HANDBOOK OF SPORTS AND LOTTERY MARKETS

HANDBOOK OF SPORTS AND LOTTERY MARKETS Edited by Donald B. Hausch University of Wisconsin, Madison William T. Ziemba University of British Columbia Oxford University University of Reading F.I ASP,V I F,R AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO North-Holland is an imprint of Elsevier L< JJO*S

List of Contributors Preface Introduction to the Series xvi xix xxiii Part I Industry Studies 1 1 Pari-Mutuel Horse Race Wagering Competition from Within and Outside the Industry 3 Richard Thalheimer and Mukhtar M. AH 1. Introduction 4 2. Competition from Casino Gaming 5 3. Competition from State Lotteries 7 4. Competition from Professional Sports 8 5. Competition from Live Racing 8 6. Competition from Simulcast Wagering 11 7. Summary and Conclusions 13 References 14 2 Modeling Money Bet on Horse Races in Hong Kong 17 John Bacon-Shone and Alan Woods 1. Introduction 18 2. Variables examined. 18 2.1. Outcome Variables 18 2.2. Independent Variables 19 3. Results and Discussion 19 4. Conclusion 21 References 22 Appendix: 31 Independent Variables Examined (Excluding Quadratic Terms) 23 vii

viii Contents Part II Utility, Probability, and Pace Estimation 25 3 Empirical Evidence on the Preferences of Racetrack Bettors 27 Bruno Jullien and Bernard Salanie 1. Introduction 28 2. Some Stylized Facts 30 3. Expected Utility 33 4. Distortions of Probabilities 36 5. Reference Points and Asymmetric Probability Weights 39 6. Heterogeneous Preferences 42 7. Exotic Bets 45 8. Concluding Remarks 46 References 47 4 Approximating the Ordering Probabilities of Multi-Entry Competitions by a Simple Method 51 Victor S.Y.Lo and John Bacon-Shone 1. Introduction 52 2. Theoretical Results of the Limiting Cases 53 3. A Simple Approximation 56 3.1. Empirical Analysis for the Approximated Henery Model 56 3.2. Empirical Analysis for the Stern Model 57 4. Conclusion 59 References 60 Appendix: Proof of Theorem 1 61 5 Modeling Distance Preference and Pace Character in Thoroughbred Turf Racing 67 David Edelman 1. Background 68 2. Case Study 1: Sha Tin (Hong Kong, SAR, PRC) 69 3. Case Study 2: Randwick (Sydney, Australia) 71 4. Qualitative Questions 77 4.1. Do Distance Specialists Exist? 77 4.2. Pace, Class, and Time: The Central Paradox of Racing 78 4.3. Jockeys: Distance or Pace Preference? 79 5. Discussion 80 References 80

ix Part III Favorite-Longshot Bias in the Win Market 81 6 The Favorite-Longshot Bias: An Overview of the Main Explanations 83 Marco Ottaviani and Peter Norman S0rensen 1. Introduction 84 2. Notation 87 3. Misestimation of Probabilities 87 4. Market Power by Informed Bettors 89 5. Preference for Risk 90 6. Heterogeneous Beliefs 93 7. Market Power by Uninformed Bookmaker 95 8. Limited Arbitrage 96 9. Simultaneous Betting by Insiders 97 10. Timing of Bets 99 10.1. Early Betting 99 10.2. Late Betting 99 References 100 7 Examining Explanations of a Market Anomaly: Preferences or Perceptions? 103 Erik Snowberg and Justin Wolfers 1. Introduction 104 2. Preferences Expected Utility Models with Linear Probabilities 108 3. Perceptions The Weighting of True Probabilities 111 4. Perceptions Informational Effects 112 5. Definition of Models and Implications for Combinatoric Bets 114 6. Using Combinatoric Markets to Test the Models 119 6.1. Testing Conditional Independence 123 6.2. Relaxing Conditional Independence Further 125 1. Conclusion ^ 129 References 130 Appendix A: Pricing of Combinatoric Bets Using Conditional Independence 134 Appendix B: Data 135 8 Unifying the Favorite-Longshot Bias with Other Market Anomalies 137 Russell S. Sobel and Matt E. Ryan 1. Introduction 138 2. Biases Found in the Previous Literature 138 3. What Causes the Favorite-Longshot Bias at the Racetrack? 140 3.1. The Casual Bettor 143

