 6th International Conference on Gambling and Risk Taking, Eadington W.R. and Cornelius J.A. (eds), Reno: Institute for the Study of Gambling and Commercial Gaming, 228–58. Bruce A.C. and Johnson J.E.V. (1992) ‘Toward an explanation of betting as a leisure pursuit’, Leisure Studies 11: 201–18. Busche K. (1994) ‘Efficient market results in an Asian setting’, in Efficiency of Racetrack Betting Markets, Hausch D.B., Lo V.S.Y. and Ziemba W.T. (eds), Academic Press: London, 615–17. Busche K. and Hall C.D. (1988) ‘An exception to the risk preference anomaly’, Journal of Business, 61: 337–46. Dowie J. (1976) ‘On the efficiency and equity of betting markets’, Economica, 43: 139–50. Figlewski S. (1979) ‘Subjective information and market efficiency in a betting model’, Journal of Political Economy, 87: 75–88. Gabriel P.E. and Marsden J.R. (1990) ‘An examination of market efficiency in British racetrack betting’, Journal of Political Economy, 98: 874–85. Gilovich T. and Douglas C. (1986) ‘Biased evaluations of randomly determined gambling outcomes’, Journal of Experimental Social Psychology, 22: 228–41. Greene W.H. (1996) Econometric Analysis (3rd edn), New York: Prentice Hall International. Henery R.J. (1985) ‘On the average probability of losing bets on horses with given starting price odds’, Journal of the Royal Statistical Society, 4: 342–9. Johnson J.E.V. and Bruce A.C. (1992) ‘Successful betting strategies: evidence from the UK offcourse betting market’, in Gambling and Commercial Gaming: Essays in Business Economics, Philosophy and Science, Eadington W.R. and Cornelius J.A. (eds), Reno: Institute for the Study of Gambling and Commercial Gaming, 635–56. Kahneman D. and Tversky A. (1979) ‘Prospect theory: an analysis of decision under risk’, Econometrica, 47: 263–91. Kopelman R.E. and Minkin B.L. (1991) ‘Toward a psychology of pari-mutuel behavior: test of Gluck’s Law’s’, Psychological Reports, 68: 701–2. Lindley D.V., Tversky A. and Brown R.V. (1979) ‘On the reconciliation of probability assessments’, Journal of the Royal Statistical Society, 142(2): 146–80. Poulton E.C. (1977) ‘Quantitative subjective assessments are almost always biased, sometimes completely misleading’, British Journal of Psychology, 68: 409–25. Quandt R.E. (1986) ‘Betting and equilibrium’, The Quarterly Journal of Economics, 101: 201–7. Quirin W.L. (1979) Winning at the Races: Computer discoveries in thoroughbred handicapping, New York: William Morrow. Shin H.S. (1991) ‘Optimal betting odds against insider traders’, Economic Journal, 101: 1179–85. Shin H.S. (1992) ‘Prices of state-contingent claims with insider traders, and the favouritelongshot bias’, Economic Journal, 102: 426–35.

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Shin H.S. (1993) ‘Measuring the incidence of insider trading in a market for statecontingent claims’, Economic Journal, 103: 1141–53. Thaler R.H. (1985) ‘Mental accounting and consumer choice’, Marketing Science, 4: 199–214. Thaler R.H. (1988) ‘Anomolies–the winner’s curse. Journal of Economic Perspectives, 1: 191–202. Thaler R.H. and Johnson E.J. (1990) ‘Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice’, Management Science, 36: 643–60. Thaler R.H. and Ziemba W.T. (1988) ‘Anomolies–pari-mutuel betting markets: racetracks and lotteries’, Journal of Economic Perspectives, 2: 161–74. Tuckwell R.H. (1983) ‘The thoroughbred gambling market: efficiency, equity and related issues’, Australian Economic Papers, 22: 106–8. Vaughan Williams L and Paton D. (1997) ‘Why is there a favourite-longshot bias in British racetrack betting markets?’ Economic Journal, 107: 150–8.

17 Market efficiency analysis requires a sensitivity to market characteristics Some observations on a recent study of betting market efficiency A.C. Bruce and J.E.V. Johnson

Introduction In a recent contribution to Applied Economics Letters, Vaughan Williams and Paton (1997) (hereafter VWP) develop the debate relating to market efficiency in the context of betting markets by examining the proposition that information efficiency is dependent upon a perceived element of information inefficiency in the relevant market. Information efficiency is defined as ‘an absence of unexploited opportunities for arbitrage’. The specific test of efficiency employed relates to the existence or otherwise of a differential between returns to winning horses in a sample of parallel UK pari-mutuel and bookmaker-based horse-race betting markets. Perceived information inefficiency is identified as being associated with ‘a marked movement in bookmakers’ odds’. The conclusion suggests that the presence of such information inefficiency signals induces bettors to act so as to eliminate the cross-market returns differential, whereas in the absence of these inefficiency signals, information inefficiency endures in the form of a returns differential. The paper raises interesting questions, but invites critical comment relating to the terminology employed, the conclusion drawn and aspects of the methodology and analysis. A general observation which is pertinent to the majority of the points developed below is that the investigation of data relating to betting markets, and the subsequent interpretation of results, demands an understanding of and willingness to accommodate the institutional peculiarities of this type of market. The failure of the paper under discussion to acknowledge the idiosyncrasies of betting market structure and process results in inappropriate methodologies and misleading interpretation. In making this general observation, it should equally be noted that shortcomings in context awareness are not uncommon in studies of betting markets, where the susceptibility of data to analysis of general market efficiency issues may deflect the researcher from influences associated with the specific context. A recent example of this is the influential work of Gabriel and Marsden (1990, 1991) (and see, for a critique, Bruce and Johnson, 1996).

Market efficiency analysis 301 In the context of these general observations, our more specific criticisms of the VWP paper are as follows: 1

2

3

From a terminological perspective, the characterization of a marked movement in odds as a signal of perceived information inefficiency appears curious in that advocates of the informational efficiency of markets might equally interpret such a movement as indicative of a responsive and efficient information transmission mechanism. It appears especially curious given that the conclusion of VWP is that the presence of this phenomenon is associated with markets which are informationally efficient. The conclusion represents a significantly overstated interpretation of the results. The results as presented invite, at most, the more qualified conclusion that information efficiency, as defined, obtains only where (a) an inefficiency signal is present and (b) the signal is associated with the pattern of betting activity relating to the winning horse. The design of the study, and in particular its exclusive focus on significant odds movements associated with winners (which, obviously, cannot be identified as such in advance), denies analysis of inefficiency signals relating to non-winning horses. Most importantly, we learn nothing of the potential presence of inefficiency signals associated with non-winners in the 379 markets (over 74 per cent of the sample) where winning horses were not the subject of significant odds movement. Yet it is undoubtedly the case that many of these markets would have featured betting patterns which satisfied the criterion for identifying an inefficiency signal. Moreover, the focus on winners which carry inefficiency signals neglects the wider market context in which these winners are located. It may be the case that a single betting market is characterized by several inefficiency signals as defined by VWP. Under such circumstances, a focus on just one signal (that related to the winner), and not necessarily the strongest such signal within a market, appears difficult to justify. In simple terms, the methodology employed does not permit a reliable basis for discriminating between markets which either meet or fail to meet the inefficiency signal criterion. The criterion for identifying an inefficiency signal is itself contentious for a number of reasons. The authors define the signal as occurring where the ratio (OP/SP) of the bookmakers’ opening price (OP) to the starting price (SP) or vice versa (SP/OP) exceeds 1.4.

This ‘1.4 rule’ is blunt in the sense that it implies that equivalent proportional changes in different areas of the distribution of odds are equivalent in terms of the market activity required to induce the changes, or in other words that movements with equivalent OP/SP ratios from, for example, 25/1 to 20/1 and 5/1 to 4/1 are indicative of a similar weight of market activity (money wagered) in each case. This is not tenable, however. The money wagered/odds response relationship is not linear across the odds distribution: a relatively modest wager which induces an odds change in the higher odds range may have no effect

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whatever in a lower odds range. This problem is compounded by the fact that the odds scale in bookmaker markets is not continuous in terms of usage. Conventionally, especially in the higher odds range, only a limited menu of odds is used. Thus, for example, if money is wagered on a horse at odds of 50/1, any resultant adjustment of odds means at least a movement to the next (albeit infrequently used) odds of 40/1 (OP/SP = 1.25) and very often a movement to the more frequently used 33/1 (OP/SP = c. 1.5). The criterion is thus likely to be oversensitive in identifying small expressions of market sentiment as inefficiency signals in the longer odds range. A related issue is that a simple focus on the ratio of OP to SP or vice versa fails to accommodate other factors which might be expected to sensitize the perceptions of bettors. These might include the timeframe over which the movement takes place, the timing of the movement within the total life of the betting market and the number of discrete odds movements within the aggregate movement. A related problem concerns the fact that the odds employed to determine the OP/SP ratio are merely reflections of underlying subjective probabilities of success held by bettors and bookmakers. A true test of efficiency characteristics should arguably focus instead on differences between subjective and objective probabilities rather than differences in odds per se. To illustrate: an OP/SP ratio of 1.5 is consistent with each of the following odds movements; 1/2–1/3; 6/4-evens; 3/1–2/1; 15/1–10/1; 45/1–30/1. Yet these odds movements are associated with changes in subjective probability of between 12.5 and 50 per cent. This suggests that the ratio employed to identify signals of market inefficiency contains a raft of non-equivalent alterations in subjective views as to the race result. A further problem with the OP/SP ratio relates to the general tendency for odds to lengthen from their opening values. Awareness of this by bettors with inside information means that they are likely to place bets only once the drift in odds has occurred. This tendency is compounded by the informational advantages associated with delaying bet placement (e.g. the opportunity to observe horses’ behaviour, the general pattern of betting activity). What this combination of factors suggests is that a more appropriate indicator of market inefficiency is the ratio of maximum odds to SP. To illustrate: a horse with opening odds of 10/1 which drifts to 20/1 before shortening to 10/1 would not feature using the VWP 1.4 ratio, despite displaying a clear signal of insider activity. Irrespective of the validity of the form of ratio employed to identify inefficiency, the authors fail to offer a justification for the use of the critical ratio value of 1.4. In the absence of any sensitivity analysis, this rather arbitrary figure fails to allay fears that the significance of the results may simply be due to an anomaly which would disappear if a different critical value were employed. The 1.4 rule also suggests a potential bias in that its use restricts the number of races with identified inefficiency to 130. Given that only 17 of the original sample of races were won by horses with odds of greater than 20/1 and only 31 by horses with odds of greater than 15/1, the method employed suggests that there are very few data relating to horses with high odds which moved substantially.

Market efficiency analysis 303 4

5

6

7

A remarkable feature of the results, which arouses suspicions of bias in the sample, is that of the 130 races where there was an inefficiency signal associated with the race winner, there were only 42 cases where the winner’s odds shortened significantly, but 88 where the winner’s odds lengthened significantly. Such a result is extraordinary given the dominance of studies pointing to the relative efficiency of horse-race betting markets and runs contrary to studies which have focused specifically on odds movements as a basis for measuring efficiency (Crafts, 1985). It is particularly odd that this result is permitted to pass without comment. The assumption of equivalence of marked inward and marked outward movements of odds as inefficiency signals invites comment because the nature of the signals would seem to differ markedly in each case. Shortening odds for a particular horse reflect a movement of market sentiment in its favour and identify it as a clear focus for further market activity vis-à-vis other horses in the race. By contrast, lengthening odds for a horse may deter bettors, but any re-routing of their bets is likely to be dispersed across all other horses in the race. The former seems, a priori, a much more potent signal. While acknowledging that the results relating to the split sample lend support to the hypothesis that it is movements in odds per se which are significant, rather than the direction of movement, the original motivation for the hypothesis is not made clear. A more practical concern relates to the implication that, where potential gains from arbitrage are identifiable, such arbitrage activity is necessarily available to bettors. This is unrealistic. For example, in the off-course market, which accounts for around 90 per cent of all betting activity, bettors are invariably located in a betting office which facilitates betting in one form of market only, the bookmaker market. Facilities for betting in the parallel pari-mutuel market were not generally available during the period from which the authors draw their data and thus effective arbitrage opportunities were extremely limited off-course. Even where bookmakers were prepared to accept wagers at parimutuel odds, the evolving pattern of pari-mutuel odds during the active market period was not available to bettors, so that the informational basis for conducting effective arbitrage was absent. Finally, one could argue that even with full reporting of pari-mutuel market activity, bettors can never be wholly confident of arbitrage benefits when the returns in the pari-mutuel market are unknown until after the close of the market. A further factor in relation to the study under scrutiny is that the OP/SP ratio which identifies inefficiency is, by definition, unobservable until the opportunity to bet has ceased, that is after the start of the race. Thus, it is impossible to both observe and act upon an inefficiency signal. Finally, VWP do not specify whether the standard error estimates reported in columns 3 and 4 of Table 2 are robust to heteroscedasticity. If they are, the justification for including a heteroscedasticity measure is unclear. If they are not, then the significance of the omitted variables questions the specification of the underlying model.

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Taken together, the observations outlined above appear to compromise seriously the results generated by the VWP study. While some of the issues raised may, individually, be susceptible to corrective attention, the more serious concern is that the design and interpretation of the study is fundamentally inadequate in its ability to recognize, comprehend and take account of the unique characteristics of horse-race betting markets. This invites the more general observation that caution should be exercised in the use of any specific market context as a lens through which to examine general market phenomena.

References Bruce, A. C. and Johnson, J. E. V. (1996) ‘Market power in British pari-mutuel and bookmaker-based horserace betting markets: an empirical analysis’, University of Nottingham, School of Management and Finance Discussion Paper, 1996.11. Crafts, N. (1985) ‘Some evidence of insider knowledge in horserace betting in Britain’, Economica, 52: 295–304. Gabriel, P. E. and Marsden, J. R. (1990) ‘An examination of market efficiency in British racetrack betting’, Journal of Political Economy, 98: 874–85. Gabriel, P. E. and Marsden, J. R. (1991) ‘An examination of market efficiency in British racetrack betting: errata and corrections’, Journal of Political Economy, 99: 657–9. Vaughan Williams, L. and Paton, D. (1997) ‘Does information efficiency require a perception of information inefficiency?’ Applied Economics Letters, 4: 615–17

18 Efficiency characteristics of a market for state-contingent claims A.C. Bruce and J.E.V. Johnson

Introduction This chapter presents a new body of analysis that develops the debate regarding the efficiency characteristics of a market for state-contingent claims, the UK horse-race betting market. A hitherto unavailable source of data relating to the UK pari-mutuel betting market is used to explore the existence of differences in returns between that market and the parallel bookmaker-based market. This offers a more comprehensive investigation of an issue addressed by the influential work of Gabriel and Marsden (1990, 1991). The results invite a reconsideration of the degree, form and origins of market efficiency within the aggregate horse-race betting market. The chapter is organized as follows. The next section provides a brief review of the literature relating to betting market efficiency issues, while the following section compares the parallel bookmaker and pari-mutuel betting markets via analyses of the menu of odds available in the two markets. Some conclusions are developed in the final section IV.

Betting market efficiency: existing literature A recurring focus in the study of betting market efficiency has been the identification of subgroups of the total betting population which systematically realize above average rates of return (e.g. Snyder, 1978; Figlewski, 1979; Asch et al., 1984; Crafts 1985). Recent work has embraced a consideration of insider effects (Shin, 1991, 1992, 1993; Schnytzer and Shilony, 1995; Vaughan Williams and Paton, 1997a), information costs (Terrell and Farmer, 1996) or perceptions of inefficiency (Vaughan Williams and Paton, 1997b; Bruce and Johnson, 2000) on efficiency. A common theme across these studies has been their focus on one or other of the two main forms of betting market, the pari-mutuel or the bookmaker market. Within the efficiency literature, Gabriel and Marsden’s (1990, 1991) work is distinctive in realizing a particular advantage of the UK horse-race betting market: pari-mutuel and bookmaker markets co-exist and, consequently, distinctive processes of odds formation can be compared over a common set of events.

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Gabriel and Marsden (1990, 1991) focused on a comparison of the rates of return to equivalent bets placed on ‘winning’ horses in each of the two market forms. Specifically, they compared returns to starting price (SP) bets in the bookmaker market with returns to equivalent bets placed in the pari-mutuel market. As a result the odds under comparison in each market are equally uncertain at the time of bet placement.1 Gabriel and Marsden’s contention was that in an efficient aggregate market, any difference in odds (and expected returns differential across markets) would generate the incentive for arbitrage activity which would in turn lead to an iteration towards returns equivalence. The results for the aggregate sample indicated that the mean returns to a 10 pence stake on equivalent winning horses were 81.55 pence in the pari-mutuel market and 63.37 pence in the bookmaker market, a highly significant difference. Various extensions to the analysis were then presented involving the exclusion of those horses with high pari-mutuel odds values from the analysis on the basis that such data could introduce an inflationary bias into the pari-mutuel returns figure. Accordingly, Gabriel and Marsden excluded all horses with odds of, respectively, greater than 20/1, 15/1 and 10/1 to reduce any inflationary bias in parimutuel returns, using, separately, pari-mutuel and bookmaker values as the basis for exclusion. Whilst the SP-defined categories, favoured by the authors in their interpretation, offered consistent evidence for highly significant cross-market distinctions, the pari-mutuel-defined categories provided a more ambivalent picture.

Available odds and notional returns Data The more comprehensive analysis of parallel betting markets which follows features details of the amounts wagered in the pari-mutuel market on each of 19,396 horses in 2,109 races in the UK between 1 June and 31 August 1996, thereby providing the basis for the calculation of a pari-mutuel odds value for each horse. The ability to analyse odds in relation to all horses constitutes a significant advantage over the earlier work. First, the ‘all runner’ analysis avoids biases associated with a ‘winner only’ methodology, where each betting market is represented by one price statistic only. A single price offers only a partial perspective on the market in which it features, with no insight into the broader characteristics (e.g. distribution of prices) within each market. Additionally, the ‘winner only’ focus involves an over-representation of shorter-odds horses and an under-representation of longer-odds horses, thereby restricting the range where the pari-mutuel odds might be expected significantly to exceed bookmaker odds. The comprehensive pari-mutuel data are complemented by details of the odds of each horse in the sample at the culmination of the relevant bookmaker market, that is the starting price or SP.

