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.

1. Warming upWimbledonCommentatorsAn exampleCorrelation and causalityWhy statisticsSports data and human behaviorWhy tennis?Structure of the bookFurther reading2. RichardMeeting RichardFrom point to gameThe tiebreakServing first in a setDuring the setBest-of-three versus best-of-fiveUpsetsLong matches: Isner-Mahut 2010Rule changes: the no-ad ruleAbolishing the second serviceFurther reading3. ForecastingForecasting with RichardFederer-Nadal, Wimbledon final 2008Effect of smaller ?pKim Clijsters defeats Venus Williams, US Open 2010Effect of larger ?pDjokovic-Nadal, Australian Open 2012In-play bettingFurther reading4. ImportanceWhat is importance?Big points in a gameBig games in a setThe vital seventh gameBig setsAre all points equally important?The most important pointThree importance profilesFurther reading5. Point dataThe Wimbledon data setTwo selection problemsEstimators, estimates, and accuracyDevelopment of tennis over timeWinning a point on service unraveledTesting a hypothesis: men versus womenAces and double faultsBreaks and rebreaksAre our summary statistics too simple?Further reading6. The method of momentsOur summary statistics are too simpleThe method of momentsEnter Miss MarpleRe-estimating p by the method of momentsMen versus women revisitedBeyond the mean: variation over playersReliability of summary statistics: a rule of thumbFiltering out the noiseNoise-free variation over playersCorrelation between opponentsWhy bother?Further reading7. QualityObservable variation over playersRankingRound, bonus, and malusSignificance, relevance, and sensitivityThe complete modelWinning a point on serviceOther service characteristicsAces and double faultsFurther reading8. First and second serviceIs the second service more important than the first?Differences in service probabilities explainedJoint analysis: bivariate GMMFour service dimensionsFour-variate GMMFurther reading9. Service strategyThe server's trade-offThe y-curveOptimal strategy: one serviceOptimal strategy: two servicesExistence and uniquenessFour regularity conditions for the optimal strategyFunctional form of y-curveEfficiency definedEfficiency of the average playerObservations for the key probabilities: Monte CarloEfficiency estimatesMean match efficiency gainsEfficiency gains across matchesImpact on the paycheckWhy are players inefficient?Rule changesServing in volleyballFurther reading10. Within a matchThe idea behind the point modelFrom matches to pointsFirst results at point levelSimple dynamicsThe baseline modelTop players and mental stabilityLessons from the baseline modelNew ballsFurther reading11. Special points and gamesBig pointsBig points and the baseline modelServing first revisitedThe tossFurther reading12. MomentumStreaks, the hot hand, and winning moodWhy study tennis?Winning mood in tennisBreaks and rebreaksMissed breakpointsThe encompassing modelFurther reading13. The hypotheses revisitedWinning a point on service is an iid processIt is an advantage to serve first in a setEvery point (game, set) is equally important to both playersThe seventh game is the most important game in the setAll points are equally importantThe probability that the service is in, is the same in the men's singles as in the women's singlesThe probability of a double fault is the same in the men's singles as in the women's singlesAfter a break the probability of being broken back increasesSummary statistics give a precise impression of a player's performanceQuality is a pyramidTop players must grow into the tournamentMen's tennis is more competitive than women's tennisA player is as good as his or her second servicePlayers have an efficient service strategyPlayers play safer at important pointsPlayers take more risk when they are in a winning moodTop players are more stable than othersNew balls are an advantage to the serverReal champions win the big pointsThe winner of the toss should select to serveWinning mood existsAfter missing breakpoint(s) there is an increased probability of being broken in the next gameAppendix A: List of symbolsWinning probabilitiesScore probabilities and importanceService probabilitiesQualityOperatorsMiscellaneous variablesRandom/unexplained partsParametersMiscellaneous symbolsAppendix B: Data, software, and mathematical derivationsData Program RichardMathematical derivationsBibliographyIndex