See all ›

40 CitationsSee all ›

28 ReferencesSee all ›

1 Figure# Home advantage in professional tennis

Abstract

Home advantage is a pervasive phenomenon in sport. It has been established in team sports such as basketball, baseball, American football, and European soccer. Attention to home advantage in individual sports has so far been limited. The aim of this study was to examine home advantage in professional tennis. Match-level data are used to measure home advantage. The test used is based on logit models, and consistent specification is addressed explicitly. Depending on the interpretation of home advantage, restrictions on the specification of the model need to be imposed. We find that although significant home advantage exists for men, the performance of women tennis players appears to be unaffected by home advantage.

Figures

Home Advantage in Professional Tennis!

Ruud H. Koning!

.

May 9, 2009

Abstract

Home advantage is a pervasive phenomena in sport. It has been well-established

in team sports as basketball, baseball, and American football in the US, and soccer

in Europe. Less attention has been given to home advantage in individual sports.

In this paper we examine the existence of home advantage in professional tennis.

We use match-level data to measure home advantage. Our test is based on logit-

models, and consistent speciﬁcation is addressed explicitly. Depending on the in-

terpretation of home advantage, restrictions on the speciﬁcation of the model need

to be imposed. We ﬁnd that signiﬁcant home advantage exists for men, but such an

advantage cannot be found for women.

Keywords: home advantage, tennis, logit model, consistent speciﬁcation.

1INTRODUCTION

Home advantage is a well established phenomena in different professional sports; a

recent overview is given in Stefani (2008). Most of the published results concern home

advantage in team sports, although it is well known that the medal count of a coun-

try organizing Olympic Games tends to be higher than expected (Balmer, Nevill, and

Williams, 2001, 2003). Because most of the elements of the Olympic competition are

individual events, this suggests that home advantage exists in individual sports as well.

Only a few studies focus explicitly on home advantage in individual sports. A small

but signiﬁcant home advantage in speed skating is established in Koning (2005), and

Nevill, Holder, Bardsley, Calvert, and Jones (1997) document little evidence of home

advantage in professional tennis and golf. In this paper, we estimate home advantage

!This paper has beneﬁtted from research assistance by Wim Siekman, Stefanie Bouw, and Tirza de Rond.

!Department of Economics & Econometrics, Faculty of Economics and Business, University of Gronin-

gen, PO Box 800, 9700 AV Groningen, The Netherlands, r.h.koning@rug.nl.

1

(c) 2009 www.rhkoning.com

in professional tennis, using a different methodology from the ones used before. Our

approach uses individual match outcomes as opposed to individual player performance

at a tournament level. The contribution of this paper is three fold. First, we propose a

logit model to analyze outcomes of tennis matches. Home advantage is deﬁned in the

context of this model, and special care is taken to obtain a logically consistent model

speciﬁcation. Second, we measure not only home advantage in individual matches, but

also as improved access to tournaments for home players. Third, we use a much ex-

panded data set compared to earlier studies. This allows us to assess whether home

advantage has changed over time and/or varies between type of tournament.

The plan of the paper is as follows. In section 2 we present a literature review and

introduce our measures of home advantage. Speciﬁcation of the model is presented in

section 3. A description of the data and empirical results are given in section 4 and

section 5 concludes.

2LITERATURE REVIEW

Home advantage is a well established phenomena in different professional sports. Re-

cent overviews documenting and interpreting its existence are given in Nevill, Balmer,

and Wolfson (2005) and the articles following in that special issue, and Stefani (2008).

Usually, home advantage is deﬁned as ‘the consistent ﬁnding that home teams in sports

competitions win over 50% of the games played under a balanced home and away

schedule’ (Courneya and Carron, 1992). However, in the context of individual sports,

where winners are usually determined in a tournament held in a ﬁxed location, this def-

inition is not applicable. Instead, a deﬁnition of home advantage as in Koning (2005)

is more useful: ‘Home advantage is the performance advantage of an athlete, team or

country when they compete at a home ground compared to their performance under

similar conditions at an away ground’.

