Analyzing Wimbledon: The Power of Statistics

269 Pages·2014·1.63 MB·English

by  Franc Klaassen

ANALYZING WIMBLEDON
The game of tennis raises many challenging questions to a statisti-
cian. Is it true that serving first in a set gives an advantage? Or
servingwithnewballs? Istheseventhgameinasetparticularlyim-
portant? 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. This book
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
a ‘winning mood’ actually exists in tennis. Aimed at readers with
someknowledgeofmathematics andstatistics, thebookusestennis
(Wimbledon in particular) as a vehicle to illustrate the power and
beauty of statistical reasoning.
Franc Klaassen is Professor of International Economics at the Uni-
versity of Amsterdam. After obtaining masters degrees in econo-
metrics and economics and a PhD at Tilburg University, he moved
to the University of Amsterdam in 1999. Klaassen is a fellow of the
Tinbergen Institute and was a visiting fellow at the University of
Wisconsin-Madison. His main research interests are the empirical
analysis of international economics and finance, fiscal policy, and
sports, mainly tennis, on which he has published widely. He is an
enthusiastic tennis player and, as a junior, was selected to train
with the Royal Dutch Lawn Tennis Association for nine years.
Jan R. Magnus is Emeritus Professor at Tilburg University and
Visiting Professor of Econometrics at the VU University Amster-
dam. He studied econometrics and philosophy at the University of
Amsterdam, where he obtained his PhD in Economics. He worked
attheUniversitiesofAmsterdam,Leiden,andBritishColumbiabe-
foremoving to theLondonSchoolof Economics in 1981. In1996 he
was appointed Research Professor of Econometrics at Tilburg Uni-
versity. Magnus held visiting positions at University of California
San Diego, New Economic School of Moscow, European University
Institute in Florence, and University of Tokyo, among others. He
is author or coauthor of eight books and more than one hundred
scientific papers.
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Analyzing Wimbledon
The Power of Statistics
Franc Klaassen
Amsterdam School of Economics,
University of Amsterdam, The Netherlands
Jan R. Magnus
Department of Econometrics & Operations Research,
VU University Amsterdam, The Netherlands
1
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Includesbibliographicalreferencesandindex.
ISBN978-0-19-935595-2(cloth: alk.paper)–ISBN978-0-19-935596-9(paperback:
alk.paper)1. WimbledonChampionships(Wimbledon,London,England)2.
Tennis–Statistics. I.Magnus,JanR.II.Title.
GV999.K582014
796.342094212–dc23 2013026355
135798642
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To my parents (FK)
To Eveline de Jong (JM)
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Contents
Preface xiii
Acknowledgements xv
1 Warming up 1
Wimbledon . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Commentators . . . . . . . . . . . . . . . . . . . . . . . . 2
An example . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Correlation and causality . . . . . . . . . . . . . . . . . . 4
Why statistics? . . . . . . . . . . . . . . . . . . . . . . . . 5
Sports data and human behavior . . . . . . . . . . . . . . 6
Why tennis? . . . . . . . . . . . . . . . . . . . . . . . . . 8
Structure of the book . . . . . . . . . . . . . . . . . . . . 9
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Richard 13
Meeting Richard . . . . . . . . . . . . . . . . . . . . . . . 13
From point to game . . . . . . . . . . . . . . . . . . . . . 15
The tiebreak . . . . . . . . . . . . . . . . . . . . . . . . . 17
Serving first in a set . . . . . . . . . . . . . . . . . . . . . 18
During the set . . . . . . . . . . . . . . . . . . . . . . . . 20
Best-of-three versus best-of-five . . . . . . . . . . . . . . . 21
Upsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Long matches: Isner-Mahut 2010 . . . . . . . . . . . . . . 24
Rule changes: the no-ad rule . . . . . . . . . . . . . . . . 27
Abolishing the second service . . . . . . . . . . . . . . . . 28
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 30
viii Contents
3 Forecasting 33
Forecasting with Richard . . . . . . . . . . . . . . . . . . 34