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Analysis and results The analysis of the dataset follows the procedure established by Gabriel and Marsden (1990, 1991) with both aggregated and defined subsets of data compared. Overall, pari-mutuel odds exceed bookmaker odds on 41 per cent more occasions than vice versa; a Wilcoxon signed ranks test, which also incorporates information about the size of the margin between pairs of odds, confirms that there is a significant difference between the two sets of odds (z = –40.76, p < 0.01, N = 19,393). The mean pari-mutuel odds (20.55/1) are significantly greater than the mean bookmaker odds (14.99/1; t = 15.53, p < 0.01, N = 19,393). The difference between mean pari-mutuel and bookmaker returns is marginally larger than that reported by Gabriel and Marsden (1991). The results of the analysis of the truncated datasets are presented in Table 18.1. Replication of the two bases for truncating the dataset employed by Gabriel and Marsden yields quite differing results. Using the comprehensive dataset, the SP-based truncation offers a consistent picture across the odds range, with highly significant superiority of mean pari-mutuel odds over mean SPs confirmed by non-parametric tests. This corroborates the earlier analysis by Gabriel and Marsden (1990, 1991). However, a truncation criterion based on bookmaker odds is flawed; it manifestly fails to exclude horses with very high pari-mutuel odds, the exclusion of which formed the rationale for Gabriel and Marsden’s truncation. By contrast, the pari-mutuel-based truncation necessarily removes from analysis those horses with very high pari-mutuel odds values. The results based on a pari-mutuel truncation (in conjunction with the ‘all runners’ dataset) provide an illuminating contrast with the ‘winner only’ analysis. Gabriel and Marsden’s analysis offered equivocal results, but Table 18.1 demonstrates a notably more consistent picture, with mean SPs significantly exceeding mean pari-mutuel odds in all odds categories. Non-parametric tests confirm that SP odds are generally higher than pari-mutuel odds when high pari-mutuel odds are excluded from the analysis. In order to investigate more precisely in which odds Table 18.1 Truncated comparisons of pari-mutuel and bookmaker odds Odds of horses in sample

N

Mean odds Parimutuel

Pari-mutuel ≤ 20/1 Pari-mutuel ≤ 15/1 Pari-mutuel ≤ 10/1 SP ≤ 20/1 SP ≤ 15/1 SP ≤ 10/1

SP

Paired samples test: t

13,891 7.80(5.16)a 7.88(6.00) –2.57b 12,173 6.44(3.90) 6.71(4.77) –9.12b 9,585 4.83(2.57) 5.26(3.57) –16.42b 15,656 12.73(15.04) 8.65(5.47) 21.07b 13,152 7.91(12.34) 6.84(3.82) 10.78b 10,566 5.92(12.31) 5.40(2.69) 4.52b

Notes a Standard deviation in parentheses. b Significant at 0.01 level.

Sign test: z

Wilcoxon signed rank test: z

–3.05b –10.37b –21.56b –16.05b –6.52b –3.42b

–4.73b –6.02b –21.69b –33.16b –20.34b –6.04b

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Table 18.2 Categorized comparisons of pari-mutuel and bookmaker odds Pari-mutuel odds of horses in sample (P)

N

Mean odds

p > 20/1 15/1 < p ≤ 20/1 10/1 < p ≤ 15/1 5/1 < p ≤ 10/1 5/2 < p ≤ 5/1 1/1 < p ≤ 5/2 p ≤ 1/1

5,445 58.22(251.64)a 32.96(25.17) 7.42b 1,698 17.39(1.43) 16.23(7.06) 6.86b 2,561 12.40(1.45) 12.04(4.90) 3.87b 4,176 7.31(1.42) 7.65(3.10) –8.00b 3,138 3.77(0.72) 4.26(1.30) –25.42b 1,675 1.86(0.42) 2.33(2.57) –7.50b 470 0.70(0.01) 1.26(0.25) –2.20

Pari-mutuel

SP

Paired Sign samples test: z test: t –48.30b –18.57b –18.50b –2.52b –18.84b –23.11b –11.32b

Wilcoxon signed rank test: z –45.69b –16.44b –15.76b –0.90b –23.68b –26.21b –12.99b

Notes a Standard deviation in parentheses. b Significant at 0.01 level.

ranges SPs exceed pari-mutuel odds a finer grid of comparisons than that employed by Gabriel and Marsden is constructed (see Table 18.2). The results of this analysis indicate that mean SPs significantly exceed mean pari-mutuel odds for all pari-mutuel odds categories up to and including 10/1. This relationship is reversed for horses with pari-mutuel odds greater than 10/1. Non-parametric tests confirm that SPs on individual horses generally exceed pari-mutuel odds in the lower (parimutuel) odds ranges and that pari-mutuel odds exceed SPs in the higher (pari-mutuel) odds ranges. Interpretation of results The overall picture which emerges from the methodologically superior parimutuel odds-based truncation (Table 18.1 and Table 18.2) is of evidence for pervasive inefficiency in terms of cross-market returns differentials. There is also evidence of heterogeneity in the form of inefficiency, with pari-mutuel superiority over bookmaker odds confined to the range beyond 10/1, but the reverse in the shorter odds zones. This contrasts sharply with Gabrie1 and Marsden’s (1991), SP-based truncation method, which finds superiority of pari-mutue1 over bookmaker market odds in all odds zones. These earlier results are, of course, unsurprising given that, with the SP-based truncation, the 20/1 or shorter and 15/1 or shorter odds categories each contain values of SPs odds which might be expected to have much higher pari-mutue1 odds equivalents. To illustrate, in the ‘all runners’ dataset, the mean pari-mutuel odds value of the 1,344 horses with SP odds of 20/1 is 29.26/1. In this context, the probability of reporting a statistically significant mean odds differential using an SP-based exclusion criterion is clearly very high, but the material significance of such an outcome is compromised by the nature of the methodology. The superiority of returns to bettors in bookmakers markets (compared with pari-mutuel returns) in the lower odds ranges is to some extent counterintuitive

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given the imbalance between supplier and buyer power (in the former market) coupled with the necessarily inverse relationship between bookmaker and bettor returns. Each would tend to generate an expectation of inferior returns to bettors in this market, compared with those available to bettors in the pari-mutuel market, where supplier and consumer returns are non-competitive. In particular relation to the shorter-odds ranges, the identified reversal in relative magnitudes of pari-mutuel and bookmaker market returns may suggest bookmakers’ sensitivity to the competitive nature of their operation in the most highly populated odds range of 10/1 or less which induces them to offer ‘value’ in terms of higher odds relative to the alternative pari-mutuel market in this range. The disproportionately high density of high stakes bets in the lower-odds range may be influential here, where bookmakers are motivated in part by the turnover (see Tuckwell, 1983) they can achieve as well as by their margins. Equally, it can be argued that the lack of competition for bets on longer-odds horses leads to bookmakers offering relatively poor value odds on these horses. In addition, the fear of adverse selection (see Shin, 1992, 1993) by insiders also results in bookmakers artificially shortening the longer odds. In explaining sustained cross-market returns disparity, the particular conditions operating in the two markets are important. Within the short duration of a betting market for a particular race, the opportunities for arbitrage by on-course bettors2 are constrained by the normally distinct and separate location of the bookmaker and pari-mutuel markets, which, particularly in a turbulent market context, represents a critical practical constraint. For off-course bettors, location in a betting office significantly constrains arbitrage opportunities since some betting operators do not accept pari-mutuel bets. More fundamentally, the ability to engage in cross-market arbitrage is compromised by the simple fact that the odds (and potential returns) associated with a bet placed in a parimutuel market or a bet placed at SP are unknown until after the market has closed. As such, it is impossible to guarantee that an apparent advantage associated with one or other form of market during the active market period will be reflected in the final odds. In particular, any pari-mutuel bet that seeks to capitalize on a current premium of pari-mutuel over bookmaker odds will tend to diminish that premium.

Conclusion This chapter has offered an extension and development of an ongoing debate into the efficiency properties of a market for state-contingent claims, the horserace betting market. The results invite a perspective on the incidence and nature of inefficiency which contrasts in significant respects with earlier investigations. A variety of factors, including revenue considerations in the bookmaker utility function, the exercise of market power and the fear of adverse selection are cited as influential in shaping the pattern of comparative returns across markets, whilst practical constraints on arbitrage act to maintain differentials.

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Notes 1 The SP of a horse represents the odds available from a leading bookmaker at the racetrack at the close of the betting market. In pari-mutuel markets, odds are mechanistically determined by the application of a formula that takes account of the distribution of betting turnover (net of operator costs) across horses. In the active trading period for each market form, the final odds at which bets will be settled are necessarily unknown. 2 The bookmakers’ odds and pari-mutuel odds are determined by betting activity at the racetrack. However, a significant proportion of betting activity occurs in off-track betting offices. This activity is to some extent reflected in the final SPs and pari-mutuel odds since the off-track betting offices have facilities for channelling some of the money taken in these offices (horses backed at bookmaker and pari-mutuel odds) directly to the on-course market.

References Asch, P., Malkiel, B. G. and Quandt, R. E. (1984) ‘Market efficiency in racetrack betting’, Journal of Business, 57: 165–75. Bruce, A. C. and Johnson, J. E. V. (2000), ‘Market efficiency analysis requires a sensitivity to market characteristics: some observations on a recent study of betting market efficiency’, Applied Economics Letters, 7: 199–202. Crafts, N. F. R. (1985) ‘Some evidence of insider knowledge in horse race betting in Britain’, Economica, 52: 295–304. Figlewski, S. (1979) ‘Subjective information and market efficiency in a betting market’, Journal of Political Economy, 87: 75–88. Gabriel, P. E. and Marsden, J. R. (1990) ‘An examination of market efficiency in British racetrack betting’, Journal of Political Economy, 98: 874–85. Gabriel, P. E. and Marsden, J. R. (1991) ‘An examination of market efficiency in British racetrack betting: errata and corrections’, Journal of Political Economy, 99: 657–9. Schnytzer, A. and Shilony, Y. (1995) ‘Inside information in a betting market’, Economic Journal, 105: 963–71. Shin, H. S. (1991) ‘Optimal betting odds against insider traders’, Economic Journal, 101: 1179–85. Shin, H. S. (1992) ‘Prices of state-contingent claims with insider traders, and the favourite–longshot bias’, Economic Journal, 102: 426–35. Shin, H. S. (1993) ‘Measuring the incidence of insider trading in a market for statecontingent claims’, Economic Journal, 103: 1141–53. Snyder, W. (1978) ‘Horse-racing: the efficient markets model’, Journal of Finance, 78: 1109–18. Terrell, D. and Farmer, A. (1996) ‘Optimal betting and efficiency in pari-mutuel betting markets with information costs’, Economic Journal, 106: 846–68. Tuckwell, R. H. (1983) ‘The thoroughbred gambling market: efficiency, equity and related issues’, Australian Economic Papers, June: 106–18. Vaughan Williams, L. and Paton, D. (1997a) ‘Why is there a favourite–longshot bias in British racetrack betting markets?’ Economic Journal, 107: 150–8. Vaughan Williams, L. and Paton, D. (1997b) Does information efficiency require a perception of information inefficiency?’ Applied Economics Letters, 4: 615–17.

19 Market ecology and decision behaviour in state-contingent claims markets A.C. Bruce and J.E.V. Johnson

Introduction Market ecology embodies characteristics that define the setting for transactions, including the market form, its processes and protocols, information and incentive characteristics, and the form of buyer–supplier relationships and communication. The aim of this chapter is to investigate the influence of aspects of market ecology on behaviour within markets, specifically to develop an understanding of the role of market ecology in explaining the differential incidence of a well-established anomaly in markets for state-contingent claims. The anomaly in question, discussed in greater detail below, relates to the tendency for subjective probabilities to underestimate systematically the objective probability of high probability outcomes and to overestimate the probability of low probability events. The chapter is structured as follows. The first section explores the link between aspects of market ecology and market outcomes and reviews some of the more influential contributions to the literature in this area. The second section introduces the main features of the market that forms the context for this study, while the third section introduces the particular form of bias under investigation and reviews the literature relating to its origins and incidence. The following sections introduce an ecology-based classification of markets, from which testable propositions relating to differential incidence of bias are developed. The next section presents and interprets results. Some concluding remarks follow.

Market ecology and market behaviour The potential influence of the environmental characteristics of markets, or market ecology, on the behaviour of market participants and, hence, market outcomes has commanded increasing attention in recent years. A special issue of the Journal of Economic Behavior and Organization (Vol. 39:1, 1999) exemplifies contemporary interest in the interface between psychology and economics as a means of examining the processes of economic behaviour as well as the outcomes. Murnighan and Ross (1999) in particular point to the potential for

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collaborative approaches to the understanding of decision-making behaviour. Within this general area, the emergence of experimental economics features, as a dominant theme, the impact of market process and institution on market outcomes. This reflects a view that structural variables (e.g. firm size, market concentration) that dominate the industrial organisational approach to explaining market outcomes can be limited in explanatory power. The extension of economists’ traditional focus beyond observed and measurable outcomes to consideration of the processes involved in economic agents’ behaviour has generated an interest in the context within which such processes operate and in those aspects of the environment that influence them. Various ecological aspects of the trading context are held to influence outcomes. Smith (1989), for example, emphasises the importance of interaction between ‘environmental’ and ‘institutional’ influences on behaviour. Here, environmental influences include agent characteristics such as preferences, resource endowments and technologies that, ultimately, may be condensed into individual supply and demand schedules. Institutional influences include the language, rules, conventions, protocols and processes within which market dialogue and transactions are conducted. Both environmental and institutional influences affect the behaviour, signals, messages and actions forthcoming from agents that translate into observable outcomes. Plott’s (1989) perspective on institutions is somewhat narrower than that of Smith, focusing solely on processes of price formation (e.g. different auction models). However, even within this narrower ecology Plott (p. 1111) argues that market institutions have a substantial influence on performance and this influence sometimes outweighs the importance of market concentration and relative firm size, which have been the traditional centre of attention for industrial organisation theorists. More recently, Waller et al. (1999) emphasise the importance of three types of factor for market behaviour. In addition to ‘institutional’ factors, which essentially mirror Smith’s definition, they cite the importance of both incentives and learning opportunities. The analysis that follows draws on the above perspectives in developing testable propositions regarding the influence of ecological distinctions on outcomes in different forms of market. Particular emphasis is placed on the roles of price formation, information and learning characteristics, and institutional features in drawing distinctions between market ecologies.

A market for state-contingent claims In general terms, a participant in a market for state-contingent claims makes decisions regarding the nature and degree of involvement in the market, based on a subjective evaluation of the likely market outcome (state), where this outcome determines the impact on the participant’s welfare. As such, analysis of markets for state-contingent claims allows important insights into various

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aspects of, inter alia, information processing, decision-making processes and attitudes to uncertainty. Speculative financial markets constitute perhaps the most significant form of state-contingent environment, and the context for this chapter is a particular form of speculative financial market, the horse-race betting market: ‘In its simplest formulation, the market for bets in an n-horse race corresponds to a market for contingent claims with n states in which the ith state corresponds to the outcome in which the ith horse wins the race’ (Shin, 1992, p. 1142). The price of a bet is determined by the horse’s odds. Employing notation suggested by the state-contingent claims and Arrow–Debreu securities literature, the purchase price of a claim on a horse is denoted by π. This claim will pay £1 if the horse wins, but nothing if it loses. If the horse’s odds are a to b then π = b/(a + b). Among the advantages of horse-race betting markets as a medium of market ecology investigation are their finite lives and unequivocal outcomes. Additionally, betting market activity is well documented, and there is a large number of independent betting events, each with its own market. Although the term ‘the horse-race betting market’ may be used to describe the sum of activity in this area, for most purposes it is unrealistic to view the market for horse-race betting in the United Kingdom as a uniform entity. Rather, it comprises a body of activity, capable of segmentation at two main levels, by generic market form and by specific market type. This segmentation enables the identification of subgroups of markets with distinctive ecological characteristics, thereby facilitating insights into the relationship between environment and behaviour. The remainder of this section explains the fundamental distinctions between the two generic market forms that operate in parallel in the UK and describes the basis for a second layer of classification based on specific race type. The detailed justification for the classification is presented in later in the chapter. Generic market form: bookmaker versus pari-mutuel At the generic level, there are two forms of betting market that operate in parallel for all UK horse-races, the bookmaker market and the pari-mutuel market. There are a number of fundamental ecological differences between these market forms. Bookmaker markets involve market dialogue between supply- and demandside agents, bookmakers and bettors. This dialogue is initiated by bookmakers at the racecourse (i.e. in the ‘on-course’ market) announcing sets of odds (or ‘prices’) for horses in a particular race. Bettors respond according, inter alia, to the perceived attractiveness of the odds and their subjective assessment of the horse’s probability of success. Based on the pattern of betting and their own subjective evaluation of the evolving information set, bookmakers adjust the sets of odds to reflect, to some degree, the relative weight of bettor investment on different horses and to manage their own exposure to losses. The odds in the market will continue to evolve for a period of around 20 minutes until the horserace begins, at which point the market closes. At the end of the race, the result is declared, and winning bettors are paid according to the odds that applied at the time they placed their bets.

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The pari-mutuel market operates in a quite different way. Odds relating to horses are determined solely by the pattern of relative bettor demand according to a predetermined formula. Bets are settled at the odds prevailing at the close of the market. Thus for any pari-mutuel market, the odds for horse i running in race j, Oijt , represent the amount that a bettor wagering £1 on horse i will win if that horse wins race j. These odds are determined as follows: nj

t ij

O =

∑h i =1

ij

(1 − d )

hij

−1

(1)

where nj = number of runners in race j, d = pari-mutuel deduction to cover costs (0.16 for the relevant sample period),1 and hij = amount bet on horse i in race j. Whilst the pattern of relative odds varies through the life of the pari-mutuel market, as in the bookmaker market, a significant distinction is the fact that bettors in the pari-mutuel market cannot guarantee their rate of return to a winning bet by ‘taking’ the odds at the time of bet placement. Thus, the ultimate return to a winning bet is unknown at the time of bet placement. The above provides an introduction to the differences in institution and process between generic market forms. The significance of these differences in explaining differential incidence of decision bias is explained more fully below. Specific market type: levels and types of race The aggregate population of horse races (and associated betting markets) may also be segmented at another layer, by race type. Thus, it is possible to distinguish between, for example, higher grade and lower grade races in terms of the quality of participating horses. A key ecological discriminator here (see Waller et al., 1999) relates to the degree to which event-specific information is publicly available. The detailed ecological differences between these race types that underpin the classification are developed more fully below.

Market behaviour: the favourite–longshot bias In investigating the influence of market ecology on market behaviour, various forms of measurable market outcome could be considered. In this study, the focus for analysis is an empirically well-established market phenomenon: the tendency for market participants subjectively to under/over-estimate the objective probability of high/low probability outcomes. In the context of horse-race betting markets, this phenomenon is known as the ‘favourite–longshot bias’, defined as the propensity for the subjective probabilities implicit in odds to under/overstate the objective probabilities of high/low objective (or realised) probabilities.

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Whilst the general objective of this chapter is to throw light on the role of ecological factors on market outcomes, rather than an investigation of the favourite–longshot bias per se, it is instructive to review briefly the literature relating to the phenomenon. Empirical evidence for the favourite–longshot bias and interest in its economic origins is well established in the economics literature. Dowie’s (1976) study provides early evidence based on a large-scale survey of UK data, where, for example, the objective probability of success of all horses with odds of 33/1 was 0.005, compared with a probability implied by the odds of 0.029. More recent studies (e.g. Thaler and Ziemba, 1988; Bird and McCrae, 1994), whilst suggesting some difference in the exact pattern of observed bias, offer dimensionally similar results. In terms of offering a rationale for the bias, a number of studies favour explanations based on aspects of the behaviour of demand-side agents, such as the tendency of bettors to discount potential losses associated with their choice (Henery, 1985) or to discount or deny linkage between losses and the bettor’s skill (Gilovich and Douglas, 1986). The non-pecuniary rewards associated with betting are also cited as potentially influential (e.g. Quandt, 1986; Gabriel and Marsden, 1990; Bruce and Johnson, 1992). The work of Shin (1991, 1992, 1993), by contrast, explains bias in terms of supply-side behaviour, specifically the risk-averse pricing behaviour of bookmakers, insuring themselves against adverse selection by informationally privileged bettors. Those studies that explain the bias in terms of supply- and/or demand-side influences pay little attention to the potential impact of market ecology, despite the fact that the studies cover a diverse range of generic market forms and specific market types. More recently, however, Vaughan Williams and Paton (1997) suggest that the characteristics of particular race types may serve to influence supplier behaviour, hence contributing to observed bias, though the main emphasis of this contribution is to develop and test Shin’s earlier approach. The specific objective of this chapter is to develop and refine the investigation of the role of market ecology in adding to our understanding of the favourite–longshot bias.