In this paper, we consider tennis so we need to deﬁne ‘performance’ more pre-

cisely. Also, we need to be more explicit about ‘similar conditions at an away ground’

since this is a unobserved (counterfactual) situation. We deal with this last issue in the

context of the empirical models we use in the next two sections. As far as performance

is concerned, one can think of two different measures of performance of a tennis player

in a given tournament. The ﬁrst is the tournament ranking of a player. The winner of a

tournament receives tournament raking 1, the losing ﬁnalist tournament ranking 2, the

losing semi-ﬁnalist tournament raking .3 C4/=2, and so on. The other measure of per-

formance is winning a particular match. The ﬁrst measure is related to the sum (during

a tournament) of the second measure. Since we want to test for the existence of home

2

(c) 2009 www.rhkoning.com

advantage, we also need to make ‘similar conditions at an away ground’ operational.

We discuss that issue in the context of the statistical models below.

Home advantage is usually attributed to four factors:

"crowd support;

"familiarity with local circumstances;

"fatigue due to travel time;

"speciﬁc rules that favor either the home or away team.

Crowd support may help a home player to perform better, to prevent him or her giv-

ing up sooner, and intimidate the opponent (assuming that that is not a home player).

It is less likely that crowd support inﬂuences the decisions made by referees in ten-

nis, as these are usually not from the home country. Moreover, the introduction of the

‘challenge’, where a player can ask for a video replay to see if a ball is in or out,

has decreased reliance on decisions by the referee and line judges. Unfortunately, we

don’t have data on the consistency of the crowd (that is, the ratio of home supporters

to away supporters) so we cannot assess the inﬂuence of consistency of the crowd on

home advantage as in Nevill, Newell, and Gale (1996). The argument of crowd sup-

port in the case of tournament style competitions can be broadened to include local

sponsor interests. Individual tennis players are frequently sponsored by sponsors from

their home country. Such sponsors may be present at the tournament, or the player may

be involved in promotional activities during the tournament. In any case, good perfor-

mance of a player on hoe ground makes it easier to renew existing contracts or ﬁnd new

sponsors. The importance of home sponsor support will be greater for subtop players

than for top players, who are usually sponsored by sponsors operating globally. Famil-

iarity with local circumstances may be relevant if players from, say Spain, have had

the opportunity to practice much more on gravel tennis courts than other players. As

tournament venues are usually not used for practice, only the type of surface may be

a factor in determining home advantage. It is unlikely that home advantage is caused

by travel fatigue for away players. All players travel from tournament to the next tour-

nament, travel time does not vary very much between players. Moreover, during the

tournament the players reside in hotels close to the venue. Finally, rules favor home

players to the extent that tournament organizers have some leeway to allow a player

to enter the tournament for other reasons than his or her world ranking. In particular,

most tournaments offer wild-cards to local players, giving home players home advan-

tage through improved access to the tournament. In section 4 we will establish whether

this is indeed the case.

3

(c) 2009 www.rhkoning.com

Home advantage in tennis has been studied before, mainly in Nevill et al. (1997)

and Holder and Nevill (1997). In these papers, the measure of performance is the tour-

nament ranking of a player and the central question that is answered is whether or

not home players achieve a better than expected tournament ranking given their world

ranking at the time of the tournament. The data used to test for home advantage are the

four Grand Slam tournaments of 1993 (the Australian Open, the French Open, Wim-

bledon, and the US Open). Home advantage is estimated by ﬁrst estimating a model

where the log of tournament rank is regressed on the log of the world rank of a player.

This baseline model is then extended with a dummy measuring home advantage (al-

lowing for a different intercept for home players), and an interaction term between

home advantage and log world rank (allowing for a different slope for home players).

In both papers, the authors ﬁnd little evidence of home advantage. Home players per-

form signiﬁcantly better only in the Wimbledon tournament, there is no evidence of

home advantage in the other three tennis tournaments. Holder and Nevill attribute this

ﬁnding to ‘an anomaly of the data collection’ (p. 556): in their study ranks are missing

for away players at Wimbledon with a rank lower than 100, but world rank is available

for all home players. Our data used below do not suffer from this issue. The approach

by Holder and Nevill is based on an implicit comparison between the performance of a

home player with a certain world rank and an away player with that same rank. Since

the strength (world rank) of the opponents does not enter as a covariate, one has to

assume that the tournament draws for both players are identical.