3.2. The Serious or Regular Bettor 144 3.3. The Arbitrageur 148 4. Is it Risk or Information? 150 5. Can the Model Explain the Biases in Other Markets? 156 6. Conclusion 157 References 158 The Favorite-Longshot Bias in S&P 500 and FTSE 100 Index Futures Options: The Return to Bets and the Cost of Insurance 161 Robert G. Tompkins, William T. Ziemba, and Stewart D. Hodges 1. Introduction 162 2. Methodology 166 3. Results 170 3.1. Results for Quarterly Options on Stock Index Futures 174 3.2. Results for Monthly Options on Stock Index Futures 175 4. Conclusions 178 References 179 Part IV Weak Market Efficiency 181 10 Efficiency of Racing, Sports, and Lottery Betting Markets 183 William T. Ziemba 1. Introduction 184 2. Extent of Gambling in the U.S. 187 3. Racetrack Betting Markets 190 3.1. Introduction to Racetrack Betting 190 3.2. Win Market' 190 3.3. Place and Show Markets 195 3.4. Place and Show Probabilities 196 3.5. Optimal Capital Growth 201 3.6. Implementing the System and Empirical Results 203 3.7. Does the System Still Provide Profits? 206 3.8. Exotic Markets 207 3.9. Cross-Track Betting 208 4. The Football Betting Market 209 5. The Basketball Betting Market 211 6. Lotteries 212 6.1. Introduction to Lotteries 212 6.2. Inefficiencies with Unpopular Numbers 214 References 217

XI 11 Point Spread and Odds Betting: Baseball, Basketball, and American Football 223 Hal S. Stern 1. Introduction 224 2. Efficiency of Odds Betting Markets 224 2.1. Horse Race Betting 224 2.2. Baseball 226 3. Efficiency of Point Spread Betting Markets 227 3.1. American Football 227 3.2. Basketball 230 4. Relationship of Point Spread and Odds Betting 230 4.1. Normal Distribution Result 231 4.2. Applications of the Normal Approximation 233 5. The Normal Model and Mid-Event Wagering 234 6. Summary 236 References 237 12 Comparing Efficiency of the Over/Under-Bets on NFL and NBA Games 239 Joseph Golec and Maurry Tamarkin 1. Introduction 240 2. The Sports Betting Market: Setting Point Spreads and Over/Unders 240 3. NFL and NBA Betting Market Efficiency 242 4. Conclusion 249 References 251 13 Arbitrage and Risk Arbitrage in Team Jai Alai 253 Daniel Lane and William T. Ziemba 1. Introduction 254 2. The Arbitrage 258 3. Risk Arbitrages 261 4. Final Remarks 269 References 271 PartV Semi-Strong Form Efficiency 273 14 Semi-Strong Form Information Efficiency in Horse Race Betting Markets 275 M. Sung and J. E. V. Johnson 1. Introduction 276 2. Semi-Strong Form Efficiency in Horse Race Betting Markets: Single Variable Models 277 2.1. Arbitrage Between Parallel Markets 278 2.2 Professional Predictions 285

xii Contents 2.3. Betting Volume 289 2.4. Post Position 290 2.5. Pedigree 291 2.6. Distance Preference 292 2.7. Single Variable Models: Overview 292 3. Semi-Strong Form Efficiency in Horse Race Betting Markets: Multiple Variable Models 293 3.1. Distribution-Based Methods 294 3.2. Distribution-Free Methods 298 3.3. Multiple Variable Models: Overview 300 4. Semi-Strong Form Efficiency in Horse Race Betting Markets: Conclusion 301 References 302 15 The Dosage Breeding Theory for Horse Racing Predictions 307 Marshall Gramm and William T. Ziemba 1. Introduction 308 2. The Racetrack as a Sequence of Markets 310 3. The Dosage Index and Performance Measures 311 4. Data Acquisition 314 5. Application of Breeding Information and Performance Measures to Refine Estimated Win Probabilities for the Kentucky Derby 314 6. The Kelly Betting Model 320 7. The Kentucky Derby, 1981-2007 322 8. The Preakness Stakes, 1946-2006 327 9. The Belmont Stakes, 1946-2006 329 10. Conclusions 330 References 331 Appendix A: Data Sources 333 A.I Public's Wagering 333 A.2. Pedigrees 333 A.3. Chef-de-Race Listings 333 A.4. Experimental Free Handicap Listings 334 A.5. Results of the Kentucky Derby and Major Races Prior to the Kentucky Derby 334 Appendix B: Kentucky Derby, Preakness, and Belmont Winners, 1946-2006 334 16 Efficiency in Horse Race Betting Markets: The Role of Professional Tipsters 341 Bruno Deschamps and Olivier Gergaud 1. Introduction 342 2. The Model 343 3. Data 345 3.1. Tips and Rewards Rules 345

