The favorite longshot bias
in ATP and WTA tennis
What is the best strategy: playing favorites or risk-love?
ERASMUS UNIVERSITY ROTTERDAM
Erasmus School of Economics
October 2014
Author:
Student ID:
Study Program:
Thesis Supervisor:
Jacky Quint
363710
Master Economics and Business: Accounting & Finance
Prof. Dr. E.A. de Groot
1
Abstract
The favorite longshot bias is a phenomenon where bettors overvalue longshots and undervalue
favorites. This results in the fact that a betting on favorites in sport matches give a higher return than
betting on the underdogs, also called the longshots. Most literature is focused on the bias in horse
racing, this is also the sport where the bias is found for the first time.
In this paper, the favorite longshot bias in the tennis sport is investigated. This paper uses a large
dataset, which contains 37.220 odds from ATP and WTA tournament in the years 2009 to 2013.
The results do not show an existence of a favorite longshot bias. In addition, there is no strong
evidence for a favorite longshot bias in WTA or ATP tournaments separately. Investigating the bias
per years or surface does show a bias in ATP tournaments in 2011 and ATP tournaments on hardcourt (outdoor), but the overall conclusion is an absent of a favorite longshot bias.
2
Preface
This thesis is the result of a research assignment in order to finalize the Master degree in Business &
Economics (Accounting & Finance).
I greatly appreciate the help of my supervisor Prof. Dr. E.A. de Groot. I would like to thank him for all
the valuable comments and feedback, but especially for his patience when I was struggling for
months with choosing a subject. I also would like to express my gratitude to all others who have
contributed, directly or indirectly, to this thesis.
Jacky Quint
Rotterdam, October 2014
3
Table of Contents
Abstract ................................................................................................................................................... 2
Preface .................................................................................................................................................... 3
1.
Introduction .................................................................................................................................... 6
2.
Literature review............................................................................................................................. 8
2.1
The early evidence .................................................................................................................. 8
2.2
Favorite longshot bias in other sports .................................................................................. 10
2.3
Favorite longshot bias in tennis ............................................................................................ 11
2.4
Contradicting literature ........................................................................................................ 12
3.
Research question & hypotheses.................................................................................................. 15
4.
Methodology................................................................................................................................. 18
4.1
Data ....................................................................................................................................... 18
4.2
Statistical research ................................................................................................................ 19
5.
Results ........................................................................................................................................... 20
5.1
Results ATP and WTA tournament (2009-2013) ................................................................... 21
5.2
Results gender....................................................................................................................... 23
5.3
Results over the years ........................................................................................................... 26
5.3.1 Results over the years - ATP and WTA tournaments ........................................................... 26
5.3.2 Results over the years – ATP and WTA tournaments separately ........................................ 30
5.4
Results surface ...................................................................................................................... 37
5.4.1 Results surface - ATP and WTA tournaments ...................................................................... 37
5.4.2 Results surface - ATP and WTA tournaments separately .................................................... 41
6.
Conclusion ..................................................................................................................................... 46
7.
Discussion...................................................................................................................................... 49
7.1 Contribution ................................................................................................................................ 49
7.2 Limitations & further research.................................................................................................... 49
References ............................................................................................................................................ 50
Appendix ............................................................................................................................................... 52
A.
Overview of ATP tournaments .................................................................................................. 52
4
B.
Overview of WTA tournaments ................................................................................................ 55
C.
Historical winners Australian Open 1950-2014 ........................................................................ 57
D.
Historical winners Roland Garros 1950-2014 ........................................................................... 58
E.
Historical winners Wimbledon 1950-2014 ............................................................................... 59
F.
Historical winners US Open 1950-2014 .................................................................................... 60
5
1. Introduction
The introduction of this master thesis will introduce the research topic and current state of
knowledge. The research question and the research methodology of the study will be briefly
presented. The main empirical findings and the contribution of the study will discussed shortly.
Finally, the structure of the thesis is provided.
Griffith (1949) mentions the favorite-longshot bias for the first time. The favorite longshot bias is a
phenomenon where bettors overvalue longshots and undervalue favorites. This results in the fact
that a betting on favorites in sport matches give a higher return than betting on the underdogs, also
called the longshots. In the early literature, there is a lot of investigation on horse racing (Ali 1977,
Arsch & Malkiel 1982 and McGlothlin 1956). Later, there was more investigation according to the
bias in other sports, like football (Andrikogiannopoulou & Papakonstantinou 2011, Cain, et al. 2000
and Vlastakis et al, 2008) and golf (Shmanske, 2005) and tennis (Forrest & Mchale, 2007). In section
2, the literature overview, many articles that support this favorite longshot bias are discussed.
The current literature (Forrest & Mchale, 2007 and Cain et al, 2003) suggest that there will be a
favorite longshot bias in tennis matches. There is also a lot of contradicting literature that found a
reverse favorite longshot bias, but this is mainly in other kind of sports. As will be conclude from the
literature review in section 2, there is a lot of research done according to the favorite longshot bias
in different sports, but not much according to tennis. In addition, does this study have a much larger
database and more specific results than other studies (Forrest & Mchale, 2007 and Cain et al, 2003).
This study aims to answer the following research question:
‘Is there a favorite longshot bias in ATP and WTA tennis?’
To answer this question, data is collected from www.oddsportal.com. The total database contains
18.610 tennis matches, which automatically will result in 37.220 odds. This odds will be distributed
in categories and the mean return per category will be calculated. After this calculation the results
will be analyzed by a t-test.
6
The results do not show an existence of a favorite longshot bias. In addition, there is no strong
evidence for a favorite longshot bias in WTA or ATP tournaments separately. Investigating the bias
per years or surface does show a bias in ATP tournaments in 2011 and ATP tournaments on hardcourt (outdoor), but the overall conclusion is an absent of a favorite longshot bias. This is not in line
with the current literature of favorite longshot bias in the tennis sport (Forrest & Mchale, 2007 and
Cain et al, 2003).
This thesis is structured as follows. In the next section the literature will be reviewed. To have a good
overview, there are tables with summaries of the relevant literature. Thereafter the research
question and the hypothesis development are discussed. In section 4 the data and the empirical
research are explained. Then section 5 contains the results of this research. After analyzing the
results, in section 6 and 7 these results will be conclude and discussed.
7
2. Literature review
This section contains a literature overview which is divided in four parts. The first part goes back to
the early literature about the favorite longshot bias. After the history, the literature about the
favorite longshot bias in other sports is discussed. The third part contains literature of the favorite
longshot bias in tennis. As the favorite longshot bias is not found by everyone, in the last part the
contradicting literature is discussed.
To have a clear overview of the articles which provide insight for the research, the tables 1 to 4 are
used. This tables give a summary of the articles by writing the author(s), date, title, research
question, time period and outcomes of the article. In some papers there are more outcomes than
explained in the tables, but those outcomes are not directly relevant for this study.
2.1 The early evidence
This section goes back to the history of the favorite longshot bias which is mainly based on the horse
racing sport.
The very first who came up with the favorite longshot bias was Griffith (1949). He researched if
bettors at horse race tracks were able to predict the exact probabilities of a horse winning the race.
The data he used were horse race tracks in the United Kingdom in 1947. He found out that the
bettors tend to overvalue the longshot horses and they undervalue the favorite horses.
In 1956 McGlothlin did a similar research like Griffith, which was also based on the behavior during
horse racing. He looked at the behavior of bettors during race tracking, especially during the day.
The same favorite longshot bias as Griffith (1949) was found. The results of his research also show
that betting on favorites becomes more valuable during the day.
Almost 20 years later, in 1977 Ali also investigated the favorite longshot bias, but he used far more
data than Griffith (1949) and McGlothlin (1956). Ali’s dataset was based on races from 1970 till 1974
which contains 20.507 races in total. There was also another advantage comparing to Griffith (1949).
Griffith worked divided the groups based on odds, which means that there was a chance that two
competing horses were in the same group. In the research of Ali there was no possibility that two
competing horses were in the same group. The results of the investigation of Ali shows a favorite
longshot bias in every year (1970-1974).
8
A few years after in 1982 Arsch and Malkiel also did research on horse racing. The research question
they wanted to answer was: Do all horses go off at odds that reflect their true probability of winning
or is there a systematic tendency to over bet longshots and under bet favorites? And they came to
the same conclusion as their predecessors: the favorite longshot bias exists. The odds are a good
indication of how horses will finish.
Table 1: Literature summary ‘The early evidence’.
The table below summarizes the academic articles that are discussed in 2.1 The early evidence.
Author(s)
Date
Title
Research
question
Time
period
Outcomes
Ali, M.M.
1977
Probability and
utility estimates
for racetrack
bettor.
Is there a favorite
longshot bias in
horse racing?
19701974
In every racetrack in each year exists
a favorite longshot bias.
Arsch, P., &
Malkiel, B.G.
1982
Racetrack
Betting and
Informed
Behavior.
Do all horses go
off at odds that
reflect their true
probability of
winning or is
there a
systematic
tendency to
overbet longshots and
underbet
favorites?
1978
A favorite longshot bias exists. The
odds are a good indication of how
horses will finish.
Griffith, R.
1949
Odds
Adjustments by
American
Horse-Race
Bettors.
Are bettors at the
horse race tracks
in the United
Kingdom able to
predict the exact
probabilities of a
horse winning the
race?
1947
The bettors over valuated the
chances of a longshot horse to win
the race.
McGlothlin,
W.H.
1956
Stability of
Choices among
Uncertain
Alternatives.
Is there a
difference in
behavior of horse
race track bettors
during the day?
19471953
The same favorite longshot bias as
Griffith (1949) was found. The results
also show that betting on favorites
becomes more valuable during the
day.
9
2.2 Favorite longshot bias in other sports
After all the research which was done on the favorite longshot bias in horse race tracking, from the
year 2000 there came more research on the favorite longshot bias in other sports. In this section
those articles are discussed. The articles based on the tennis sport are discussed in section 2.3.
In 2000 Cain et al. did research about the favorite longshot bias in UK football. Therefore the
research question of this study was: Does the favorite longshot bias appear in UK football? The study
shows that the same favorite longshot bias is found as in horse racing. The bias appears in betting on
the results of the game (home win, away win or a draw), but also In betting on specific scores.
Shmanske (2005) did examination of the extent to which the odds predict the outcome. He studied
the golf-betting market, but did that with a small dataset. The data only contains the PGA TOUR
events for the 2002 season. There was evidence found for a positive favorite longshot bias; betting
on favorites will pay the highest return to bettors, but because of the small dataset size, the results
are doubtful.
Vlastakis, Dotsis & Markellos (2008) did an assessment of the international efficiency of the
European football betting market by examining the forecast ability of match outcomes. The data
contains the European football league games from 2002 to 2004. In the results of the study a
favorite longshot bias was found.
Three years later, Andrikogiannopoulou & Papakonstantinou (2008) also investigate football games.
They examine whether the prices set by bookmakers on large number of soccer events are efficient.
The dataset they used contains 10.000 soccer matches. Besides the match results, they also looked
at the behavior of bettors. A favorite longshot bias was found for the matches in the years from
2005 to 2009. They also found a favorite longshot bias looking at the outcomes of the soccer
matches. For example the winning of home and away games of favorites were underbetted. Looking
at the results of the behavior of bettors, they found out that only 2% of the bettors constantly bet on
the favorite, while 6% of the bettor bet on the underdog.
10
Table 2: Literature summary ‘Favorite longshot bias in other sports’.
The table below summarizes the academic articles that are discussed in 2.2 Favorite longshot bias in other
sport.
Author(s)
Date
Title
Research
question
Time
period
Outcomes
Andrikogian
nopoulou,
A., &
Papakonsta
ntinou, F.
2011
Market
Efficiency and
Behavioral
Biases in the
Sports Betting
Market.
Examine whether
the prices set by
bookmakers on
large number of
soccer events are
efficient.
20052009
A favorite longshot bias occurs in
soccer matches.
Cain, M.,
Law, D. and
Peel, D.
2000
The favouritelongshot bias
and market
efficiency in UK
football betting.
Does the favorite
longshot bias
appear in UK
football?
19911992
There appears to be a favorite
longshot bias.
Shmanske,
S.
2005
Odds-setting
efficiency in
gambling
markets:
Evidence from
the PGA Tour.
Examination of
the extent to
which the odds
predict the
outcome.
2002
A favorite longshot bias exists.
Vlastakis,
N., Dotsis,
G., &
Markellos,
R.N.
2008
How efficient is
the European
football beting
market?
Assessment of
the international
efficiency of the
European football
betting
market by
examining the
forecast ability of
match outcomes.
20022004
A favorite longshot bias exists.
2.3 Favorite longshot bias in tennis
As seen in sections 2.1 and 2.2 there is a lot of research on the favorite longshot bias in horse racing
and football. In table 3, the articles about the favorite longshot bias in tennis are summarized. This
are only two articles and the article of Cain et al. (2003) contains besides tennis also study on boxing,
cricket, horserace, snooker and tennis.
Cain et al. (2003) investigated the returns on bets in different kinds of sports, namely boxing, cricket,
horserace, snooker and tennis. In each sport they used a very small amount of data, which lead to
very poor returns. The sample, which was used to study tennis, only contains 91 matches of
Wimbledon in 1996. The data which will be used in this thesis will be over 200 times larger.