An ecological classification of horse-race betting markets This section has two main aims. First, it explains the basis for an ecology-based classification of horse races and their associated betting markets; second, the classification is used to develop two testable propositions relating to the differential incidence of bias. The ecological distinctions between generic market forms: the bookmaker and pari-mutuel markets The discussion of the ecological distinctions between bookmaker and parimutuel markets focuses on five aspects of the market environment that draw on the market ecology literature discussed above.

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Odds determination The first significant ecological distinction relates to the processes of odds (i.e. price) determination in the two market forms. Odds in bookmaker markets are co-determined via the interaction of active supply and demand sides, whereas odds in pari-mutuel markets are determined solely by the demand-side activity. It might be argued that the existence of an active and professional supply side (i.e. bookmakers) in bookmaker markets would tend to induce alignment between the probability inherent in odds and the actual probability, thus producing less bias compared with pari-mutuel markets. However, this view neglects the fact that bookmakers (as the market makers) may, under certain circumstances, have an incentive to offer odds that feature deliberate misalignment (e.g. to protect themselves from adverse selection). It should also be remembered that while the odds in a bookmaker market are co-determined, odds outcomes emerge in a non-systematic way via the interaction of supply- and demand-side sentiment and behaviour. Consequently, it is reasonable to view bookmaker markets as susceptible to both supply- and demand-side (and interactive) drivers of favourite–longshot bias. By contrast, pari-mutuel markets, though susceptible to demand-induced bias such as that resulting from the employment of heuristics, are insulated both from supply-induced bias and from biases that are a product of interactions of supply- and demand-side influences. Thus, there might be reasonable grounds for expecting a more pronounced favourite–longshot effect in bookmaker markets. Buyer-supplier relationship A second ecology-based distinction between market forms relates to the differential nature of the buyer–supplier relationship. Bookmaker markets involve an adversarial relationship between buyers and suppliers since an inverse relationship exists between the returns to bettors and the returns to bookmakers. In pari-mutuel markets, however, the shares of total betting revenue for the market operator and the bettors remain fixed. As a result, bettors in bookmaker markets must, in addition to attempting to select the winning horse, form a view as to the value or ‘reasonableness’ of the odds relating to each horse. To the extent that consideration of ‘value’ complicates the bettor’s judgmental task, it might be expected to impact negatively on rational choice and promote a more random pattern of activity. Any such effect would involve a greater tendency to bet on low probability (high odds) horses, thus contributing to favourite–longshot bias. By contrast, bettors in parimutuel markets are free to focus exclusively on the selection, in the knowledge that the operator’s ‘take’ from the market is predetermined. Supply-side structure The added complexity discussed above that may be regarded as deflecting the attention of the bettor from the central task in bookmaker markets is compounded

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by the fact that the supply sides of bookmaker markets are imperfectly competitive. They comprise a range of suppliers offering odds that are both different at any point in time and that evolve at different rates and in a non-systematic way. Hence, the bettor faces significant search costs in locating the most favourable odds in bookmaker markets, whilst pari-mutuel bettors face a unique set of odds offered by a monopoly operator. Again, this additional consideration for bettors in bookmaker markets might induce a degree of randomness and associated bias in the pattern of betting activity as the focus on the core decision task becomes blurred. Rate of return insurance An additional distinction between market forms with the potential to influence the incidence of bias is the differential opportunity to guarantee the rate of return at which a successful bet will be rewarded. Bets in bookmaker markets fix the odds at which returns are settled; bets in pari-mutuel markets necessarily involve odds uncertainty. If the ability to insure odds is regarded by some bettors as utility-enhancing, they may be prepared to sacrifice some value in order to secure odds insurance. Hence, some deviation between odds-implied and actual probabilities, which may manifest itself as favourite–longshot bias, may be tolerated in bookmaker markets. Additionally, the non-availability of fixed odds in pari-mutuel markets may result in a more sophisticated consideration of the relationship between odds and actual probability, which might be expected to promote closer alignment between these variables. Information environment and learning opportunities It is sensible to consider together the differential opportunities for learning and the differential nature and availability of market-relevant information between bookmaker and pari-mutuel settings. This reflects the view that learning opportunities are largely a function of the quantity and form of information made available to bettors. Differences in information availability reflect the distinction between the computer-based, formula-driven pari-mutuel setting and the more organic bookmaker market. To summarise a set of arguments presented in Johnson and Bruce (2001), there are grounds for suggesting that participants in pari-mutuel markets are informationally privileged vis à vis those in bookmaker markets in terms of (a) the availability of continual updates of the market as a whole, including size of the aggregate market in financial terms, (b) the standardised formula that translates betting patterns into odds, and (c) the unique odds for any betting event at any time, compared with differing odds from different bookmakers. As a basis for rational decision-making, it is thus argued that the information environment in pari-mutuel markets is superior to that available to bettors in bookmaker markets. Thus, it is anticipated that deviations from rational betting behaviour, as evidenced by favourite–longshot bias, are less likely in

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Table 19.1 Pari-mutuel and bookmaker markets: ecological distinctions Factor

Pari-mutuel market

Bookmaker market

Odds determination

Demand-determined (formulaic) Non-adversarial

Co-determined (organic) Adversarial

Monopolistic Uncertain Technologically advanced, non-complex, objective

Imperfectly competitive Insurable Technologically primitive, relatively complex, supplier influenced Relatively low

Buyer-supplier relationship Supply-side structure Rate of return Information environment Scope for buyer learning

Relatively high

pari-mutuel markets. Equally, the more uniform presentation of odds data in pari-mutuel markets fosters a more favourable learning environment, as odds evolve according to invariable rules. In the absence of a common basis for odds formulation across bookmaker markets, opportunities for learning through repeated exposure to such markets are more limited. The more organic nature of the bookmaker market renders it more susceptible to unpredictable influences such as bookmakers’ subjective views as to race outcome. Such influences might again induce a more significant random component in betting behaviour and, thus, a greater propensity for favourite–longshot bias. The above discussion suggests a range of ecological characteristics that might affect the incidence of favourite–longshot bias. These ecological features and their differential incidence across market forms are summarised in Table 19.1 and may be formalised in the following testable proposition: Proposition 1: Pari-mutuel markets will be characterised by a lower incidence of favourite–longshot bias than bookmaker markets. The ecological distinctions between specific market types: informationally opaque and informationally transparent markets Shin (1993) and Vaughan Williams and Paton (1997) introduce the notion of races (markets) that, in terms of their informational characteristics, are considered more or less susceptible to ‘insider’ activity. Certain types of race may be regarded, respectively, as informationally relatively transparent and relatively opaque. The significance of this distinction lies in its potential to explain differential opportunities for undetected exploitation of privileged information. In simple terms, races (and markets) that are subject to a high degree of public and media interest, scrutiny and analysis are regarded as less susceptible to insider influence due to the relative difficulty of concealing and exploiting information in such settings. In terms of the favourite–longshot bias, the contention is that races that are vulnerable to insider effects induce bookmakers to set odds

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‘defensively’ to limit their exposure to informed bettors. As noted earlier, the greatest potential exposure relates to successful ‘insider’ betting on horses with long odds; hence bookmakers tend to ‘over-shorten’ the odds of longshots, thereby inducing favourite–longshot bias. The analysis that follows defines two distinct groups of races that are, respectively, informationally transparent and informationally opaque. The groups are defined in the following sections. Transparent This category incorporates all high grade races (Class A–C races) that usually offer the highest prize money and attract the better quality horses. Higher grade races tend to attract considerable and overt attention in terms of media speculation and analysis, and the featured horses in such events are generally more exposed in terms of their public profile. There is consequently less scope for the covert holding of privileged information. Opaque This category comprises all lower grade (Class D–H), non-handicap races.2 The basis for regarding these races as relatively informationally opaque relates to a number of aspects. First, ‘non-handicap’ races often include horses with very little exposed public form and, frequently, horses racing for the first time in public whereas handicap races generally require all horses to have run in at least three races. Second, and relatedly, the trainers and owners of horses in this type of race often have, by virtue of the race conditions, greater discretion in determining a key variable, the weight carried by their horse. This clearly contrasts with handicap races, where weights are assigned by the ‘official handicapper’ on the basis of the horses’ previous performances. As such, in this type of lower class, non-handicap race, weights are often determined by various individuals’ subjective evaluations of a blend of public- and privately-held information. Finally, more prosaically, lower grade non-handicaps are renowned as vehicles for activity by informationally privileged bettors whose actions are based on knowledge of planned ‘coups’ by a particular horse’s ‘connections’ (e.g. owner, trainer). This effect may be amplified by the fact that such low grade races attract modest prize money so that connections may view them more as opportunities to make money via betting rather than via the prize fund. The isolation of lower grade, non-handicap races offers a clear basis for comparison between two distinct sets of race types defined by their respective informational transparency and opacity. The above discussion provides strong a priori grounds for expecting the informationally transparent markets to feature a lower incidence of bias relative to more opaque markets. In bookmaker markets informational transparency offers a more comprehensive knowledge resource for bettors and reduces the vulnerability of bookmakers to the actions of informationally privileged bettors.

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Each factor would tend to reduce favourite–longshot bias in informationally transparent bookmaker markets. For pari-mutuel forms of transparent markets, the supply-side effect is absent, but the superior informational base enjoyed by bettors might still be expected to reduce bias relative to opaque markets. Hence, to formalise the proposition, Proposition 2. Informationally transparent market types will be characterised by a lower incidence of favourite–longshot bias for both generic market forms (pari-mutuel and bookmaker) than informationally opaque market types.

Testing the ecology-based classification of horse-race betting markets: data and procedures Data characteristics The principal data used in this chapter relate to details of quantities staked in the pari-mutuel market on 19,162 horses that participated in 2,078 horse races in the UK between 1 June and 31 August 1996. These data were made available to the authors by the UK monopoly operator of pari-mutuel horse race betting, the Horserace Totalisator Board (the ‘Tote’). They allow the computation of pari-mutuel odds for each horse in each race in the sample, thereby representing a comprehensive picture of pari-mutuel betting activity and providing a complete profile of each of the 2,078 individual betting markets from a broad crosssection of 49 racetracks. Since the racetracks are distributed across the UK, the results are unlikely to be biased by any potential location-specific influences (e.g. a larger proportion of informationally privileged racegoers at racetracks located close to major racehorse training centres). This represents a significant improvement over the informational basis with which earlier studies of UK parimutuel activity have operated. Thus, for example, both Gabriel and Marsden (1990, 1991) and Vaughan Williams and Paton (1997) confine their analysis of pari-mutuel markets to winning horses. The reason for this is that the Tote merely declares odds of the winning horse; odds of all other participants, had they won, are not published. Of course, the value of analysis based on scrutiny of just one set of odds (or price) within a much larger market is open to question, but the data set employed in the current study overcomes this difficulty. The pari-mutuel market information is augmented by details of the odds in the bookmaker market for each horse in the sample, thus allowing direct comparison of betting activity between the two market forms over a common set of events. It should be emphasised that the odds declared for bookmaker markets and the odds declared in the pari-mutuel market are based on the closing price in the relevant on-course market. These on-course markets co-exist within the confines of the relevant racecourse, and there is open access for bettors to either market. The importance of this point lies in the assurance that the data reflect parallel betting activity both in terms of a homogeneous set of events and a homogeneous set of bettors.

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In addition to the market-specific data, information regarding the type (e.g. grade, handicap/non-handicap) and the result of each race is collated from publicly available sources. Procedures A central aim of the procedures employed here is to test the contention that the favourite–longshot bias is influenced by market form and market type. This involves conducting two stages of analysis to investigate the existence and origin of the favourite–longshot bias, where bias is evidenced by the pattern of deviation between the subjective (implicit in the odds) and the objective (or observed) probabilities of success associated with horses across the odds range. In both stages of the analysis, a conditional logit modelling procedure is employed. An overview of this procedure is now provided (full details are given in the Appendix) prior to an explanation of the two stages in its application to the data. In describing the procedure, it is important to understand the distinctions between pari-mutuel and bookmaker markets in terms of the probabilities inherent in the odds in each market. The derivation of odds in a pari-mutuel (Tote) betting market is explained in Equation (1) above. As these odds reflect the aggregated judgements of all Tote bettors, they may be used to assess these bettors’ degree of belief concerning a horse’s probability of success. Given that Tote bettors are aware of the level of deduction from the Tote pool (this is widely publicised) and that prevailing Tote odds are widely displayed at the racecourse, it is expected that ‘the odds on a given bet will be bid to a level that reflects the market’s best estimate of the true probability of winning it’ (Figlewski, 1979, p. 80). Consequently, if a rational Tote bettor’s subjective probability of horse i winning race j (with nj runners) is pijt , she is likely to continue to stake money on horse i, up to the amount, hij, such that nj

Oijt =

1 − pijt pijt

or

∑h i =1

ij

(1 − d )

hij

− 1.

(2)

A bettor, having staked £ xi on horse i in race j, would make a profit of £ xi × O tij if horse i won race j. In bookmaker markets, starting prices (SPs) are those odds available at the racecourse immediately prior to the start of the relevant race; that is at the culmination of the period of approximately 15–20 minutes which constitutes the active market period. At the start of this market period, the odds on offer reflect the subjective views of bookmakers as to the relative probabilities of success of the competing horses, adjusted according to Shin (1992) to embody an element of insurance against the activity of informationally privileged traders. Throughout the life of the market, the pattern of betting activity and bookmakers’ competitive behaviour will generate movement in the odds of each horse. These

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movements are reinforced by the activity of off-course bookmakers who control their risk exposure by betting, via their agents, in the on-course market. At the end of the market period, therefore, the odds (Oijb ) offered in relation to horse i in race j are related to a combination of bettors’ and bookmakers’ subjective probabilities of horse i’s chance of winning (Pijb ) in the following manner: Oijb =

1 − pijb pijb

(3)

Both Pijt and P ijb represent forms of subjective probability, associated, respectively, with bettors and a combination of bettors and bookmakers. In each of the market forms described above, where the observed or objective probability of a group of horses with a particular set of odds differs from the probability implied by the odds, this discrepancy represents evidence of market inefficiency in the sense that available information is not fully reflected in the odds available. If the objective probability of horses with high odds (low odds) is consistently less (greater) than the probability implied by the odds, this would suggest that favourite–longshot bias is present. In order to assess the degree of favourite–longshot bias in the two markets, a conditional logit procedure is developed (McFadden, 1974) for modelling the objective probability of success for horse i in race j with particular Tote odds (model 1) and with particular bookmaker odds (model 2). For both models an index of winningness, Wij, is defined for horse i in race j, such that the horse with the largest value of Wij will win the race. For model 1, Wij is defined as a polynomial of the natural logarithm of the Tote odds, O tij , together with a random error term, eij. A polynomial is employed since the precise nature of the relationship between the odds and a horse’s objective chance of success is unknown. In model 2, bookmaker odds, Oijb replace Tote odds in the winningness index. These indices are used (see Appendix) to develop a formula relating the objective probability of horse i winning race j (as evidenced by the results of the 2,078 races in the sample) to a function (Equation A.5 in Appendix) incorporating the Tote bettors’ subjective estimates of horse i’s chance of success (model 1) and the bookmaker/bettors’ subjective estimates of its chance of success (model 2). Model 1 and model 2 are estimated by applying a conditional logit procedure (McFadden). Maximum likelihood procedures in LIMDEP are used to determine the coefficients of the parameters employed in these models. For horse i in race j, Equations (A.5) and (A.7) were employed (see Appendix) to determine the predicted probability of o o success, Pij , Pij derived, respectively, from the Tote odds and bookmaker odds. This process was repeated for each horse in all Jk races. Since a conditional logit model was employed, then for a given race, j, t

nj

ot

b

nj

ob

∑ P ij = ∑ Pij = 1

i=1

i=1

ot

For horse i in race j, with particular Tote odds, O tij , a unique value of P ij is obtained. However, horses that run in different races, but that share the same

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odds value (i.e. O tij = O tik) may not share the same predicted probability of o o success. Thus, there is no guarantee that P ij = P ik . This implies that for each value of Tote odds, O tk a range of probability estimates is obtained, depending upon the race in which the horse ran (see Appendix). To estimate a unique probability of success for horse k, with particular Tote odds O tk, irrespective of the race in which it runs, curve-fitting facilities within SPSSX were employed. A similar procedure was used to assign unique probabilities of success to horses with particular bookmaker odds values. Graphs are then drawn to relate subjective probabilities (determined from both Tote and bookmaker markets) to the horses’ objective probabilities of success. A reference function is also constructed that shows perfect alignment between subjective and objective probabilities. Deviations from this line indicate the degree of favourite–longshot bias in each market form (Tote and bookmaker) when the objective probability for a horse with long (short) odds is lower (higher) than the odds imply. In line with Proposition 2 indicated above, models were also developed to compare the favourite–longshot bias evident in informationally transparent markets (Class A–C races) with that in informationally opaque markets (non-handicap, class D–H races) for both pari-mutuel and bookmaker market forms. t

t

Results and interpretation The results of the conditional logit estimations are reported in Tables 19.2–19.4. The six models involving (a) bookmaker odds and (b) Tote odds developed using data from ‘all races’, ‘Class A–C races’ and ‘non-handicap/class D–H races’ were all highly significant. Polynomials of degrees greater than those indicated in Tables 19.2–19.4 were tried, but they introduced insignificant terms and did not improve upon the explanatory power of the models indicated. In order to assess the degree of favourite–longshot bias, curve-fitting procedures in SPSSX were employed to represent the relationship between the objective probability of a horse winning and its Tote and bookmaker odds. The results of these procedures are also given in Tables 19.2–19.4. Polynomials of degrees greater than one, in the case of the Tote odds model, developed using data from ‘all races’ in the sample and degrees greater than two for all other models were tried. However, they introduced insignificant terms and did not improve the explanatory power of the polynomials indicated under ‘curve-fitting results’ in Tables 19.2–19.4. The resulting polynomials are used to construct Figures 19.1–19.3. These depict the natural logarithm of the probability of success for horses with particular Tote odds and bookmaker odds, for the ‘all races’ (Figure 19.1), the ‘Class A–C’ (Figure 19.2) and the ‘non-handicap/class D–H’ samples (Figure 19.3). These figures also include a reference line that represents the situation where odds are a perfect predictor of success (i.e. prob = 1/(1 + odds)). Deviations below (above) the reference line indicate that the odds overestimate (underestimate) the objective probability of success. It is clear from Figure 19.1 that bookmaker odds increasingly overestimate

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Table 19.2 Results of conditional logit estimations and curve-fitting procedures for models 1 and 2 (all races) Variable

Coefficient

SE

Model 1: independent variable: Ln (Tote odds) ln(Oijt )a –0.6286 0.0558 [ln(Oijt )]2 –0.0729 0.0170 Model χ2 = 6,817.58 (2 degrees of freedom), Log likelihood = 3,727.03 Number of observations: 2,078

b/SE

Significance

–11.268 0.0000 –4.293 0.0000 [χ2 (0.001) = 13.82]

Curve-fitting results ln( pkT ) = − 0.5117 − 0.9574ln(Okt ) R2 = 0.98, degrees of freedom = 19.161, F = 796,057 (p < 0.0001) Model 2: independent variable: Ln (bookmaker odds) –0.5888 0.0695 ln(Oijb) a [ln(Oijb)]2 –0.1331 0.0225 Model χ2 = 6,914.80 (2 degrees of freedom) Log likelihood = 3,677.59 Number of observations: 2,078

