Journal of Sports Economics
http://jse.sagepub.com
Competitive Balance and Match Uncertainty in Grand-Slam Tennis:
Effects of Seeding System, Gender, and Court Surface
Julio del Corral
Journal of Sports Economics 2009; 10; 563 originally published online May 6, 2009;
DOI: 10.1177/1527002509334650
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Articles
Competitive Balance and Match
Uncertainty in Grand-Slam
Tennis
Journal of Sports Economics
Volume 10 Number 6
December 2009 563-581
# 2009 SAGE Publications
10.1177/1527002509334650
http://jse.sagepub.com
hosted at
http://online.sagepub.com
Effects of Seeding System, Gender, and
Court Surface
Julio del Corral
Fundación Observatorio Económico del Deporte
University of Oviedo
This article tests whether the increase in seeded players in tennis grand-slam
tournaments from 16 to 32 in 2001 led to decreased competitive balance. In doing
so, two alternative measures of competitive balance for single-elimination
tournaments are proposed based on the performance of seeded players. Likewise, the
differences in competitive balance due to gender and court surface are also analyzed.
Additionally, using data from tennis grand-slam matches from 2005 to 2008, this
article analyzed the determinants of ex post match level uncertainty with probit models.
Keywords:
competitive balance; seeding system; match uncertainty; tennis
Introduction
Competitive balance in sports has attracted a lot of research in the past. The
considerable interest from sports economists on this issue is driven by the fact that
participants need each other to produce at all requires a basic interdependence. In
other words, sports firms have to avoid monopoly (Neale, 1964). This is in sharp contrast to other types of business firms, for which the monopoly is the preferred market
Author’s Note: Correspondence concerning this article should be addressed to Julio del Corral, Department of
Economics/Fundación Observatorio Económico del Deporte, University of Oviedo, Avda del Cristo s/n,
33006 Oviedo, Spain; e-mail: [email protected]. ‘‘I have received helpful comments from Paloma
Corrales, Kiran Gajwani, Juan Prieto, Daniel Solı́s, graduate student Cornell seminar participants, X IASE
Meeting placed in Gijón participants and two anonymous referees. The author would also like to thank
Julio del Corral Sr. and Pelayo González for their research assistance. Lastly, the author acknowledges the
Spanish Ministry of Science and Technology for his FPU fellowship. Any remaining errors are the sole
responsibility of the author’’.
563
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564 Journal of Sports Economics
structure. Neale explained this peculiar fact of sport economics with the well-known
Louis-Schmelling paradox, in which the heavyweight champion of the world needed
a strong contender to maximize profits. Hence, several studies analyzing the demand
for sports have focused on the uncertainty of outcome hypothesis.1 Szymanski
(2003) stated that while the evidence is far from unambiguous, there is some support
for the belief that attendance is positively affected by competitive balance. For this
reason, there are several studies that have analyzed what happened to competitive
balance over time (e.g., Garcı́a & Rodrı́guez, 2007; Horowitz, 1997; Koning, 2000).
Manuscripts that analyze changes in competitive balance as a result of changes in
business practice are more interesting than those that merely analyze competitive
balance over time (Fort & Maxcy, 2003). For instance, Balfour and Porter (1991)
tested the effect of free agency in the National Football League (NFL) and in Major
League Baseball (MLB). Vrooman (1995) analyzed whether the salary cap and free
agency policies altered competitive balance in MLB, the NFL, and the National
Basketball Association (NBA). Schmidt (2001) tested the effects of expansion in the
MLB. Haugen (2008) tested whether the three-point victory rule changed competitive balance in some European soccer leagues. La Croix and Kawaura (1999)
investigated how the change from an open-bidding regime to a player draft regime
affected competitive balance in the professional Japanese baseball leagues.
All the above-mentioned articles analyzed the effect of some policy on competitive balance in team sports. However, as Neale pointed out in his Louis-Schmelling
paradox, competitive balance is also important in individual sports. Likewise, organizers of individual sports events are also able to alter competitive balance within a
competition. For instance, they can change the scoring system or some rules of the
game.2 In addition, they can provide advantages to stronger competitors such as
seedings (tennis) or the assignment of lanes (swimming). These practices tend to
decrease competitive balance (Sanderson, 2002).
This article aims to analyze the impact of a change in an individual sport policy on
competitive balance. In particular, in 2001, the tennis grand-slam tournaments (i.e.,
the Australian Open, the French Open, Wimbledon, and the U.S. Open) changed the
number of seeded players from 16 to 32. The expected outcome of this change was to
decrease competitive balance. This article tests this hypothesis using data obtained
from the grand-slam tournaments from 1994 to 2008. Thus, the sample is split into
two periods: 1994-2000 and 2002-2008. In the first sampling period, the number of
seeded players was 16, whereas in the second period the number of seeded players
was 32. Given the nature of single elimination tournaments, traditional measures
of competitive balance, such as the Gini coefficient or the Herfindahl-Hirschman
index, cannot be used. Hence, to measure the competitive balance in these
tournaments are proposed two alternative measures based on the performance of the
seeded players.
It is important to note that this article is not the first to analyze competitive balance in individual sports. Previously, Rohm, Chatterjee, and Habibullah (2004)
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del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis
565
investigated the degree of competition at Wimbledon from 1968 to 2001, using the
degree of dominance among the top four seeds. Their results support the idea that
competitiveness at Wimbledon has been extremely high. Also using Wimbledon
data, Magnus and Klaassen (1999) analyzed the advantage for the seeded players.
