Analyzing Wimbledon: The Power of Statistics

ISBN : 9780199355952

Franc Klaassen; Jan R. Magnus
272 Pages
161 x 234 mm
Pub date
Jan 2014
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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.


1. Warming up
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
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
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
Miscellaneous variables
Random/unexplained parts
Miscellaneous symbols
Appendix B: Data, software, and mathematical derivations
Data Program Richard
Mathematical derivations

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.

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