11
In 2007 there was a study from Forrest & Mchale which investigate the favorite longshot bias in
tennis tournaments with a larger dataset. In their study they used 17.000 possible odds, which
means that this study is still more than 2 times bigger with 37.220 possible odds. The paper finds an
positive bias throughout the range of odds.
Table 3: Literature summary ‘Favorite longshot bias in tennis’.
The table below summarizes the academic articles that are discussed in 2.3 Favorite longshot bias in tennis.
Author(s)
Date
Title
Research
question
Time
period
Outcomes
Cain, M.,
Law, D. and
Peel, D.
2003
The favouritelongshot bias,
bookmaker
margins and
insider trading
in a variety of
betting markets.
Does the
favouritelongshot bias
exists in a variety
of sports betting
markets? (boxing,
cricket,
horserace,
snooker and
tennis)
19891997
A favorite longshot bias was found,
though there still appears to be
some doubt about its exact nature.
Forrest, D.,
& Mchale, I.
2007
Anyone for
Tennis
(Betting)?
Is there a positive
longshot bias in
single’s men
tennis matches?
2002 2005
There is a positive longshot bias. (the
study is based on 17.000 possible
bets)
2.4 Contradicting literature
In this subsection, the contradicting literature is discussed, because not all academic articles found a
favorite longshot bias. There are investigations which found that the favorites are the ones that are
overvalued, while the underdogs are undervalued, this is called the reverse favorite longshot bias.
The results of the articles discussed in this section are in contradictory to what is found by most of
the literature in section 2.1 to 2.3.
Table 4: Literature summary ‘Contradicting literature’.
The table below summarizes the academic articles that are discussed in 2.4 Contradicting literature.
Author(s)
Date
Title
Research
question
Time
period
Outcomes
Busche, K.
and Hall, C.D.
1988
An exception to the
risk preference
anomaly
Does the favorite
longshot bias
appear in Hong
Kong horse
racing?
19811987
No favorite longshot bias was
detected.
12
Busche, K.
and Walls,
W.D.
2000
Decision costs and
betting market
efficiency
Examination of
the linkage
between
decision costs
and market
efficiency in the
context of
racetrack betting
markets.
No favorite longshot bias was
detected.
Dixon, M.J.,
& Pope, P.
2004
The value of
statistical forecasts
in the UK
association.
Evaluation of
the economic
significance of
statistical
forecasts of UK
Association
Football match
outcomes in
relation to
betting market
prices.
19931996
A reverse favorite longshot
bias; high odds for longshots
and small odds for high
probability outcomes.
Paul, R.J., &
Weinbach,
A.P.
2005
Bettor
Misperceptions in
the NBA : The
Overbetting of
Large Favorites and
the ''Hot Hand''.
Is there a
favorite longshot
bias in NBA
Basketball
games?
19952002
Systematic bettor
misperceptions and evidence of
the overbetting of favorites was
found.
Vaughan
Williams, L.
and Paton, D.
1998
Why are some
favourite-longshot
biases positive and
some negative?
Is there a
favorite longshot
bias in
horseraces in
Britain?
1992
A bias absent in the case of
wagering on ‘higher-grade
handicap’ races.
Woodland,
L.M., &
Woodland,
B.M.
1994
Market Efficiency
and the FavoriteLongshot bias: The
Baseball Betting
Market.
Does the favorite
longshot bias
appear in the
legal gambling
market for major
league baseball?
19791989
There is a reverse favorite
longshot bias in baseball.
Woodland, L.
and
Woodland, B.
2001
Market Efficiency
and Profitable
Wagering in the
National Hockey
League: Can Bettors
Score on
Longshots?
Is the favoritelongshot bias
confined to the
racetrack?
19901996
There is a reverse favorite
longshot bias in hockey. They
even found a profitable strategy
betting on the underdogs.
In the Asian racetrack market there are a few investigations who found a reverse favorite longshot
bias, namely; Busche & Hall (1988), Busche & Walls (2000). Vaughan Williams & Paton (1998) found
a reverse favorite longshot bias by investigating 5903 horses running (510 horseraces) in Britain.
13
Dixon & Pope (2004) did research in the fixed odds football betting market. In this study the odds of
the matches are fixed before the game, which means that there is no influence of betting behavior.
The results of this study show that there is a reverse favorite longshot bias in UK football from 1993
to 1996.
Paul & Weinbach (2005) looked at the NBA basketball point spread betting market. The results show
systematic bettor misperceptions. Using a strategy of betting the underdogs rejecting the null of a
fair bet, a reverse favorite longshot bias is found. Betting these home underdogs not only rejects a
fair bet, but it also shown to reject the null of no profitability. Another profitable betting strategy
according to this article is betting against winning streaks.
Actually, Woodland & Woodland (1994) were one of the first investigators who found a reverse
favorite longshot bias. They found this reverse bias in the major league baseball games from the
years 1979 to 1989. These results were not in line with the previous literature. In this study they also
tested the market efficiency. Because the results gave a reverse favorite longshot bias, which means
that betting on the underdogs will give smaller losses than betting on favorites, the market may be
inefficient.
After the study in 1994, Woodland & Woodland did a similar research in 2001, but this time they
investigate the hockey sport. In this study they tested the two same things as in 1994, namely the
existence of the favorite longshot bias and the market efficiency. Also in this research they found a
reverse favorite longshot bias. The results also show an inefficient betting market. They create a
strategy where they bet the underdog in away games in the period 1990 to 1996, which makes 11%
profit in those years. There is no doubt looking at the results; there is definitely a reverse favorite
longshot bias.
14
3. Research question & hypotheses
After reviewing the existing literature in section 2, you can conclude that there are a lot articles
about the favorite longshot bias in different kinds of sports, but there is not much according to
tennis. A larger and more recent research on the favorite longshot bias in tennis will contribute to
the existing literature.
The research question that is addressed in the thesis is:
‘Is there a favorite longshot bias in ATP and WTA tennis?’
Besides the favorite longshot bias in general, this study will look at the favorite longshot bias in other
aspects in tennis; like gender, surface and years. The following four hypotheses will be investigated.
H1: There exists a favorite longshot bias in ATP and WTA tennis.
H2: The favorite longshot bias is stronger in women tournaments.
H3a: The favorite longshot bias is becoming stronger over the years.
H3b: The favorite longshot bias is becoming stronger over the years in ATP tournaments.
H3c: The favorite longshot bias is becoming stronger over the years in WTA tournaments.
H4a: At gravel tournaments occurs a stronger favorite longshot bias than in hard-court tournaments.
H4b: At gravel tournaments occurs a stronger favorite longshot bias than in hard-court tournaments
in ATP tournaments.
H4c: At gravel tournaments occurs a stronger favorite longshot bias than in hard-court tournaments
in WTA tournaments.
The expectation of the first hypothesis is based on the outcomes Forrest & Mchale (2007). This
article is discussed in section 2.3. The outcome of this research was that there exists a favorite
longshot bias in tennis. Based on this article, the expectation is the same for this study, which means
that a favorite longshot bias in ATP and WTA tennis exists.
For the other tree hypothesis, it is hard to have an expectation, because there are no articles that
looked at the favorite longshot bias for men and women, the surface or the trend over the years
before. So the hypotheses are not based on literature, but on own experience and interest.
15
The expectation of the second hypothesis is that a favorite longshot bias exist in men and women
tournaments, but in women tournaments the bias will be stronger. This expectation is based on the
fact that the differences in level in women tennis are bigger than in men’s tennis. This means that
favorites are playing much better tennis than the underdogs and the gap between favorites and
underdogs is bigger in women tennis. The favorites in women tennis are more constant and there is
less chance to have a ‘surprising’ win of an underdog in WTA tennis.
The third hypothesis tests the trend of the favorite longshot bias over the years. The last years the
favorites (top 10 players) are getting better and better. In Appendix C to F the results of the 4 grand
slam tournaments from 1950 to 2014 are presented. For example looking at the ATP winners of
Roland Garros you see that Rafael Nadal won from 2005 till 2014, except of 2009. In the years before
there was no one who won so much Roland Garros titles in a row. This is also the case with ATP
Wimbledon – Federer / Sampras, WTA Wimbledon – Williams, WTA Roland Garros – HeninHardenne, ATP US Open Federer and WTA US Open Williams. The trend is not visible in every
category in every tournament, but if you look at the overall results, you see that in the recent years
there are more the same winners than in the earlier years. This means the favorites are getting
better and the difference in level with the underdogs are getting bigger. This is the reason why the
expectation that the favorite longshot bias is becoming stronger over the years.
The last hypothesis tests the favorite longshot bias at different kind of surfaces. Most tournaments
investigated in this study, are played on gravel (30%) and hard-court (59%). Only 11% of the
tournaments in this study are played on grass, that why this surface is excluded in the hypothesis.
The expectation is that in gravel tournaments there is a stronger bias than in hard-court
tournaments (indoor and outdoor). The expectation is also based on the historical results in
Appendix C to F. Comparing Roland Garros (gravel) with Australian Open and US Open (both hardcourt), we see more the same winners in Roland Garros. This can be an indication that favorite
players who prefer gravel are more constant at winning games, than players who have a preference
for hard-court. This means that the gap in level between gravel players is larger, than the gap
between hard-court players is smaller. The favorite longshot bias in gravel tournaments should be
stronger, because the chance of a ‘surprising’ win of an underdog is lower at this surface.
A reason for the gap in level can be that there are more player who love to play on hard-court, than
players who prefer gravel. This means there is more competition in the top favorites players on
hard-court. However, it is also possible that it is harder to become very good at playing on gravel and
16
it is easier to become a favorite on hard-court. The reason for this is not very important for the
hypothesis.
17
4. Methodology
The first subject which is discussed in this section is the dataset. Then the methodology is explained
by working out the statical research and statical tests which are used for the results of this thesis.
4.1 Data
This study will contain data of all ATP and WTA tournaments over the past 5 years (2009-2013). In
Appendix A and B an overview of all those tournaments is attached. For every tournament the
official tournament name, country, surface and number of matches is included. There are in total
18.610 matches included in this study. These are only single matches, so every match contains two
players. Those two players each got an odd, so this study contains 37.220 odds. That is a lot if you
compare this to other studies; Forrest & Mchale (2007) 8.500 matches/17.000 odds, Cain et al (2003)
91 matches/182 odds. Only the official tournament matches are included, there are no qualification
matches in this study.
The data is collected from: http://www.oddsportal.com/results/#tennis.
The data will be tested for four different subjects namely; totally, men vs women, the surface and
the trend over the years. In the table below, an overview of those categories is given.
Table 5: Data distribution per hypotheses subject
Men vs. Women
ATP
24.152
WTA
13.068
Total
37.220
Trend over the years
2009
7.328
2010
7.372
2011
7.462
2012
7.474
2013
7.584
Total
37.220
Surface
Grass
Gravel
Hard-court (i)
Hard-court (o)
Total
4.330
10.596
5.608
16.686
37.220
18
4.2 Statistical research
The research design used in this study is derived from Forrest & Mchale (2007). First, for all 37.220
players the odds are turned into winning probabilities, by using the next formula:
Winning Probability = 1/odds
For example: if Federer has a winning odd of 1,05, the win probability is 1/1.05 = 95%. This is done
for all 37.220 players who played a match in ATP and WTA tournaments over the last 5 years.
The next step is to divide all the odds in categories based on their probability. The next 20 categories
will be used:
Table 6: Probability categories
1.
0-5%
11.
50-55%
2.
5-10%
12.
55-60%
3.
10-15%
13.
60-65%
4.
15-20%
14.
65-70%
5.
20-25%
15.
70-75%
6.
25-30%
16.
75-80%
7.
30-35%
17.
80-85%
8.
35-40%
18.
85-90%
9.
40-45%
19.
90-95%
10.
45-50%
20.
95-100%
In Forrest & McHale (2007) they use probability categories of 10%, which means this study is more
specific by using probability categories of 5%.
After the distribution in categories, the mean return per category was calculated. The return will be
determined by betting 1 euro per match.
Mean return of category i: ∑ returns
Ni
Statistical tests
First calculate the standard deviation of every category. Then there will be a T-test for every
category.
T-statistic =
Mean Return
Standard Deviation / √𝑵
19
5. Results
This section will provide the results and findings of the study as described in section 4. More
specifically, section 5.1 will presents the results of all ATP and WTA tournaments in the past 5 years
(2009-2013). To see if there is a difference in favorite longshot bias between men (ATP) and women
(WTA), in section 5.2 the ATP and WTA tournaments are investigated separately. In section 5.3 the
trend over the last 5 years is studied. In the last section the results of the influence of surfaces on
the favorite longshot bias are presented.
In every section a table with the results is presented which contains the probability, the mean return
and the standard deviation for every category. In the last column the result of the t-test for every
category is calculated. The t-test is significant when it is below -2 or above 2 which means -2 < t < 2
is insignificant. In the analyzing the results, we look at the categories 1 to 7 for the underdogs and
categories 15 to 20 for the favorites. When there are many significant t-values we can conclude that
there is a favorite longshot bias.