They found no evidence for differences between men and women with regard to the
difficulty of achieving an upset. Du Bois and Heyndels (2007) studied match-specific
uncertainty, inter-seasonal uncertainty, and indicators for long-term uncertainty in
men’s and women’s tennis. To do so, they analyzed the tightness of several grandslam finals, the coefficient of variation of ranking points for the top 10 players, and
the Spearman rank correlation coefficient between two consecutive seasons. They
found that the share of new top 10 players was larger in men (Association of Tennis
Professionals [ATP] Tour) than in women (Women’s Tennis Association [WTA]
Tour). However, they claim that there is no difference in competitive balance
between WTA and ATP, using indicators for match-specific and seasonal uncertainty. Boulier and Stekler (1999) found that 53% of male players and 63% of female
players were seeded players in the 4th round of tennis grand slams.
Therefore, the objective of the article is threefold. First, two alternative measures of competitive balance in single-elimination tournaments, based on the
performance of seeded players, are proposed. Second, those measures are used
to analyze competitive balance in tennis grand-slams tournaments. Specifically,
whether the increase in the number of seeded players from 16 to 32 in 2001 led
to a decrease in competitive balance is tested. Likewise, the effects of gender and
court surface differences are investigated. Third, the determinants of upset are
tested using discrete choice models in grand-slam matches.3 The data consist of
more than 4,000 tennis matches from the tennis grand-slam tournaments played
in 2005, 2006, 2007, and 2008.
The rest of the article is organized as follows. The following section describes the
context of professional tennis and the tennis seeding system. This is followed by an
analysis of competitive balance in elimination tournaments. Subsequently, the data
are presented. Then the results of competitive balance and match uncertainty are
shown. Finally, we draw some conclusions from our analysis.
Professional Tennis and Tennis Seeding System
Professional tennis is split into the ATP (men) and WTA (women) tours. The most
important and prestigious tournaments in the tennis circuits are the grand-slam tournaments (i.e., the Australian Open, the French Open, Wimbledon, and the U.S.
Open). Competition in those tournaments begins with 128 players in its main draws4
and its prize money and prestige is much higher in grand-slam tournaments than in
other tournaments. Hence, the incentive to perform well in those tournaments is so
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566 Journal of Sports Economics
high that it is very unlikely that players treat the event as a practice or underperforming because the player does not want to risk aggravating an injury.
A tennis match is comprised of an odd number of sets (three or five). A set
consists of a number of games (a sequence of points played with the same player serving), and games, in turn, consist of points (Paserman, 2007). Men play to the best of
five sets, while women play to the best of three sets in grand-slam tournaments.
Assuming that the probability of winning a set by the favorite player is the same
throughout the match,5 probability theory tells us that the larger the number of sets
played, the higher the probability that the favorite wins.6 On the contrary, Magnus
and Klaassen (1999) argued that it may be that men are more equal in quality than
women. Therefore, it will be interesting to test the differences in competitive balance
and match uncertainty among gender.
As stated in Du Bois and Heyndels (2007), a critical dimension of tennis’ structure
is the playing surface because it determines the speed of the game and thus the strategy of the game. The Australian Open and the U.S. Open are played on hard courts,
whereas the French Open and Wimbledon are played on clay and grass courts,
respectively.7 From a theoretical point of view, underdogs are believed to use riskier
strategies than favorites (Dixit, 1987). Moreover, given that, in general, fewer ‘‘winners’’ hits are needed to win a point on quick surfaces than on less quick surfaces, the
quicker the court, the more effective risky strategies should be. Thus, we expect that
outcome uncertainty will be higher on grass than on hard courts and clay.
Public preferences, especially in the final rounds of elimination tournaments, are
assumed to be to watch both contests between popular contestants8 and even, rather
than uneven, matches. Hence, to protect top contestants from early elimination and
ensure that strong will play the strong in later round matches (Sanderson & Siegfried,
2003), organizers of elimination tournaments produce seeding positions based on previous performances.9 Thus, the seeding system can be viewed as a tool for organizers
to decrease competitive balance. The seeding system in tennis’ grand slams has
evolved over time. The number of seeded players has been 8, 12, 16, and currently
32, since the 2001 French Open. However, in 1924 a seeding system was introduced
in which up to four representatives of a nation were drawn in the four different quarters
of the draw. In 1927, full seeding was carried out and competitors were selected
according to ability, irrespective of nationality. Since 1975, the seeding system has
been based on computer rankings.4 Moreover, Wimbledon is the only tournament that
has traditionally used the power to ignore these rankings and select seeds using their
own criteria. In particular, a committee adjusted seedings subjectively. As a result, top
clay court specialist players protested the unfairness of Wimbledon’s seeding system
by boycotting Wimbledon in 2000. However, other professionals like Brad Gilbert
(Andre Agassi’s coach) claimed to not understand why other grand-slam tournaments
did not follow the All England Club’s example with regard to assigning seeds.