(4)b

–8.472 0.0000 –5.912 0.0000 [χ2 (0.001) = 13.82]

Curve-fitting results ln(pkB) = −0.707 − 0.5465ln(O bi j) − 0.1414[ln(O bi j)]2 R2 = 0.996, degrees of freedom = 19,160, F = 2,409,709 (p < 0.0001)

(5)b

Notes a Oijt and O bij = odds of horse i in race j, in Tote and bookmaker markets, respectively. b pkT and pkB = objective probabilities of a horse with Tote odds of Okt and bookmaker odds of Okb, respectively.

horses’ probabilities of success as odds increase from about 2.5/1. Tote odds on the other hand do not overstate the horses’ chance of success to any appreciable degree. Whilst Tote odds do apparently underestimate horses’ probabilities of success for odds below 1/1, the underestimation is not appreciable. In addition, the limited number of runners with odds below 1/1 in the sample makes these estimates less reliable. The demand-side influences on the favourite–longshot bias therefore appear limited in effect. In summary, Figure 19.1 appears to confirm Proposition 1 that pari-mutuel markets are characterised by a lower incidence of the favourite–longshot bias than bookmaker markets. Whilst the rationale for the results that follow assigns particular significance to the ecological distinctions between the market forms, it is important at least to acknowledge the possibility of alternative explanatory factors. For example, it might be suggested that the populations that bet, respectively, in bookmaker and pari-mutuel markets may be quite distinct in terms of risk attitudes, cognitive styles or preferences, thereby generating materially distinct behaviours and outcomes across markets. However, there is no evidence within the literature to suggest that each market type is associated with a distinct sub-population. Rather, it is a common perception that these physically adjacent markets compete with each other for customers. It is certainly the case that the specialist media routinely and regularly conduct comparisons

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Table 19.3 Results of conditional logit estimations and curve-fitting procedures for models 1 and 2 (Class A–C races) Variable

Coefficient

SE

Model 1: independent variable: Ln (Tote odds) ln(Oijt )a –0.8513 0.0674 Model χ2 = 1,177.68 (1 degree of freedom), Log likelihood = 680.83 Number of observations: 361

b/SE

Significance

–12.64 0.0000 [χ2 (0.001) = 10.83]

Curve-fitting results ln(pkT ) = −0.8050 − 0.7339In(Okt ) − 0.0216[ln(Okt )]2 R2 = 0.990, degrees of freedom = 34.23, F = 158,311 (p < 0.0001) Model 2: independent variable: Ln (bookmaker odds) –1.0009 0.0779 ln(Oijb)a Model χ2 = 1,134.64 (1 degree of freedom) Log likelihood = 672.35 Number of observations: 361

(6)b

–12.84 0.0000 [χ2 (0.001) = 10.83]

Curve-fitting results ln(pkB) = −0.5815 − 0.8441ln(Obk ) − 0.0306[ln(O bk )]2 R2 = 0.981, degrees of freedom = 3423, F = 86,459 (p < 0.0001)

(7)b

Notes a Oijt and O bij and are odds of horse i in race j, in Tote and bookmaker markets, respectively. b pkT and pkB and are objective probabilities of a horse with Tote odds of Okt and bookmaker odds of Okb, respectively.

between returns in pari-mutuel markets and bookmaker markets across a range of bet types. Additionally, the vigorous promotional and product development activity of the monopoly pari-mutuel operator in the UK (often citing direct value comparisons with bookmaker market returns) suggests that it perceives the aggregate customer population not to be segmented by market form. As indicated above, there are a number of differences between the two market forms that might contribute to greater favourite–longshot bias in bookmaker markets. Bookmakers, for example, have the opportunity to set odds in a manner to protect themselves from those with privileged information, and this has been shown to lead to the favourite–longshot bias. In addition, it has been argued above that demand-side influences on the bias are less marked in pari-mutuel markets. Bettors in pari-mutuel markets have the opportunity to develop a more sophisticated awareness of the relationship between odds and probability than bettors in bookmaker markets as a result of the more uniform, consistent and comprehensive (e.g. size of aggregate market) information environment. Further, for bettors in bookmaker markets, the search for the most favourable odds may detract from the central task of selecting the likely winner. Similarly, some tolerance of deviation between subjective and objective probabilities in bookmaker markets may be explained by the utility derived from the opportunity to insure the rate of return at which bets are settled. All of these factors suggest that market form is influential in affecting the degree of favourite–longshot bias. In particular

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Table 19.4 Results of conditional logit estimations and curve-fitting procedures for models 1 and 2 (non-handicap, Class D–H races) Variable

Coefficient

SE

Model 1: independent variable: Ln (Tote odds) ln(Oijt )a –0.6269 0.0748 [ln(Oijt )]2 –0.1077 0.02613 Model χ2 = 2,537.44 (2 degrees of freedom), Log likelihood = 1,316.07 Number of observations: 849

b/SE

Significance

–8.386 0.0000 –4.123 0.0000 [χ2 (0.001) = 13.82]

Curve-fitting results ln(pkT ) = −0.7814 − 0.5786ln(Okt ) − 0.1147[ln(Okt )]2 R2 = 0.997, degrees of freedom = 7157, F = 1,333,161 (p < 0.0001) Model 2: independent variable: Ln (bookmaker odds) –0.5956 0.0883 ln(Oijb)a [ln(Oijb)]2 –0.1530 0.0321 Model χ2 = 2,577.16 (2 degrees of freedom) Log likelihood = 1,296.22 Number of observations: 849

(8)b

–6.746 0.0000 –4.772 0.0000 [χ2 (0.001) = 13.82]

Curve-fitting results ln( pkB) = − 0.6731 − 0.5618ln(O bi j) − 0.1599 [ln(O bi j)]2 R2 = 0.997, degrees of freedom = 7,157, F = 1,394,924 (p < 0.0001)

(9)b

Notes a Oijt and O bij and are odds of horse i in race j, in Tote and bookmaker markets, respectively. b pkT and pkB and are objective probabilities of a horse with Tote odds of Okt and bookmaker odds of Okb, respectively.

the results presented in Table 19.2 and Figure 19.1 appear to confirm Proposition 1 that pari-mutuel markets are characterised by a lower incidence of favourite– longshot bias than bookmaker markets. Seen together, Figures 19.2 and 19.3 provide a means of comparing the degree of favourite–longshot bias across different market types, in particular between informationally transparent markets (Class A–C races) and informationally opaque markets (non-handicap, Class D–H). Figure 19.2 indicates almost perfect correlation between Tote odds and the reference line, suggesting no favourite–longshot bias in Tote odds in Class A–C races. This contracts with a marked favourite–longshot bias in non-handicap, Class D–H races (Figure 19.3). Similarly, whilst bookmaker odds display only a small degree of favourite–longshot bias in Class A–C races (Figure 19.1), there is a significantly greater bias in non-handicap, Class D–H races (Figure 19.3). These results confirm Proposition 2, namely that informationally transparent market types feature a lower incidence of favourite–longshot bias for each generic market form compared with informationally opaque market types. A number of demand- and supply-side reasons have been suggested for these results. In particular, markets with comparatively transparent information afford bettors the opportunity for more sophisticated analyses of each horse’s chance of success.

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2

Ln (objective win probabilities)

0 −2 −4 −6 Reference

−8

(prob=1/(1+odds))

−10 −12

Tote odds

−14

Bookmaker odds

−16 −1.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Ln (odds)

Figure 19.1 Favourite–longshot bias in Tote versus bookmaker markers (all races).

2

Ln (objective win probabilities)

0 −2 −4 −6 Reference

−8

(prob=1/(1+odds))

−10 −12

Tote odds

−14

Bookmaker odds

−16 −1.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Ln(odds)

Figure 19.2 Favourite–longshot bias in Tote versus bookmaker markets (Class A–C races).

Equally, where information is lacking, bettors will have less of a basis for discriminating between horses, resulting in a more even distribution of bets across all horses in a race and contributing to a favourite–longshot bias. Figure 19.3 clearly demonstrates the presence of demand-side-induced bias, whereby the Tote odds (determined solely by demand factors) display a significant degree of

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Ln (objective win probabilities)

0 −2 −4 −6 Reference

−8

(prob=1/(1+odds))

−10 −12

Tote odds

−14

Bookmaker odds

−16 −1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Ln (odds)

Figure 19.3 Favourite–longshot bias in Tote versus bookmaker markets (non-handicap, Class D–H).

favourite–longshot bias in the informationally opaque markets. However, the lack of favourite–longshot bias in Tote betting for informationally transparent markets suggests that the demand-side influences on the bias operate through the information disadvantages associated with certain market types. Bookmaker markets, in addition to being subject to demand-induced bias, are also subject to influences on the supply side. Where bookmakers set odds defensively to protect themselves against holders of privileged information, this behaviour will be most pronounced in relation to longshots since relatively small bets on these horses (by privileged ‘insiders’) can result in larger losses for the bookmakers. In comparing Figures 19.2 and 19.3 it is clear that the favourite– longshot bias is more evident in the informationally opaque markets, precisely the markets in which holders of privileged information are most likely to operate. Consequently, the empirical evidence supports Proposition 2, that informationally transparent market types will be characterised by a lower incidence of favourite–longshot bias for each generic market form than informationally opaque market types. It is also interesting to note that Figures 19.2 and 19.3 each demonstrate greater favourite–longshot bias in bookmaker than in parimutuel markets, once again confirming proposition 1.

Conclusions This chapter seeks to explore the influence of market ecology on behaviour within markets. In particular, the objective is to examine the role of market form and market type on the incidence of a well-established anomaly (favourite–

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longshot bias) in markets for state-contingent claims. The horse-race betting market in the UK is selected for analysis since it offers the prospect of parallel generic market forms (bookmaker versus pari-mutuel) and distinct market types (high class versus low class races). Conditional logit analysis of patterns of betting activity between the two market forms and two market types allows a clear insight into the differential impacts of market ecology on the favourite– longshot bias. The results suggest that both market form and market type have a substantial influence on the nature of the favourite–longshot bias and provide evidence for both demand- and supply-side origins for the market distortion. In more general terms, it appears that market ecology may play a significant role in the incidence of distortion in markets for state-contingent claims. In particular, it is tempting to suggest that distortions are likely to increase when market conditions favour insider trading or cause bias in traders’ behaviour.

Appendix In order to model the objective probability of success for horses with particular Tote odds (model 1), an index, Wij, is defined for horse i in race j as a polynomial of the natural logarithm of the Tote odds together with a random error term, eij, as follows: m

( )

r

Wij = ∑ ar ln Oijt  + eij . r =0

(A.1)

Wij is constructed such that, for a given race, the horse with the largest value of Wij will win; it might therefore be thought of as an index of winningness. Wij cannot be observed directly, but the horse that wins race j can be determined. Consequently, if horse i* is observed to win race j, with nj runners, this implies Wi*j > max Wij ∀i≠ o i*. The probability of horse i* winning race j (Pi*j ) is therefore given as follows: t

piO*tj = prob (Wi* j ) > (Wij ) , ∀i ≠ i*,

(A.2)

m r r m  = prob  ∑ ar  ln Oit* j  + ei* j > ∑ ar  ln Oijt  + eij  , i = 1, 2,... nj     r= 0  r=0 

( )

m

( )

r

m

r

= prob[eij < ∑ ar  ln(Oit* j )  − ∑ ar  ln(Oijt )  + ei * j ] r =0

(A.3)

(A.4)

r =0

Wij cannot be observed, hence the observed variables are defined as follows: yij = 1 (if Wij = Max(W1 j, W2j ,...........Wnjj), yij = 0 otherwise. The probability that a particular horse wins race j is conditional on the ‘winningness index’ for all other horses in that race. Consequently, it can be shown that if the error terms, eij, are assumed to be independent and distributed according to the double exponential distribution, then the predicted probability of horse i winning race j is given as follows:

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A.C. Bruce and J.E.V. Johnson r   m exp  ∑ ar ln Oijt    for i = 1, 2K n (A.5) pij = p (yij = 1| Wij , ∀i ≠ i *)= n j  r =0m j r   exp  ∑ ar ln Oijt   ∑ i =1  r =0 

( )

( )

For a given value of m, mt, the parameters ar (r = 1, 2, . . . mt) in Equation (5) are determined by maximising the joint probability of observing the results of all Jk races in the sample under the assumption of independence across bets. Consequently, for m = mt the values of ar (r = 1, 2, . . . mt) are determined such that the following likelihood function, L, is maximised (employing maximum likelihood procedures in LIMDEP): Jk

L = ∏ pi* j .

(A.6)

j =1

This procedure is repeated to produce r models where r = 1, . . . m. The most parsimonious model is then chosen for which the coefficients of ar (r = 1, 2, . . . m) are all significant at the 5 per cent level. Employing the selected model, the predicted probabilities of success (pij) for each horse in the sample are determined. Since a conditional logit model is n employed, these sum to unity within a given race, (∑ P oij = 1). However, since i=1 the pattern of odds and operator’s margins (due to variations in breakage) vary between races, the predicted probability of success for horses with the same odds but running in different races may not be equal. Thus, if Oijt = Oilt , it is probable that P oij ≠ P oil. The aim is to provide a best estimate for the probability of success for a horse running in any race with Tote odds of a particular value. Consequently, curvefitting facilities in SPSS are employed to define the appropriate function (Ft) for determining a unique predicted probability of winning ( pkT ) for horses with particular Tote odds, Okt, irrespective of the race in which they run. A second model is developed, replacing Tote odds with bookmaker odds in the above procedures. Consequently, Equation (A.5) becomes j

t

t

pOb ij

t

s  n exp  ∑ as ln Oijb    = n j  s =0n s exp ∑ as ln Oijb  ∑ i =1 r =0

( )

(A.7)

( )

where pijOb = probability of horse i winning race j, derived from the bookmaker odds of horse i and Oijb = bookmaker odds for horse i in race j. In a similar manner to that indicated above, the appropriate function (Fb) is defined (using curve-fitting facilities in SPSS) to determine for a horse with odds O kb its objective probability of winning, irrespective of the race in which it runs

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P kB. A reference function (FR) is also constructed, which assumes that the subjective probability inherent in horse i’s odds (Oib ) are equal to its predicted probability of winning (pi):

pi =

1 ⋅ 1 + Oib

(A.8)

Functions Ft and Fb are then drawn alongside FR to compare the degree to which Tote and bookmaker odds, respectively, overestimate and/or underestimate the winning probability of horses with particular odds. This provides a means for determining whether the favourite–longshot bias is more pronounced in the Tote or bookmaker markets.

Notes 1 Tote odds are also affected by ‘breakage’, whereby odds are only declared to the nearest 0.1. For example, if Equation (1) produces the value 2.16, the odds actually used to calculate return would be 2.10. The degree of breakage in any given race is not constant, and consequently, the operator’s margin will vary to some degree across races. 2 Races are categorised as either handicap or non-handicap. Horses cannot normally run in handicaps until they have run in at least three non-handicap races. Each horse that runs in a handicap is allocated (by the ‘official handicapper’) a weight to carry based on its previous performances. The weights are set by the handicapper in such a way that, based on previous performances of horses, the horses are expected to finish in a dead-heat. This goal is rarely achieved but the differential weights carried by horses generally create very competitive races.

References Bird, R. and McCrae, M. (1994) ‘Racetrack betting in Australia: a study of risk preferences and market efficiency’, in Eadington, W.R. and Cornelius, J.A. (eds). Proceedings of the 7th International Conference on Gambling and Risk Taking. Institute for the Study of Gambling and Commercial Gaming, Reno, pp. 228–58. Bruce, A.C. and Johnson, J.E.V. (1992) ‘Toward an explanation of betting as a leisure pursuit’, Leisure Studies 11: 201–18. Dowie, J. (1976) ‘On the efficiency and equity of betting markets’, Economica, 43: 139–50. Figlewski, S. (1979) ‘Subjective information and market efficiency in a betting market’, Journal of Political Economy, 87: 149–63. Gabriel, P.E. and Marsden, J.R. (1990) ‘An examination of market efficiency in British racetrack betting’, Journal of Political Economy, 98: 874–85. Gabriel, P.E. and Marsden, J.R. (1991) ‘An examination of market efficiency in British racetrack betting: Errata and corrections’, Journal of Political Economy, 99: 657–9. Gilovich, T. and Douglas, C. (1986) ‘Biased evaluations of randomly determined gambling outcomes’, Journal of Experimental Social Psychology, 22: 228–41. Henery, R.J. (1985) ‘On the average probability of losing bets on horses with given starting price odds’, Journal of the Royal Statistical Society, 4: 342–9. Johnson, J.E.V. and Bruce, A.C. (2001) ‘Calibration of subjective probability judgments

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in a naturalistic setting’, Organizational Behavior and Human Decision Processes, 85: 265–90. McFadden, D. (1974) ‘Conditional logit analysis of qualitative choice behaviour’, in Zarembka, P. (ed.). Frontiers in Econometrics: Economic Theory and Mathematical Economics. Academic Press, New York, pp. 105–42. Murnighan, J.K. and Ross, T.W. (1999) ‘On the collaborative potential of psychology and economics’, Journal of Economic Behavior and Organization, 39: 1–10. Plott, C.R. (1989) ‘An updated review of industrial organization: applications of experimental methods’, in Schmalensee, R. and Willig, R.D. (eds). Handbook of Industrial Organization Volume II. Elsevier, Amsterdam, pp. 1109–76. Quandt, R.E. (1986) ‘Betting and equilibrium’, The Quarterly Journal of Economics, 101: 201–7. Shin, H.S. (1991) ‘Optimal betting odds against insider traders’, Economic Journal, 101: 1179–85. Shin, H.S. (1992) ‘Prices of state-contingent claims with insider traders, and the favourite–longshot bias’, Economic Journal, 102: 426–35. Shin, H.S. (1993) ‘Measuring the incidence of insider trading in a market for statecontingent claims’, Economic Journal, 103: 1141–53. Smith, V.D. (1989) ‘Theory, experiment and economics’, Journal of Economic Perspectives, 3: 151–69. Thaler, R.H. and Ziemba, W.T. (1988) ‘Anomalies – pari-mutuel betting markets, racetracks and lotteries’, Journal of Economic Perspectives, 2: 161–74. Vaughan Williams, L. and Paton, D. (1997) ‘Why is there a favourite–longshot bias in British racetrack betting markets?’, Economic Journal, 107: 150–8. Waller, W.S., Shapiro, B. and Sevcik, G. (1999) ‘Do cost-based pricing biases persist in laboratory markets?’, Accounting, Organizations and Society, 24: 717–39.