In our approach below, we use match level data, and we relate the outcome of a

match to observed covariates. Other studies have identiﬁed relevant covariates that we

can use in our baseline model or as variables to moderate the effect of home advantage.

In a recent paper, del Corral (2009) estimates match uncertainty in tennis. He shows

that Grand Slam tournaments have become less competitive since 2002 when the num-

ber of seeded players was increased from 16 to 32. According to his empirical results,

competitiveness in tennis varies by sex, round, and surface. Also, he shows that upsets

are mainly determined by quality differences between players (as measured by the dif-

ference in their rankings). In his empirical analysis, he does not take home advantage

into consideration.

Klaassen and Magnus (2001, 2003) model the probability of winning a tennis match

differently. In Klaassen and Magnus (2001) they focus on winning a point in a game,

instead of winning a complete match. In that paper, the probability of winning the next

point by the player who serves depends on time-constant covariates (quality difference

between players, absolute quality of the match) and on time-varying covariates (who

won the previous point, ﬁrst point of the game, importance of the next point). Klaassen

4

(c) 2009 www.rhkoning.com

and Magnus (2001) that the probability of winning the next point depends positively

on the quality difference between both players, and positively on the absolute quality

of the match. Their focus is on testing whether or not points are independently identi-

cally distributed, so their attention for other covariates is limited. They do report that

they experiment with some other covariates, but home advantage is not one of them.

Klaassen and Magnus (2003) follow up on that paper and consider the probability that

a player wins a match (instead of the next point). This problem is close to the one we

consider in the next section. They estimate the probability that the better player (as

measured by world ranking) wins against the weaker player. Difference of quality is

the main covariate. Again, they do not take home advantage into account.

3MOD EL SP EC IFI CATI ON

In this paper, we take ‘winning a match’ as the measure of performance in tennis.

The main reason to prefer this measure over tournament ranking is that it allows us

to measure home advantage while taking a given draw into account. When estimating

the performance of a home player, it matters if a home player with world rank, say, 50

plays a top ten player in the ﬁrst round, or a lucky qualiﬁer. Considering the availability

of individual match data, we can estimate the probability of winning a match easily,

and let this probability depend on certain covariates. Obviously, home advantage and

quality of the players are important covariates to be included in a model. However, the

use of match data imposes restriction on the speciﬁcation that can be estimated. This

issue we address ﬁrst.

Consider two arbitrary tennis players, Aand B. Since Aand Bare chosen arbitrar-

ily, we do not know which one is the higher ranked player, or which one plays at home.

One can consider these players as being drawn randomly from the pool of participants

in a tournament. The individual characteristics of Aand Bare measured as vectors

xAand xB. This vector xmay include world ranking, height, weight, age, number of

career wins, etc. Also, there are variables that are common to both players, such as the

time of the match, or the surface, and these common characteristics are denoted by the

vector zAB. The probability that Awins against Bis denoted as Pr.A > B/. We model

this probability by a logit model:

Pr.A > B/ D1

1Ce!f .xA;xB;zAB /#!.f .xA;x

B;z

AB//: (1)

The term f .xA;x

B;z

AB/is also known as the index of the logit model. From equa-

5

(c) 2009 www.rhkoning.com

tion (1), the probability that Adoes not win, and therefor Bwins is

Pr.B > A/ D1$Pr.A > B/ De!f.xA;xB;zAB/

1Ce!f .xA;xB;zAB /

D1

1Cef .xA;xB;zAB /D!.$f .xA;x

B;z

AB//:

Alternatively, it follows directly from equation (1) that

Pr.B > A/ D1

1Ce!f .xB;xA;zAB /D!.f .xB;x

A;z

AB//:

Hence, consistent model speciﬁcation requires that

f .xA;x

B;z

AB/D$f .xB;x

A;z

AB/for all xA;x

B;z

AB:(2)

If we assume that the index is linear

f .xA;x

B;z

AB/Dˇ0

1xACˇ0

2xBCˇ0

3zAB;

with ˇ1,ˇ2, and ˇ3vectors of parameters to be estimated, restriction (2) takes the form