To end this argument among tennis professionals, in 2001, four grand slams
agreed that the number of seeded players would be increased to 32 and the seed order
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del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis
567
could be determined using a formula that assesses not only actual ranking but also
past performance on the event’s playing surface. In particular, Wimbledon developed a new seeding system for men in which the 32 highest ranked players would
be selected for seeding. However, the seeds would be changed by constructing a
new indicator that summed the total ranking points, plus a 100% increase for points
earned for all grass court tournaments in the past 12 months, as well as an additional 75% increase in points earned for the best grass court tournaments in the
prior 12 months. However, for women, the seeding order followed the ranking list,
except where, in the opinion of the committee, the grass court credentials of a
particular player necessitated a change, in the interest of achieving a balanced
draw. Still, the other grand-slam tournaments preferred to stick to the ATP/WTA
rankings. The ATP welcomed the decision to seed 32 players at the grand-slams
tournaments instead of 16 players, but it was opposed to determining the order
based on a surface-based system. Given that, by its very nature, a surface-specific
system is highly technical and likely to be understood by very few fans, the ATP
preferred to produce the seeds with a surface-biased base rather than to use a more
complex seeding system.
Competitive Balance in Elimination Tournaments
Most individual sports events are organized on an elimination tournament basis.11
Given that the tournament design of a single elimination tournament is far from that
of a league, measures of a leagues’ competitive balance, such as the dispersion of
winning percentage, Herfindahl-Hirschman Indexes, and so on (see Humphreys,
2002) cannot be adopted for individual sports tournaments. Therefore, it is necessary
to look for alternative measures. However, very few articles have attempted to measure competitive balance in single elimination tournaments. Boulier and Stekler
(1999) proposed using the relative frequency with which 16 seeded players reached
the 4th round in tennis grand-slam tournaments. In this article, we propose to extend
this idea to all rounds. Thus, a competitive balance measure for each round can be
computed as the percentage of the seeded contestants who achieved a round, out
of the seeded contestants who should achieve12 such rounds—if seeds were perfect
predictors. For instance, if the players who achieve the final round are the first and
third seeded, the measure will be 50%.
An advantage of this measure is that it is bounded between 0 and 100, so it is very
easy to interpret: the closer to 100, the poorer the competitive balance. The main
drawback is that it does not account for the quality of the players who ‘‘surprisingly’’
advance to some rounds. For instance, it provides the same measure of competitive
balance if the final is played by the first and third seeded players and by the first
seeded and an unseeded contestant. Obviously, an effective measure should indicate
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568 Journal of Sports Economics
higher competitive balance in the latter situation. An alternative measure that overcomes such problem is given by
P
ðn þ 1Þ seedp ij
i
CBj ¼ P
100;
ððn þ 1Þ seedt Þij
ð1Þ
i
where i denotes seeded players, j denotes round, p denotes players who have
achieved round j, t denotes players who should achieve round j according to their
seed number, seed is the seed position, and n is the total number of seeded players.
Therefore,
if the number of seeded players is 16, the CB will be 96.77%
16þ14
if the final is achieved by the first and third seeded players and
16þ15 100
51.61%
16
16þ15
100 if the final is achieved by the first seeded and an unseeded
player.
Data
Two kinds of data were gathered. To analyze competitive balance, we collected
the round reached by seeded players in tennis grand-slam tournaments from 1994
to 2008. To do so, draws were consulted or the information was obtained from
Wikipedia.
However, to study match-specific uncertainty, data from the matches in grandslam tournaments since 2005 to 2008 were used. In particular, we collected the
results of the matches and whether the player was either qualified from the qualification round or obtained a wild card. Additionally, we collected some individual characteristics such as the ranking at the time of the tournament, the best previous
ranking, country, height, weight, and date of birth of the players that were involved
in the tournaments. Most data were gathered from the Web sites of the ATP
(www.atptennis.com) and WTA (www.sonyericssonwtatour.com), but some data
were gathered from the Web site www.tennis-data.co.uk.13 Each draw is composed
of 128 players. Thus, 127 matches for both men and women are played in each tournament. In total, we gathered data on 4,064 matches.
Tournaments’ Competitive Balance Results
In this section, we tested whether the increase in the number of seeded players
from 16 to 32 led to decreased competitive balance in tennis grand-slam tournaments. To do so, the performance of the top 16 seeded players is analyzed during two
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del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis
569
Figure 1
Evolution of the Percentage of the Seeded Players (16) that Achieve the
Expected Round Using a 3-Year Moving Average
100
Men
35
35
55
55
%
%
75
75
100
Women
1994
1998
2002
Year
Semifinal
Third
2006
Fourth
Second
1994
1998
2002
Year
Semifinal
Third
2006
Fourth
Second
different periods: 1994-2000 and 2002-2008. In the first period, there were 16 seeded
players, while in the second period there were 32.
A way to compare competitive balance between both periods is by calculating the
competitive balance measures proposed above, using the performance of the top 16
seeded players. Therefore, to compute the percentage of seeded players who
achieved the expected round, only the performance of the top 16 seeded players
should be analyzed. Likewise, n in equation (1) is 16 to compute the CB measure.
Figures 1 and 2 show the evolution over time of the average across tournaments
of the percentage of seeded players who achieved the expected round and the CB
measure, in some rounds.14 To avoid that the inherent noise of the data cause some
problems, both figures have been made using a 3-year moving average. It is noteworthy to indicate that all points in the figures are averages of 3 years of data using
the same number of seeded players.