20 Calibration of subjective probability judgements in a naturalistic setting J.E.V. Johnson and A.C. Bruce

Introduction Analysis of the factors which affect the quality of human judgement has generated considerable research within disciplines which share an interest in decision processes and outcomes: economics, psychology and management in particular. A feature of the resulting literature is the degree of consensus which has emerged regarding the factors which inhibit the quality of human judgement and the decisions which result. In particular, there is a growing body of evidence of discrepancies between individuals’ subjective probability estimates and the relevant objective probabilities. This consensus of poor calibration reflects the outcome of research conducted mainly within the dominant methodological tradition of laboratory-based, experimental enquiry. The principal aim of this chapter is to offer a complementary body of analysis which explores decision-making in a non-experimental and naturalistic environment. Whilst it is acknowledged that experimentation can be conducted within a natural setting, throughout this chapter the term naturalistic is defined as a natural environment which has not been artificially manipulated (i.e. a nonexperimental setting). This chapter highlights a number of factors which previous laboratorybased experiments identify as likely to improve calibration. A particular naturalistic setting, the UK horse-race betting market, is then introduced. This environment, it is argued, embodies many of the features likely to induce accurate subjective probability estimates and it is an investigation of the calibration of bettors in this market which forms the main empirical focus of this study. The chapter proceeds as follows. The second section offers a brief review of the diverse literature devoted to the investigation of the quality of human judgements in general and explores the calibration literature in some detail. In particular, the consensus of poor calibration to emerge from laboratory experiments is highlighted and alternative explanations for these results are offered. The less uniform results reported in naturalistic calibration studies are explored and factors which appear to be influential in inducing good calibration are highlighted. The third section discusses the motivation for examining decisions made

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in the UK horse-race betting market. In particular this identifies the degree to which this setting embodies those features likely to lead to good calibration whilst simultaneously satisfying the received requirements for naturalistic enquiry into decision-making. The fourth section outlines the data employed in the study together with an overview of the procedures used to analyse the data (these are more fully developed in the Appendix). The fifth section presents the results of the analysis and the sixth section interprets their significance. Some conclusions are developed in the last section.

Calibration – literature review The diverse literature addressing the quality of human judgement identifies a range of factors which can inhibit performance and lead to poor calibration. Before discussing the specific findings of calibration studies it is instructive to categorize the literature exploring the quality of human judgement in general. A useful taxonomy groups factors inhibiting decision performance according to whether they are associated with, respectively, the decision-maker, the decision task or the decision environment. An important focus of the literature addressing the decision-maker is the limited cognitive capacity of the individual. This may result in reliance on heuristic principles which are designed to render more manageable the set of decision-relevant information. However, it has been demonstrated that these can lead to a range of systematic biases (e.g. Cohen, 1993b; Eiser and van der Pligt, 1988; Kahneman et al., 1982; Kahneman and Tversky, 1972; Russo and Shoemaker, 1989; Tversky and Kahneman, 1974) which may in turn lead to poor calibration. An important element of the literature addressing task characteristics concerns task complexity. Research in this area invites the general conclusion that the quality of human judgement is negatively related to complexity, defined in terms of alternatives and attributes (e.g. Ford et al., 1989; Hogarth, 1975; Malhotra, 1982; Timmermans, 1993; Wright, 1975). A range of variables associated with the decision environment has been shown to affect the quality of judgement. For example, the presence of other decision-makers may compromise performance via pressure to conform (Janis and Mann, 1972) or to justify actions (Curley et al., 1986). In addition there is evidence to suggest that individuals may have more difficulty in framing rational responses to tasks within a tense or highly charged setting (Bruce and Johnson, 1992), thereby inhibiting calibration. The range of potentially influential factors associated with the decisionmaker, the task or the environmental characteristics suggests that any observed errors in human judgement should be regarded as unremarkable. Indeed, this is reflected in the calibration studies discussed below. von Winterfeldt and Edwards (1986) conclude that ‘research evidence about calibration is abundant but significantly hard to make sense of’ (p. 27). Despite this view, we attempt to summarize the literature and draw some conclusions from the research evidence; in particular we attempt to identify factors which may be expected to foster good

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calibration. This review discusses, respectively, the results of laboratory experiments and naturalistic studies. Laboratory experiments The main finding to emerge from experimental studies conducted in the laboratory is that, with few exceptions, individuals’ subjective probability judgments are not well calibrated. Three distinct effects are dominant in explaining poor calibration. A number of studies demonstrate overconfidence in subjective probability estimates associated with events which are difficult to discriminate and under-confidence associated with events that are easier to discriminate – the hard-easy or discriminability effect (e.g. Baranski and Petrusic, 1994, 1995; Lichtenstein and Fischhoff, 1977; Lichtenstein et al., 1977; Stratigakos, 1994; Suantek et al.). There is also consistent evidence of relative overestimation in tasks with lower base-rate probabilities and relative underestimation in tasks involving higher base rates – the base-rate effect (Ferrell, 1994; Lichtenstein et al. 1982; Lindsay and Norman, 1972). In addition, individuals have been shown to overestimate the probability of events which are favourable to them and to underestimate the probability of events which they see as undesirable (Lindsay and Norman, 1972; Zakay, 1983). In terms of the causal origins of these effects, three broad accounts can be discerned in the literature: a cognitive bias account, which suggests that miscalibration results from the inappropriate manner in which individuals process and evaluate information, perhaps resulting from the employment of particular heuristics or arising from a particular risk attitude; a methodological account, which argues that miscalibration is simply an artefact of the artificial and misleading tasks subjects are required to perform in experimental calibration studies; and a combined account, which suggests a combination of individual and methodological sources for the poor calibration. These alternative forms of explanation are well exemplified in the debate surrounding the source of the hard–easy effect (see Suantek et al., 1996, for a useful review). It has been argued, for example, that this effect has a cognitive basis. Individuals are believed to employ a range of heuristics which result in bias in memory search or in the formation of opinions, leading to insensitivity to task difficulty (Ferrell and McGoey, 1980; Griffin and Tversky, 1992; Koriat et al. 1980; Sniezek et al. 1990). Alternatively, it has been suggested that the hard–easy effect is an artefact of the experimental methods employed; specifically, individuals internalize, through observation, the validities of certain cues to make judgements within particular environments. This allows them to make accurate judgements within their familiar natural environments. However, it is argued that subjects are often presented with misleading and artificial tasks in experiments, involving perhaps non-representative questions which are outside the subjects’ experience and for which the cues they normally employ are invalid. Miscalibration results (Björkman, 1994; Gigerenzer et al., 1991; Juslin, 1993, 1994). Proponents of

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this view point to the fact that small changes in experimental design can produce results which suggest good or poor judgement (Ayton and Wright, 1994; Beach et al., 1987; Pitz, 1977). For example, it has been demonstrated that subjects ignore base-rate probabilities when presented with these by the experimenter, but take them into account when allowed to develop their own base-rate probabilities (Gigerenzer et al., 1988). The essence of the methodological account is that heuristics may lead to biases in the static tasks presented in some laboratory experiments, but that these can be functional in dynamic real-world environments (Hogarth, 1980). Wider concerns associated with laboratory-based experiments are explored elsewhere (Beach and Lipshitz, 1993; Cohen, 1993a, 1993b; Hammond, 1993; Lipshitz, 1993; Orasanu and Connolly, 1993) and these can be summarized as follows (Eiser and van der Pligt, 1988): ‘Experimental demonstrations (of human fallibility) may depend to a large extent on the use of hypothetical problems that violate assumptions that people might reasonably make about apparently similar situations in everyday life’ (p. 96). It has also been argued that the overconfidence observed may simply be an artefact of the open-ended probability scales employed in some studies (Fischhoff and Bruine de Bruin, 1999) or result from regression of the error component in individuals’ estimates toward the mean (Erev et al., 1994). The foregoing accounts suggest either a cognitive or a methodological basis for the hard-easy effect. Alternatively, it has been argued that individuals possess an internal confidence variable which is partitioned in a particular manner to produce responses. It is suggested that the hard-easy effect results because subjects receive insufficient information concerning task difficulty to alter sufficiently the partition when task difficulty changes. Consequently, insufficient adjustment is likely to occur when inadequate cues regarding discriminability are given (Suantek et al., 1996). This combined account may therefore be seen as incorporating cognitive and methodological elements. It is evident from the above discussion of the hard–easy effect that explaining the particular causal form or route via which a factor exerts its influence on calibration may not be straightforward and, as such, there would appear to be scope for further investigation of the underlying causal influences of alleged effects. To summarize this section, the overwhelming impression to emerge from laboratory-based experiments is that of poor calibration amongst subjects, though some (Beach et al., 1987) argue that this impression arises due to a clear citation bias toward studies showing poor performance. In addition, as indicated above, a growing body of literature highlights the role played by inappropriate experimental methods in producing miscalibration. Despite these criticisms, a number of more recent studies control rigorously for some of the possible pitfalls associated with unrepresentative research design, yet still report miscalibration (e.g. Brenner et al., 1995; Griffin and Tversky, 1992; Keren, 1997). Thus, it appears that a degree of genuine miscalibration remains in well-designed laboratory studies.

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Naturalistic studies It has been suggested that the miscalibration observed in many laboratory experiments would be removed by observing, in their own task domain, the behaviour of individuals who are experienced in making judgements (Bazerman, 1994; Beach et al., 1987; Ferrell, 1994). However, the research evidence in this regard is mixed. Experienced estate agents (Northcraft and Neale, 1987), professional auditors (Joyce and Biddle, 1981; Smith and Kida, 1991), members of the armed forces (Hazard and Peterson, 1973), CIA agents (Cambridge and Shreckengost, 1980) and casino gamblers (Lichtenstein and Slovic, 1971) have all been shown to make biased probability judgements associated with the employment of various heuristics. In addition, a number of studies have shown that physicians employ a variety of heuristics which cause biased decisions and poorly calibrated probability judgements (Bennett, 1980; Christensen-Szalanski et al., 1983; Detmer et al., 1978; Einhorn, 1972; Elstein et al., 1978; Lusted, 1977). By contrast, other naturalistic studies have demonstrated that individuals in certain fields, with experience and domain-specific knowledge, are well calibrated. In particular, excellent calibration has been reported in the prediction of future interest rates by bankers (Kabus, 1976), prediction of R&D success by experienced managers (Balthasar et al., 1978), prediction of finishing position by horserace bettors (Hoerl and Fallin, 1974), prediction of the ability to make contracts by expert bridge players (Keren, 1991) and predictions by experienced weather forecasters (Murphy and Brown, 1985; Murphy and Winkler, 1977). In addition, experienced auditors appear to be better calibrated than naive subjects (Joyce and Biddle, 1981; Smith and Kida, 1991; Tomassini et al., 1982). Conditions for good calibration The generally poor calibration observed in laboratory experiments involving naive subjects and the mixed results from naturalistic studies involving experienced decision-makers within their own task domains suggest some conditions under which it is more likely that good calibration will be achieved (Phillips, 1987): 1

Expertise appears to aid calibration. As noted above, more experienced subjects generally achieve better calibration (e.g. Joyce and Biddle, 1981; Smith and Kida, 1991; Tomassini et al., 1982). However, the variability of calibration in naturalistic studies suggests that experience or expertise are not sufficient conditions for good calibration. Poor calibration by experienced subjects may result from their unfamiliarity with the characterization of uncertainty in terms of probabilities (Ferrell, 1994). Consequently, it might be argued that subjects experienced in their own task domain, who habitually assess situations in probability terms (e.g. weather forecasters), are more likely to be better calibrated (Phillips, 1987). Additionally, Shanteau (1992) has suggested that task characteristics may account for

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J.E.V. Johnson and A.C. Bruce differences observed in the quality of experts’ judgements; specifically, that more competent performance is likely if the decisions involve stimuli that are relatively constant, the tasks undertaken are repetitive, and where decision aids are widely available. Training and feedback within the specific decision domain appear to influence calibration. However, poor calibration amongst physicians who receive outcome information suggests that feedback per se is not sufficient. The ecological model predicts that training will improve calibration if outcome feedback allows individuals to learn judgement-relevant cues and cue validities (McClelland and Bolger, 1994). This appears to require practice with homogeneous tasks, particularly where forecasting is performed on a sequential and repetitive basis. Consequently, homogeneity of task, with regular immediate feedback unconfused by extraneous information, appears to assist good calibration (Lock, 1987). Poor calibration by physicians might then be explained by the heterogeneity of conditions which they are required to assess and the time lag between initial judgement and eventual feedback. Motivation for accurate judgements has been identified as an important factor influencing calibration (Beach et al., 1987). Research with experienced auditors, for example, has clearly demonstrated that calibration improves when incentives are provided for accurate judgements (Ashton, 1992). The research discussed above suggests that calibration in naturalistic settings is often better than in laboratory settings. It is argued that individuals become aware, for example, that some data sources in real-world environments involve redundant and unreliable data and that they must develop approaches, such as changing hypotheses, to handle the environment’s complex and dynamic nature (Omodei and Wearing, 1995). In short, it is argued that (McClelland and Bolger, 1994, p. 462): through interaction with the natural environment the ecological validity of cues becomes internalized through the process of observing the frequencies of co-occurrences of environmental events and these become the cue validities used in the probabilistic mental model they employ.

5

It is claimed that laboratory experiments often involve more static decisionmaking tasks involving reliable and diagnostic data, where subjects whose cognitive processes are attuned to their natural environment are likely to be poorly calibrated (Gigerenzer et al., 1991; Juslin, 1993, 1994). A number of studies suggest that calibration associated with prediction is likely to be better than that associated with individuals’ assessment of the accuracy of their memory. The latter is tested in the typical general knowledge tests often employed in calibration studies. Research has demonstrated that individuals employ different cognitive processes when assessing the probabilities of future events and it is suggested that these processes are less subject to bias (e.g. Wright, 1982; Wright and Ayton, 1988).

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Having identified a set of factors which the literature suggests might contribute to a high degree of calibration, the following section introduces the environment which forms the basis for empirical enquiry in this study, the UK horserace betting market.

Horserace betting markets as a naturalistic decision setting This section introduces the empirical setting for the analysis which follows and examines the degree to which it embodies the characteristics identified in the previous section as conducive to a high degree of calibration. An obvious starting point, given the focus of this chapter on naturalistic behaviour, is to consider in some detail the credentials of the horserace betting market as a natural setting, this being a criterion identified as significant in promoting calibration. Orasanu and Connolly (1993) argue that the full richness, dynamism and uncertainty of a natural context involving individual decision-makers involves a setting characterized by: • • • • • •

ill-structured problems uncertain, dynamic environments shifting, ill-defined, competing goals action-feedback loops time stress high stakes (i.e. rewards–penalties associated with decisions are meaningful to the decision-makers).

We now consider each of these factors in turn in relation to the horserace betting market, before exploring the degree to which the setting embodies further factors with the potential to encourage calibration: 1

2

A naive view of horserace betting would suggest that it cannot be viewed as an ill-structured problem since it simply involves the selection of one horse from a number of alternatives. However, in reality, horse-race betting involves a number of features of ill-structured problems. First, there is no unique way of addressing the task, a feature of ill-structured problems noted by Orasanu and Connolly (1993). A variety of views exists as to those factors which are more or less important in determining race outcome. These include previous performances of horses, weights carried by horses, horses’ trainers and jockeys, racecourse type and conditions. There is certainly no consensus on a process for combining these factors. In addition, the bettor must decide whether to gamble on one or several horses in a given race and must choose the particular form of bet. The only structural certainties in a horserace are that there exists a particular number of runners, that ex post the finishing order can be unequivocally determined and that the bet will be settled. Horserace betting markets are quintessentially uncertain and dynamic environments. The uncertainty resides in the uniqueness of each event in terms

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J.E.V. Johnson and A.C. Bruce of participants, location, conditions, the elusiveness of precedent and the fundamental unpredictability of the participants’ relative performance. The market is a dynamic environment in the sense that the evolving pattern of relative betting on different horses is reflected in continuously changing broadcast forecasts of the anticipated odds of each horse. This informational turbulence in relation to market activity is compounded by ongoing changes in factors relevant to the race itself, e.g. the demeanour and behaviour of horses in the pre-race period. Shifting, ill-defined, or competing goals are invariably a characteristic of bettors. Bruce and Johnson (1992) observe that bettors are motivated by a variety of factors, including financial reward, intellectual challenge and excitement. For many, the motivation is a cocktail of factors, where the different elements in the mix may themselves be susceptible to variation in relative importance. The subjective evaluation of horses’ chances of success, central to the activity of bettors, is based on the observation and analysis of each horse’s evolving portfolio of race performances as well as reports relating to its training progress, the form of its trainer, jockey, and so on. Actionfeedback loops are thus critical to the formulation and continual modification of models designed to improve decision accuracy. Bettors receive immediate and unequivocal feedback on decisions in the form of race outcome. Time stress is endemic to betting markets in that the life of the market in relation to a particular race generally extends to around 30 minutes. Whilst high levels of stress have been shown to have a damaging effect on decision quality (Janis and Mann, 1977), moderate levels of stress may actually lead to better decisions (Eiser and van der Pligt, 1988). It is difficult to quantify the levels of time stress involved at the race track, but the 30 minutes in which the betting market operates prior to most races should provide sufficient time for bettors to make reasonably sound decisions, especially since most races take place in the afternoon. This allows bettors to conduct analysis at leisure during the preceding morning. Finally, as regards high stakes, the level of financial commitment which the bettor makes is, of course, at the bettor’s discretion. Thus, one might argue that betting may or may not constitute a high stakes game. More importantly, however, ‘much decision research involves subjects who are not invested in the task to the same level as they would be outside the laboratory’ (Orasanu and Connolly, 1993, p. 10).