20
5.1 Results ATP and WTA tournament (2009-2013)
Appendix A shows an overview of all ATP and WTA tournaments in the last 5 years (2009-2013). In
total 18.610 matches are played during this tournament. Every player has an odd, so this means that
there are 37.220 odds in this study. Below you find the outcomes of all the ATP and WTA
tournaments in the last 5 years (2009-2013).
Table 7: Results of all ATP and WTA tournaments in the last 5 years (2009-2013)
All ATP and WTA tournaments 2009-2013
Category
Total
Probability
1
1-5%
2
3
Number
of games
Mean return
category
Standard
deviation
T-test
122
-0,470
3,354
-1,548
5-10%
1.034
-0,483
2,502
-6,209
10-15%
1.274
-0,345
2,182
-5,647
4
15-20%
1.518
-0,168
2,036
-3,218
5
20-25%
1.980
-0,163
1,736
-4,178
6
25-30%
2.083
-0,179
1,523
-5,351
7
30-35%
2.308
-0,113
1,395
-3,883
8
35-40%
2.392
-0,070
1,274
-2,684
9
40-45%
2.443
-0,085
1,149
-3,670
10
45-50%
2.300
-0,040
1,055
-1,838
11
50-55%
1.791
-0,064
0,954
-2,826
12
55-60%
2.205
-0,079
0,865
-4,288
13
60-65%
2.606
-0,035
0,782
-2,273
14
65-70%
2.386
-0,056
0,710
-3,829
15
70-75%
2.324
-0,036
0,633
-2,760
16
75-80%
2.087
-0,015
0,553
-1,255
17
80-85%
2.063
-0,021
0,480
-1,970
18
85-90%
1.482
-0,023
0,404
-2,191
19
90-95%
1.561
-0,029
0,334
-3,481
20
95-100%
1.261
-0,013
0,203
-2,186
37.220
-2,487
24,124
ATP and WTA tournaments are played at the highest level of professional tennis. The past five years
18.610 matches were played. Those matches were divided in probability categories. Probability
category 1 contains the biggest ‘underdogs’ . The betting market gives those players 1 – 5% chance
to win the game. The other way around, category 20 (chance: 95-100%) are the most favorite
players. In the fifth column ‘Mean return category’, the mean return when betting 1 euro on all the
21
players in the category is given. In every category this contains a negative value, this means that in
every category you lose money.
What stands out in table 1 is the pattern of the mean return. Lower probability categories contains a
more negative return, and higher probability categories a lower negative return. For every betted
euro in category 1, the bettor receives €0,53 back. Betting one euro in category 20 will one average
give €0,987 back. To make it more clear the graph below is added.
Graph 1: Development of the mean return of all ATP and WTA tournaments in the last 5 years (2009-2013)
ATP and WTA tournaments (2009-2013)
0.000
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
-0.100
-0.200
-0.300
Mean return
-0.400
-0.500
-0.600
The mean return line gets more to the 0-point on the X-as while the category becomes higher.
As said before, every category had a negative return, which means that there is no chance to make a
profit on betting on the tennis tournaments. Even though, betting on favorite players will generate
the least negative return and is the best strategy possible.
Looking at the last column we see a lot of t-values below -2 of above 2 which means a lot of
significant results. In category 1 to 7 there are 6 significant values, which is an indication for a
favorite longshot bias. However, in the categories 15 to 20 we see also 5 significant values. Based on
this you cannot really speak of a bias.
22
5.2 Results gender
Table 8: Results of all ATP and WTA tournaments separately in the last 5 years (2009-2013)
ATP matches (Men)
Category
Total
Probability
Number
of games
Mean
return
category
Standard
deviation
WTA matches (Women)
T-test
Number
of games
Mean
return
category
Standard
deviation
T-test
1
1-5%
105
-0,384
3,610
-1,091
17
-1,000
0,000
0,000
2
5-10%
692
-0,391
2,686
-3,832
342
-0,669
2,071
-5,971
3
10-15%
812
-0,393
2,113
-5,299
462
-0,261
2,298
-2,445
4
15-20%
951
-0,213
1,987
-3,307
567
-0,093
2,114
-1,045
5
20-25%
1.219
-0,186
1,720
-3,783
761
-0,126
1,763
-1,966
6
25-30%
1.306
-0,238
1,482
-5,806
777
-0,078
1,585
-1,380
7
30-35%
1.509
-0,130
1,388
-3,629
799
-0,081
1,410
-1,623
8
35-40%
1.601
-0,068
1,276
-2,141
791
-0,073
1,272
-1,621
9
40-45%
1.614
-0,073
1,151
-2,532
829
-0,110
1,144
-2,771
10
45-50%
1.522
-0,023
1,056
-0,835
778
-0,075
1,051
-1,998
11
50-55%
1.146
-0,052
0,956
-1,842
645
-0,084
0,950
-2,257
12
55-60%
1.440
-0,097
0,866
-4,231
765
-0,046
0,863
-1,473
13
60-65%
1.747
-0,049
0,785
-2,584
859
-0,007
0,776
-0,261
14
65-70%
1.553
-0,061
0,711
-3,366
833
-0,046
0,707
-1,881
15
70-75%
1.553
-0,023
0,628
-1,435
771
-0,063
0,644
-2,727
16
75-80%
1.323
0,000
0,543
-0,004
764
-0,041
0,568
-2,014
17
80-85%
1.270
-0,012
0,474
-0,929
793
-0,034
0,490
-1,976
18
85-90%
938
-0,017
0,398
-1,336
544
-0,033
0,414
-1,842
19
90-95%
982
-0,023
0,326
-2,249
579
-0,040
0,348
-2,746
20
95-100%
869
-0,018
0,213
-2,536
392
0,000
0,178
0,048
24.152
-2,451
24,369
13.068
-2,960
20,646
23
Graph 2: Development of the mean return of ATP and WTA tournaments separately in the last 5 years (20092013)
WTA Tournaments (2009-2013) - ATP/WTA
0.000
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
-0.200
-0.400
ATP (men)
-0.600
WTA (women)
-0.800
-1.000
-1.200
Graph 2 shows the line of the mean return for ATP tournaments (men) and WTA tournaments
(women) separately. The higher the probability category, the closer the line gets to the x-as, so it is
clear that there is a favorite longshot bias in both genders.
The line of the WTA (women) gets faster to the x-as than the ATP (men). For the WTA tournaments
from category 4 the mean return is higher than -0,2 and fluctuate between -0,2 and 0,00 in
categories 4 to 20. The line of the mean return in ATP tournaments shows a more stable upward
curve. The higher the category, the higher the return. Only at category 12 the mean return bounces
a bit back.
After all, looking at category 1 (longshot), we see that the WTA tournaments have a lower return
than the ATP tournaments. Looking at category 20 (favorites) we see that in WTA tournaments you
have no profit or loss (return is €0) and in ATP tournament you have a loss of €0,018.
Looking at the last column we see a lot of t-values below -2 of above 2 which means a lot of
significant results. Looking at the ATP tennis, in categories 1-7 there are 6 significant t-values and in
category 15-20 there are 2 significant t-values. In WTA tennis, in categories 1-7 there are 2
significant t-values and in category 15-20 there are 3 significant t-values. The significant results in
the underdogs categories are an indication for the existence of a favorite longshot bias. In WTA
24
tennis there are only 2 significant t-values in underdog categories. Based on the lack of significant
results, we can doubt about the existence of a favorite longshot bias. In the underdog categories of
ATP tournaments there are 6 out of 7 significant t-values, but also in the favorite categories there
are a lot of significant t-values. Based on this you cannot really speak of the existence of a bias.
25
5.3 Results over the years
5.3.1 Results over the years - ATP and WTA tournaments
After looking at the difference between men and women in the previous section, this section will show results over the last 5 years separately.
Table 9: Results of all ATP and WTA tournaments sorted by year (2009-2013)
2009
Category
Total
Probability
Number
of
games
2010
Mean
return
category
Standard
deviation
T-test
Number
of
games
2011
Mean
return
category
Standard
deviation
T-test
Number
of
games
Mean
return
category
Standard
deviation
T-test
1
1-5%
11
-1,000
0,000
0,000
5
-1,000
0,000
0,000
24
-1,000
0,000
0,000
2
5-10%
191
-0,315
2,850
-1,525
166
-0,779
1,642
-6,112
187
-0,627
2,066
-4,147
3
10-15%
282
-0,276
2,193
-2,110
242
-0,225
2,364
-1,481
264
-0,387
2,162
-2,905
4
15-20%
319
-0,052
2,137
-0,432
277
-0,248
1,958
-2,109
306
-0,042
2,154
-0,345
5
20-25%
392
-0,183
1,728
-2,099
421
-0,107
1,781
-1,236
387
-0,187
1,722
-2,132
6
25-30%
412
-0,231
1,490
-3,153
442
-0,147
1,542
-2,008
434
-0,150
1,547
-2,022
7
30-35%
389
-0,057
1,425
-0,785
468
-0,168
1,367
-2,653
495
-0,199
1,352
-3,274
8
35-40%
444
-0,124
1,254
-2,090
469
-0,112
1,261
-1,923
504
-0,051
1,281
-0,894
9
40-45%
472
-0,058
1,155
-1,087
483
-0,065
1,154
-1,230
480
-0,098
1,146
-1,880
10
45-50%
490
-0,015
1,058
-0,320
449
-0,097
1,046
-1,970
446
-0,059
1,055
-1,187
11
50-55%
385
-0,049
0,955
-1,014
399
-0,084
0,954
-1,751
325
-0,107
0,949
-2,038
12
55-60%
474
-0,130
0,867
-3,270
427
-0,037
0,864
-0,889
422
-0,014
0,860
-0,345
13
60-65%
530
-0,047
0,786
-1,378
529
-0,037
0,783
-1,076
486
-0,041
0,783
-1,151
14
65-70%
441
-0,042
0,706
-1,259
456
-0,042
0,706
-1,274
515
-0,070
0,715
-2,211
15
70-75%
408
-0,033
0,633
-1,043
475
-0,028
0,630
-0,961
489
-0,004
0,619
-0,159
16
75-80%
401
-0,003
0,545
-0,126
438
-0,016
0,554
-0,590
447
-0,003
0,546
-0,123
17
80-85%
424
-0,007
0,469
-0,290
415
-0,040
0,495
-1,662
398
-0,027
0,485
-1,123
18
85-90%
296
-0,066
0,442
-2,567
309
-0,011
0,393
-0,486
302
-0,024
0,404
-1,036
19
90-95%
352
-0,044
0,353
-2,359
293
-0,044
0,353
-2,134
314
-0,039
0,347
-2,016
20
95-100%
215
-0,016
0,218
-1,062
209
-0,004
0,186
-0,342
237
0,002
0,162
0,176
7.328
-2,748
21,264
7.372
-3,291
20,032
7.462
-3,129
20,357
26
2012
Category
Total
Probability
Number
of
games
2013
Mean
return
category
Standard
deviation
T-test
Number
of
games
Mean
return
category
Standard
deviation
T-test
1
1-5%
43
-0,485
3,380
-0,942
39
0,090
4,754
0,118
2
5-10%
264
-0,448
2,580
-2,823
226
-0,330
2,911
-1,706
3
10-15%
256
-0,387
2,130
-2,914
230
-0,463
2,057
-3,410
4
15-20%
304
-0,314
1,880
-2,915
312
-0,197
2,021
-1,721
5
20-25%
393
-0,037
1,830
-0,405
387
-0,307
1,608
-3,759
6
25-30%
395
-0,234
1,480
-3,152
400
-0,134
1,556
-1,725
7
30-35%
478
0,010
1,450
0,158
478
-0,139
1,383
-2,193
8
35-40%
480
-0,099
1,260
-1,722
495
0,028
1,305
0,478
9
40-45%
491
-0,184
1,120
-3,636
517
-0,024
1,164
-0,462
10
45-50%
415
-0,050
1,060
-0,955
500
0,010
1,058
0,220
11
50-55%
342
0,000
0,960
0,004
340
-0,079
0,956
-1,527
12
55-60%
402
-0,101
0,870
-2,336
480
-0,104
0,868
-2,628
13
60-65%
517
0,016
0,770
0,484
544
-0,064
0,790
-1,902
14
65-70%
491
-0,014
0,700
-0,447
483
-0,108
0,723
-3,277
15
70-75%
465
-0,099
0,660
-3,258
487
-0,019
0,627
-0,681
16
75-80%
404
-0,029
0,560
-1,055
397
-0,026
0,559
-0,910
17
80-85%
417
-0,038
0,490
-1,580
409
0,008
0,455
0,375
18
85-90%
274
-0,003
0,380
-0,131
301
-0,010
0,394
-0,452
19
90-95%
323
-0,009
0,310
-0,534
279
-0,008
0,305
-0,417
20
95-100%
320
-0,013
0,200
-1,168
280
-0,027
0,232
-1,966
7.474
-2,518
24,070
7.584
-1,902
25,727
27
In the tables above, the pattern of the less negative return in the higher categories and the higher
negative return in the lower categories still emerges.