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570 Journal of Sports Economics
Figure 2
Evolution of the CB Measure Using a 3-Year Moving Average
75
100
Men
55
35
35
55
%
%
75
100
Women
1994
1998
2002
Year
Semifinal
Third
2006
Fourth
Second
1994
1998
2002
Year
Semifinal
Third
2006
Fourth
Second
From both figures, it seems that there is a structural break point, especially for
men, in the year 2001, when the 32-player seeding system was adopted. In particular,
both measures take higher values in the second period of analysis. Therefore, competitive balance has been lower since the new seeding system was adopted. Moreover, it can be seen that the measures take higher values especially for men. Thus,
it seems that competitive balance is lower in the 32-player seeding system. Still,
regression analysis should be used to get a clearer picture of the effects of the change
in the number of seeded players. Before doing that, however, Table 1 provides the
average of the percentage of expected seeded players who get some rounds and
Table 2 provides the average of the CB measure.
Wimbledon carried the lowest percentages of seeded players who advanced to the
2nd and 3rd rounds; however, Wimbledon is also the tournament with the highest
percentage of the four top seeded players in the semifinals. Thus, lower seeded players were more likely to lose in the preliminary rounds in Wimbledon than in other
tournaments. Likewise, the French Open is characterized by the lowest predictive
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571
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88%
(7%)
78%
(9%)
66%
(9%)
62%
(20%)
55%
(17%)
54%
(37%)
36%
(50%)
Women
82%
(9%)
66%
(15%)
52%
(16%)
49%
(19%)
48%
(33%)
36%
(36%)
36%
(50%)
Men
85%
(9%)
72%
(13%)
59%
(14%)
55%
(20%)
52%
(26%)
45%
(37%)
36%
(49%)
Both
Australian Open
86%
(10%)
79%
(12%)
63%
(11%)
58%
(15%)
54%
(29%)
36%
(31%)
14%
(36%)
Women
82%
(5%)
64%
(10%)
48%
(11%)
38%
(17%)
30%
(33%)
21%
(43%)
0%
(0%)
Men
French Open
Note: Standard deviations are shown in parentheses.
Winner
Final
Semifinal
Quarterfinal
1/8 Final
3rd Round
2nd Round
Tournament
Gender
84%
(8%)
72%
(13%)
55%
(13%)
48%
(19%)
42%
(33%)
29%
(37%)
7%
(26%)
Both
89%
(10%)
72%
(11%)
58%
(9%)
60%
(11%)
57%
(27%)
50%
(34%)
43%
(51%)
Women
81%
(11%)
60%
(15%)
45%
(14%)
42%
(17%)
50%
(26%)
61%
(35%)
71%
(47%)
Men
Wimbledon
85%
(11%)
66%
(14%)
52%
(13%)
51%
(17%)
54%
(26%)
55%
(34%)
57%
(50%)
Both
90%
(9%)
81%
(11%)
64%
(12%)
63%
(11%)
57%
(25%)
64%
(36%)
36%
(50%)
Women
83%
(9%)
66%
(12%)
50%
(9%)
42%
(18%)
48%
(21%)
36%
(36%)
36%
(50%)
Men
US Open
86%
(10%)
73%
(14%)
57%
(13%)
52%
(18%)
53%
(23%)
50%
(38%)
36%
(49%)
Both
88%
(9%)
78%
(11%)
63%
(11%)
60%
(14%)
56%
(24%)
51%
(35%)
32%
(47%)
Women
Men
All
82%
(9%)
64%
(13%)
49%
(13%)
43%
(18%)
44%
(29%)
38%
(39%)
36%
(48%)
Table 1
Percentage of Seeded Players Who Achieve Each Round With 16 Seeded Players (1994-2008)
85%
(9%)
71%
(14%)
56%
(14%)
52%
(18%)
50%
(27%)
45%
(38%)
34%
(48%)
Both
572
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91%
(6%)
83%
(8%)
73%
(8%)
71%
(17%)
72%
(17%)
81%
(20%)
77%
(34%)
Women
85%
(9%)
73%
(15%)
60%
(17%)
60%
(20%)
63%
(25%)
63%
(23%)
86%
(17%)
Men
88%
(8%)
78%
(13%)
67%
(14%)
65%
(19%)
68%
(21%)
72%
(23%)
81%
(27%)
Both
Australian Open
89%
(10%)
84%
(10%)
71%
(10%)
69%
(13%)
77%
(17%)
75%
(20%)
79%
(18%)
Women
83%
(8%)
65%
(13%)
50%
(14%)
49%
(16%)
50%
(30%)
52%
(34%)
57%
(37%)
Men
French Open
Note: Standard deviations are shown in parentheses.