ˇ0

1xACˇ0

2xBCˇ0

3zAB D$ˇ0

1xB$ˇ0

2xA$ˇ0

3zAB

ˇ0

1.xACxB/Cˇ0

2.xBCxA/C2ˇ0

3zAB D0:

If this is to hold for all xAand xB, clearly ˇ3must be zero. In other words, covariates

common to both players (such as surface, or day of the week) cannot enter the index as

main effects. Also, the ﬁrst two terms in the sum collapse to

.ˇ1Cˇ2/0.xACxB/D0:

If this is to hold for all xAand xB, we have ˇ2D$ˇ1and the index must satisﬁes

f .xA;x

B;z

AB/Dˇ0

1xACˇ0

2xBCˇ0

3zAB Dˇ0

1.xA$xB/: (3)

In other words, only differences between covariates can enter the index. From an intu-

itive point of view, this is straightforward. Suppose the only covariate is a dummy hA

taking the value 1 if the player Aplays at home. Also, suppose home advantage is posi-

tive. If player Balso plays at home (so player Aand Bare of the same country, playing

in their home country), it is not possible that the winning probabilites of both player

Aand player Bincrease due to the home advantage. Note that another implication of

6

(c) 2009 www.rhkoning.com

restriction (3) is that the model cannot have an intercept.

Klaassen and Magnus (2001, 2003) do not address this identiﬁcation issue explic-

itly. In Klaassen and Magnus (2001) a restriction as in (2) does not appear in their linear

probability model because there is no restriction between the probability that player A

wins the next point when he serves, and that player Bwins the next point when he

serves. Both players do not serve simultaneously for the next point. In Klaassen and

Magnus (2003) they estimate a logit model as implied by (3), without discussing the

general nature of the identiﬁcation problem above. They do impose one restriction

based on the observation that Pr.A > B/ D1

2if both players are equally strong: they

do not include an intercept in the logit model.

In this framework we measure home advantage by estimating the coefﬁcient "in

ˇ0.xA$xB/C".hA$hB/:

If both players are playing at home, hA$hBis zero, and this is also the case if both play-

ers meet away. If Aplays at home and Bdoes not, Ais expected to have a home advan-

tage of "(on the logit scale), if Bplays at home and Adoes not, Ahas a disadvantage

of ". In other words, Bhas an advantage of ". If home advantage exists, we should

ﬁnd "> 0 and signiﬁcant.

In this setup it is easy to moderate the effect of home advantage. Home advantage

may vary with common covariates, for example, it may be weaker in Grand Slam tour-

naments. There are two possibilities to include moderating variables. First, one can

condition on values of xA$xBor zAB and estimate the model for each subgroup. In

other words, one estimates a model as (1) for each value of the moderating variable

(for example, tournament is a Grand Slam tournament or tournament is not a Grand

Slam tournament). Second, one can include interactions as covariates in the index, for

example zABhA$zABhB. In this case, it is not necessary to include main effects in the

index since these will have zero coefﬁcient according to (3).

4DATA AND TESTS

We assess participation in tournaments and estimate the model of the previous section

using data on both professional men and women tennis tournaments. We have data

on 22811 matches for men, over the period 2000 to 2008 (partially). The dataset con-

tains information on the outcome of the match, the tournament, the date of play, round

within the tournament, surface of the court, and the ﬁnal result. Also, the dataset has

information on the world ranking of both players at the beginning of the tournament,

7

(c) 2009 www.rhkoning.com

Table 1: Access to tennis tournaments, men (2000-2008) and women (2007-2008)

home ERHERAtail number

men

Grand Slam 0:10 221:4 178:7 0:18 37

Masters 0:11 140:8 116:1 0:21 90

International 0:18 206:0 85:7 0:80 474

women

Tier I 0:13 152:8 88:3 0:28 19

Tier II 0:11 129:8 63:4 0:49 29

Tier III/IV 0:10 204:8 90:9 0:88 62

home indicators, and (ﬁxed) betting odds before the match. The men dataset has three

tournament types (in decreasing order of importance): Grand Slam, Masters, and In-

ternational tournaments. The dataset for women has the same information, but is much

smaller in size: 2896 matches played in 2007 and 2008. Tournament types that we can

distinguish are Tier I and Grand Slam tournaments, Tier II and Tier III/IV tournaments.