Graph 3: Development of the mean return of ATP and WTA tournaments in the last 5 years (2009-2013)
0.200
0.000
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
-0.200
2009
-0.400
2010
2011
-0.600
2012
2013
-0.800
-1.000
-1.200
Graph 3 shows the line of the mean returns per year. It is hard to see which favorite longshot bias is
the strongest, but in every year there the line goes upwards.
In category 1 in 2013 there is a positive return of €0,090. In this category there are 39 matches and
one match is won by an underdog which gives a high return and therefore the mean return is
positive. Also category 8, 10 and 17 of 2013 matches will give you a positive return.
The favorite longshot bias is based on underdogs and favorites, which means we have to look at
category 1 (underdogs) and category 20 (favorites). In table 10 a quick overview of the returns is
added. In every year, except of 2013, the return in category 20 is higher than in category 1. Based on
these facts, you might be able to conclude that, a favorite longshot bias exists in every year, except
of 2013.
28
Table 10: Mean return in category 1-7 and 15-20 over the years
Year
Mean return category 1-7
Mean return category 15-20
2009
-0,178
-0,027
2010
-0,221
-0,025
2011
-0,235
-0,015
2012
-0,204
-0,231
2013
-0,037
-0,014
Looking at table 10, we see that for every year the underdog categories generate a lower mean
return than the favorite categories, except of 2012. Based on those numbers, you might be able to
conclude that, a favorite longshot bias exists in every year, except of 2012.
It is hard to look if the trend is becoming stronger over the years. If you look at the categories 1-7
the return gets lower till 2011 and from there the return gets higher. In the favorite categories the
return till 2011 becomes higher, but in 2012 there is a very low result of -0,231. The results are not
showing a clear trend over the years.
If we compare the t-values in the years with the t-values of section 5.1 and 5.2, we see a lot more
insignificant results. Because of those insignificant t-values (-2 < t < 2) we can doubt about the
existence of a favorite longshot bias. It is interesting to test the ATP and WTA tournaments
separately, because this might lead better t-values. With better t-values the doubt about the
existence of a favorite longshot bias could disappear. In 5.3.2 we test the data over the years for ATP
and WTA tournaments separately.
29
5.3.2 Results over the years – ATP and WTA tournaments separately
This section starts with the results of the ATP tournaments in table 11 and the WTA tournament in table 12. After that we discuss those results.
Table 11: Results of all ATP tournaments sorted by year (2009-2013)
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of games categorie deviation
11
135
182
197
235
256
259
295
309
323
243
300
364
285
266
262
249
184
228
149
4.732
-1,000
-0,291
-0,360
-0,258
-0,180
-0,362
-0,006
-0,125
-0,004
0,002
-0,042
-0,141
-0,086
-0,052
-0,024
0,017
0,004
-0,057
-0,011
-0,018
0,000
2,916
2,078
1,913
1,741
1,386
1,452
1,253
1,164
1,058
0,957
0,867
0,793
0,709
0,630
0,532
0,460
0,434
0,308
0,219
T-test
Category
Probability
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
0,000
-1,158
-2,335
-1,895
-1,586
-4,181
-0,068
-1,717
-0,055
0,026
-0,689
-2,807
-2,059
-1,240
-0,631
0,517
0,135
-1,785
-0,557
-1,001
Total
Number
Mean
of
return Standard
games categorie deviation
3
119
141
162
238
273
305
308
323
285
248
264
354
293
320
271
236
185
171
145
-1,000
-0,691
-0,382
-0,094
-0,137
-0,137
-0,223
-0,140
-0,054
-0,066
-0,068
-0,060
-0,057
-0,032
0,004
-0,025
-0,027
-0,010
-0,061
0,000
0,000
1,934
2,152
2,139
1,770
1,549
1,341
1,254
1,155
1,052
0,957
0,867
0,787
0,703
0,615
0,560
0,487
0,393
0,372
0,170
T-test
0,000
-3,899
-2,106
-0,559
-1,198
-1,460
-2,898
-1,953
-0,847
-1,060
-1,125
-1,130
-1,360
-0,790
0,108
-0,729
-0,838
-0,339
-2,135
0,005
4.644
30
2011
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of games categorie deviation
24
126
165
194
249
273
322
344
320
305
200
290
320
349
329
282
259
190
194
169
4.904
-1,000
-0,708
-0,358
-0,032
-0,268
-0,266
-0,238
-0,060
-0,067
-0,069
-0,095
-0,038
-0,057
-0,064
0,010
0,033
0,008
-0,032
-0,043
0,008
0,000
1,886
2,222
2,153
1,655
1,467
1,330
1,279
1,153
1,054
0,955
0,863
0,787
0,714
0,612
0,521
0,457
0,412
0,352
0,137
2012
T-test
0,000
-4,215
-2,070
-0,205
-2,559
-2,993
-3,207
-0,870
-1,034
-1,140
-1,399
-0,750
-1,284
-1,676
0,299
1,074
0,265
-1,072
-1,683
0,743
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of games categorie deviation
41
161
165
201
243
254
314
308
330
276
223
270
341
312
305
262
263
180
205
214
-0,460
-0,165
-0,486
-0,452
-0,060
-0,221
-0,063
-0,055
-0,184
-0,024
0,001
-0,098
0,015
-0,045
-0,069
-0,037
-0,034
0,015
0,005
-0,031
3,458
3,150
1,945
1,704
1,809
1,488
1,417
1,281
1,126
1,060
0,956
0,865
0,769
0,706
0,647
0,566
0,492
0,360
0,284
0,237
T-test
0,000
-0,665
-3,210
-3,763
-0,519
-2,364
-0,782
-0,753
-2,973
-0,372
0,023
-1,852
0,368
-1,123
-1,866
-1,060
-1,124
0,575
0,263
-1,884
4.868
31
2013
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
26
151
159
197
254
250
309
346
332
333
232
316
368
314
333
246
263
199
184
192
0,635
-0,222
-0,381
-0,200
-0,278
-0,209
-0,097
0,024
-0,049
0,034
-0,059
-0,138
-0,056
-0,107
-0,037
0,010
-0,013
-0,003
-0,015
-0,042
5,781
2,983
2,193
2,021
1,629
1,513
1,402
1,307
1,159
1,059
0,960
0,869
0,789
0,723
0,636
0,537
0,474
0,388
0,316
0,259
T-test
0,000
-0,913
-2,190
-1,390
-2,721
-2,182
-1,218
0,337
-0,772
0,594
-0,944
-2,824
-1,364
-2,622
-1,071
0,298
-0,440
-0,121
-0,654
-2,244
5.004
32
Table 12: Results of all WTA tournaments sorted by year (2009-2013)
2009
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mean
Proba- Number
return
Standard
bility
of games categorie deviation
1-5%
0
0,000
0,000
5-10%
56
-0,372
2,709
10-15%
100
-0,123
2,392
15-20%
122
0,282
2,428
20-25%
157
-0,188
1,715
25-30%
156
-0,017
1,628
30-35%
130
-0,157
1,368
35-40%
149
-0,123
1,259
40-45%
163
-0,161
1,134
45-50%
167
-0,048
1,058
50-55%
142
-0,061
0,956
55-60%
174
-0,113
0,870
60-65%
166
0,038
0,763
65-70%
156
-0,024
0,703
70-75%
142
-0,048
0,640
75-80%
139
-0,042
0,569
80-85%
175
-0,022
0,482
85-90%
112
-0,081
0,457
90-95%
124
-0,105
0,418
95-100%
66
-0,011
0,218
2.596
2010
T-test
0,000
-1,027
-0,513
1,283
-1,372
-0,129
-1,312
-1,188
-1,807
-0,584
-0,766
-1,708
0,636
-0,435
-0,899
-0,868
-0,593
-1,866
-2,799
-0,407
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mean
Proba- Number
return
Standard
bility
of games categorie deviation
1-5%
2
-1,000
0,000
5-10%
47
-1,000
0,000
10-15%
101
-0,006
2,628
15-20%
115
-0,466
1,656
20-25%
183
-0,068
1,800
25-30%
169
-0,164
1,534
30-35%
163
-0,065
1,412
35-40%
161
-0,059
1,276
40-45%
160
-0,085
1,155
45-50%
164
-0,152
1,038
50-55%
151
-0,109
0,950
55-60%
163
0,000
0,860
60-65%
175
0,004
0,775
65-70%
163
-0,059
0,711
70-75%
155
-0,093
0,656
75-80%
167
-0,001
0,544
80-85%
179
-0,059
0,507
85-90%
124
-0,013
0,396
90-95%
122
-0,021
0,325
95-100%
64
-0,015
0,221
2.728
T-test
0,000
0,000
-0,024
-3,015
-0,512
-1,389
-0,585
-0,589
-0,932
-1,870
-1,405
0,004
0,074
-1,067
-1,760
-0,017
-1,549
-0,352
-0,701
-0,527
33
2011
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mean
Proba- Number
return
Standard
bility
of Games categorie deviation
1-5%
0
0,000
0,000
5-10%
61
-0,458
2,404
10-15%
99
-0,434
2,070
15-20%
112
-0,061
2,165
20-25%
138
-0,039
1,833
25-30%
161
0,046
1,662
30-35%
173
-0,127
1,395
35-40%
160
-0,032
1,289
40-45%
160
-0,162
1,132
45-50%
141
-0,039
1,059
50-55%
125
-0,128
0,942
55-60%
132
0,037
0,853
60-65%
166
-0,011
0,776
65-70%
166
-0,082
0,721
70-75%
160
-0,034
0,634
75-80%
165
-0,066
0,583
80-85%
139
-0,092
0,529
85-90%
112
-0,011
0,391
90-95%
120
-0,034
0,338
95-100%
68
-0,013
0,214
2558
2012
T-test
0,000
-1,488
-2,088
-0,299
-0,249
0,349
-1,199
-0,311
-1,807
-0,433
-1,516
0,502
-0,179
-1,458
-0,684
-1,445
-2,056
-0,285
-1,111
-0,499
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
2
-1,000
0,000
103
-0,890
1,115
91
-0,209
2,425
103
-0,045
2,168
150
0,000
1,857
141
-0,259
1,463
164
0,150
1,501
172
-0,179
1,235
161
-0,184
1,121
139
-0,101
1,052
119
-0,002
0,962
132
-0,108
0,870
176
0,018
0,773
179
0,040
0,677
160
-0,157
0,673
142
-0,015
0,555
154
-0,045
0,501
94
-0,038
0,422
118
-0,034
0,342
106
0,022
0,101
2606
T-test
0,000
-8,099
-0,821
-0,211
0,000
-2,101
1,282
-1,901
-2,086
-1,131
-0,025
-1,422
0,316
0,786
-2,941
-0,333
-1,125
-0,883
-1,080
2,192
34
2013
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mean
Proba- Number
return
Standard
bility
of Games categorie deviation
1-5%
13
-1,000
0,000
5-10%
75
-0,549
2,765
10-15%
71
-0,646
1,716
15-20%
115
-0,191
2,031
20-25%
133
-0,363
1,571
25-30%
150
-0,010
1,622
30-35%
169
-0,215
1,350
35-40%
149
0,038
1,306
40-45%
185
0,022
1,175
45-50%
167
-0,038
1,057
50-55%
108
-0,121
0,951
55-60%
164
-0,039
0,864
60-65%
176
-0,082
0,794
65-70%
169
-0,109
0,725
70-75%
154
0,020
0,606
75-80%
151
-0,084
0,590
80-85%
146
0,047
0,419
85-90%
102
-0,024
0,408
90-95%
95
0,007
0,286
95-100%
88
0,005
0,155
2.580
T-test
0,000
-1,720
-3,172
-1,010
-2,662
-0,075
-2,068
0,358
0,253
-0,459
-1,327
-0,573
-1,367
-1,960
0,401
-1,744
1,349
-0,590
0,240
0,290
35
In tables 13 and 14 below the mean return in the underdog categories (1-7) and in the favorite
categories (15-20) are given. In every year you see that the return on favorites is higher than on
underdogs, which can be an indication for a favorite longshot bias.
Table 13: Mean return in category 1-7 and 15-20 over the years at ATP tournaments
Year
Mean return category 1-7
Mean return category 15-20
2009
-0,238
-0,012
2010
-0,236
-0,018
2011
-0,292
0,001
2012
-0,223
-0,030
2013
-0,200
-0,017
Table 14: Mean return in category 1-7 and 15-20 over the years at WTA tournaments
Year
Mean return category 1-7
Mean return category 15-20
2009
-0,071
-0,052
2010
-0,197
-0,037
2011
-0,131
-0,046
2012
-0,171
-0,051
2013
-0,287
-0,006
As said in section 5.3.1 we wanted to test the results over the years for ATP and WTA tournaments
separately, with the goal of getting more t-values that are significant. Looking at the t-values in table
11 and 12, we see that they are actually becoming more insignificant.
When testing the ATP and WTA tournaments separately, the results becoming more insignificant.
When we put all the data together, the results are looking fine and significant, but when we split
them apart, the results show a whole other point of view. This is not in line with the literature of
Forrest & Mchale, 2007 and Cain et al, 2003.