Winner
Final
Semifinal
Quarterfinal
1/8 Final
3rd Round
2nd Round
Tournament
Gender
86%
(9%)
75%
(14%)
61%
(16%)
59%
(18%)
64%
(28%)
64%
(30%)
68%
(31%)
Both
92%
(7%)
78%
(9%)
64%
(8%)
68%
(15%)
73%
(18%)
85%
(17%)
81%
(28%)
Women
84%
(13%)
66%
(18%)
52%
(16%)
53%
(18%)
62%
(25%)
76%
(30%)
91%
(25%)
Men
Wimbledon
88%
(11%)
72%
(15%)
58%
(14%)
60%
(18%)
68%
(22%)
80%
(24%)
86%
(26%)
Both
92%
(8%)
86%
(11%)
73%
(13%)
75%
(12%)
81%
(12%)
85%
(20%)
82%
(28%)
Women
85%
(8%)
71%
(12%)
57%
(10%)
53%
(15%)
65%
(19%)
74%
(26%)
69%
(40%)
Men
U.S. Open
89%
(8%)
78%
(13%)
65%
(14%)
64%
(17%)
73%
(18%)
79%
(24%)
76%
(34%)
Both
91%
(8%)
83%
(10%)
70%
(10%)
71%
(14%)
76%
(16%)
82%
(19%)
80%
(27%)
Women
Table 2
The CB Measure of Competitive Balance With 16 Seeded Players (1994-2008)
84%
(9%)
69%
(14%)
55%
(15%)
54%
(17%)
60%
(25%)
66%
(29%)
76%
(33%)
Men
All
88%
(9%)
76%
(14%)
63%
(15%)
62%
(18%)
68%
(22%)
74%
(26%)
78%
(30%)
Both
del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis
573
Table 3
Number of Seeded Players Who Achieve the Predicted Round
Determinants
All
Model 1
DSEED16
DMASC
HARD
CLAY
R3
R4
R5
R6
R7
R8
R2HARD
R3HARD
R4HARD
R5HARD
R6HARD
R7HARD
R8HARD
R2CLAY
R3CLAY
R4CLAY
R5CLAY
R6CLAY
R7CLAY
R8CLAY
R2GRASS
R3GRASS
R4GRASS
R5GRASS
R6GRASS
R7GRASS
R8GRASS
Constant
Observations
R2
**
4.1
10.3***
2.1
11.8***
14.2***
29.2***
33.3***
34.9***
40.3***
51.0***
96.2***
784
.30
Women
Model 2
**
4.1
10.3***
Model 1
0.3
Model 2
0.3
88.4***
392
.32
Model 1
8.0
***
Model 2
8.0***
6.6**
18.1***
18.0***
33.1***
39.0***
37.6***
43.4***
46.1***
2.4
5.5
10.4**
25.3***
27.6***
32.3***
37.2***
55.9***
28.3*** (1)
15.4** (1)
0.8 (1)
3.3 (1)
4.9 (2)
9.8 (2)
21.4*** (2)
26.8*** (3)
14.5** (2)
1.8 (2)
8.9 (3)
15.2** (3)
28.6*** (3)
50.0*** (3)
27.7*** (2)
9.2 (3)
5.6 (3)
6.3 (2)
3.6 (1)
1.8 (1)
(1)
64.4***
784
.35
Men
45.8*** (1)
36.6*** (1)
22.1*** (1)
19.2** (1)
13.4 (2)
16.1* (2)
7.1 (2)
43.3*** (2)
36.6*** (2)
20.1** (2)
15.2 (3)
10.7 (3)
7.1 (3)
28.6*** (3)
46.0*** (3)
29.5*** (3)
15.2 (3)
17.0* (2)
14.3 (1)
7.1 (1)
(1)
43.0***
392
.34
93.6***
392
.29
10.9 (2)
5.8 (1)
20.5** (1)
25.9*** (1)
23.2*** (2)
35.7*** (1)
35.7*** (2)
10.3 (3)
7.6 (1)
23.7** (2)
33.0*** (3)
41.1*** (3)
50.0*** (3)
71.4*** (3)
9.4 (1)
11.2 (3)
26.3*** (3)
29.5*** (2)
21.4** (1)
107 (2)
(1)
75.4***
392
.38
Notes: In parentheses, the ranking of the coefficients relative to the other two surfaces in the same round
and model are shown.
*, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.
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574 Journal of Sports Economics
Table 4
CB Determinants
All
Model 1
DSEED16
DMASC
HARD
CLAY
R3
R4
R5
R6
R7
R8
R2HARD
R3HARD
R4HARD
R5HARD
R6HARD
R7HARD
R8HARD
R2CLAY
R3CLAY
R4CLAY
R5CLAY
R6CLAY
R7CLAY
R8CLAY
R2GRASS
R3GRASS
R4GRASS
R5GRASS
R6GRASS
R7GRASS
R8GRASS
Constant
Observations
R2
***
3.6
12.6***
1.3
5.3***
12.0***
25.1***
25.6***
19.7***
13.9***
10.0***
96.5***
784
.25
Women
Model 2
***
3.6
12.6***
Model 1
0.7
Model 2
0.7
89.5***
392
.16
Model 1
7.8
***
Model 2
7.8***
0.1
11.0***
15.5***
29.2***
30.7***
24.0***
18.0***
8.5**
2.7
0.4
8.5***
20.9***
20.5***
15.4***
9.7***
11.5***
2.3 (1)
8.0* (1)
20.2*** (1)
21.4*** (1)
15.7*** (1)
10.5** (2)
7.6* (2)
0.0 (3)
11.6** (2)
25.4*** (2)
27.2*** (3)
22.6*** (3)
22.5*** (3)
18.3*** (3)
1.8 (2)
14.2*** (3)
27.9*** (3)
25.8*** (2)
18.5*** (2)
5.7 (1)
(1)
94.3***
784
.27
Men
10.6** (1)
3.2 (1)
8.1 (1)
8.5 (1)
4.5 (1)
1.5 (2)
1.8 (2)
7.7 (3)
2.4 (3)
10.0 (3)
11.8* (3)
4.0 (3)
5.9 (3)
2.2 (3)
11.0* (2)
2.9 (2)
17.3*** (2)
13.0** (2)
8.3 (2)
4.0 (1)
(1)
80.9***
392
.17
91.0***
392
.25
6.0 (2)
19.2*** (1)
32.4*** (1)
34.4*** (1)
26.8*** (2)
22.4*** (2)
13.4* (2)
7.8 (3)
25.6*** (2)
40.9*** (2)
42.6*** (2)
41.2*** (1)
39.0*** (3)
34.4*** (3)
7.4 (1)
25.4*** (3)
38.6*** (3)
38.5*** (3)
28.6*** (3)
15.5* (1)
(1)
95.0***
392
.28
Notes: In parentheses, the ranking of the coefficients relative to the other two surfaces in the same round
and model are shown.
*, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.
power of seeds, especially from the quarterfinals. When comparing the difference in
competitive balance between men and women, we found that competitive balance is
lower for women than for men (the only exception is the winner round of Table 1).
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del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis
575
Tables 3 and 4 show the determinants of the competitive balance measures using
regression analysis. In doing so, a different observation is considered for each round
of each tournament for men and women. Thus, there are 784 observations,15 of which
392 belong to women and 392 to men. Those measures are evaluated using ordinary
least squares (OLS) regression with a number of dummy variables. The first dummy
variable takes the value of one if the tournament had 16 seeded players and zero otherwise (DSEED16). A negative coefficient is expected for this variable. Another dummy
variable represents gender (DMASC) and takes the value of one for men’s matches.
Likewise, a set of dummies for surface (HARD, CLAY, and GRASS) and dummies for
round were also used. Those sets of dummies were interacted in Model 2.
The coefficient of DSEED16 is negative and significant in the models for all
players.16 Thus, the increase in the number of seeded players led to decreased competitive balance in tennis grand-slam tournaments. However, if the sample is split
into men and women, this coefficient is not significant for women but takes a lower
and significant value for men. Thus, the change in the number of seeded players
affected men’s and women’s grand-slam tournaments differently.
Moreover, average competitive balance measures are lower for men than for
women by more than 10%. Therefore, men’s tournaments are characterized by a
much higher competitive balance than women’s tournaments. Finally, with respect
to court surfaces, clay turned out to be the type of court surface in which the
competitive balance is highest, if all rounds are aggregated. This result could be
qualified using the results from Model 2. Thus, in general, clay is the surface that
produces the most competitive balance, especially in the final rounds. In the preliminary rounds, Wimbledon is the tournament generally characterized by the highest
competitive balance.
Match-Specific Uncertainty Results
The biggest ex post match uncertainty outcome happens when the underdog beats
the favorite. Following Abrevaya (2002), this outcome is labeled as upset. To analyze
upset determinants, we estimated probit models in which the dependent variable takes
the value of one when there is an upset and zero otherwise. Two kinds of covariates are
used. The first refers to the characteristics of the match, while the second refers to
players’ characteristics. To control for match characteristics, we used dummies for the
court surface (i.e., HARD, CLAY, and GRASS) where GRASS is the reference category and a set of dummies controls for the round of the match. With regard to court
surface, we expected that the quicker the surface, the higher the likelihood of upsets.
Thus, it is expected that the lowest coefficient would belong to clay surface and the
highest to grass surface. Likewise, the round dummies are expected to be lower when
advancing round because Gilsdorf and Sukhatme (2007) found that the larger the
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576 Journal of Sports Economics
difference in prizes between the winner and the loser, the less likely the upset, but
upsets will be less likely on 1st rounds due to the seeding system because seeded player
are going to face between them. Thus, it is unclear which effect will predominate.
With respect to the player characteristics, the following variables were used.
A measure of the ex ante quality differences between players (DIFRANKING)
was constructed as the difference between players’ rating measures (Rating ¼
8 log(Rank)), which was proposed by Klaassen and Magnus (2001).17 The main
advantage of this measure is that it assumes that quality in tennis is a pyramid. The
expected value of the coefficient of this value is negative. Moreover, we included
the age of the favorite (AGEF) and the age of the underdog (AGEU). Older players
are more experienced than younger ones but may also lose some of their abilities and
incentives. Hence, it was not clear, which sign the coefficient of those variables
would take. However, with a large data set, the coefficients of those variables are
likely to demonstrate that young players are more likely to improve their ranking
than old players. Therefore, a negative coefficient for AGEU and a positive coefficient for AGEF were expected. In addition, a dummy variable for players who played
in the qualification round (DPREV) and a dummy variable for wild cards players18
(DWILD) were introduced. Moreover, because countries could specialize in producing players with particular surface skills (e.g., Spain with clay), dummy variables for
countries with enough observations were interacted with the surface dummies.19 In
tennis, the height of the players is correlated positively with service skills (i.e., the
taller player is the one more likely to serve fast). As a result, we assumed that differences in height could influence upsetting. Therefore, we include the height difference (DIFHEIGHT) between the favorite and the underdog, with the coefficient
expected to be negative because the higher height difference between the favorite
and the underdog the less likely are upsets. Lastly, we created a dummy variable that
takes the value of 1 if the player is a former top 10 player at a minimum of five 5 years
ago. The model includes variables for if the former top-10 player is the underdog
(EXTOP10U) or the favorite (EXTOP10F). The expected values of those coefficients
are negative for EXTOP10F and positive for EXTOP10U. This is based on the expectation that former top 10 players will remember how to play well if they are motivated
enough. Finally, to test whether the differences between men and women are significant, we used gender dummy variables (i.e., DMALE and DFEMALE). Likewise,
those variables were interacted to test for joint differences between gender and court
in an alternative specification for which GRASS*DMALE was the reference.
