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Contents 1 Introduction 1 Jim Albert and Ruud H. Koning 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Patterns of world records in sports (2 chapters) . . . . . . 2 1.1.2 Competition, rankings and betting in soccer (3 articles) . . 2 1.1.3 An investigation into some popular baseballmyths (3 chapters) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.4 Uncertainty of attendance at sports events (2 chapters) . . 4 1.1.5 Home advantage, myths in tennis, drafting in hockey pools, American football . . . . . . . . . . . . . . . . . . . . . 4 1.2 Website . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Modelling the development of world records in running 7 Gerard H. Kuper and Elmer Sterken 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Modelling world records . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Cross-sectional approach . . . . . . . . . . . . . . . . . . 10 2.2.2 Fitting the individual curves . . . . . . . . . . . . . . . . 11 2.3 Selection of the functional form . . . . . . . . . . . . . . . . . . 12 2.3.1 Candidate functions . . . . . . . . . . . . . . . . . . . . . 12 2.3.2 Theoretical selection of curves . . . . . . . . . . . . . . . 17 2.3.3 Fitting the models . . . . . . . . . . . . . . . . . . . . . . 18 2.3.4 The Gompertz curve in more detail . . . . . . . . . . . . 18 2.4 Running data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Results of fitting the Gompertz curves . . . . . . . . . . . . . . . 23 2.6 Limit values of time and distance . . . . . . . . . . . . . . . . . 26 2.7 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . 28 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3 The physics and evolution of Olympic winning performances 33 Ray Stefani 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Running events . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 The physics of running . . . . . . . . . . . . . . . . . . . 34 3.2.2 Measuring the rate of improvement in running . . . . . . . 37 iii iv Statistical Thinking in Sports 3.2.3 Periods of summer Olympic history . . . . . . . . . . . . 38 3.2.4 The future of running . . . . . . . . . . . . . . . . . . . . 40 3.3 Jumping events . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3.1 The physics of jumping . . . . . . . . . . . . . . . . . . . 40 3.3.2 Measuring the rate of improvement in jumping . . . . . . 44 3.3.3 The future of jumping . . . . . . . . . . . . . . . . . . . 45 3.4 Swimming events . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4.1 The physics of swimming . . . . . . . . . . . . . . . . . 45 3.4.2 Measuring the rate of improvement in swimming . . . . . 47 3.4.3 The future of swimming . . . . . . . . . . . . . . . . . . 49 3.5 Rowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.5.1 The physics of rowing . . . . . . . . . . . . . . . . . . . 50 3.5.2 Measuring the rate of improvement in rowing . . . . . . . 52 3.5.3 The future of rowing . . . . . . . . . . . . . . . . . . . . 53 3.6 Speed skating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.6.1 The physics of speed skating . . . . . . . . . . . . . . . . 54 3.6.2 Measuring the rate of improvement in speed skating . . . 55 3.6.3 Periods of winter Olympic history . . . . . . . . . . . . . 56 3.6.4 The future of speed skating . . . . . . . . . . . . . . . . . 58 3.7 A summary of what we have learned . . . . . . . . . . . . . . . . 58 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4 Competitive balance in national European soccer competitions 63 Marco Haan, Ruud H. Koning and Arjen van Witteloostuijn 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Measurement of competitive balance . . . . . . . . . . . . . . . . 64 4.3 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Can national competitive balance measures be condensed? . . . . 72 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5 Statistical analysis of the effectiveness of the FIFA World Rankings 77 Ian McHale and Stephen Davies 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 FIFA¿s ranking procedure . . . . . . . . . . . . . . . . . . . . . . 78 5.3 Implications of the FIFA World Rankings . . . . . . . . . . . . . 79 5.4 The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.5 Preliminary analysis . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.5.1 Team win percentage, in and out of own confederation . . 80 5.5.2 International soccer versus domestic soccer . . . . . . . . 