Only in 2011 at ATP tournaments, we see significant t-values. Also, table 13 shows a higher return at
favorites than underdogs in 2011 ATP tournaments. Based on those results we can say that there is a
favorite longshot bias in 2011 ATP tournaments.
36
5.4 Results surface
5.4.1 Results surface - ATP and WTA tournaments
Table 15: Results of all ATP and WTA tournaments sorted by surface
Grass
Category
Total
Probability
Gravel
Number
of
games
Mean
return
category
Standard
deviation
T-test
Number
of
games
Mean
return
category
Standard
deviation
T-test
1
1-5%
25
1,586
7,153
1,109
47
-1,000
0,000
0,000
2
5-10%
142
-0,444
2,716
-1,950
265
-0,506
2,560
-3,214
3
10-15%
169
-0,359
2,157
-2,165
382
-0,469
1,980
-4,627
4
15-20%
218
-0,157
2,046
-1,135
392
-0,058
2,120
-0,541
5
20-25%
218
-0,057
1,834
-0,456
595
-0,196
1,710
-2,783
6
25-30%
242
-0,057
1,595
-0,558
547
-0,184
1,520
-2,842
7
30-35%
266
-0,180
1,364
-2,151
667
-0,110
1,400
-2,036
8
35-40%
251
0,045
1,309
0,540
758
-0,069
1,280
-1,495
9
40-45%
261
-0,141
1,138
-2,008
683
-0,037
1,160
-0,832
10
45-50%
257
-0,038
1,055
-0,582
680
0,004
1,060
0,103
11
50-55%
182
-0,071
0,953
-1,001
429
-0,089
0,950
-1,932
12
55-60%
239
-0,073
0,866
-1,306
627
-0,106
0,870
-3,061
13
60-65%
275
0,008
0,776
0,169
770
-0,048
0,780
-1,704
14
65-70%
258
-0,102
0,722
-2,263
703
-0,071
0,710
-2,657
15
70-75%
270
-0,010
0,621
-0,274
695
-0,039
0,640
-1,606
16
75-80%
238
-0,081
0,589
-2,132
573
-0,013
0,550
-0,577
17
80-85%
212
-0,025
0,486
-0,756
580
-0,019
0,480
-0,976
18
85-90%
204
-0,053
0,432
-1,739
412
-0,039
0,420
-1,866
19
90-95%
221
-0,021
0,327
-0,972
436
-0,012
0,310
-0,830
20
95-100%
182
-0,029
0,235
-1,651
355
-0,006
0,190
-0,620
4.330
-0,261
28,375
10.596
-3,067
20,690
37
Hard-court (i)
Category
Total
Probability
Hard-court (o)
Number
of
games
Mean
return
category
Standard
deviation
T-test
Number
of
games
Mean
return
category
Standard
deviation
T-test
1
1-5%
1
-1,000
0,000
0,000
49
-1,000
0,000
0,000
2
5-10%
76
-0,214
2,998
-0,623
551
-0,519
2,338
-5,208
3
10-15%
132
-0,030
2,645
-0,132
591
-0,331
2,196
-3,667
4
15-20%
222
-0,331
1,847
-2,674
686
-0,182
2,039
-2,333
5
20-25%
304
-0,080
1,805
-0,777
863
-0,197
1,702
-3,392
6
25-30%
358
-0,200
1,508
-2,509
936
-0,198
1,513
-4,008
7
30-35%
366
-0,082
1,413
-1,113
1.009
-0,108
1,397
-2,453
8
35-40%
398
-0,060
1,279
-0,932
985
-0,104
1,262
-2,581
9
40-45%
384
-0,062
1,156
-1,047
1.115
-0,110
1,144
-3,209
10
45-50%
349
0,065
1,058
1,141
1.014
-0,107
1,048
-3,251
11
50-55%
343
-0,050
0,955
-0,974
837
-0,055
0,955
-1,658
12
55-60%
345
-0,160
0,868
-3,432
994
-0,035
0,861
-1,284
13
60-65%
401
-0,051
0,786
-1,310
1.160
-0,030
0,781
-1,323
14
65-70%
389
-0,077
0,717
-2,122
1.036
-0,025
0,702
-1,163
15
70-75%
371
-0,034
0,633
-1,025
988
-0,043
0,636
-2,104
16
75-80%
360
-0,011
0,551
-0,384
916
-0,001
0,544
-0,042
17
80-85%
329
-0,047
0,501
-1,710
942
-0,011
0,473
-0,746
18
85-90%
217
-0,009
0,390
-0,341
649
-0,008
0,388
-0,551
19
90-95%
175
-0,042
0,355
-1,582
729
-0,039
0,345
-3,051
20
95-100%
88
-0,024
0,241
-0,950
636
-0,010
0,197
-1,252
5.608
-2,503
21,707
16.686
-3,113
20,521
38
Graph 4: Development of the mean return of ATP and WTA tournaments per surface
ATP and WTA Tournaments (2009-2013) Surface
2.000
1.500
1.000
Grass
0.500
Gravel
Hard-court (i)
Hard-court (o)
0.000
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
-0.500
-1.000
-1.500
39
Table 16: Mean return in category 1-7 and 15-20 per surface
Year
Mean return
Mean return
category 1-7
category 15-20
Grass
-0,150
-0,036
Gravel
-0,233
-0,023
Hard-court (i)
-0,151
-0,028
Hard-court (o)
-0,239
-0,019
As said before, the favorite longshot bias is based on underdogs and favorites, so categories 1-7
(underdogs) and category 15-20 (favorites) are the most important. In table 12 a quick overview of
the returns per surface is added. Looking at table 16 we see at every surface a lower return in the
underdogs categories compared to the favorites, which can be a indication for the existence of a
favorite longshot bias.
If we compare the t-values in the years with the t-values of section 5.1 and 5.2, we see a lot more
insignificant results. Especially the results of gravel and hard-court (i) are insignificant. Because of
those insignificant t-values (-2 < t < 2) we can doubt about the existence of a favorite longshot bias
at those surfaces. It is interesting to test the ATP and WTA tournaments separately, because this
might lead better t-values. With better t-values the doubt about the existence of a favorite longshot
bias could disappear. In 5.4.2 we test the data per surface for ATP and WTA tournaments separately.
40
5.4.2 Results surface - ATP and WTA tournaments separately
This section starts with the results of the ATP tournaments in table 17 and the WTA tournament in table 18. After that, we discuss those results.
Table 17: Results of all ATP tournaments sorted by surface
Grass
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Number
of Games
20
94
116
136
129
145
184
165
178
169
126
155
186
168
189
145
124
129
148
124
2.830
Mean
return
Standard
categorie deviation
2,233
7,902
-0,488
2,449
-0,465
1,995
-0,153
2,057
-0,061
1,838
-0,119
1,570
-0,246
1,330
-0,009
1,300
-0,205
1,119
0,012
1,059
-0,080
0,954
-0,098
0,865
0,033
0,769
-0,076
0,718
0,028
0,602
-0,046
0,571
-0,030
0,490
-0,060
0,440
-0,010
0,309
-0,040
0,254
Gravel
T-test
1,264
-1,933
-2,511
-0,866
-0,377
-0,914
-2,514
-0,087
-2,449
0,152
-0,939
-1,411
0,586
-1,377
0,643
-0,961
-0,693
-1,556
-0,386
-1,746
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
42
-1,000
0,000
179
-0,391
2,899
250
-0,469
1,985
256
-0,114
2,072
377
-0,159
1,752
370
-0,283
1,450
480
-0,107
1,402
529
-0,079
1,274
482
-0,088
1,148
493
-0,007
1,055
302
-0,078
0,956
448
-0,116
0,870
553
-0,023
0,780
489
-0,039
0,703
496
-0,049
0,639
396
0,010
0,537
362
-0,017
0,478
277
-0,037
0,419
286
-0,014
0,313
249
-0,006
0,182
7316
T-test
0,000
-1,806
-3,740
-0,879
-1,765
-3,759
-1,669
-1,427
-1,685
-0,143
-1,411
-2,828
-0,708
-1,218
-1,709
0,371
-0,696
-1,480
-0,758
-0,494
41
Hardcourt
(i)
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Number
of Games
1
70
118
198
272
311
316
344
335
297
291
299
350
331
324
312
294
194
153
82
4.892
Mean
return
Standard
categorie deviation
-1,000
0,000
-0,147
3,117
-0,182
2,464
-0,306
1,882
-0,119
1,778
-0,244
1,476
-0,085
1,411
-0,053
1,281
-0,030
1,162
0,095
1,058
-0,057
0,955
-0,164
0,869
-0,073
0,790
-0,094
0,721
-0,029
0,631
-0,005
0,546
-0,029
0,488
-0,010
0,391
-0,033
0,343
-0,029
0,249
Hardcourt
(o)
T-test
0,000
-0,394
-0,802
-2,287
-1,100
-2,915
-1,066
-0,760
-0,465
1,546
-1,013
-3,266
-1,731
-2,378
-0,841
-0,147
-1,031
-0,347
-1,186
-1,050
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
42
-1,000
0,000
349
-0,414
2,546
328
-0,385
2,117
361
-0,255
1,960
441
-0,288
1,617
480
-0,235
1,485
529
-0,137
1,382
563
-0,085
1,269
619
-0,046
1,158
563
-0,109
1,051
427
-0,022
0,959
538
-0,042
0,861
658
-0,080
0,791
565
-0,056
0,711
544
-0,013
0,624
470
0,009
0,539
490
0,006
0,459
338
0,011
0,366
395
-0,032
0,335
414
-0,017
0,210
9.114
T-test
0,000
-3,039
-3,294
-2,475
-3,740
-3,470
-2,275
-1,593
-0,980
-2,460
-0,484
-1,137
-2,582
-1,856
-0,476
0,343
0,299
0,550
-1,872
-1,691
42
Table 18: Results of all WTA tournaments sorted by surface
Grass
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
5
-1,000
0,000
48
-0,359
3,202
53
-0,127
2,480
82
-0,165
2,041
89
-0,050
1,839
97
0,035
1,636
82
-0,030
1,434
86
0,147
1,329
83
-0,004
1,174
88
-0,136
1,046
56
-0,050
0,959
84
-0,027
0,869
89
-0,045
0,792
90
-0,149
0,732
81
-0,100
0,658
93
-0,137
0,614
88
-0,018
0,484
75
-0,040
0,422
73
-0,045
0,361
58
-0,005
0,190
1.500
Gravel
T-test
0,000
-0,776
-0,374
-0,732
-0,258
0,212
-0,193
1,026
-0,035
-1,217
-0,391
-0,285
-0,531
-1,935
-1,370
-2,154
-0,346
-0,812
-1,060
-0,214
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
5
-1,000
0,000
86
-0,746
1,658
132
-0,469
1,986
136
0,047
2,223
218
-0,258
1,648
177
0,022
1,636
187
-0,119
1,388
229
-0,047
1,281
201
0,086
1,175
187
0,033
1,065
127
-0,116
0,953
179
-0,081
0,867
217
-0,111
0,794
214
-0,146
0,730
199
-0,013
0,627
177
-0,065
0,580
218
-0,022
0,479
135
-0,041
0,425
150
-0,009
0,307
106
-0,007
0,198
3.280
T-test
0,000
-4,171
-2,715
0,246
-2,315
0,181
-1,171
-0,551
1,038
0,424
-1,374
-1,250
-2,061
-2,928
-0,292
-1,499
-0,693
-1,135
-0,365
-0,373
43
Hardcourt (i)
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Hardcourt (o)
Number
Mean
of
return
Standard
Games categorie deviation
0
0,000
0,000
6
-1,000
0,000
14
1,247
3,726
24
-0,543
1,551
32
0,243
2,024
47
0,090
1,696
50
-0,067
1,440
54
-0,106
1,278
49
-0,282
1,093
52
-0,108
1,052
52
-0,014
0,959
46
-0,137
0,873
51
0,097
0,750
58
0,020
0,691
47
-0,063
0,649
48
-0,054
0,583
35
-0,198
0,588
23
-0,003
0,395
22
-0,109
0,430
6
0,037
0,008
716
T-test
0,000
0,000
1,253
-1,715
0,680
0,366
-0,331
-0,609
-1,804
-0,742
-0,103
-1,060
0,926
0,224
-0,661
-0,641
-1,989
-0,037
-1,184
11,000
Category
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total
Probability
1-5%
5-10%
10-15%
15-20%
20-25%
25-30%
30-35%
35-40%
40-45%
45-50%
50-55%
55-60%
60-65%
65-70%
70-75%
75-80%
80-85%
85-90%
90-95%
95-100%
Mean
Number
return
Standard
of Games categorie deviation
7
-1,000
0,000
202
-0,700
1,920
263
-0,264
2,294
325
-0,100
2,124
422
-0,101
1,783
456
-0,159
1,542
480
-0,076
1,415
422
-0,128
1,253
496
-0,190
1,123
451
-0,105
1,047
410
-0,088
0,950
456
-0,027
0,862
502
0,034
0,765
471
0,011
0,689
444
-0,079
0,649
446
-0,011
0,550
452
-0,031
0,488
311
-0,029
0,410
334
-0,048
0,357
222
0,005
0,168
7.572
T-test
0,000
-5,179
-1,868
-0,848
-1,162
-2,205
-1,180
-2,106
-3,773
-2,123
-1,881
-0,660
1,003
0,342
-2,568
-0,404
-1,338
-1,264
-2,447
0,407
44
In tables 19 and 20 below the mean return in the underdog categories (1-7) and in the favorite
categories (15-20) are given. At every surface, except hard-court (i), you see that the return on
favorites is higher than on underdogs, which can be an indication for a favorite longshot bias. At
hard-court (i) in ATP and WTA tennis the return in categories 1 to 7 is higher than in the categories
15-20, which can be an indication for a reverse favorite longshot bias.