We estimated two alternative specifications for all players, as well as a model for
men’s matches and another for women’s matches. Thus, we estimated four models of
upset determinants. Table 5 shows the estimates as well as the marginal effects.20
As expected, the difference in quality between contestants is negatively correlated
with the probability of upset and is significant in all models. The variable DMALE
has a negative coefficient but is not significant. The estimated coefficients of the
court surface dummies are not significant at any confidence level. The only
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577
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0.025***
0.022***
0.204***
0.147
0.229***
0.424***
0.007**
0.401
0.404
0.285
0.252
0.389
0.005
3,952
.12
2,070
0.235
0.424***
0.075
0.031
0.093
(0.008)
(0.007)
(0.068)
(0.049)
(0.070)
(0.148)
(0.002)
(0.127)
(0.119)
(0.084)
(0.074)
(0.108)
(0.002)
(0.135)
(0.024)
(0.010)
(0.030)
ME
0.103
0.032
0.191
0.223
0.179*
0.025***
0.022***
0.205***
0.151
0.231***
0.428***
0.007**
0.403
0.406
0.287
0.253
0.390
0.008
3,952
.12
2,069
0.107
0.424***
Coefficient
Model 2
(0.033)
(0.010)
(0.064)
(0.075)
(0.060)
(0.008)
(0.007)
(0.068)
(0.050)
(0.071)
(0.150)
(0.002)
(0.128)
(0.120)
(0.084)
(0.074)
(0.108)
(0.002)
(0.135)
ME
(0.006)
(0.004)
(0.074)
(0.076)
(0.112)
(0.236)
(0.002)
(0.308)
(0.249)
(0.193)
(0.179)
(0.196)
(0.055)
(0.044)
(0.030)
0.141
0.100
0.020**
0.013
0.227**
0.229
0.389***
0.657***
0.008*
1.021**
0.988**
0.799**
0.775*
0.941**
0.192
1,930
.16
966
(0.128)
ME
0.764
0.414***
Coefficient
Model 1 (Women)
Note: ME, marginal effect measured at the means of the other variables.
*, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.
All models include country effects interacted with the surface for favorite and underdog, respectively.
CONSTANT
DIFRANKING
DMALE
HARD
CLAY
HARD*DFEMALE
HARD*DMALE
CLAY*DFEMALE
CLAY*DMALE
GRASS*DFEMALE
AGEF
AGEU
DPREV
DWILD
EXTOP10F
EXTOP10U
DIFHEIGHT
DROUND1
DROUND2
DROUND3
DROUND4
DROUND5
DROUND6
Observations
Pseudo-R2
Log likelihood
Coefficient
Model 1
Table 5
Upset Probit Results
0.031***
0.036***
0.138
0.061
0.083
0.359***
0.009**
0.022
0.014
0.070
0.101
0.007
0.054
2,022
.15
1,030
0.143
0.248
0.011
0.453***
Coefficient
ME
(0.010)
(0.011)
(0.045)
(0.020)
(0.026)
(0.122)
(0.003)
(0.007)
(0.004)
(0.022)
(0.033)
(0.002)
(0.017)
(0.045)
(0.081)
(0.142)
Model 1 (Men)
578 Journal of Sports Economics
exception is the coefficient for GRASS*DFEMALE, which is positive in Model 2.
Therefore, the hypothesis that quicker courts have higher match-specific uncertainty
is only supported by the data for women.
The coefficients for AGEF and AGEU are positive and negative, respectively.
This suggests that younger players tend to perform better than older players, given
the ranking and other covariates. Similar results were found by Gilsdorf and
Sukhatme (2007), using data from men’s matches. The coefficients of EXTOP10U
are positive and EXTOP10F are negative, reflecting that players who were top 10
players several years before tend to make more upsets as underdog and to lose less
matches as favorites than other players. Moreover, this effect is higher for women
than for men. Finally, the coefficient of DIFHEIGHT is negative in all models,
reflecting that if the difference in height between the favorite and the underdog is
positive, the upset likelihood will be reduced. If the difference is negative (i.e., the
underdog is taller than the favorite), then the upset-likelihood will increase.
Conclusions
In this article, we tested whether the increase in the number of seeded tennis players in grand-slam tournaments from 16 to 32 in 2001 led to a decrease in competitive
balance. To do that, we proposed two measures of competitive balance based on the
performance of the seeded players. The results indicated that the outcome of the
change in the seeding system differed by gender. In particular, competitive balance
decreased significantly for men. For women, no significant effect on competitive balance was incurred as a result of the change. Moreover, the competitive balance measured by the performance of seeded players is much higher for men than for women.
Furthermore, Wimbledon faced the highest amount of competitive balance in the
preliminary rounds, while in the final rounds, the opposite was found.
Additionally, we analyzed the upset determinants using probit models. We found
that quality difference is the main determinant of upsets. Moreover, conclusive evidence of differences among surfaces and gender were not found.