Our empirical strategy to test the existence of home advantage is as follows. First,

we test for home advantage through better access to tournaments for home players.

Then, we focus of home advantage given the set of participants of a tournament. We

start by ﬁnding a baseline model that explains the outcome of a match satisfactorily.

Of course, this speciﬁcation satisﬁes consistency condition (3) of the previous section.

Then, we extend this baseline speciﬁcation with a home advantage dummy to assess

whether or not home advantage exists. Finally, we establish whether a home advantage

effect, if any, is moderated by other variables.

First, we consider improved access to tournaments as a type of home advantage. In

tennis, the organization of a tournament has the option to give so called ‘wild cards’

to eligible players (see for example Chapter VII, article 7.12 of the ATP Rule Book).

These wild cards are entries in the main draw of the tournament, and are awarded at

‘the sole discretion of the tournament’. Usually, they are given to players from the home

country, young and talented players, or players who make a comeback after an injury.

Wimbledon winner of the men’s tournament in 2001, Goran Ivaniˇ

sevi´

c, participated in

that tournament on a wild card, while being ranked only 125th on the World Ranking at

that moment. High ranked players are guaranteed entry to a tournament, lower ranked

players may have to play a qualiﬁcation tournament or depend on a wild card.

There are no standard measures for home advantage through improved access to

a tournament. We propose to measure improved access by looking at the world ranks

8

(c) 2009 www.rhkoning.com

of weaker participants of a tournament. A tournament with krounds has 2kpartic-

ipants. Hence, the strongest draw possible would have players with world ranking 1

to 2k. In practice, players with a weaker ranking than 2kwill also participate, for ex-

ample because they receive a wild card from the organization of the tournament, or

because they qualify through a qualiﬁcation tournament that precedes the main tour-

nament. Especially tournaments of lower importance are played simultaneously and

therefor one would expect that more lower ranked players participate in such tourna-

ments. Organizers have to contract enough players to have a complete schedule, and a

player can participate in only one tournament at a given moment in time. Should home

players have improved access to tournaments through this mechanism, we should ﬁnd

that among the weaker participants , home players are weaker than away players. We

measure this as follows. If the best players participate in a tournament, the weakest

observed rank is 2k. The number of players with a lower rank (i.e., ranked on a higher

position than 2k), and their ranks, indicate the strength of the tournament. For each

tournament in our sample, we calculate the median position of home and away play-

ers ranked lower than 2k. Then, this median is averaged over all tournaments, and the

results are in columns labeled ERHfor home players and ERAfor away players in ta-

ble 1. The numbers should be interpreted as follows. In Grand Slam tournaments for

men, 128 players participate. In an average Grand Slam tournament, the median rank

of home players whose rank is weaker than 128, is 224.5. The same number is 178.2

for away players. Participating home players not in the top 128 of the world ranking

are of lesser quality than participating away players not in the top 128 of the world

ranking. This effect is found for all types of tournaments, both for men and women.

The difference is signiﬁcant as can be established using a permutation test approach.

For each tournament, we condition on the observed ranks of the weaker players (those

with a world rank weaker than 2k) and the number of home players. The ‘home’ label

is then permuted over the observed ranks and we calculate the average median ranks

for home players and away players, and its difference, for this permutation. We repeat

this procedure a large number (10000) of times to obtain the distribution of the dif-

ference of the average median ranks, under the null hypothesis that the ranks of home

players and away players are distributed similarly (that is, according to the observed

ranks of the weaker players for each tournament). The p-values of the observed differ-

ences obtained from Table 1 is 0 in all six cases. Moreover, notice that the difference is

largest in tournaments of lowest importance, as expected. In the ﬁfth column we give

the fraction of players with a lower rank than 2k. 18% of the players in Grand Slam

tournaments for men are ranked lower than 128. Clearly, this fraction is much higher

for the least important types of tournament in our dataset, both for men and women.