82 5.6 Forecasting soccer matches . . . . . . . . . . . . . . . . . . . . . 84 5.7 Using the FIFA World Rankings to forecast match results . . . . . 84 5.7.1 Reaction to new information . . . . . . . . . . . . . . . . 85 5.7.2 A forecasting model for match result using past results . . 86 5.8 Conclusion Table of Contents v Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6 Forecasting scores and results and testing the efficiency of the fixed-odds betting market in Scottish league football 91 Stephen Dobson and John Goddard 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.3 Regression models for goal scoring and match results . . . . . . . 95 6.4 Data and estimation results . . . . . . . . . . . . . . . . . . . . . 97 6.5 The efficiency of the market for fixed-odds betting on Scottish league football . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7 Hitting in the pinch 111 Jim Albert 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.2 A breakdown of a plate appearance: four hitting rates . . . . . . . 112 7.3 Predicting runs scored by the four rates . . . . . . . . . . . . . . . 113 7.4 Separating luck from ability . . . . . . . . . . . . . . . . . . . . . 114 7.5 Situational biases . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.6 A model for clutch hitting . . . . . . . . . . . . . . . . . . . . . . 124 7.7 Clutch stars? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.8 Related work and concluding comments . . . . . . . . . . . . . . 130 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8 Does momentum exist in a baseball game? 135 Rebecca J. Sela and Jeffrey S. Simonoff 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 Models for baseball play . . . . . . . . . . . . . . . . . . . . . . 136 8.3 Situational and momentum effects . . . . . . . . . . . . . . . . . 138 8.4 Does momentum exist? . . . . . . . . . . . . . . . . . . . . . . . 140 8.4.1 Modeling transition probabilities . . . . . . . . . . . . . . 140 8.4.2 Modeling runs scored . . . . . . . . . . . . . . . . . . . . 144 8.5 Rally starters and rally killers . . . . . . . . . . . . . . . . . . . . 149 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 9 Inference about batter-pitcher matchups in baseball from small samples153 Hal S. Stern and Adam Sugano 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 9.2 The batter-pitcher matchup: a binomial view . . . . . . . . . . . . 154 9.3 A hierarchical model for batter-pitcher matchup data . . . . . . . 155 9.3.1 Data for a single player . . . . . . . . . . . . . . . . . . . 155 9.3.2 A probability model for batter-pitcher matchups vi Statistical Thinking in Sports 9.3.3 Results - Derek Jeter . . . . . . . . . . . . . . . . . . . . 158 9.3.4 Results - multiple players . . . . . . . . . . . . . . . . . . 160 9.4 Batter-pitcher data from the pitcher¿s perspective . . . . . . . . . 160 9.4.1 Results - a single pitcher . . . . . . . . . . . . . . . . . . 161 9.4.2 Results - multiple players . . . . . . . . . . . . . . . . . . 163 9.5 Towards a more realistic model . . . . . . . . . . . . . . . . . . . 163 9.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10 Outcome uncertaintymeasures: how closely do they predict a close game? 167 Babatunde Buraimo, David Forrest and Robert Simmons 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10.2 Measures of outcome uncertainty . . . . . . . . . . . . . . . . . . 169 10.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 10.4 Preliminary analysis of the betting market . . . . . . . . . . . . . 172 10.5 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 10.6 Out-of-sample testing . . . . . . . . . . . . . . . . . . . . . . . . 175 10.7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . 176 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 11 The impact of post-season play-off systems on the attendance at regular season games 179 Chris Bojke 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 11.2 Theoretical model of the demand for attendance and the impact of play-off design . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 11.3 Measuring the probability of end-of-season outcomes and game significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 11.4 The data: the 2000/01 English Football League 2nd tier . . . . . . 185 11.5 Statistical issues in the measurement of the determinants of attendance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 11.5.1 Skewed, non-negative heteroscedastic data . . . . . . . . 