Clearly, horserace betting markets largely meet Orasanu and Connolly’s (1993) requirements for naturalistic research. This is particularly important in relation to the observation of betting behaviour, since it has been concluded (Anderson and Brown, 1984, p. 407) that ‘gambling behaviour . . . differs to a significant degree in the real and laboratory situations’. Specifically, as noted above, individuals are often well adapted to handling real-world environments

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which involve redundant and unreliable data and hence good calibration can be expected under such conditions. In addition to the influence of natural setting, four further factors were identified in the previous section as conducive to good calibration. Thus, potentially positive influences on calibration were associated, respectively, with the degree of expertise of decision-makers, opportunities for relevant training in the decision task, motivation or incentive, and the prediction of future as opposed to the estimation of existing outcomes. The first two of these factors may be taken together in the sense that expertise may be regarded as a product of training via repeated exposure to similar forms of decision problem. In terms of expertise, whilst some individuals who bet at the racetrack may be unfamiliar with the betting task, it seems reasonable to suggest that most will be operating in a familiar environment and will embody a degree of expertise. The development of expertise in horserace betting is enhanced by the opportunity for repeated exposure to similarly configured decision problems. Thus, the task of selecting winners in a series of races is a repetitive process involving analysis of a reasonably consistent set of stimuli. This opportunity for training or learning is reinforced by the existence of unequivocal feedback in the form of race results and the availability of a range of decision aids in the form of racing systems and models, form guides and specialist media analysis. Whilst there is no empirical evidence for the degree to which decision aids are employed by bettors, the range of products available suggests that demand exists for such aids. In addition, casual observation at UK racetracks suggests that most bettors appear to consult some form of racing publication when making their selection. These conditions are consistent with those identified by Shanteau (1992) as likely to be associated with competent performance by those familiar with the task domain. Equally, it has been empirically observed that violations of rationality are reduced under the multiple play conditions which exist at the racetrack (Keren, 1991; Keren and Wagenaar, 1987; Lopes, 1981, 1996; Weddell and Bochenholt, 1990). So far as motivation and incentive are concerned, each would appear to be present as features of decision-making in horserace betting markets. Importantly here, participation in horse-race betting is a voluntary act, so that it seems reasonable to assume that those who engage in betting are motivated to do so. In terms of incentive for good calibration, the material, and perhaps psychological, benefits or penalties which are attached to decision outcomes seem likely to be influential in incentivizing strong performance. Finally, drawing on the literature which distinguishes between estimation of existing and future outcomes, the essence of the horserace betting decision is that it is a prediction of a future outcome. Indeed, the window within which betting is permitted in relation to a particular event is closed by the start of the event itself, in racetrack parlance ‘the off’. Hence, the conditions exist for any perceived advantage in terms of calibration to manifest itself in this setting. This section has sought to demonstrate that the empirical setting for the analysis presented below is characterized by a number of factors held to promote

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good calibration. Consequently, the proposition explored here is that a high degree of calibration is likely to be observed when examining decisions made by bettors in the UK pari-mutuel horserace betting market. Operation of horse-race betting markets In the United Kingdom two distinct forms of horserace betting market operate in parallel, the bookmaker market and the pari-mutuel market. The analysis which follows is based exclusively on data relating to the latter, and it is thus important to understand the operation of the pari-mutuel market in terms of the processes and mechanisms involved in determining market outcomes. This reflects the emergent view (see, for example, Hey, 1992; Smith, 1989) that it is not merely the measurable structural characteristics (e.g. relative firm size, number of firms) of markets which influence outcomes, but equally the idiosyncrasies of market process, the organization and nature of dialogue between demand- and supply-side agents, and the formal and informal rules by which agents engage in trade. Each of these may contribute to an understanding or explanation of observed outcomes. As Hey (1991, p. 186) observes: ‘One message that does seem to emerge from the little theory that there is, however, is that the outcome does depend quite crucially on the precise market trading mechanism’. This is a theme which is explicitly acknowledged in interpreting the results which follow. A separate pari-mutuel betting market exists for each horserace run in the United Kingdom. Within each market, the simplest form of bet (on which this study focuses) involves decision-makers (bettors) selecting a particular horse to win that race.1 The bettor must also decide the size of bet to place (the stake). The selection and stake information are electronically recorded by the parimutuel operator (in the United Kingdom, the Horserace Totalizator Board, the Tote). All bets must be placed in the period (typically 30 minutes) prior to the start of the relevant race. Once the result of the race is known, the returns to winning bettors are determined as follows. A set percentage or take (currently 16 per cent in the United Kingdom) is deducted from the aggregate of stakes wagered to cover operator costs and profit. The remaining sum is then divided pro rata between winning bettors. For example, in a race with an aggregate betting turnover (after take deduction) of £500, where three winning bets were placed with stakes of £50, £30 and £20, respectively, the Tote returns to each winning bet would be £250, £150 and £100, respectively (including stake), equivalent to odds in a bookmaker market of 4/1. Bettors are made aware of the continuously evolving pattern of Tote odds available on each horse via computerized display screens. However, they cannot secure a particular set of odds on their selection, odds being determined ex post in the manner explained above. This study employs the proportions of money placed on each horse in a race as a proxy for the bettors’ subjective view of the probability of each horse’s chance of success (the justification for this is given later in this section under

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Procedures). In the past, the accurate estimation of the proportion of money placed on each horse in the United Kingdom has not been possible since only the Tote odds, not the proportions of money, are declared. This creates two problems: first, Tote odds are publicly declared rounded down to the first decimal place. Consequently, with an aggregate betting turnover (after ‘take’ deducted) of £550 and with winning bets totalling £150, the declared Tote odds would not be [(550/150) –1]/1 (i.e. 2.666/1) but 2.60/1. This fractional deduction from winning bets (which is retained as profit by the pari-mutuel operator) is known as breakage and varies according to the distribution of aggregate betting turnover and stakes on the winning horse. A knowledge of the declared Tote odds on each horse would not, therefore, provide a clear picture of the relative amount of money staked on each horse. The second and more fundamental difficulty is that only the odds relating to winning horses are publicly declared in the UK pari-mutuel market. Consequently, a common limitation of previous pari-mutuel analyses in the United Kingdom (e.g. Gabriel and Marsden, 1990) is their reliance on a single, potentially inaccurate, estimate of bettors’ subjective probability in each race. As indicated above, a bookmaker market operates in parallel with the parimutuel market in the United Kingdom. Whilst a potential advantage of employing bookmaker data is that odds are declared on each runner in each race, bookmaker odds arise from a combination of bettors’ subjective beliefs as to race outcomes (reflected by the relative amounts wagered) and bookmakers’ subjective opinions of the likely race outcomes. A study which relied on an analysis of bookmaker odds would therefore fail to isolate the decision preferences of bettors, whereas, this study employs a database which enables bettors’ aggregate subjective probabilities concerning each horse’s chance of success to be determined.

Method Data The data on which the empirical part of this chapter is based were supplied to the authors as a result of an agreement with the Tote – the United Kingdom’s sole pari-mutuel horserace betting operator. They provide details of staking levels in the pari-mutuel market on each of 19,396 horses in 2,109 races in the United Kingdom between 1 June and 31 August 1996. For each race details were collected of the aggregate amount of money staked on each horse. These data represent the aggregate betting decisions of those choosing to attend the racetrack and, consequently, it is expected that most of these will be familiar with the betting task. Individual bettors were unaware that their decisions were under scrutiny. This dataset offers, for the first time, the opportunity to view the full profile of staking behaviour in a large sample of races in the United Kingdom. The sample incorporates data from a broad cross-section of 49 racetracks, distributed across the United Kingdom, thereby avoiding any potential location-specific

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bias. The staking data enable us to estimate the bettors’ aggregate opinion regarding each horse’s probability of success. The method employed to estimate the subjective probabilities is outlined in the following section. Preliminary analysis of the data reveals that the average amount of money bet on a race was £9,093.10 ($14,076 at June/August 1996 exchange rate) (σ = £16,468.0). On average, 10.88 per cent of the money staked on any given race was bet on a particular horse, with a minimum of 0.06 per cent and a maximum of 97.44 per cent. The above information is augmented by published data on race outcomes. Horses were grouped into categories on the basis of the proportion of money staked on those horses. The proportion of horses within each group which won their race was calculated and this was employed as the objective probability of success for the group of horses. The results are displayed in Table 20.1. This indicates that, generally, those horses which attracted higher proportions of stakes won relatively more often than those which attracted lower proportions of stakes. This preliminary analysis suggests that bettors’ assessment of the horses’ probability of success, as evidenced by their staking patterns, is reasonably sound. The following section explains the basis for a more precise analysis of the accuracy of bettors’ subjective probability judgements. Procedures The basis for the measurement of the performance adopted in this chapter is the congruence between the subjective probability of success of a horse (embedded in the decisions of all those who bet in the pari-mutuel market) and the objective probability of success (revealed by race outcomes). This form of performance measure has been referred to as calibration (Goodwin and Wright, 1992). In determining the bettors’ subjective assessment of a horse’s chance of success, we calculate the proportion of money wagered in a race on that particular horse. Table 20.1 Comparison of bettor’s aggregate subjective probability judgements and horses’ observed (objective) probability of success Proportion of money staked on an individual horse in a race

Mean subjective probability

Mean objective Probability

0.0–0.1 0.1–0.2 0.2–0.3 0.3–0.4 0.4–0.5 0.5–0.6 0.6–0.7 0.7–0.8 0.8–0.9 0.9–1.0 Total

0.05 0.14 0.24 0.34 0.44 0.54 0.64 0.73 0.83 0.97

0.04 0.13 0.26 0.32 0.47 0.68 0.82 0.69 1 1

n 11,795 4,590 1,850 679 309 120 38 13 1 1 19,396

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This represents a straightforward aggregation of the independent decisions of many individual bettors regarding which horse to bet and the size of stake to wager. Since a simple aggregation is employed we would expect the combined judgements to reflect any negative decision quality influences which are present. Consequently, congruence between the objective and subjective probability assessments is interpreted as indicative of a generally high level of decision quality. Perfect calibration requires that for a particular set of horses, where the aggregate bettors’ assessment of the subjective probability of success of each of these horses is 1/n, that these horses win, on average, 1 in n races. It is argued that bettors will continue to place money on a given horse until the proportion of money on that horse accurately reflects their opinion of that horse’s chance of winning. Clearly, there will be differences of opinion amongst bettors in the market and it has been argued that (Figlewski, 1979) ‘the odds on a given bet will be bid to a level that reflects the market’s best estimate of the true probability of winning it’ (p. 80). Consequently, the aggregate staked on each horse reflects the decisions of all bettors in the pari-mutuel market and provides an indication of their probability judgements. As such, the proportion of money placed on horse i in race j can be used as a measure of the bettors’ subjective probability concerning horse i’s chance of success in race j, pijs (Asch et al., 1984; Figlewski, 1979). Consequently:

pijS =

hij

(1)

nj

∑h i =1

ij

where hij is the total amount staked on horse i in race j and nj is the number of runners in race j. Our aim is to assess to what extent the bettors’ subjective assessment of horse i’s chance of success in race j, pijs , is a reflection of the horse’s true or objective probability of success, poij. Perfect calibration would imply that for all horses pijs = poij . To test for perfect calibration we employ a conditional logit model, originally developed to analyse shopping choice (McFadden, 1974), to model the objective probability of horse i winning race j based solely on the bettors’ subjective probability assessment. We assume that each horse in race j can be assigned an index of winningness Wij, such that the horse with the largest value of Wij will win the race. We define Wij as Wij = β pijS + ξij

(2)

where β is a parameter to be estimated, which measures the importance of the bettors’ aggregate subjective probability of horse i, in determining its winning potential and ξij are the measurement errors.

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If bettors’ subjective assessments of each horse’s chance of success perfectly match the objective probabilities, then β would equal 1 since Equation (7) (see Appendix) would imply pijs = poij . However, miscalibration will result in a β which deviates from 1. If β > 1, it suggests that bettors under-bet the favourite and over-bet the longshots (i.e. a greater proportion of stakes are bet on longshots than their objective probabilities merit and vice versa for the favourite). If β < 1 it can be implied that bettors over-bet the favourite and under-bet the longshots. A full explanation of the derivation of the model and the procedures employed to estimate β is given in the Appendix. We now turn to the results of applying these procedures to estimate β.

Results We report the results of the conditional logit estimation in Table 20.2, obtained using the maximum likelihood procedures in LIMDEP. The model is highly significant, which suggests that reliance can be placed on the estimated value for β. The objective probability of success, poij , was estimated using Equation (7) (see Appendix) for each of the 19,396 horses in the sample. Curve-fitting facilities within SPSS revealed that the functional relationship between pis and poi was: po = –.0059 + 1.0554 ps [R2 = 0.999, degrees of freedom = 19,394, F = 1.4E + 7( p < .0001)]. Figure 20.1 depicts this relationship and offers a comparison with the situation where bettors’ subjective probability estimates are perfectly calibrated (i.e. po = ps). It is clear from Figure 20.1 that whilst there is a widening of the gap between objective and subjective probabilities as subjective probability increases, over the range of subjective probabilities which make up the majority of the sample (i.e. 0–0.8: 99.9 per cent of data) there is a remarkable degree of calibration. To test if the apparent differences between poij and pijs are significant, a t-test was conducted on the estimated value of β in Equation (7). This reveals that β is not significantly different from one at the 1 per cent level (t = 2.46, p > 0.0129, n = 2109). This is a striking result given the large sample size and implies that bettors’ probability judgements are very well calibrated. Table 20.2 Results of conditional logit estimation Estimated value

Standard error

t ratio

Significance

β Restricted log likelihood Unrestricted log likelihood Model χ2

1.0802 –4,492.93 –3,749.2 1,394.2

0.0327

33.09

0

Number of observations

19,396

(1 degree of freedom)

{χ2(0.001) = 1,083}

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1.2 1

Objective probability

0.8 0.6 0.4 0.2 0 −0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bettors’ subjective probability

Figure 20.1 Comparison of objective probabilities with bettors’ subjective judgements. Notes —  perfect calibration. …  predicted relationship.

Discussion The almost perfect calibration observed here is in sharp contrast to the poor calibration identified in the majority of laboratory experiments, but is in line with other non-experimental studies conducted in naturalistic settings (e.g. Murphy and Brown, 1985; Murphy and Winkler, 1984). In particular, the results are consistent with Hoerl and Fallin’s (1978) observation of a strong correlation observed between the ranking of subjective and objective probabilities in a horse-race betting context. In interpreting the results four themes are explored. First, an explanation is offered in terms of the congruence between betting market characteristics and factors identified in earlier studies as conducive to good calibration. Second, the potential significance of aggregation effects is addressed. The third section acknowledges the influence of particular features of the environment in which decisions are made and the fourth section develops this theme with a particular focus on the environmental characteristics which operate in a pari-mutuel betting market. Perspectives from the calibration literature It is tempting to point to the favourable calibration conditions which exist in the betting market as a likely explanation for the results. Thus a case may be made

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for each of the following factors, discussed in detail above, as contributing, perhaps in an interactive manner, to the calibration observed here: the experience of most racetrack bettors, their regular assessment of uncertainty situations in probabilistic terms, the regular and unequivocal feedback of decision performance, the bettors’ financial and non-financial motivation for making accurate judgements, and the degree to which the bettors’ cognitive processes are attuned to their particular decision setting. Further factors are the predictive, repetitive and uniformly configured nature of the betting decision, involving consistent stimuli and the use of decision aids. Aggregation – combining individual decisions It is possible that, despite the favourable calibration conditions, the results observed may arise because certain biases present in an individual bettor’s decisions are being counterbalanced by opposite biases in other bettors’ decisions. This seems plausible in principle; indeed, there is a considerable literature which addresses issues relating to the aggregation of individual judgements and, in particular, the erroneous outcomes which inappropriate forms of aggregation may generate. One issue here is the possibility of collusive behaviour between individual decision-makers, but in relation to the data used in this study, explicit collusion would appear highly unlikely. Individuals who believe themselves to be holding privileged information have a strong incentive not to divulge it. This incentive is particularly powerful in a parimutuel market, where returns to a successful decision are non-insurable. Another issue which has emerged as problematic in relation to aggregation procedures in general, ambiguity of outcome, is not a concern here, there being an unequivocal outcome to each decision event. Aggregation – environmental and institutional effects It may be instructive to explore in greater detail how the particular characteristics of the trading environment which create the context for the decision processes may be influential in determining observable outcomes. Recent attention has focused on seeking to understand the influence of aspects of market process on behaviour. Thus, for example, Smith (1989) stresses the importance of the interaction between environmental and institutional characteristics in explaining behaviour. The former can be condensed into individual demand and supply schedules, whereas the latter include the particular arrangements which exist for communication within a market: the language, processes, rules, conventions and protocols of market dialogue, via which initial positions translate into trading outcomes. Waller et al., (1999) link the aggregation issue to the role of market setting by stressing the potential importance of three types of factors: institutional effects, that is the framework of rules and conventions within which individuals engage in trading activity; incentives; and learning opportunities associated with the presence and nature of information within the market setting.

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The pari-mutuel market environment An approach to the understanding of decision processes and market outcomes, which seeks to integrate perspectives from the psychology and economics literatures, offers a fertile basis for explaining the degree of calibration observed here in pari-mutuel betting markets. In essence, it invites a consideration of whether there may be aspects of the market setting which explain the resilience of the market in aggregate to potentially distortive influences. The remainder of this section explores this line of enquiry. Following Waller et al.’s (1999) survey, we consider the potential impact of the institutional characteristics of the pari-mutuel betting market. An important feature of horserace betting in the United Kingdom is the existence of parallel pari-mutuel and bookmaker-based markets. This virtually unique situation may help to explain high calibration within UK pari-mutuel markets in two respects. First, the existence of a parallel bookmaker-based market provides bettors in UK pari-mutuel markets with a yardstick, against which to compare pari-mutuel activity and relative price evolution. The ability to observe activity in the bookmaker-based market, where returns to privileged information are insurable via the taking of a particular price, may provide a useful guide to the existence of such information and, more generally, a more sophisticated understanding of the nature of value in both bookmaker and pari-mutuel markets. It may be significant here that studies of pari-mutuel market activity in the United States, where there is no parallel market, suggest a susceptibility of pari-mutuel bettors to the types of bias in decision-making which leads to miscalibration, most noticeably here the favourite–longshot bias (e.g. Snyder, 1978). Whilst there is no direct empirical evidence that UK racetrack bettors do make comparisons between the odds available in the parallel bookmaker and pari-mutuel markets, these markets exist in close physical proximity, making comparison and choice of betting in either market relatively easy for racetrack bettors. In addition, computer screens at various locations throughout the racetrack display the latest available pari-mutuel odds and bookmaker odds. It would therefore seem likely that bettors seeking to maximize their return would engage in at least some casual comparison of odds before placing their bets. In support of this view, literature exploring the efficiency of racetrack betting markets suggests that where odds discrepancies exist between two parallel markets these are usually removed by arbitrage activity (e.g. Ali, 1979). A second possible influence associated with parallel markets is that parimutuel bettors in the United Kingdom are able to focus more sharply on the decision problem under consideration, compared with bettors in the bookmaker market, who have the additional task of comparing the value inherent in the odds offered by competing bookmakers. In a bookmaker-based market, the returns to the set of bookmakers and the set of winning bettors are determined by the interplay of active supply- and demand-side participants; the market is adversarial and as such the search by bettors for value among the set of bookmakers becomes a legitimate distraction from the central decision task, with potentially

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negative consequences for decision quality. However the nature of odds determination in the pari-mutuel market means that returns to the set of winners are always a fixed proportion of the total betting pool. The market is thus nonadversarial in the sense that the supplier and the set of winning bettors always share the total betting pool in a given proportion. Bettors in pari-mutuel markets are therefore confronted with only a single odds value for each horse and they can therefore focus directly on the task of selecting the appropriate horse on which to bet, with potentially positive implications for calibration. The presence of incentives in promoting efficiency in aggregate outcome may also be important in the pari-mutuel market context. Here, Waller et al. (1999, p. 720) observe: ‘The effects of incentives in markets may be enhanced by the presence of multiple, selfinterested participants who affect each other’s payoff through the institution.’ The significance of this in relation to pari-mutuel betting markets is striking. It seems uncontroversial to suggest that individual bettors are motivated primarily by self-interest in arriving at their betting decisions. Moreover, it is a distinctive feature of pari-mutuel markets that participants, via their actions, directly influence the return to other participants, rates of return to winning bets being a function of the pattern of betting activity in this type of market. This is in marked contrast to bookmaker-based markets, where the opportunity to insure the rate of return to a winning bet reduces the interdependence between payoffs. As regards the potential impact of learning on calibration, it may be significant that there is the opportunity for participants to engage repeatedly in the particular form of market process and therefore to become familiar with the rhythms, interactions, processes and outcomes of the market. To this degree, it seems reasonable to suggest that decision-makers in the market have the opportunity to establish a sophisticated basis for interpreting developing market information. In particular relation to probability calibration, it has been observed (Goodwin and Wright, 1992) that ‘performance-demonstrated expertise in probability judgements is underpinned by practice and regular performance feedback’ (p. 215). A review of some of the variants of decision-making models (Lipshitz, 1993) clearly indicates the potential for learning benefits. Thus, with Noble’s situation assessment model, an important factor in the ability to assess a decision problem is its similarity to previously experienced problems. Equally, in terms of Klein’s (1989) recognition-primed decisions the ‘crucial role of domain-specific knowledge or experience in proficient decision-making’ has been acknowledged (Lipshitz, 1993, p. 109). Relatedly, it has been observed (Orasanu and Connolly, 1993, p. 12) that: ‘Experience enables a person to seek information that will be helpful in coping with the situation, and to generate a limited set of plausible diagnoses, options or hypotheses, rather than wasting precious time and energy on low-payoff leads’. It was suggested above that many of the bettors attending racetracks are likely to have some experience of betting. Previous research suggests that experienced bettors do learn to undertake a great deal of research and to assess a range of factors associated with the outcome of a race (Neal, 1998; Rosecrance, 1988).

