Table of contents for Statistical thinking in sports / editors, Ruud H. Koning and James H. Albert.

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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.