190 11.5.2 Clustering of attendance within teams and unobserved heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . 192 11.5.3 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . 192 11.5.4 Final statistical model . . . . . . . . . . . . . . . . . . . 193 11.6 Model estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 194 11.6.1 Choice of explanatory variables . . . . . . . . . . . . . . 194 11.6.2 Regression results . . . . . . . . . . . . . . . . . . . . . . 195 11.7 The impact of the play-off system on regular league attendances . 197 11.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 12 Measurement and interpretation of home advantage 203 Table of Contents vii Ray Stefani 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 12.2 Measuring home advantage . . . . . . . . . . . . . . . . . . . . . 204 12.3 Rugby union, soccer, NBA . . . . . . . . . . . . . . . . . . . . . 207 12.4 Australian rules football, NFL and college football . . . . . . . . . 211 12.5 NHL hockey and MLB baseball . . . . . . . . . . . . . . . . . . 212 12.6 Can home advantage become unfair? . . . . . . . . . . . . . . . . 214 12.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 13 Myths in Tennis 217 Jan Magnus and Franc Klaassen 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 13.2 The data and two selection problems . . . . . . . . . . . . . . . . 218 13.3 Service myths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 13.3.1 A player is as good as his or her second service . . . . . . 223 13.3.2 Serving first . . . . . . . . . . . . . . . . . . . . . . . . . 224 13.3.3 New balls . . . . . . . . . . . . . . . . . . . . . . . . . . 226 13.4 Winning mood . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 13.4.1 At the beginning of a final set, both players have the same chance of winning the match . . . . . . . . . . . . . . . . 230 13.4.2 In the final set the player who has won the previous set has the advantage . . . . . . . . . . . . . . . . . . . . . . . . 231 13.4.3 After breaking your opponent¿s service there is an increased chance that you will lose your own service. . . . . . . . . 232 13.4.4 After missing break points in the previous game there is an increased chance that you will lose your own service . . . 233 13.5 Big points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 13.5.1 The seventh game . . . . . . . . . . . . . . . . . . . . . . 234 13.5.2 Do big points exist? . . . . . . . . . . . . . . . . . . . . . 235 13.5.3 Real champions . . . . . . . . . . . . . . . . . . . . . . . 237 13.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 14 Back to back evaluations on the gridiron 241 David J. Berri 14.1 Why do professional team sports track player statistics? . . . . . . 241 14.2 The NFL¿s quarterback rating measure . . . . . . . . . . . . . . . 242 14.3 The Scully approach . . . . . . . . . . . . . . . . . . . . . . . . . 243 14.4 Modeling team offense and defense . . . . . . . . . . . . . . . . . 244 14.5 Net Points, QB Score and RB Score . . . . . . . . . . . . . . . . . 252 14.6 Who is the best? . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 14.7 Forecasting performance in the NFL . . . . . . . . . . . . . . . . 254 14.8 Do different metrics tell a different story? . . . . . . . . . . . . . 259 14.9 Do we have marginal physical product in the NFL? . . . . . . . . 260 viii Statistical Thinking in Sports References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 15 Optimal drafting in hockey pools 263 Amy E. Summers, Tim B. Swartz and Richard A. Lockhart 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 15.2 Statistical modelling . . . . . . . . . . . . . . . . . . . . . . . . . 264 15.2.1 Distribution of points . . . . . . . . . . . . . . . . . . . . 264 15.2.2 Distribution of games . . . . . . . . . . . . . . . . . . . . 266 15.3 An optimality criterion . . . . . . . . . . . . . . . . . . . . . . . 268 15.4 A simulation study . . . . . . . . . . . . . . . . . . . . . . . . . 269 15.5 An actual Stanley Cup playoff pool . . . . . . . . . . . . . . . . . 273 15.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Referenc.e.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 References 277 List of authors 291 Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
Library of Congress Subject Headings for this publication:
Sports -- Statistical methods.
Sports -- Statistics.