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Consequently, it is likely that their experience enables them to capitalize on the benefits available from learning. The capacity to benefit from the learning potential of repeated exposure to pari-mutuel betting markets may be amplified by the high degree of uniformity between markets, particularly in terms of time frame, structural characteristics and mode of information presentation. This uniformity reduces the requirement on the part of agents to organize, codify or configure the market data prior to interpretation and consequent action, allowing a greater focus on the decision problem per se. Relatedly, during the active market period in pari-mutuel betting markets, the continuously updated price information appears in wholly numerical form, thereby excluding the possibility of potentially distortive framing effects associated with verbal description and interpretation of market characteristics. The current study complements laboratory enquiry by exploring calibration in a naturalistic context. However, unlike laboratory experiments it does not permit the isolation, manipulation and scrutiny of particular variables influencing the quality of judgement. It is therefore not possible to attribute the excellent calibration observed to the impact of any specific variable. In addition, since the data employed here relate to aggregated judgements, it is not possible to offer conclusions regarding individual behaviour. In particular it should be stressed that evidence of aggregate calibration is not necessarily indicative of good calibration at the individual level. However, it is instructive to observe that the conditions identified above as likely to be favourable to calibration are associated with decisions made by pari-mutuel bettors in the United Kingdom and weather forecasters (Murphy and Brown, 1985). Each of these groups has now been shown to be well calibrated. However, the conditions required for good calibration, identified above, are also associated with other betting environments where biases in gamblers’ decisions have been observed (e.g. casino gamblers – Lichtenstein and Slovic, 1971). An important difference between pari-mutuel horserace betting markets and the gambling environments where biases have been identified is that features of aggregation of individual judgements exist in the former but not in the latter. It might therefore be speculated that aggregation associated with pari-mutuel horse-race betting markets is an important determinant of good calibration.

Conclusions The principal contribution of this chapter is the insight it offers into the performance of human judgement in a naturalistic setting which is characterized by many of the factors held to aid calibration. The results support the view that in favourable environments individuals can make excellent subjective probability judgements. The current study does not permit the isolation of those specific factors which contribute to good calibration. However, it is speculated that a number of features of the decision-maker and the decision task may help to improve subjective probability judgements, including experience of the task

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domain, regular and unequivocal feedback, motivation for accuracy, practice in probabilistic judgements, a naturalistic setting for which the decision makers’ cognitive processes are attuned, and appropriate aggregation of individual judgements. Further studies employing betting data may help to isolate the determinants of the good calibration observed here. For example, examination of the calibration of bettors’ judgements at the beginning and end of the racing day may help to establish the role of feedback, particularly if the bettor’s individual financial success or failure that day is taken into consideration. Similarly, there would appear to be scope for segmenting betting activity to shed light on the influence of expertise, use of decision support systems and staking levels on the degree of calibration achieved. More broadly, it seems reasonable to suggest that extension of naturalistic investigation over a wider range of settings involving a differing set of characteristics may help to enrich further the understanding of decision performance which emerges from the experimental environment.

Appendix: Derivation of model and procedures employed to test for miscalibration If horse i* is observed to win race j, which has nj runners, then this implies that nature has chosen i*. If we assume that nature is rational, this would imply that the horse with the highest index of winningness will win the race (i.e. Wi*j > Wij for i = 1,2, . . ., nj). Consequently, piO* j = prob (Wi* j > Wij , i = 1, 2,L , n j )

(

(3)

= prob β piO* j + ξi* j > β pijS + ξij , i = 1, 2,L , n j

)

(4)

We obviously cannot observe Wij, but we can observe whether horse i is successful (i.e. wins the race). The observed variables are defined as follows: sij = 1 if Wij = Max (W1 ,W2 ,...,Wnj ), sij = 0 otherwise.

Hence

(

)

(

p sij = 1| pijs = prob β pis* j + ξ i* j > β pijs + ξ ij, i = 1, 2,L n j

)

(5)

It can be shown (McFadden, 1974) that if the error terms, ξij, are assumed to be independent and identically distributed according to the double exponential distribution, then the probability of horse i winning race j is given as follows: O ij

(

s ij

p = p sij = 1| p

)=

(

exp β pijS nj

(

)

∑ exp β pijS i =1

)

for i = 1, 2,L n j

(6)

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If the bettors’ probability judgements are perfectly calibrated then the proportion of money bet on horse i in race j will be equal to its objective probability of success; i.e. pijs = poij . However, the model represented in Equation (6) does not include this simple case. This presents a problem, since our aim is to explore the degree to which bettors’ judgements are perfectly calibrated. It has been suggested (Bacon-Shone et al., 1992) that this difficulty can be overcome by replacing pijs with ln pijs in Equation (6). As a result Equation (6) becomes: O ij

p

(p ) = p (s = 1| ln (p ))= ∑ (p ) ij

s ij

β

S ij

nj

i =1

S ij

β

for i = 1, 2,L nj

(7)

The parameter β in Equation (7) is determined by maximizing the joint probability of observing the results of the 2,109 races in the sample. Consequently, if the estimated objective probability associated with horse i*, which won the jth race, is designated poi*j then we find β which maximizes the likelihood function L, such that: 2109

L = C piO* j

(8)

j =1

A formal assessment of the degree of calibration of bettors’ subjective probabilities is conducted, employing the estimated values of β in Equation (7). These values provide a direct measurement of the degree of calibration of bettors’ subjective probabilities. If, for example, β = 1, it can be implied that bettors’ probability judgements are perfectly calibrated, since Equation (7) would imply pijs = poij . The greater is the deviation of β from 1, the poorer is the calibration. The assumptions adopted concerning the error terms, ξij, in Equation (5) (i.e. independent and identically distributed according to the double exponential distribution) imply that the estimate of β, derived from a large sample such as that employed here, is approximately normally distributed with a mean of β and a standard deviation which can be consistently estimated by the standard errors provided by the maximum likelihood procedures in LIMDEP. Thus we can test the null hypothesis, H0: β = 1, by employing a t-test, since β – 1 has a limiting normal distribution. SE Clearly, for a given race j, each pijs will lead to a single predicted value for poij (employing Equation 8). However, several races may involve horses with associated subjective probabilities of the same value. Each of these subjective probabilities (i.e. pijs = piks = pils etc. = ps) may be associated with a different value for the objective probability of success (i.e. it is probable that poij ≠ poik ≠ poil etc.). Consequently, we employ curve-fitting facilities in SPSS to determine the appropriate functional relationship between the subjective and objective probabilities such that, for a given subjective probability, ps, a unique objective

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probability, p0, may be determined. The resulting functions are graphed to provide a visual check on the degree of calibration.

Note 1 In practice, a variety of bets is possible. A bet may be placed on a single horse to win or to be placed (i.e. to finish in the first three) in a race. In addition, a variety of more exotic bets is available, the success of which is determined by the performance of more than one horse. The simplest and most popular bet remains the bet on a single horse to win a particular race – it is these bets which form the basis of the investigation detailed in this chapter.

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Index

Abelson, R.P. 50 Abt, V.74 ‘accumulators’ 175–82 action-feedback loops 340 ‘adverse-selection’ problem 278–9 advertising, betting shops 184 Agnew 38, 74, 117 Aiken, L. 138, 153 Alavi, M. 145, 153 alcohol consumption 35 Aldag, R. 145, 153 Aldrich, J.H. 295 Ali, M.M. 247, 248, 270, 349 alternative-based complexity 59–60, 63–72, 74–83, 86–7, 96–8 ‘ambiguity avoidance’ 86, 89, 92–3 analytical potential, betting markets 118–20 Anderson, G. 8–9, 10, 27, 28, 38, 76, 119, 181, 207, 236, 340 Applegate, L. 131 Arenson, S.J. 142, 153, 173, 202 Arrow-Debreu securities 233, 313 Asch, P. 12, 32, 43, 44–5, 48, 173, 250, 256, 270, 284, 305, 345 Ashburner, L. 145–6, 153, 199, 203 Ashton, R.H. 338 assertiveness, gender differences 148–9 attribute-based complexity 59–60, 63–72, 74–83, 86–7, 96–8 Australian betting markets 44 Ayton, P. 286, 336, 338 Bacon-Shone, J.H. 122, 284, 353 Baker, T. 148, 153, 179, 201 Balthasar, H.U. 337 Baranski, J.V. 335 bargaining studies 147, 150 Bariff, M. 139–40, 155

Barki, H. 140, 153 Barnett, J.H. 147, 153, 200, 205 Baron, J. 75, 86, 89, 92, 96, 97, 110, 118 Bazerman, M.H. 337 Beach, L.R. 336, 337, 338 Bem, S.L. 151, 154 Benbasat, I. 132, 133, 139, 140, 141, 149, 152, 154 Bendig, A.W. 201 Bennett, M.J. 337 Benter, W. 259 Berkowitz, L. 148, 154, 201 Berry, B. 144, 173, 204 bet placement, timing 11–13, 28–39, 48–55 bets, payment of tax on 231–48 betting: motivation for 1–3; as opportunity for gain 42–6 betting activity, distribution of 77–82 betting data, scope of 28–30 betting as leisure pursuit 10–22 betting markets: analytical potential 118–20; ecological classification 315–20; efficiency in 44–5; information in 42–6; naturalistic enquiry 64–5; operation of 342–3 betting offices: environment 8–9, 34, 35–6, 46, 49–55, 270; nature and image 184, 190; social function 9–10 betting slips 10–11, 29–31, 47, 64–5, 66, 75–6, 87, 98–9, 119, 174, 188, 207, 238, 271 bettors: ‘informed class’ of 31–2, 43–56; subsets of 14–15, 16–22 Biddle, G.C. 337 Biggs, F.D. 108, 110 Billings, R.S. 93, 97, 110 Bird, R. 44, 250, 255–6, 278, 286, 315 Birley, S. 144, 146, 151, 154, 199, 203

360

Index

Björkman, M. 335 Block, J.H. 135, 154, 201, 207 Bochenholt, U. 341 Bolger, F. 338 Bolton, R.N. 173 bookmaker market: betting as leisure pursuit study 5–23; complexity effects study 86–94; complexity impact study 74–83; consumption value study 228–48; decision-making under risk study 117–30; ecological distinction with pari-mutuel market 315–18; excitement costing study 25–39; male/female betting behaviour study 172–82; naturalistic research 63–72; performance, risk taking and confidence study 184–96; risk strategy under task complexity study 96–113; successful betting strategies study 42–56 bookmakers 315–18; access to privileged information 251–2; analysis of decisionmaking 277–97 Braddock, P. 99, 100 Brehmer, B. 75, 118, 121 Breiman, L. 258 Brenner, L.A. 336 Brim, O. 201 British Market Research Bureau 208 Brochhaus, R. 213 Broverman, I.K. 135, 154, 200 Brown, B.G. 337, 347, 351 Brown, B.R. 163 Brown, J.L. 74, 117 Brown, R.I.F. 8–9, 10, 27, 28, 38, 47, 76, 80, 119, 181, 207, 236, 340 Bruine de Bruin, W. 336 Brush, C. 199 Burke, R.J. 136–7, 160, 202 Busche, K. 284, 293 buyer–supplier relationship 316 calibration: conditions for 337–9; literature 347–8; overview 225–6 Cambridge, R.M. 337 Capon, N. 69, 92, 108 Carey, G.L. 135, 154, 200 Carlson, K. 200 Ceci, S.J. 122, 173, 250, 266 Chaganti, R. 146, 154, 199, 203, 204, 205 Chammah, A.M. 162 Chapman, R.G. 173, 254 Chervany, N. 144, 155 children, studies using 173, 202–3

Chiu, C. 87, 98, 118, 147, 157, 207 Christensen-Szalanski, J.J.J. 337 closing odds 250–67 Cochran, W.G. 79 Coet, L.J. 142, 143, 155, 173, 200, 202 cognitive abilities, gender differences 136–41 cognitive capacity: challenges to 66–7, 117–18; limits of 74–5 cognitive processes: suspension of 16, 50–1; see also non-cognitive processes Cohen, A.R. 201 Cohen, M.S. 334 Collins, N.W. 199 Collinson, D. 199 comparative performance and complexity 121–3 complex decisions: gender differences 180; impact of complexity 66–72; naturalistic inquiry 64–5; overview 63–4 complexity: and decision-making 96–8; definition of 66–7; effect on performance 117–30; effect on risk taking 86–94; empirical study of impact 74–83; impact of 59–62, 66–72; and participation 67–8; and performance 70–1; and risk strategy 68–70, 108; see also task complexity confidence and gender 141–5, 173, 177–8, 180–1, 189, 194–5, 201, 203 Connolly, T. 99, 339, 340, 350 consumption value of gambling 222, 234–6 Cooke, S. 198 ‘cool’ environments 34, 35–6 Coombs, C.H. 141, 155 Cooper, J. 148, 165, 179, 200, 201 Cooper, R.E. 200 Cornish, D.B. 7 costing excitement 2, 25–39 Coton, M. 99 Crafts, N.F.R. 43, 122, 250, 251, 252, 255–6, 303, 305 Crandall, V.C. 155 Crano, W.S. 148, 155, 202 cross-validation 261–2 cultural norms 135, 151, 205 cultural pressures 143, 202–3 Curley, S.P. 75, 86, 89, 92, 97, 110, 112, 113, 118, 334 Cvetkovich, G. 200 databases: betting behaviour study 10–11; complexity impact study 66;

Index 361 excitement-related influences study 30–1; gender differences in leisure behaviour study 188; successful betting strategies study 46–7 Davis, G.B. 139 Davis, R. 69, 92, 108 decision quality and gender 134–6, 203–4 decision style 145–60 decision support system (DSS) design and gender: agenda for future research 150–2; current guidelines 132–3; decision quality 134–6; decision style 145–50; motivation and abilities 136–41; overview 127–8, 131–2; research in gender and decision taking 133–4; risk taking and confidence 141–5 Deem, R. 185 Dennis, A.R. 141 design guidelines, DSS 132–3 design phase, decision taking 149 Detmer, D.E. 337 Dexter, A.S. 152 Dhaliwal, J.S. 132 Dialeschki, M.D. 185 Dickerson, M.G. 9, 18, 27, 28, 29, 38, 47, 49–50, 120, 181, 207 Dickson, G. 144, 155 discriminability 75, 96, 335–6 Dixey, R. 9 Doerner, D. 70, 75, 118, 121 dominance, violation of 222, 231–4 Dorros, K. 142, 159, 200 Dos Santos, B. 139–40, 155 Douglas, C. 8, 27, 278, 315 Dowie, J. 20, 43, 278, 286, 315 Downes, D.M. 7, 8, 9, 27 Drucker, P.F. 198 Duncan, D. 100 Dunning, E. 25, 26 ‘each way’ bets 90–3, 100–1, 103–7, 109, 175–82; gender differences 189, 192–3, 210–11 Eagly, A. 135, 146–7, 148, 151, 155, 172, 186, 187, 201, 202, 205 early races 223–4, 269–76 Ebbeson, E.B. 200 ecological classification, betting markets 315–20; testing of 320–3 Edwards, W. 334 Einhorn, H.J. 86, 337 Eiser, J.R. 16, 38, 50, 74, 75, 93, 96, 118, 334, 336 Elias, N. 25, 26

Elstein 337 environmental effects 348 epistemic reasoning 82 Erev, I. 336 Estes, R. 135–6, 144, 155, 172, 173, 178, 186, 190, 195, 203, 206 Etzioni, A. 38 event-specific information 12, 14–15 excitement 8–9, 39 excitement costing: discussion 36–9; literature 26–7; methodology 27–31; overview 2, 25–6; prediction of win probabilities 295–7; procedures and results 31–6 exotic bets 237, 275 expertise as aid to calibration 337–8, 341, 347–51 Extel 11, 47 ‘extreme’ complexity effects 111–12 Fallin, H.K. 337, 347 familiarity and risk propensity 143, 145 Farmer, A. 305 Fatkin, L.T. 135–6, 141–2, 143, 147, 156, 157, 172, 173, 178, 180, 186, 194, 203, 204 favourite–longshot bias: data and methodology 280–2; interpretation of results 290–4; literature 278–80; and market behaviour 314–15; overview 223, 277–8; procedures 282–7; results 287–90 favourites: propensity to select 20–2; and risk aversion 88–9, 90–3 feedback as influence on calibration 338 female betting behaviour 128–9, 172–82 female-built models, DSS 144–5, 152 female decision-makers, role of 199–200 female-oriented tasks 137, 139, 201, 204 feminine socially valued characteristics 151–2 Ferrell, W.R. 335, 337 Figlewski, S. 251, 284, 305, 321, 345 Filby, M.P. 6, 7, 9, 25, 37 financial commitment 340 financial gain 7 financial modelling study 212–14 financial penalties of complexity 80–1 financial return and motivation 15–17 Firestone, J. 185 Fischhoff, B. 68, 101, 335, 336 Fjelsted, O. 152, 156 ‘flat’ races 99, 251 ‘followship’ behaviour 279

362

Index

Ford, J.K. 69, 86, 92, 108, 118, 334 ‘forecasts’ 175–82; male/female bets 191–2, 211 ‘form’ 77 framing, DSS 139 Freedman, J.L. 148, 156, 201 Frisch, D. 75, 86, 89, 92, 97 Furnham, A. 7, 83 Gabriel, P. 39, 224, 278, 300, 305–6, 307, 308, 315, 318, 343 gain, opportunities for 42–6 Gallupe, R. 141, 156 Garvin, A.D. 142, 164, 200 gender and betting behaviour: discussion 178–81; method 174–5; overview 128–9, 172–4; results 175–8 gender and decision-making: decision quality 134–6; empirical tests 205–14; managers 129–30, 198–216; research in 133–4 gender differences: decision-making 127–30; decision-making and betting 186–8; leisure behaviour 129, 184–96 gender issues and DSS design 131–65 generic market forms 315–18 Gerritann, J.C.M. 146, 156, 203 Gigerenzer, G. 335, 336, 338 Gilovich, T. 8, 27, 236, 269, 278, 315 Ginsburg, H. 141, 156, 204 Gluck’s Second Law: discussion 274–6; literature 269–71; method 271; overview 222–3; results 271–4 goals: gender differences 146–7, 150; uncertainty of 340 Goodhue, D. 152, 156 Goodwin, P. 344, 350 Goslar, M. 145, 149, 156 Grand National 6 Greene, W.H. 296 Griffin, D. 335, 336 Griffiths, M.D. 74, 80 group decision support systems (GDSS) 133, 134–41, 150 group pressure 148–9, 150 ‘groupthink’ 17, 51 Gutek, B. 135, 162, 200 Hall, C.D. 284, 293 Hall, D. 100 Halpern, D.F. 136, 137, 156, 204 handicaps 77–80, 81–2, 88–93, 100–1, 103–7, 110–13, 120, 122–3 Haney, M. 200

hard–easy effect 335–6 Hardwick, J. 140, 153 Harper, R. 200 Harvey, I. 6, 7, 9, 25, 37 Hausch, D.B. 250–51, 259 Hazard, T.H. 337 Henderson, K.A. 185 Henery, R.J. 20, 278, 315 Herschel, R. 136, 139, 141, 156, 172, 186, 190 Hey, J.D. 342 Higbee, K.L. 28 high class races 319, 323–8 high-risk bets, gender definitions 179–80 Hiltz, S.R. 150 Hisrich, R. 199 Hodgson, R.C. 146, 157, 205 Hoerl, A.E. 337, 347 Hoffman, L.R. 135, 136, 157, 160, 186, 200, 201–2 Hofstede, G. 134, 157, 200 Hogarth, R.M. 75, 86, 87, 117–18, 334, 336 Holding, C.S. and D.H. 138, 157 Hong, Y. 87, 98, 118, 147, 157, 207 Horserace Totalisator Board see Tote Hosseini, J. 135–6, 144, 155, 172, 173, 178, 186, 190, 195, 203, 206 Hovland, C.L. 148, 157, 201 Huber, G. 131–2, 157 Hudgens, G.A. 135–6, 141–2, 143, 147, 156, 157, 172, 173, 178, 180, 186, 194, 203, 204 Hunsaker, P.L. 135, 136, 137, 147, 162, 172, 186, 190, 200, 201–2 Hyde, J.S. 137–8, 158, 204 ‘hypervigilance’ 17 ‘illusion of control’ 8 incentive for betting 341, 347–51 individual decisions, combining 348 individualistic cultures 200 influenceability, gender differences 148–9, 150, 179, 201, 202 information: betting markets 42–6; role in decision-making 38–9; in uncertain markets 339–40; use of 221–6 information environment 317–18; development of 30–9 ‘information overload’ 50–1 informationally opaque/transparent markets 318–20 ‘informed class’ of bettors 31–2, 43–56 institutional effects 348