Federer-Nadal, Wimbledon final 2008 . . . . . . . . . . . . 36
Effect of smaller p¯ . . . . . . . . . . . . . . . . . . . . . . 38
Kim Clijsters defeats Venus Williams, US Open 2010 . . . 40
Effect of larger p¯ . . . . . . . . . . . . . . . . . . . . . . . 41
Djokovic-Nadal, Australian Open 2012 . . . . . . . . . . . 42
In-play betting . . . . . . . . . . . . . . . . . . . . . . . . 44
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Importance 49
What is importance? . . . . . . . . . . . . . . . . . . . . . 49
Big points in a game . . . . . . . . . . . . . . . . . . . . . 50
Big games in a set . . . . . . . . . . . . . . . . . . . . . . 52
The vital seventh game . . . . . . . . . . . . . . . . . . . 54
Big sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Are all points equally important? . . . . . . . . . . . . . . 57
The most important point . . . . . . . . . . . . . . . . . . 58
Three importance profiles . . . . . . . . . . . . . . . . . . 59
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Point data 65
The Wimbledon data set . . . . . . . . . . . . . . . . . . . 65
Two selection problems . . . . . . . . . . . . . . . . . . . 67
Estimators, estimates, and accuracy . . . . . . . . . . . . 70
Development of tennis over time . . . . . . . . . . . . . . 72
Winning a point on service unraveled . . . . . . . . . . . . 74
Testing a hypothesis: men versus women . . . . . . . . . . 76
Aces and double faults . . . . . . . . . . . . . . . . . . . . 78
Breaks and rebreaks . . . . . . . . . . . . . . . . . . . . . 80
Are our summary statistics too simple? . . . . . . . . . . 82
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 82
6 The method of moments 85
Our summary statistics are too simple . . . . . . . . . . . 85
The method of moments . . . . . . . . . . . . . . . . . . . 88
Enter Miss Marple . . . . . . . . . . . . . . . . . . . . . . 90
Re-estimating p by the method of moments . . . . . . . . 90
Men versus women revisited . . . . . . . . . . . . . . . . . 91
Contents ix
Beyond the mean: variation over players . . . . . . . . . . 92
Reliability of summary statistics: a rule of thumb . . . . . 94
Filtering out the noise . . . . . . . . . . . . . . . . . . . . 97
Noise-free variation over players . . . . . . . . . . . . . . . 99
Correlation between opponents . . . . . . . . . . . . . . . 100
Why bother? . . . . . . . . . . . . . . . . . . . . . . . . . 102
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 102
7 Quality 105
Observable variation over players . . . . . . . . . . . . . . 105
Ranking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Round, bonus, and malus . . . . . . . . . . . . . . . . . . 112
Significance, relevance, and sensitivity . . . . . . . . . . . 114
The complete model . . . . . . . . . . . . . . . . . . . . . 115
Winning a point on service . . . . . . . . . . . . . . . . . 116
Other service characteristics . . . . . . . . . . . . . . . . . 119
Aces and double faults . . . . . . . . . . . . . . . . . . . . 121
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 123
8 First and second service 127
Is the second service more important than the first? . . . 127
Differences in service probabilities explained . . . . . . . . 130
Joint analysis: bivariate GMM . . . . . . . . . . . . . . . 132
Four service dimensions . . . . . . . . . . . . . . . . . . . 134
Four-variate GMM . . . . . . . . . . . . . . . . . . . . . . 134
Further reading . . . . . . . . . . . . . . . . . . . . . . . . 136
9 Service strategy 137
The server’s trade-off . . . . . . . . . . . . . . . . . . . . . 137
The y-curve . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Optimal strategy: one service . . . . . . . . . . . . . . . . 140
Optimal strategy: two services . . . . . . . . . . . . . . . 141
Existence and uniqueness . . . . . . . . . . . . . . . . . . 142
Four regularity conditions for the optimal strategy . . . . 143
Functional form of y-curve . . . . . . . . . . . . . . . . . . 145
Efficiency defined . . . . . . . . . . . . . . . . . . . . . . . 146
Efficiency of the average player . . . . . . . . . . . . . . . 147
Observations for the key probabilities: Monte Carlo . . . 148
Efficiency estimates. . . . . . . . . . . . . . . . . . . . . . 149