9

(c) 2009 www.rhkoning.com

The last column in Table 1 gives the number of tournaments of each type in our dataset.

From Table 1 we conclude that there is clear evidence that home players have improved

access to tournaments, especially to tournaments of lower importance.

Now that we have established that there is home advantage by improved access to

participation in tournaments, we proceed to measure home advantage within the tour-

nament. We follow the approach discussed in the previous section, so ﬁrst we specify a

baseline model that depends on individual speciﬁc covariates only, possibly interacted

with moderating variables. In our data set, only three individual speciﬁc covariates are

available: home advantage, odds of winning as offered by different bookmakers, and

world ranking. We do not want to include odds offered by bookmakers as a covariate,

even though that information will generate a very good baseline model, see McHale and

Forrest (2005) and Koning (2009). The reason is that home advantage will be priced

into such ﬁxed odds already. In fact, if betting odds contain all relevant information on

the result of a tennis match, we could use betting odds as the dependent variable. How-

ever, McHale and Forrest (2007) and Koning (2009) show that betting odds in tennis

are not unbiased predictors of the outcome of a tennis match so we do not use betting

odds as the dependent variable. This leaves us with world ranking as the individual

speciﬁc covariate. Variables common to both players are type of tournament, quality of

the match (measured by the sum of the rankings of both players, this variable is catego-

rized in four quartiles), surface, and year. The choice between entering the difference

of world ranks in equation (1) in levels, or in logarithms with base 2 as suggested by

Klaassen and Magnus (2001) is left to the data. As our baseline speciﬁcation, we use

the model that provides the best ﬁt.

So ﬁrst, we estimate two models:

Pr.A > B/ D1

1Cexp.$ˇ.log WRA$log WRB// ;(4)

and

Pr.A > B/ D1

1Cexp.$ˇ.WRA$WRB// :(5)

To choose between these speciﬁcations we draw calibration plots in Figure 1, where

the actual outcome of a match is regressed on the predicted probabilities obtained

from models (4) and (5). If the estimated probabilities from these models are unbi-

ased estimators of the actual outcome, the calibration curve would be coinciding with

the 45-degree line. Clearly, the model with difference of the logarithm of world ranks

(model (4), top panels in Figure 1) provides a much better ﬁt than the model with dif-

10

(c) 2009 www.rhkoning.com

fitted probability

outcome

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8

men

absolute

women

absolute

men

log

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

women

log

Figure 1: Calibration of baseline model, for men and women, world ranking difference

in logs and levels.

ference of absolute levels of world ranks (model (5), lower panels in Figure 1). For

this reason, we use the difference of log world ranks only, and denote this variable as

log WR #log WRA$log WRB.

In a second step, we test whether the effect of world rank in our baseline spec-

iﬁcation needs to be moderated by interacting it with absolute quality of the match

(measured by the sum of world ranks of both players), round, and type of tournament.

We test signiﬁcance of these interactions at a 99% conﬁdence level, because of the size

of the data set. For men, it turns out that the type of tournament is signiﬁcant. The es-

timation results of the preferred speciﬁcations are given in Table 2. The ﬁrst four lines

in that table give the estimate of ˇas in model (4) for each of the tournament types

11

(c) 2009 www.rhkoning.com

Table 2: Home advantage and baseline speciﬁcations for men and women

O

ˇs.e.( O

ˇ)O

ˇs.e.( O

ˇ)

men

.log WR/%GrandSlam $0:453 0:016 $0:456 0:017

.log WR/%Masters $0:301 0:014 $0:304 0:014

.log WR/%International $0:388 0:010 $0:392 0:010

.log WR/%ATP $0:457 0:061 $0:447 0:066

HA 0:143 0:029

women

log WR $0:510 0:018 $0:517 0:020

HA 0:122 0:083

indicated. The estimated coefﬁcient is negative, as expected: if player Ahas a better

ranking than player B, he is more likely to win. The relation between world rank and

the probability of winning is slightly stronger for women, as is seen from the more

negative coefﬁcient in the ﬁrst line of the second part of Table 2. In the case of women,

none of the potentially moderating variables has a signiﬁcant effect.