Xlll 3.2. Public Information 346 3.3. Measuring Forecast Originality 347 4. Results 348 4.1. Results of Frequency Tests 348 4.2. Originality and Accuracy 348 4.3. Anti-Herding and Excess Originality 350 5. Conclusion 351 References 351 Appendix: Proof of Equation (5) 353 Part VI Prediction Markets 355 17 Index Betting for Sports and Stock Indices 357 John Haigh and Leighton Vaughan Williams 1. Background 358 2. How Index Betting Operates 360 3. Setting Spreads 362 4. Spreads in Performance Indices 365 5. Advantageous Bets 368 6. Regulation, Taxation, and Biases in Spread Betting Markets 372 References 374 Appendix A 377 Appendix B 378 Appendix C 380 18 Prediction Markets: From Politics to Business (and Back) 385 Erik Snowberg, Justin Wolfers, and Eric Zitzewitz 1. Overview 386 2. The First Prediction Markets 388 3. Markets in the Lab 391 4. Current Uses of Prediction Markets: Business and Policy 393 5. Future Directions: Decision Markets 397 6. Potential Pitfalls 398 7. Conclusion 400 References 401 19 Betting Exchanges: A Technological Revolution in Sports Betting 403 Michael A. Smith and Leighton Vaughan Williams 1. Introduction 404 2. The Operation of Betting Exchanges 404

XIV Contents 3. Empirical Models and Evidence Concerning Weak-Form Information Efficiency in Betting Exchanges 409 4. New Evidence on the Degree of Bias in Betting Exchange Odds 412 5. Conclusions 416 References 417 Part VII Soccer 419 20 Soccer Betting in Britain 421 David Forrest 1. Introduction 422 2. Development of Soccer Betting 423 3. Transactions Costs in the Fixed Odds Market 426 4. Early Study of Market Efficiency 429 5. Tipsters 431 6. Fundamental Analysis as an Aid to Soccer Betting 432 7. Technical Analysis 437 8. Sentiment 440 9 The Future of Research on Soccer Betting 443 References 444 21 Efficiency of Soccer Betting Odds Evidence from a Pan-European Electronic Market 447 Stephan Kossmeier and Simon Weinberger 1. Introduction 448 2. The Soccer Betting Market 449 3. Data Description 450 4 Efficiency Tests 451 4.1. Statistical Tests 451 4.2. Economic Tests 454 5. Conclusion 455 References 456 Part VIII Lotteries 457 22 How to Design a Lottery 459 Ian Walker 1. Introduction 460 2. The Odds of Winning a (Pari-Mutuel) Lottery 464 3. The Expected Value Calculation 465

xv 4. Higher Moments of the Prize Distribution 467 5. Econometric Methodology, Data, and Estimates 469 6. Game Design Simulations 474 7. Conclusion 476 References 477 Appendix: The Expected Value Formula 479 23 The Statistics of Lotteries 481 John Haigh 1. Introduction 482 2. Prize Structure and Winning Chances 485 3. Tests of Randomness 491 4. Gambler Choices 496 References 502 24 U.S. Lotto Markets 503 Victor Matheson and Kent Grote 1. Introduction 504 2. Differences Between American and European Lotteries 509 3. Fungibility of Lottery Revenues 512 4. Efficiency of Lottery Markets Parti 516 5. Efficiency of Lottery Markets Part 2 519 6. Efficiency of Lottery Markets Part 3 521 7. Conclusions 522 References 523 Subject Index 525 Author Index 533