Analyzing Wimbledon: The Power of Statistics

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.

Table of Contents:
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

About the Author :
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.