It is now easy to test for the presence of home advantage in individual tennis

matches, by extending the model with a home advantage dummy. The estimates of

the coefﬁcient are given in the rows labelled HA in Table 2. The effect is positive and

signiﬁcant at any reasonable level of signiﬁcance for men, and positive but insigniﬁcant

for women. From now on, we focus on home advantage for men only. Similar to our

search for a baseline speciﬁcation, we interact home advantage with variables that are

common to both players to asses whether other variables moderate the home advantage

effect. Home advantage does not vary by type of tournament. We do ﬁnd that home

advantage varies signiﬁcantly with the absolute quality of the match, as measured by

the sum of the world rankings of both players. We recode the quality variable into four

quartiles, so that the ﬁrst quartile corresponds to matches of high quality (the sum of

both rankings is low), and the fourth quartile corresponds to matches of lowest qual-

ity. The estimation results are given in Table 3 and it appears that home advantage is

stronger in games of high quality, and decreases to zero for games of lowest quality.

Home advantage may tip the balance in a match between two very good players, and

is not important in deciding the outcome in a match between two weak players. In

fact, home advantage does not seem to exist in a match between two weak players.

That outcome is determined by relative world ranking and the type of tournament. We

also examine whether home advantage varies with other common characteristics of the

12

(c) 2009 www.rhkoning.com

Table 3: Home advantage interacted with quality of match (men)

O

ˇs.e.( O

ˇ)

.log WR/%GrandSlam $0:455 0:017

.log WR/%Masters $0:305 0:014

.log WR/%International $0:387 0:010

.log WR/%ATP $0:441 0:066

HA %Q10:341 0:067

HA %Q20:261 0:063

HA %Q30:109 0:057

HA %Q4$0:006 0:048

match, as the type of surface, year, country, round in the tournament, or being the fa-

vorite. Not one of these variables turns out to be signiﬁcant, so we conclude that our

ﬁnal speciﬁcation in Table 3 is quite robust.

To interpret the relative magnitude of home advantage compared to the effect of

differences in world ranking, we use an equivalence scale. Consider two players Aand

Bwho play a match away. Suppose we were to substitute player Aby another player,

A", who plays at home. Because player A"plays at home, he can be a lower ranked

player than player A, and still have the same winning probability against player B.

This, of course, is due to home advantage. Let ıHA be the effect of home advantage.

Then the world ranking of player A"playing at home that is equivalent to the world

ranking of player Aplaying away follows from

ıHA Cˇ.log WRA!$log WRB/Dˇ.log WRA$log WRB/:

A player with world rank WRA!D2!ıHA =ˇ WRAwho plays at home has an equal win-

ning probability against player Bas a player with world rank WRAwho does not play

at home. The estimates of Table 3 are translated into the factor 2!ıHA=ˇ in Table 4. It is

clear that this factor decreases for all tournament types when matches of lesser quality

is considered. The magnitude of the estimates are large. Consider a match in a Grand

Slam tournament., between the world rank number 3 and the world rank number 7, both

playing away. This match is in the ﬁrst quartile of the quality distribution. According

to the results in Table 4, a home player with world rank 12 (&1:68 %7) has the same

probability of winning against the world rank 3 player as the away player with world

rank 7. Home advantage amounts to ﬁve places on the world ranking in this case.

13

(c) 2009 www.rhkoning.com

Table 4: Home advantage expressed as equivalence factor (men)

GrandSlam Masters International ATP

Q11:680 2:169 1:842 1:708

Q21:488 1:810 1:597 1:507

Q31:181 1:282 1:217 1:188

Q41:000 1:000 1:000 1:000

5CONCLUSIONS

In this paper, we have tested for the existence of home advantage in professional ten-

nis, both for men and women. Home advantage was measured along two dimensions:

as improved access to tournaments, and as an increased probability of winning a tennis

match, given the relative strength of both players. Our main ﬁndings are as follows.