Index 363 instructions, female preference for 140–1, 201–2 ‘insurance’ features of bets 187 intellectual challenge 7–8 intelligence phase, decision taking 149 interactive effects, alternative-/attributebased complexity 110 investment choices, female confidence in 204 irrational gamblers 230 Isen, A.M. 275 jack-knifing 261–2 Jacklin, C. 137, 143–4, 147, 148, 160, 201 Jacoby, J. 67, 69, 70, 74, 81, 86, 92, 97, 108, 109, 111, 117, 118, 122 Jamieson, B.D. 202 Janis, I.L. 17, 50–1, 148, 157, 201, 334, 340 Jones, O. 250–67 Joyce, E.J. 337 Juslin, P. 335, 338 Kabus, I. 337 Kahneman, D. 38, 74, 86, 97, 117, 280, 292, 334 Kanter, R.M. 135, 146, 158, 200, 205 Karson, M.J. 147, 153, 200, 205 Kass, N. 158, 179 Keen, P. 139 Keinan, G. 142, 158, 173 Kelly betting 258–61 Kelly, J.A. 136, 148–9, 151, 158, 159, 172, 202 Keren, G. 38, 74, 86, 97, 117, 336, 337, 341 Kerstholt, J.H. 97, 109 Kida, T. 67, 69, 70, 74, 86, 93, 109, 117, 118, 121, 337 King, K.M. 27 King, W. 152, 164 King, W.R. 141, 159 Klayman 92, 108 Klein, G.A. 350 Klein, N.M. 75, 96, 97, 118, 122 Knights, D. 199 knowledge engineering 131 Kogan, N. 142, 159, 200, 201 Kohlberg, L. 146, 159, 205 Kolmogorov–Smirnov test 263 Konsynishi, B. 152, 156 Kopelman, R.E. 269–70, 293 Koriat, A. 335

Kramer, R. 146, 159, 205 Kretch, D. 201 Kunreuther, H. 75, 118 Kusyszyn, I. 27 laboratory-based research 335–6; ecological limitations 99, 118; need for caution 64 Ladbroke Racing 6, 10, 30, 47, 80, 87, 119, 174, 237, 271, 281 Ladouceur, R. 212 Lafferty, T. 28 Landers, W.F. 202 Langer, E.J. 8 late races 223–4, 269–76 Layman, J. 69 learning opportunities 317–18 legislation 184 leisure behaviour, gender differences: database and procedures 188–9; decision-making and betting 186–8; overview 128, 184–6; results and analysis 190–5 leisure pursuits: database 10–11; excitement in 2–3, 25–39; motivation 6–10, 11–14; overview 1–3, 5–6; rationale and tests 14–22; timing and price decision 11–14 leisure, female entitlement to 185 Lenney, E. 142, 143, 159, 201 Letarte, A. 8 Levi, A. 50 Levin, I.P. 137, 142, 143, 159, 186, 194, 204 Lichtenstein, S. 335, 337, 351 Liker, J.K. 122, 173, 251, 266 Lindgren, H.E. 179 Lindley, D.V. 286 Lindsay, P.H. 335 Linn, M.C. 138, 158, 159, 204 Lipshitz, R. 350 Lo, V.S.Y. 251 Lock, A. 338 locus of control questionnaires 213–14 log likelihood tests 258 Lohman, D.F. 138, 159, 204 long-odds 256, 269–76 longshot–favourite bias see favourite–longshot bias Lopes, L.L. 341 low-risk bets, gender definitions 178–9 lower class races 319–20, 323–9 Lusted, L.B. 337 Lynn, D.B. 135, 137, 160, 200

364

Index

McClelland, A.G.R. 338 Maccoby, E. 137, 143–4, 147, 148, 160, 201 McCrae, M. 44, 250, 255–6, 278, 286 McDavid, J. 148, 163 McDermott, P.J. 142, 143, 155, 173, 200, 202 McDonald, C.D. 142, 162, 194, 204 McFadden, D. 322, 345 McGee, M. 138, 161 McGlothlin, W.H. 250, 270 McGoey, P.J. 335 Machina, M. 228 McLintock, A. 144 McPhee, K.A. 138, 163, 204 Maddala, G.S. 252 Maier, N.R.F. 135, 136–7, 157, 160, 186, 200, 201–2 male betting behaviour 128–9, 172–82 male-built models, DSS 144–5, 152 male-oriented tasks 137, 139, 201, 204 Malhotra, N.K. 67, 69, 74, 75, 78, 92, 93, 96, 97, 99, 108, 109, 110, 112, 118, 334 management support systems (MSS) 132–3 managerial decision-making 138–9 managerial population, empirical study 206–12 managers, decision-making, risk and gender: empirical tests 205–14; literature review 200–5; overview 129–30, 198–9; role of female decisionmakers 199–200 managers, male/female decision styles 145–6 Mann, L. 17, 50–1, 334, 340 Mann, R. 131, 132, 160 March, J.G. 38 Marcus, S. 93, 97, 110 marginal odds 43 market behaviour 311–12; favourite–longshot bias 314–15 market ecology 311–33 market efficiency analysis 223–4, 300–4 market forms 313–14, 315–18 market imperfection 43 market segmentation 313 market type 314 market, state-contingent claims 312–14 Marsden, J.R. 39, 224, 278, 300, 305–6, 307, 308 315, 318, 343 Marshall, J. 148, 161, 204 masculine cultures 200 masculine socially valued characteristics 151–2

Masters, R. 135, 161, 172, 190, 204–5 mathematical problem solving, gender differences 138 Maurer, R.J. 142, 161, 202 media 191–2, 207 Meece, J.L. 137, 161 Meier, R. 135, 161, 172, 190, 204–5 methodological innovation 55–6 Metzger, M.A. 39, 270, 275 Meyer, R.J. 75, 86, 110, 118 Meyer, W.J. 201 Middlebrook, P.N. 148, 161 Miller, S. 141, 156, 204 Milton, G.A. 135, 136, 151, 161, 200, 201, 202, 206 mimetic excitement 26 Minkin, B.L. 269–70, 293 Mintel Gambling Reports 6, 184 miscalibration, testing for 352–4 Mittman, B.S. 140 model: price information study 251–8; test of miscalibration 352–4 model testing: cross-validation and jackknifing 261–2; features of winning bets 264–7; Kelly betting 258–61; log likelihood tests 258; parametric bootstrapping 262–4 Montgomery, G.T. 202 Moon, C.E. 200 Moore, J.H. 140 morning line odds 43 Morris, S. 247 Morrison, D.F. 103 motivation: for accurate judgements 338; for betting 341, 347–51; and DSS 140; gender differences 136–41; overview 1–3, 6–10 motivation, off-course betting: database 10–11; excitement in 2–3, 25–39; overview 1–3, 5–14; rationale and tests 14–22; timing and price decision 11–14 ‘multiple’ bets 175–82, 211–12 multivariate analysis: of behaviour 96–113; of variance 69, 88, 102–3 Murnighan, J.K. 311–12 Murphy, A.H. 337, 347, 351 Murphy, P. 26 Nakamura, C. 202 National Lottery 230 naturalistic research: complex decisions 63–72; multivariate analysis of behaviour 96–113 Neal, M. 350

Index 365 Neale, M.A. 337 Nelson, F.D. 295 Nicholson, N. 145–6, 161, 173, 180–1, 186, 195, 203, 204 Nieva, V.F. 135, 162, 200 Noe, F.P. 142, 162, 194, 204 non-cognitive processes, restraints on 50–1 non-compensatory strategies 96–7 non-favourites 88–9 non-handicap races 319–20, 323–9 Norman, D.A. 335 Northcraft, G.B. 337 notional returns 306–9 O’Brien, R. 223–48 odds: availability and notional returns 306–9; changes in 250–67; determination of 251–8, 316; early/late races 271–3; implications 88; male/female selection 191–4; marginal/morning line 43; movement of 300–4; public reporting of 280; range of 121–2; size of 101–13; UK market 42–56 off-course betting see bookmaker market Oldak, R. 138, 163, 204 Olshavsky, R.W. 69, 97, 108, 110 Omodei, M.M. 338 Onken, J. 38, 74, 83, 86, 92, 97, 108, 117, 122–3 opaque markets 319–20 opening price (OP) 301–4 Orasanu, J. 99, 339, 340, 350 outsiders, propensity to select 20–2 Paquette, L. 67, 69, 70, 74, 86, 92–3, 109, 117, 118, 121 parallel betting markets 223, 277–97 parametric bootstrapping 262–4 pari-mutuel market: analysis of decisionmaking 277–97; determination of odds in 46; ecological distinction with bookmaker market 315–18; efficiency characteristics 305–9; environment 349–51; favourite–longshot bias in 317–18; large wagers 261; market efficiency analysis 300–4; market environment 349–51; operation of 342–54; performance advantages 12; quantities staked in 320–3, 329–31; support for comparative ‘outsiders’ 270–1; see also Tote participation effects of complexity:

discussion 80–2; method 75–8; overview 74–5; results 78–80 Paton, D. 224, 250, 279, 291, 300, 301, 302, 303, 304, 305, 315, 318, 320 Payne, J.W. 69, 76, 81, 92, 93, 97, 99, 108, 111, 118 peer-group esteem 9 ‘people-oriented’ leadership style 146–7, 149, 205 performance 31–5; across bet types 187; and complexity 70–1; and excitement 31–5; and gender 175–6, 178–9, 188–9, 190–1; indicators of 48 performance effects of complexity: method 118–21; overview 117–18; results and discussion 121–3 performance penalties 97 Peterson, A.G. 138, 159, 204, 337 Petrusic, W.M. 335 Phillips, L.D. 337 Pillai’s Criterion 103 Pitz, G.E. 336 Plake, B.S. 137, 162 Plott, C.R. 312 Potashier, M.R. 142, 164, 194, 204 Poulton, E.C. 280, 292 Powell, P.L. 131–65, 198–216 Power, D. 145, 153 pre-closing odds 250–67 prediction, association with calibration 338, 341, 347–51 predictors, extracting from price curve 253–6 price forecasts, specialist media 43–4 price information, use of: description of data and model 251–8; model testing 258–67; overview 222, 250–51 pricing system, significance of 13–14 Priest, R.F. 135, 136, 137, 147, 162, 172, 186, 190, 200, 201–2 Prisoners’ Dilemma 147 probit analysis, tax decision 237 probit estimation, tax decision 240–6 probit model for estimating effect of complexity: method 87–91; overview 86–7; results and discussion 91–3 problems: gender content of 137, 139, 201, 204; structure of 339 professional gamblers 7 Prospect Theory 292 Pruit, D.G. 141, 155 Pruitt, D.B. 22 Quandt, R.E. 247, 278, 315

366

Index

quantitative skills, gender differences 137–8, 140, 203–4 Quirin, W.L. 293 races: characteristics of 51; levels and types of 314 Racing Industry Statistical Bureau 6 Rapoport, A. 162 rational economic behaviour, deviations from 221–6 real-world studies, male/female decisionmaking 136 Reason, J.L. 87, 97, 99, 118 relative odds 101–7 relative performance 70–1 relative risk 68–70, 98–113 researchers, influence of sex of 186 ‘reverse forecasts’ 175–82, 211 risk aversion 68–9, 87, 88–9, 112–13; 274–5; gender differences 142–3 risk degree 109; and motivation 15–16, 19–22 risk and gender: empirical tests 205–14; literature review 200–5; overview 198–9; role of female decision-makers 199–200 risk hedging 69–70, 108, 110–13 risk homeostasis theory 109, 112 risk preference, cross-gender definitions 189, 191–4 risk propensity: and gender 176–7, 179–80; managerial population 212–14; non-managerial population 206–12 risk strategy and complexity 68–70, 96–113 risk-neutral environments 97 Ritov, I. 75, 86, 96, 97, 110, 118 Roberts, G.C. 142, 163, 200 Rosecrance, J. 350 Rosett, R.N. 247 Ross, T.W. 311–12 Rubin, J.Z. 147, 163 Saint-Germain, M.A. 142, 163, 186, 191, 204 sample design, male/female betting behaviour study 174 Sargent, A. 147, 163, 205 Satellite Information Services (SIS) 252 Sauer, R.D. 250, 251, 252 Saunders, D.M. 8, 9, 25 Schiff, W.C. 138, 163, 204 Schnytzer, A. 249–50, 251, 256, 305 Schwartz, E. 146, 163 Scott, C. 199

Scott, M.B. 7–8 Scott Morton, M. 139 Scraton, S. 185 ‘sensation-seeking’ 8–9 sex role, identification with 202, 206 Shanteau, J. 337–8, 341 Shaw, S.M. 185 Shelton, B.A. 185 Shewan, D. 47, 207 Shilony, Y. 249–50, 251, 305 Shin, H.S. 228–48, 279, 283, 286, 291, 294, 309, 313, 315, 318, 321 show period, bets placed during 14–15, 28–39, 48–55 Shreckengost, R.C. 337 Simon, H.A. 38 simplification strategies 92–3, 117–18, 122 single bets 10, 76, 175–82; comparative male/female performance 187, 188–9, 190–1 Sistruck, F. 148, 163 skill 173 Slack, N. 198 Slovic, P. 28, 142, 143, 163, 173, 186, 200, 202–3, 337, 351 Smith, G.A. 163, 203, 204 Smith, J.E. 337 Smith, V.D. 312, 342, 348 Snedecor, G.W. 79 Sniezek, J.A. 335 Snitkin, S. 152, 164 Snyder, W.W. 39, 87, 98, 118, 305, 349 soccer 26–7 social interaction 9–10 societal norms 185 specialist media, price forecasts 43–4 speculative markets, price information 222, 250–67 spending, comparative ability 194–5 stake level 342–54; and complexity 93, 98–113; early/late races 273–4; and excitement 35–6; gender differences 194–5, 210; and motivation 15–16, 17–19; as proxy for confidence 180–1; and time periods 37 Starr, M.W. 142, 164, 194, 204 starting price (SP): and male/female bets 191–2; motivational aspects 13–14 state-contingent claims markets, market ecology/decision behaviour 225, 309–31 state-contingent claims, market efficiency: available odds and notional returns 306–9; literature 305–6; overview 224–5

Index 367 state-contingent claims, market for 312–14 Stein, J. 96, 97 stereotyping 141, 143, 151–2, 173, 200, 202–3, 205 Stevenson, L. 199 Stone, E.R. 101 Stones, I. 138, 164 ‘straight forecasts’ 175–82 Stratigakos, S. 335 Streufert, S. 111 Suantek, L. 335, 336 subjective probability judgements, calibration of: betting markets as naturalistic decision setting 339–43; calibration literature 334–9; discussion 347–51; method 343–6; overview 225–6, 333–4; results 346–7; testing for miscalibration 352–4 success, estimating probability of 142 successful bets, as percentage of bets 7 Summers, J.O. 96 Sundstroem, G.A. 68, 74, 97, 108, 110, 117 supplier–buyer relationship see buyer–supplier relationship supply-side agents 277–97 supply-side structure 316–17 Sweeney, E.J. 135, 164, 200

Tuddenham, R.D. 143, 164, 202 Turner, D.E. 8, 9, 25 turnover, UK betting/gaming 6 Tversky, A. 280, 292, 334, 335, 336

Tajfel, H. 202 Talbot, M. 9 Tang, L. 250–67 Target Group Index 208 tax 189, 195, 231–48 Teger, A.I. 22 Terborg, J. 135, 164, 200 Terrell, D. 305 Thaler, R.H. 274–5, 277, 278, 280, 284, 292, 293, 315 Thomas, G.P. 142, 164, 200 time stress 340 timing: bet placement 11–15, 28–39, 48–55; races 269–76 Timmermans, D. 69, 70, 74, 81, 87, 92, 97, 108, 110, 111, 117, 121, 334 Todd, P. 149, 164 Tomassini, L. 337 Tote: bets 175–82; data from 320–3, 329–31; operation of 342–54 track biases 293–4 training as influence on calibration 338, 341, 347–51 transparent markets 319 Tuckwell, R.H. 120, 250, 255–6, 284, 286, 292, 309

Wagenaar, W.A. 38, 74, 82, 86, 97, 117, 119, 120, 180, 236, 341 Wallach, M. 200, 201 Waller, W.S. 312, 314, 348, 349, 350 Ward, D.A. 148, 165, 202 ‘warm’ environments 34, 35–6 Watson, E.D. 146, 157, 205 Watson, J.S. 28 Wearing, A.J. 338 Weddell, D.H. 341 Welsch, H. 146, 147, 165, 203, 205 West, M. 145–6, 161, 173, 180–1, 186, 195, 203, 204 Wilde, G.T.S. 109, 112 Wilkie, W.K. 96 ‘win’ bets 90–3, 100–1, 103–7, 109, 175–82; and male/female bets 187, 189, 192–3, 210–11 win probabilities, favourites–longshots 295–7 ‘win-singles’ bets 238, 275 Winkler, R.L. 347 ‘winner’s curse’ 292 winning bets, features of 264–7 winnings: gender differences 209–10; tax payments on 231–48

UK: gender and decision-making literature 200–5; off-course betting market 42–56; turnover on betting gaming 6 US: gender and decision-making literature 200–5; pari-mutuel data 278 US National Commission on Gambling 27 user-built models, DSS 131–2, 139, 152 utility: gambling 234–6; payment of tax on wager 240–46 van der Pligt, J. 16, 38, 50, 74, 75, 93, 96, 118, 334, 336 Varro, B. 136, 137, 165, 203 Vaughan Williams, L. 224, 251, 279, 291, 300, 301, 302, 303, 304, 305, 315, 318, 320 verbal skills, gender differences 136–7, 140, 203–4 visual–spatial skills, gender differences 136–7, 140, 203–4 Voelz, C.J. 151, 165, 202 von Winterfeldt, D. 334

368

Index

Wood, W. 165, 205 Worchel, S. 148, 165, 179, 201 workplace decisions see managers Wright, G. 336, 338, 344, 350 Wright, P. 68, 70, 74, 78, 99, 111, 117, 118, 121, 334 Yadav, M.S. 75, 96, 97, 118, 122

Yates, J. 75, 76, 99, 101, 118 Young, E. 146, 147, 165, 203, 205 Zakay, D. 335 Ziemba, W.T. 250–51, 259, 277, 278, 284, 315 Zigurs, I. 141, 165 Zmud, R. 131, 165