Table 19: Mean return in category 1-7 and 15-20 over the years at ATP tournaments
Year
Mean return
Mean return
category 1-7
category 15-20
Grass
-0,178
-0,022
Gravel
-0,243
-0,020
Hard-court (i)
-0,178
-0,283
Hard-court (o)
-0,021
-0,006
Table 20: Mean return in category 1-7 and 15-20 over the years at WTA tournaments
Year
Mean return
Mean return
category 1-7
category 15-20
Grass
-0,101
-0,062
Gravel
-0,212
-0,027
Hard-court (i)
0,041
-0,081
Hard-court (o)
-0,187
-0,035
As said in section 5.4.1 we wanted to test the results over the years for ATP and WTA tournaments
separately, with the goal of getting more t-values that are significant. Looking at the t-values in table
17 and 18, we see that they are actually becoming more insignificant.
By separating between ATP and WTA tournaments, the same as in section 5.3.2 happens; the results
becoming more insignificant. When we put all the data together, the results are looking fine and
significant, but when we split them apart, the results show a whole other point of view. This is not in
line with the literature of Forrest & Mchale, 2007 and Cain et al, 2003. Only at hard-court (o)
tournaments in ATP tournaments, we see significant t-values. In addition, table shows a higher
return at favorites than underdogs in hard-court (o) tournaments. Based on those results we can say
that there is a favorite longshot bias in hard-court (o) ATP tournaments.
45
6. Conclusion
In this study the matches of all the ATP and WTA tournaments of the years 2009 to 2013 are
examined. Before we evaluate the hypotheses and conclusion of the results of section 5, we will
restate the research question and the hypotheses.
The research question which is answered in this thesis was:
‘Is there a favorite longshot bias in ATP and WTA tennis?’
Hypotheses:
H1: There exists a favorite longshot bias in ATP and WTA tennis.
H2: The favorite longshot bias is stronger in women tournaments.
H3a: The favorite longshot bias is becoming stronger over the years.
H3b: The favorite longshot bias is becoming stronger over the years in ATP tournaments.
H3c: The favorite longshot bias is becoming stronger over the years in WTA tournaments.
H4a: At gravel tournaments occurs a stronger favorite longshot bias than in hard-court tournaments.
H4b: At gravel tournaments occurs a stronger favorite longshot bias than in hard-court tournaments
in ATP tournaments.
H4c: At gravel tournaments occurs a stronger favorite longshot bias than in hard-court tournaments
in WTA tournaments.
To answer the question the odds of WTA and ATP tennis tournaments from 2009 to 2013 were
analyzed. The odds were calculated into winning probabilities and divided over 20 probability
categories. For every category the mean return and standard deviation was calculated. For every
category we did a T-test, where the results lower than -2 or higher than 2 are significant, obviously
-2 < t < 2 is insignificant.
Table 21: Hypotheses evaluation
Hypothesis
H1:
There
Accept/reject
exists
a
favorite
returns of underdogs and most t-values of underdog
longshot bias in ATP and WTA
tennis.
Remarks
The returns of favorites are mostly higher than the
categories are significant. But also the favorite
Reject
categories are significant. Based on this there is an
46
absent of favorite longshot bias.
The returns of favorites are mostly higher than the
returns of underdogs and most t-values of underdog
H2: The favorite longshot bias is
categories are significant. But also the favorite
stronger in women tournaments.
categories are significant. Based on this there is an
Reject
absent of favorite longshot bias.
H3a: The favorite longshot bias is
The returns of favorites are mostly higher than the
becoming stronger over the
returns of underdogs, but most of the t-values are
years.
insignificant. Based on this there is an absent of
Reject
favorite longshot bias.
The returns of favorites are mostly higher than the
returns of underdogs, but most of the t-values are
H3b: The favorite longshot bias is
insignificant. Only the results of 2011 contain
becoming stronger over the years
significant results. Based on this there is an absent of
in ATP tournaments.
favorite longshot bias in the years 2009, 2010, 2012
and 2013 in ATP tournaments. In 2011, a favorite
Reject
longshot bias exists.
The returns of favorites are mostly higher than the
H3c: The favorite longshot bias is
returns of underdogs, but most of the t-values are
becoming stronger over the years
insignificant. Based on this there is an absent of
in WTA tournaments.
favorite longshot bias in every year in WTA
Reject
tournaments.
H4a: At gravel tournaments
The returns of favorites are mostly higher than the
occurs a stronger favorite
returns of underdogs, but most of the t-values are
longshot bias than in hard-court
insignificant. Based on this there is an absent of
tournaments.
Reject
favorite longshot bias
The returns of favorites are mostly higher than the
H4b: At gravel tournaments
returns of underdogs, but most of the t-values are
occurs a stronger favorite
insignificant. Only the results of hard-court (o)
longshot bias than in hard-court
contain significant results. Based on this there is an
tournaments in ATP tournaments.
absent of favorite longshot bias at grass, gravel and
hard-court (o) in ATP tournaments. In hard-court (i), a
Reject
favorite longshot bias exists.
H4c: At gravel tournaments
The returns of favorites are mostly higher than the
occurs a stronger favorite
returns of underdogs, but most of the t-values are
longshot bias than in hard-court
insignificant. Based on this there is an absent of
tournaments in WTA
Reject
favorite longshot bias at every surface in WTA
47
tournaments.
tournaments.
Looking at the results of all the data together in 5.1 and the results of ATP and WTA separately in 5.2
we see many significant t-values and the mean return of favorites is often higher than underdogs. At
first sight, you see a clear favorite longshot bias in both situations. However, in section 5.3.2 and
5.4.2, we separate the ATP and WTA tournament over the years and per surface, which lead to many
insignificant results. This means that if we look at the results of all the data together, it looks all good
and significant, but if we separate it, it does not look that significant anymore. In addition, if we look
at the t-values in the results overall and sorted by gender, we see many significant t-values in
underdogs categories (1 to 7), which is a good indication of a favorite longshot bias. However, in the
favorite categories (15 to 20) we also see many significant t-values. Based on this, we made the
conclusion that there is no strong favorite longshot bias in ATP and WTA tournaments over 2009 to
2013. This is not in line with the literature of Forrest & Mchale, 2007 and Cain et al, 2003.
Only at hard-court (o) tournaments in ATP tournaments and in 2011 ATP tournaments, we see
significant t-values. However, this is such a small share that we conclude that there is no favorite
longshot bias in ATP and WTA tournament over the years or per surface.
Articles that investigate the favorite longshot bias in tennis before, found a favorite longshot bias
(Forrest & Mchale, 2007 and Cain et al, 2003). There were no tennis-related articles which found a
absent of a favorite longshot bias. In other sports, there were articles which did not found a favorite
longshot bias like; Busche & Hall 1988 (horse racing), Busche & Walls 2000 (racetrack), Vaughan
Williams & Paton 1998 (horse racing), Woodland & Woodland 1994 (baseball) and Woodland &
Woodland 2001 (hockey). The results of this study are corresponding to those contradicting
literature.f
The answer to the question is as follows:
‘No, a favorite longshot bias in tennis ATP and WTA tennis does not exists. There are only
indication for a favorite longshot bias in 2011 ATP tournaments and ATP hard-court (i)
tournaments. However, the overall conclusion is that there is an absent of a favorite longshot
bias in ATP and WTA tennis (sorted by gender, years and surface)’.
In the next section, the contribution and limitations of this study are discussed. In addition, some
interesting directions for future research are discussed.
48
7. Discussion
In this section the contribution of this study to the academic literature is discussed. The most
important limitations of this study are summarized and some interesting directions for future
research are discussed.
7.1 Contribution
As seen in the literature review in section 2, there was a lot of research on the favorite longshot bias
in different kind of sports. Most of these studies are based on horseracing, football and soccer.
Investigations on the favorite longshot bias in tennis are scarce, so a new research on the favorite
longshot bias in the tennis sport will contribute to the existing literature. Cain et al. (2003) did some
research on tennis, but they used a very small dataset whereby the results were doubtful. Forrest &
Mchale (2007) actually did a valuable study on the favorite longshot bias in tennis tournaments.
They used a dataset of 17.000 possible bets and found a favorite longshot bias. This study goes a
step further by using a dataset of 37.220 possible bets, which is 219% bigger than the dataset of
Forrest & Mchale (2007). In addition, the large dataset used in this investigation, will make this a
valuable article that contribute to the existing literature.
7.2 Limitations & further research
Looking at the conclusion in section 6, we see that all hypothesis are reject by the data. In the
literature review we did not find any articles that looked at the trend over the years of the favorite
longshot bias in tennis matches. So there is no possibility compare the results of this study with a
similar study. Also looking at the research method we do not find an explanation for the rejection of
the hypothesis. The sample we used is not too small or biased. Also there is no question of noisy
proxies or failed manipulation checks.
It is interesting to do further research on the trend over the years. In this study we looked at the
trend over 5 years (2009-2013), but you probably have to have a bigger sample size which contain
more years. For example, if you use data from the last 30 years, you might see a clearer trend than
the trend over 2009 to 2013.
49
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51
Appendix
A. Overview of ATP tournaments
Surface
Official name
Matches
20092013
Total odds
Grand Slam
Australian Open
Roland Garros
Wimbledon
US Open
Australian Open
Les Internationaux de France de Roland Garros
The Wimbledon Championships
US Open
Hard-court (o)
Gravel
Gras
Hard-court (o)
545
609
599
600
1.090
1.218
1.198
1.200
Barclays ATP World Tour Finals
Hard-court (i)
75
150
BNP Paribas Open
Sony Open Tennis
Monte-Carlo Rolex Masters
Internazionali BNL d'Italia
Mutua Madrid Open
Coupe Rogers
Western & Southern Open - Cincinnati
Shanghai Rolex Masters
BNP Paribas Masters
Hard-court (o)
Hard-court (o)
Gravel
Gravel
Gravel
Hard-court (o)
Hard-court (o)
Hard-court (o)
Hard-court (i)
454
452
261
253
255
157
257
256
222
908
904
522
506
510
314
514
512
444
ATP World Tour Finals
Londen
ATP World Tour Masters
1000
Indian Wells
Miami
Monte Carlo
Rome
Madrid
Montréal/Toronto
Cincinnati
Shanghai
Parijs
52
ATP World Tour 500
Rotterdam
Memphis
Acapulco
Dubai
Barcelona
Hamburg
Washington
Peking, Beijng
Tokio
Basel
Valencia
ABN AMRO World Tennis Tournament
U.S. National Indoor Tennis Championships
Abierto Mexicano Telcel
Dubai Duty Free Tennis Championships
Barcelona Open Banc Sabadell
bet-at-home Open - German Tennis Championships
Citi Open
China Open
Rakuten Japan Open Tennis Championships
Swiss Indoors Basel
Valencia Open 500
Hard-court (i)
Hard-court (i)
Gravel
Hard-court (o)
Gravel
Gravel
Hard-court (o)
Hard-court (o)
Hard-court (o)
Hard-court (i)
Hard-court (i)
141
150
148
144
252
202
209
147
150
154
146
282
300
296
288
504
404
418
294
300
308
292
BB&T Atlanta Open
Heineken Open
Thailand Open
SkiStar Swedish Open
Claro Open Colombia
Brisbane International
BRD Nastase Tiriac Trophy
Hard-court (o)
Hard-court (o)
Hard-court (i)
Gravel
Hard-court (o)
Hard-court (o)
Gravel
Gravel
Gravel
Hard-court (o)
Hard-court (o)
Hard-court (o)
Gravel
Gras
Gravel
Gras
Gravel
102
130
132
130
118
138
135
147
134
143
143
153
126
133
136
141
132
204
260
264
260
236
276
270
294
268
286
286
306
252
266
272
282
264
ATP World Tour 250
Atlanta
Auckland
Bangkok
Bastad
Bogota
Brisbane
Bucharest
Buenos Aires
Casablanca
Chennai
Delray Beach
Doha
Dusseldorf
Eastbourne
Gstaad
Halle
Houston
Copa Claro
Grand Prix Hassan II
Aircel Chennai Open
Delray Beach Open by The Venetian® Las Vegas
Qatar ExxonMobil Open
Power Horse Cup
Aegon International
Crédit Agricole Suisse Open Gstaad
Gerry Weber Open
US Men's Clay Court Championship
53
Kitzbuhel
Kuala Lumpur
London
Marseille
Metz
Montpellier
Moscow
Munich
Newport
Nice
Oeiras**
Sao Paulo
San Jose
's-Hertogenbosch
St. Petersburg
Stockholm
Stuttgart
Sydney
Umag
Vienna
Vina del Mar
Winston-Salem
Zagreb
bet-at-home Cup Kitzbühel
Malaysian Open, Kuala Lumpur
Aegon Championships
Open 13
Moselle Open
Open Sud de France
Kremlin Cup by Bank of Moscow
BMW Open
Hall of Fame Tennis Championships
Open de Nice Côte d’Azur
Portugal Open
Brasil Open 2013
SAP Open
Topshelf Open
St. Petersburg Open
If Stockholm Open
MercedesCup
Apia International Sydney
Vegeta Croatia Open Umag
Erste Bank Open
VTR Open
Winston-Salem Open
PBZ Zagreb Indoors
Gravel
Hard-court (i)
Gras
Hard-court (i)
Hard-court (i)
Hard-court (i)
Hard-court (i)
Gravel
Gras
Gravel
Gravel
106
128
256
134
127
78
132
139
146
103
129
212
256
512
268
254
156
264
278
292
206
258
Gravel (i)
Hard-court (i)
Gras
Hard-court (i)
Hard-court (i)
Gravel
Hard-court (o)
Gravel
Hard-court (i)
Gravel
Hard-court (o)
Hard-court (i)
51
143
140
142
131
139
128
133
131
77
131
141
102
286
280
284
262
278
256
266
262
154
262
282
12.076
24.152
Total
54
B. Overview of WTA tournaments
Matches
20092013
Total
odds
Official name
Surface
Australian Open
Les Internationaux de France de Roland Garros
The Wimbledon Championships
US Open
Hard-court
Gravel
Gras
Hard-court
542
627
620
618
1.084
1.254
1.240
1.236
WTA Championships
Commonwealth Bank Tournament of Champions
Hard-court
Hard-court
60
28
120
56
BNP Paribas Open
Sony Ericsson Open
Mutua Madrileña Madrid Open
China Open
Hard-court
Hard-court
Gravel
Hard-court
486
466
278
271
972
932
556
542
Dubai Duty Free Tennis Championships
Internazionali BNL d'Italia
Rogers Cup presented by National Bank
Western & Southern Financial Group
Toray Pan Pacific Open
Hard-court
Gravel
Hard-court
Hard-court
Hard-court
204
260
97
257
259
408
520
194
514
518
Grand Slam
Australian Open
Roland Garros
Wimbledon
US Open
Year-End Championships
WTA Championships, Istanboel
Tournament of Champions, Bali
Premier Mandatory
WTA Indian Wells
WTA Miami
WTA Madrid
WTA Peking
Premier Five
WTA Dubai
WTA Rome
WTA Montreal/Toronto
WTA Cincinnati
WTA Tokio
55
Premier
WTA Sydney
WTA Parijs
WTA Doha
WTA Charleston
WTA Stuttgart
WTA Brussel
WTA Eastbourne
WTA Stanford
WTA San Diego
WTA New Haven
WTA Moskou
Medibank International Sydney
Open GDF Suez
Qatar Ladies Open
Family Circle Cup
Porsche Tennis Grand Prix
Brussels Ladies Open
AEGON International
Bank of the West Classic
Mercury Insurance Open
New Haven Open at Yale
Kremlin Cup
Hard-court
Hard-court
Hard-court
Gravel
Gravel
Gravel
Gras
Hard-court
Hard-court
Hard-court
Hard-court
Total
135
138
156
260
132
83
130
132
28
135
132
270
276
312
520
264
166
260
264
56
270
264
6.534
13.068
56
C.
