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
