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The game of tennis raises many questions that are of interest to a statistician. Is it true that beginning to serve in a set gives an advantage? Are new balls an advantage? Is the seventh game in a set particularly important? Are top players more stable than other players? Do real champions win the big points? These and many other questions are formulated as "hypotheses" and tested statistically. Analyzing Wimbledon also discusses how the outcome of a match can be predicted (even while the match is in progress), which points are important and which are not, how to choose an optimal service strategy, and whether "winning mood" actually exists in tennis. Aimed at readers with some knowledge of mathematics and statistics, the book uses tennis (Wimbledon in particular) as a vehicle to illustrate the power and beauty of statistical reasoning.
Franc Klaassen is Professor of International Economics at University of Amsterdam. Jan R. Magnus is Emeritus Professor at Tilburg University and Visiting Professor of Econometrics at the Vrije Universiteit Amsterdam.
1. Warming up ; Wimbledon ; Commentators ; An example ; Correlation and causality ; Why statistics ; Sports data and human behavior ; Why tennis? ; Structure of the book ; Further reading ; 2. Richard ; Meeting Richard ; From point to game ; The tiebreak ; Serving first in a set ; During the set ; Best-of-three versus best-of-five ; Upsets ; Long matches: Isner-Mahut 2010 ; Rule changes: the no-ad rule ; Abolishing the second service ; Further reading ; 3. Forecasting ; Forecasting with Richard ; Federer-Nadal, Wimbledon final 2008 ; Effect of smaller ~ p ; Kim Clijsters defeats Venus Williams, US Open 2010 ; Effect of larger ~ p ; Djokovic-Nadal, Australian Open 2012 ; In-play betting ; Further reading ; 4. Importance ; What is importance? ; Big points in a game ; Big games in a set ; The vital seventh game ; Big sets ; Are all points equally important? ; The most important point ; Three importance profiles ; Further reading ; 5. Point data ; The Wimbledon data set ; Two selection problems ; Estimators, estimates, and accuracy ; Development of tennis over time ; Winning a point on service unraveled ; Testing a hypothesis: men versus women ; Aces and double faults ; Breaks and rebreaks ; Are our summary statistics too simple? ; Further reading ; 6. The method of moments ; Our summary statistics are too simple ; The method of moments ; Enter Miss Marple ; Re-estimating p by the method of moments ; Men versus women revisited ; Beyond the mean: variation over players ; Reliability of summary statistics: a rule of thumb ; Filtering out the noise ; Noise-free variation over players ; Correlation between opponents ; Why bother? ; Further reading ; 7. Quality ; Observable variation over players ; Ranking ; Round, bonus, and malus ; Significance, relevance, and sensitivity ; The complete model ; Winning a point on service ; Other service characteristics ; Aces and double faults ; Further reading ; 8. First and second service ; Is the second service more important than the first? ; Differences in service probabilities explained ; Joint analysis: bivariate GMM ; Four service dimensions ; Four-variate GMM ; Further reading ; 9. Service strategy ; The server's trade-off ; The y-curve ; Optimal strategy: one service ; Optimal strategy: two services ; Existence and uniqueness ; Four regularity conditions for the optimal strategy ; Functional form of y-curve ; Efficiency defined ; Efficiency of the average player ; Observations for the key probabilities: Monte Carlo ; Efficiency estimates ; Mean match efficiency gains ; Efficiency gains across matches ; Impact on the paycheck ; Why are players inefficient? ; Rule changes ; Serving in volleyball ; Further reading ; 10. Within a match ; The idea behind the point model ; From matches to points ; First results at point level ; Simple dynamics ; The baseline model ; Top players and mental stability ; Lessons from the baseline model ; New balls ; Further reading ; 11. Special points and games ; Big points ; Big points and the baseline model ; Serving first revisited ; The toss ; Further reading ; 12. Momentum ; Streaks, the hot hand, and winning mood ; Why study tennis? ; Winning mood in tennis ; Breaks and rebreaks ; Missed breakpoints ; The encompassing model ; Further reading ; 13. The hypotheses revisited ; Winning a point on service is an iid process ; It is an advantage to serve first in a set ; Every point (game, set) is equally important to both players ; The seventh game is the most important game in the set ; All points are equally important ; The probability that the service is in, is the same in the men's singles as in the women's singles ; The probability of a double fault is the same in the men's singles as in the women's singles ; After a break the probability of being broken back increases ; Summary statistics give a precise impression of a player's performance ; Quality is a pyramid ; Top players must grow into the tournament ; Men's tennis is more competitive than women's tennis ; A player is as good as his or her second service ; Players have an efficient service strategy ; Players play safer at important points ; Players take more risk when they are in a winning mood ; Top players are more stable than others ; New balls are an advantage to the server ; Real champions win the big points ; The winner of the toss should select to serve ; Winning mood exists ; After missing breakpoint(s) there is an increased probability of being broken in the next game ; Appendix A: List of symbols ; Winning probabilities ; Score probabilities and importance ; Service probabilities ; Quality ; Operators ; Miscellaneous variables ; Random/unexplained parts ; Parameters ; Miscellaneous symbols ; Appendix B: Data, software, and mathematical derivations ; Data Program Richard ; Mathematical derivations ; Bibliography ; Index
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- ID: 9780199355969
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