Historical winners Australian Open 1950-2014
ATP - Men
Year Winner
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Stanislas Wawrinka
Novak Đoković
Novak Đoković
Novak Đoković
Roger Federer
Rafael Nadal
Novak Đoković
Roger Federer
Roger Federer
Marat Safin
Roger Federer
Andre Agassi
Thomas Johansson
Andre Agassi
Andre Agassi
Jevgeni Kafelnikov
Petr Korda
Pete Sampras
Boris Becker
Andre Agassi
Pete Sampras
Jim Courier
Jim Courier
Boris Becker
Ivan Lendl
Ivan Lendl
Mats Wilander
Stefan Edberg
geen toernooi
Stefan Edberg
Mats Wilander
Mats Wilander
Johan Kriek
Johan Kriek
Brian Teacher
Guillermo Vilas
Guillermo Vilas
Roscoe Tanner
Mark Edmondson
John Newcombe
Jimmy Connors
John Newcombe
Ken Rosewall
Ken Rosewall
Arthur Ashe
Rod Laver
William Bowrey
Roy Emerson
Roy Emerson
Roy Emerson
Roy Emerson
Roy Emerson
Rod Laver
Roy Emerson
Rod Laver
Alex Olmedo
Ashley Cooper
Ashley Cooper
Lew Hoad
Ken Rosewall
Mervyn Rose
Ken Rosewall
Ken McGregor
Dick Savitt
Frank Sedgman
Losing finalist
Rafael Nadal
Andy Murray
Rafael Nadal
Andy Murray
Andy Murray
Roger Federer
Jo-Wilfried Tsonga
Fernando González
Marcos Baghdatis
Lleyton Hewitt
Marat Safin
Rainer Schüttler
Marat Safin
Arnaud Clément
Jevgeni Kafelnikov
Thomas Enqvist
Marcelo Ríos
Carlos Moyá
Michael Chang
Pete Sampras
Todd Martin
Stefan Edberg
Stefan Edberg
Ivan Lendl
Stefan Edberg
Miloslav Mečíř
Pat Cash
Pat Cash
Mats Wilander
Kevin Curren
Ivan Lendl
Steve Denton
Steve Denton
Kim Warwick
John Sadri
John Marks
Guillermo Vilas
John Newcombe
Jimmy Connors
Phil Dent
Onny Parun
Malcolm Anderson
Arthur Ashe
Dick Crealy
Andrés Gimeno
Juan Gisbert
Arthur Ashe
Arthur Ashe
Fred Stolle
Fred Stolle
Ken Fletcher
Roy Emerson
Rod Laver
Neale Fraser
Neale Fraser
Malcolm Anderson
Neale Fraser
Ken Rosewall
Lew Hoad
Rex Hartwig
Mervyn Rose
Frank Sedgman
Ken McGregor
Ken McGregor
WTA- Women
Year Winner
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Li Na
Viktoryja Azarenka
Viktoryja Azarenka
Kim Clijsters
Serena Williams
Serena Williams
Maria Sjarapova
Serena Williams
Amélie Mauresmo
Serena Williams
Justine Henin
Serena Williams
Jennifer Capriati
Jennifer Capriati
Lindsay Davenport
Martina Hingis
Martina Hingis
Martina Hingis
Monica Seles
Mary Pierce
Steffi Graf
Monica Seles
Monica Seles
Monica Seles
Steffi Graf
Steffi Graf
Steffi Graf
Hana Mandlíková
geen toernooi
Martina Navrátilová
Chris Evert
Martina Navrátilová
Chris Evert
Martina Navrátilová
Hana Mandlíková
Barbara Jordan
Chris O'Neil
Kerry Melville Reid
Evonne Goolagong Cawley
Evonne Goolagong Cawley
Evonne Goolagong Cawley
Margaret Court
Virginia Wade
Margaret Court
Margaret Court
Margaret Court
Billie Jean King
Nancy Richey
Margaret Court
Margaret Court
Margaret Court
Margaret Court
Margaret Court
Margaret Court
Margaret Court
Mary Carter Reitano
Angela Mortimer Barrett
Shirley Fry
Mary Carter Reitano
Beryl Penrose
Thelma Coyne Long
Maureen Connolly
Thelma Coyne Long
Nancye Wynne Bolton
Louise Brough
Losing finalist
Dominika Cibulková
Li Na
Maria Sjarapova
Li Na
Justine Henin
Dinara Safina
Ana Ivanović
Maria Sjarapova
Justine Henin
Lindsay Davenport
Kim Clijsters
Venus Williams
Martina Hingis
Martina Hingis
Martina Hingis
Amélie Mauresmo
Conchita Martínez
Mary Pierce
Anke Huber
Arantxa Sánchez Vicario
Arantxa Sánchez Vicario
Steffi Graf
Mary Joe Fernandez
Jana Novotná
Mary Joe Fernandez
Helena Suková
Chris Evert
Martina Navrátilová
Chris Evert
Helena Suková
Kathy Jordan
Martina Navrátilová
Chris Evert
Wendy Turnbull
Sharon Walsh
Betsy Nagelsen
Dianne Fromholtz Balestrat
Renáta Tomanová
Martina Navrátilová
Chris Evert
Evonne Goolagong Cawley
Evonne Goolagong Cawley
Evonne Goolagong Cawley
Kerry Melville
Billie Jean King
Margaret Court
Lesley Turner Bowrey
Nancy Richey
Maria Bueno
Lesley Turner Bowrey
Jan Lehane
Jan Lehane
Jan Lehane
Jan Lehane
Renee Schuurman
Lorraine Coghlan Robinson
Althea Gibson
Thelma Coyne Long
Thelma Coyne Long
Jenny Staley Hoad
Julia Sampson
Helen Angwin
Thelma Coyne Long
Doris Hart
57
D. Historical winners Roland Garros 1950-2014
ATP - Men
Year Winner
Losing finalist
WTA - Women
Year Winner
Losing finalist
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Novak Đoković
David Ferrer
Novak Đoković
Roger Federer
Robin Söderling
Robin Söderling
Roger Federer
Roger Federer
Roger Federer
Mariano Puerta
Guillermo Coria
Martin Verkerk
Juan Carlos Ferrero
Àlex Corretja
Magnus Norman
Andrej Medvedev
Àlex Corretja
Sergi Bruguera
Michael Stich
Michael Chang
Alberto Berasategui
Jim Courier
Petr Korda
Andre Agassi
Andre Agassi
Stefan Edberg
Henri Leconte
Mats Wilander
Mikael Pernfors
Ivan Lendl
John McEnroe
Mats Wilander
Guillermo Vilas
Ivan Lendl
Vitas Gerulaitis
Victor Pecci
Guillermo Vilas
Brian Gottfried
Harold Solomon
Guillermo Vilas
Manuel Orantes
Niki Pilic
Patrick Proisy
Ilie Năstase
Zeljko Franulovic
Ken Rosewall
Rod Laver
Tony Roche
Istvan Gulyas
Tony Roche
Nicola Pietrangeli
Pierre Darmon
Roy Emerson
Nicola Pietrangeli
Luis Ayala
Ian Vermaak
Luis Ayala
Herbert Flam
Sven Davidson
Sven Davidson
Art Larsen
Vic Seixas
Frank Sedgman
Eric Sturgess
Jaroslav Drobný
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Simona Halep
Maria Sjarapova
Sara Errani
Francesca Schiavone
Samantha Stosur
Dinara Safina
Dinara Safina
Ana Ivanović
Svetlana Koeznetsova
Mary Pierce
Jelena Dementjeva
Kim Clijsters
Venus Williams
Kim Clijsters
Conchita Martínez
Martina Hingis
Monica Seles
Martina Hingis
Arantxa Sánchez Vicario
Arantxa Sánchez Vicario
Mary Pierce
Mary Joe Fernandez
Steffi Graf
Arantxa Sánchez Vicario
Steffi Graf
Steffi Graf
Natasja Zvereva
Martina Navrátilová
Martina Navrátilová
Martina Navrátilová
Chris Evert-Lloyd
Mima Jaušovec
Andrea Jaeger
Sylvia Hanika
Virginia Ruzici
Wendy Turnbull
Mima Jaušovec
Florenţa Mihai
Renáta Tomanová
Martina Navrátilová
Olga Morozova
Chris Evert
Evonne Goolagong
Helen Gourlay
Helga Niessen
Ann Haydon-Jones
Ann Haydon-Jones
Lesley Turner
Nancy Richey
Margaret Smith
Maria Bueno
Ann Haydon-Jones
Lesley Turner
Yola Ramírez
Yola Ramírez
Zsuzsa Körmöczy
Shirley Bloomer
Dorothy Knode
Angela Mortimer
Dorothy Knode
Ginette Bucaille
Doris Hart
Shirley Fry
Doris Hart
Patricia Todd
Rafael Nadal
Rafael Nadal
Rafael Nadal
Rafael Nadal
Rafael Nadal
Roger Federer
Rafael Nadal
Rafael Nadal
Rafael Nadal
Rafael Nadal
Gaston Gaudio
Juan Carlos Ferrero
Albert Costa
Gustavo Kuerten
Gustavo Kuerten
Andre Agassi
Carlos Moyà
Gustavo Kuerten
Jevgeni Kafelnikov
Thomas Muster
Sergi Bruguera
Sergi Bruguera
Jim Courier
Jim Courier
Andrés Gómez
Michael Chang
Mats Wilander
Ivan Lendl
Ivan Lendl
Mats Wilander
Ivan Lendl
Yannick Noah
Mats Wilander
Björn Borg
Björn Borg
Björn Borg
Björn Borg
Guillermo Vilas
Adriano Panatta
Björn Borg
Björn Borg
Ilie Năstase
Andrés Gimeno
Jan Kodeš
Jan Kodeš
Rod Laver
Ken Rosewall
Roy Emerson
Tony Roche
Fred Stolle
Manuel Santana
Roy Emerson
Rod Laver
Manuel Santana
Nicola Pietrangeli
Nicola Pietrangeli
Mervyn Rose
Sven Davidson
Lew Hoad
Tony Trabert
Tony Trabert
Ken Rosewall
Jaroslav Drobný
Jaroslav Drobný
Budge Patty
Maria Sjarapova
Serena Williams
Maria Sjarapova
Li Na
Francesca Schiavone
Svetlana Koeznetsova
Ana Ivanović
Justine Henin-Hardenne
Justine Henin-Hardenne
Justine Henin-Hardenne
Anastasia Myskina
Justine Henin-Hardenne
Serena Williams
Jennifer Capriati
Mary Pierce
Steffi Graf
Arantxa Sánchez Vicario
Iva Majoli
Steffi Graf
Steffi Graf
Arantxa Sánchez Vicario
Steffi Graf
Monica Seles
Monica Seles
Monica Seles
Arantxa Sánchez Vicario
Steffi Graf
Steffi Graf
Chris Evert-Lloyd
Chris Evert-Lloyd
Martina Navrátilová
Chris Evert-Lloyd
Martina Navrátilová
Hana Mandlíková
Chris Evert-Lloyd
Chris Evert-Lloyd
Virginia Ruzici
Mima Jaušovec
Sue Barker
Chris Evert
Chris Evert
Margaret Smith-Court
Billy Jean King
Evonne Goolagong
Margaret Smith-Court
Margaret Smith-Court
Nancy Richey
Françoise Dürr
Ann Haydon-Jones
Lesley Turner
Margaret Smith
Lesley Turner
Margaret Smith
Ann Haydon
Darlene Hard
Christine Truman
Zsuzsa Körmöczy
Shirley Bloomer
Althea Gibson
Angela Mortimer
Maureen Connolly
Maureen Connolly
Doris Hart
Shirley Fry
Doris Hart
58
E.