Given that many sports events use seeds in single-elimination tournaments, the
methodology used in this article can be implemented to analyze the competitive balance in these events. This could be especially important for testing the implications
of some rule changes on competitive balance in sports and events.
Notes
1. See Borland and MacDonald (2003) or Szymanski (2003) for surveys.
2. For instance, the International Table Tennis Federation has recently banned the use of speed glue
to stick rubbers to the blade. Such a measure will certainly alter the competitive balance and will benefit
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del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis
579
players with high defensive skills. Table tennis has also made some previous changes that could affect the
competitive balance, such as the change in the scoring system and the service rule.
3. Magnus and Klaassen (1999), Boulier and Stekler (1999), Clarke and Dyte (2000), Klaassen and
Magnus (2001, 2003), Paserman (2007), and Gilsdorf and Sukhatme (2007) have previously estimated discrete choice models using tennis data.
4. Some players need to qualify to the main draw by playing the qualifying stage. If an unexpected
spot becomes available, then a lucky loser of the qualifying stage will play in the main draw.
5. Magnus and Klaassen (1999) found that there is no decrease in service dominance during a match.
6. For instance, assuming that the probability of winning a set by the favorite is .6, then the probability that the favorite wins the match is .65 within a match to the best of three sets and it is .68 if the match is
played to the best of five sets.
7. The fastest court is the grass court, followed by hard court. The slowest type of surface is the clay
surface.
8. The most popular players are usually the best classified players in the official rankings (see Pujol
& Garcı́a-del-Barrio, 2007). However, there can be some exceptions from players who garner fame
because of circumstances other than being a good player. Anna Kournikova in the beginning of the
2000’s is a good example.
9. Seeds are not only used in single elimination tournaments but also in several competitions in which
round robin matches are played and subsequently the classified players are pooled in a single elimination
tournament such as the Olympic competitions in sports, UEFA Champions League or FIFA World Cup.
See Groh, Moldovanu, Sela, and Sunde (in press) for a theoretical analysis of optimal seedings.
10. The Appendix contains an explanation of how the computer rankings are constructed.
11. See Szymanski (2003) for the economic design of individual contests.
12. The 1st and 2nd seeded players should achieve the final, the 3rd and 4th should achieve the semifinals, the 5th, 6th, 7th, and 8th should achieve the quarterfinal, and so on.
13. Data from this source have previously been used by Forrest and McHale (2007) to estimate the
relationship between returns and odds.
14. Some rounds are precluded because the figure turns fuzzy. The graphs containing all rounds are
available upon request.
15. 14 (years), times 4 (tournaments), times 7 (rounds), times 2 (genders).
16. The coefficient of DSEED16 is the same in all models 1 and 2 because model 1 and model 2
contains the same information. The only difference is that in model 2 the round dummies and surface dummies were interacted.
17. The absolute difference in the ranking was also used, but because we obtained better results with
this variable only those results are presented.
18. These wild cards are usually given to players from the country in which the tournament is played
or well-recognized players who may not have a high enough ranking.
19. The coefficients of these variables are ignored in the presentation of the results, but they are available upon request. Not surprisingly, the country effects of Spain reflect the ability of Spanish players on
clay.
20. It is important to note that it is not possible to use all observations due to missing data for some
variables (i.e., ranking, height, and age).
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580 Journal of Sports Economics
Appendix A
How Are Tennis Rankings Computed?
The ATP and WTA ranking system reflects players’ performance in tournament
play using a cumulative points system in which the number of tournament results that
comprise a player’s ranking is capped at 17 and 18 tournament results for women and
men, respectively. Both systems have some ‘‘mandatory’’ events (i.e., grand slams,
ATP Master Series, and WTA Tier I). In both cases, for each ‘‘mandatory’’ event in
which a player is not accepted, he or she may count one extra event toward his or her
ranking Thus, the ATP ranking is based on calculating, for each player, his total
points from the 13 ‘‘mandatory’’ events—the four grand slams and the nine ATP
Masters Series tournaments—and his best five results from all eligible International
Series tournaments from the past 52 weeks. The Tennis Masters Cup counts as an
additional 19th tournament for players who qualify for the circuit finale.
However, the WTA ranking is based on the player’s highest ranking points over
the past 52 weeks including her ranking points from the Mandatory Tier I Tournament and the grand-slam Tournaments, if the player qualifies. Players are ranked
on the basis of their total points. In the following table, the points awarded for each
round in the ATP and WTA ranking systems are presented.
Table A1. Points Awarded in Various Types of Tournaments (2008)
Women
Grand slam
ATP master series
Tier I (US$3,000,000)
Tier I (US$2,000,000)
Tier I (US$1,340,000)
Men
W
F
S
Q
R16
R32
W
F
S
q
R16
R32
1,000
700
450
250
140
90
1,000
500
700
350
450
225
250
125
150
75
75
35
500
465
430
350
325
300
225
210
195
125
115
110
70
65
60
45
40
35
Notes: W ¼ winner; F ¼ finalist; S ¼ semifinal; Q ¼ quarterfinal.
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Julio del Corral is a Ph D. Student at the University of Oviedo. His fields of specialization are efficiency
and productivity analysis and sports economics. He has published articles in the Journal of Sports Economics, Revista de Economia Aplicada and Journal of Dairy Science.
Downloaded from http://jse.sagepub.com at Univ de Oviedo-Bib Univ on December 2, 2009