Historical winners Wimbledon 1950-2014
ATP - Men
Year Winner
Losing finalist
WTA - Women
Year Winner
Losing finalist
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Roger Federer
Novak Đoković
Andy Murray
Rafael Nadal
Tomáš Berdych
Andy Roddick
Roger Federer
Rafael Nadal
Rafael Nadal
Andy Roddick
Andy Roddick
Mark Philippoussis
David Nalbandian
Patrick Rafter
Patrick Rafter
Andre Agassi
Goran Ivanišević
Cédric Pioline
MaliVai Washington
Boris Becker
Goran Ivanišević
Jim Courier
Goran Ivanišević
Boris Becker
Boris Becker
Stefan Edberg
Boris Becker
Ivan Lendl
Ivan Lendl
Kevin Curren
Jimmy Connors
Chris Lewis
John McEnroe
Björn Borg
John McEnroe
Roscoe Tanner
Jimmy Connors
Jimmy Connors
Ilie Năstase
Jimmy Connors
Ken Rosewall
Alex Metreveli
Ilie Năstase
Stan Smith
Ken Rosewall
John Newcombe
Tony Roche
Wilhelm Bungert
Dennis Ralston
Fred Stolle
Fred Stolle
Fred Stolle
Marty Mulligan
Chuck McKinley
Rod Laver
Rod Laver
Neale Fraser
Ashley Cooper
Ken Rosewall
Kurt Nielsen
Ken Rosewall
Kurt Nielsen
Jaroslav Drobný
Ken McGregor
Frank Sedgman
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Eugenie Bouchard
Sabine Lisicki
Agnieszka Radwańska
Maria Sjarapova
Vera Zvonarjova
Venus Williams
Serena Williams
Marion Bartoli
Justine Henin
Lindsay Davenport
Serena Williams
Venus Williams
Venus Williams
Justine Henin
Lindsay Davenport
Steffi Graf
Nathalie Tauziat
Jana Novotná
Arantxa Sánchez Vicario
Arantxa Sánchez Vicario
Martina Navrátilová
Jana Novotná
Monica Seles
Gabriela Sabatini
Zina Garrison
Martina Navrátilová
Martina Navrátilová
Steffi Graf
Hana Mandlíková
Chris Evert
Chris Evert
Andrea Jaeger
Chris Evert
Hana Mandlíková
Chris Evert
Chris Evert
Chris Evert
Betty Stöve
Evonne Goolagong
Evonne Goolagong
Olga Morozova
Chris Evert
Evonne Goolagong
Margaret Court
Billie Jean King
Billie Jean King
Judy Tegart
Ann Haydon-Jones
Maria Bueno
Maria Bueno
Margaret Court
Billie Jean King
Věra Suková
Christine Truman
Sandra Reynolds Price
Darlene Hard
Angela Mortimer
Darlene Hard
Angela Buxton
Beverly Baker Fleitz
Louise Brough
Doris Hart
Louise Brough
Shirley Fry
Margaret Osborne duPont
Novak Đoković
Andy Murray
Roger Federer
Novak Đoković
Rafael Nadal
Roger Federer
Rafael Nadal
Roger Federer
Roger Federer
Roger Federer
Roger Federer
Roger Federer
Lleyton Hewitt
Goran Ivanišević
Pete Sampras
Pete Sampras
Pete Sampras
Pete Sampras
Richard Krajicek
Pete Sampras
Pete Sampras
Pete Sampras
Andre Agassi
Michael Stich
Stefan Edberg
Boris Becker
Stefan Edberg
Pat Cash
Boris Becker
Boris Becker
John McEnroe
John McEnroe
Jimmy Connors
John McEnroe
Björn Borg
Björn Borg
Björn Borg
Björn Borg
Björn Borg
Arthur Ashe
Jimmy Connors
Jan Kodeš
Stan Smith
John Newcombe
John Newcombe
Rod Laver
Rod Laver
John Newcombe
Manuel Santana
Roy Emerson
Roy Emerson
Chuck McKinley
Rod Laver
Rod Laver
Neale Fraser
Alex Olmedo
Ashley Cooper
Lew Hoad
Lew Hoad
Tony Trabert
Jaroslav Drobný
Vic Seixas
Frank Sedgman
Dick Savitt
Budge Patty
Petra Kvitová
Marion Bartoli
Serena Williams
Petra Kvitová
Serena Williams
Serena Williams
Venus Williams
Venus Williams
Amélie Mauresmo
Venus Williams
Maria Sjarapova
Serena Williams
Serena Williams
Venus Williams
Venus Williams
Lindsay Davenport
Jana Novotná
Martina Hingis
Steffi Graf
Steffi Graf
Conchita Martínez
Steffi Graf
Steffi Graf
Steffi Graf
Martina Navrátilová
Steffi Graf
Steffi Graf
Martina Navrátilová
Martina Navrátilová
Martina Navrátilová
Martina Navrátilová
Martina Navrátilová
Martina Navrátilová
Chris Evert
Evonne Goolagong
Martina Navrátilová
Martina Navrátilová
Virginia Wade
Chris Evert
Billie Jean King
Chris Evert
Billie Jean King
Billie Jean King
Evonne Goolagong
Margaret Court
Ann Haydon-Jones
Billie Jean King
Billie Jean King
Billie Jean King
Margaret Court
Maria Bueno
Margaret Court
Karen Hantze Susman
Angela Mortimer
Maria Bueno
Maria Bueno
Althea Gibson
Althea Gibson
Shirley Fry
Louise Brough
Maureen Connolly
Maureen Connolly
Maureen Connolly
Doris Hart
Louise Brough
59
F.
Historical winners US Open 1950-2014
ATP - Men
Years Winner
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Marin Čilić
Rafael Nadal
Andy Murray
Novak Đoković
Rafael Nadal
Juan Martín del Potro
Roger Federer
Roger Federer
Roger Federer
Roger Federer
Roger Federer
Andy Roddick
Pete Sampras
Lleyton Hewitt
Marat Safin
Andre Agassi
Patrick Rafter
Patrick Rafter
Pete Sampras
Pete Sampras
Andre Agassi
Pete Sampras
Stefan Edberg
Stefan Edberg
Pete Sampras
Boris Becker
Mats Wilander
Ivan Lendl
Ivan Lendl
Ivan Lendl
John McEnroe
Jimmy Connors
Jimmy Connors
John McEnroe
John McEnroe
John McEnroe
Jimmy Connors
Guillermo Vilas
Jimmy Connors
Manuel Orantes
Jimmy Connors
John Newcombe
Ilie Năstase
Stan Smith
Ken Rosewall
Rod Laver
Arthur Ashe
John Newcombe
Fred Stolle
Manuel Santana
Roy Emerson
Rafael Osuna
Rod Laver
Roy Emerson
Neale Fraser
Neale Fraser
Ashley Cooper
Mal Anderson
Ken Rosewall
Tony Trabert
Vic Seixas
Tony Trabert
Frank Sedgman
Frank Sedgman
Art Larsen
Losing finalist
Kei Nishikori
Novak Đoković
Novak Đoković
Rafael Nadal
Novak Đoković
Roger Federer
Andy Murray
Novak Đoković
Andy Roddick
Andre Agassi
Lleyton Hewitt
Juan Carlos Ferrero
Andre Agassi
Pete Sampras
Pete Sampras
Todd Martin
Mark Philippoussis
Greg Rusedski
Michael Chang
Andre Agassi
Michael Stich
Cédric Pioline
Pete Sampras
Jim Courier
Andre Agassi
Ivan Lendl
Ivan Lendl
Mats Wilander
Miloslav Mečíř
John McEnroe
Ivan Lendl
Ivan Lendl
Ivan Lendl
Björn Borg
Björn Borg
Vitas Gerulaitis
Björn Borg
Jimmy Connors
Björn Borg
Jimmy Connors
Ken Rosewall
Jan Kodeš
Arthur Ashe
Jan Kodeš
Tony Roche
Tony Roche
Tom Okker
Clark Graebner
John Newcombe
Cliff Drysdale
Fred Stolle
Frank Froehling
Roy Emerson
Rod Laver
Rod Laver
Alex Olmedo
Mal Anderson
Ashley Cooper
Lew Hoad
Ken Rosewall
Rex Hartwig
Vic Seixas
Gardnar Mulloy
Vic Seixas
Herbert Flam
WTA- Women
Years Winner
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
Serena Williams
Serena Williams
Serena Williams
Samantha Stosur
Kim Clijsters
Kim Clijsters
Serena Williams
Justine Henin
Maria Sjarapova
Kim Clijsters
Svetlana Koeznetsova
Justine Henin-Hardenne
Serena Williams
Venus Williams
Venus Williams
Serena Williams
Lindsay Davenport
Martina Hingis
Steffi Graf
Steffi Graf
Arantxa Sánchez Vicario
Steffi Graf
Monica Seles
Monica Seles
Gabriela Sabatini
Steffi Graf
Steffi Graf
Martina Navrátilová
Martina Navrátilová
Hana Mandlíková
Martina Navrátilová
Martina Navrátilová
Chris Evert Lloyd
Tracy Austin
Chris Evert Lloyd
Tracy Austin
Chris Evert
Chris Evert
Chris Evert
Chris Evert
Billie Jean King
Margaret Smith-Court
Billie Jean King
Billie Jean King
Margaret Smith-Court
Margaret Smith-Court
Virginia Wade
Billie Jean King
Maria Bueno
Margaret Smith
Maria Bueno
Maria Bueno
Margaret Smith
Darlene Hard
Darlene Hard
Maria Bueno
Althea Gibson
Althea Gibson
Shirley Fry
Doris Hart
Doris Hart
Maureen Connolly
Maureen Connolly
Maureen Connolly
Margaret Osborne duPont
Losing finalist
Caroline Wozniacki
Viktoryja Azarenka
Viktoryja Azarenka
Serena Williams
Vera Zvonarjova
Caroline Wozniacki
Jelena Janković
Svetlana Koeznetsova
Justine Henin-Hardenne
Mary Pierce
Jelena Dementjeva
Kim Clijsters
Venus Williams
Serena Williams
Lindsay Davenport
Martina Hingis
Martina Hingis
Venus Williams
Monica Seles
Monica Seles
Steffi Graf
Helena Suková
Arantxa Sánchez Vicario
Martina Navrátilová
Steffi Graf
Martina Navrátilová
Gabriela Sabatini
Steffi Graf
Helena Suková
Martina Navrátilová
Chris Evert Lloyd
Chris Evert Lloyd
Hana Mandlíková
Martina Navrátilová
Hana Mandlíková
Chris Evert
Pam Shriver
Wendy Turnbull
Evonne Goolagong Cawley
Evonne Goolagong Cawley
Evonne Goolagong
Evonne Goolagong
Kerry Melville
Rosie Casals
Rosie Casals
Nancy Richey
Billie Jean King
Ann Haydon-Jones
Nancy Richey
Billie Jean Moffitt
Carole Graebner
Margaret Smith
Darlene Hard
Ann Haydon
Maria Bueno
Christine Truman
Darlene Hard
Louise Brough
Althea Gibson
Patricia Ward
Louise Brough
Doris Hart
Doris Hart
Shirley Fry
Doris Hart
60