First, both in men tennis and women tennis we see that home players have signiﬁ-

cant improved access to tournaments, for example through wild cards, qualiﬁcation

tournaments preceding the main draw, or direct invitation by the organization of the

tournament. This is especially prevalent in tournaments of lesser importance. Second,

using a consistent speciﬁcation to model outcomes of individual matches, we found

in men tennis a signiﬁcant and quantitatively important home advantage effect. This

effect is strongest in matches between highly skilled opponents, and absent when we

consider a match between two weak players. No such home advantage effect in indi-

vidual matches is found for women.

REFERENCES

Balmer, N.J., A.M. Nevill, and A.M. Williams (2001). Home advantage in the Winter

Olympics (1908–1998). Journal of Sports Sciences 19(2), 129–139.

Balmer, N.J., A.M. Nevill, and A.M. Williams (2003). Modelling home advantage in

the Summer Olympic Games. Journal of Sports Sciences 21(6), 469–478.

del Corral, J. (2009). Competitive balance and match uncertainty in grand slam tennis:

Effects of seeding system, gender, and court surface. Journal of Sports Economics

forthcoming.

Courneya, K.S. and A.V. Carron (1992). The home advantage in sport competitions: A

literature review. Journal of Sport and Exercise Physiology 14, 13–27.

14

(c) 2009 www.rhkoning.com

Holder, R.L. and A.M. Nevill (1997). Modelling performance at international tennis

and golf tournaments: Is there a home advantage? The Statistician 46(4), 551–559.

Klaassen, F.J.G.M. and J.R. Magnus (2001). Are points in tennis independent and

identically distributed? evidence from a dynamic binary panel data model. Journal

of the American Statistical Association 96(454), 500–509.

Klaassen, F.J.G.M. and J.R. Magnus (2003). Forecasting the winner of a tennis match.

European Journal of Operational Research 16(2), 257–267.

Koning, R.H. (2005). Home advantage and speed skating: Evidence from individual

data. Journal of Sports Sciences 23(4), 417–427.

Koning, R.H. (2009). Betting odds and market efﬁciency. Manuscript.

McHale, I.G. and D. Forrest (2005). The importance of recent scores in a forecasting

model for professional golf tournaments. IMA Journal of Management Mathemat-

ics 16(2), 131–140.

McHale, I.G. and D. Forrest (2007). Anyone for tennis (betting)? European Journal of

Finance 13(8), 156–166.

Nevill, A., N. Balmer, and S. Wolfson (2005). The extent and causes of home advan-

tage: Some recent insights. Journal of Sports Sciences 23(4), 335 – 336.

Nevill, A.M., R.J. Holder, A. Bardsley, H. Calvert, and S. Jones (1997). Identifying

home advantage in international tennis and golf tournaments. Journal of Sports

Sciences 15, 437–443.

Nevill, A.M., S.M. Newell, and S. Gale (1996). Factors associated with home ad-

vantage in English and Scottish football matches. Journal of Sports Sciences 14,

181–186.

Stefani, R.T. (2008). Measurement and interpretation of home advantage. In J. Albert

and R.H. Koning (Eds.), Statistical Thinking in Sports, Chapter 12, pp. 203–216.

Boca Raton: Chapman & Hall/CRC.

15

(c) 2009 www.rhkoning.com

Article

Home advantage is a well-documented phenomenon in many sports. Home advantage has been shown to exist for team sports (soccer, hockey, football, baseball, basketball) and for countries organizing sports tournaments like the Olympics and World Cup Soccer. There is also some evidence for home advantage in some individual sports, but there is a much more limited literature. This paper addresses... [Show full abstract]

Article

Sport is becoming an activity of increasing importance: over time more people participate in sport (active sport consumption), more time is spent watching sport (passive sport consumption). An important part of sport consumption is passive sport consumption where production and consumption are separate: (professional) athletes engage in a contest, and fans pay to watch the contest. An... [Show full abstract]

Article

Home advantage is well documented for professional baseball, basketball and ice hockey in North America. One of the possible causes of this advantage is familiarity with the local playing facility. This was investigated and quantified in an analysis of 37 teams moving to new stadiums, but in the same city, from 1987 to 2001. Home advantage during the first season in a new stadium after the... [Show full abstract]

Article

back During a tennis match broadcast on TV, a number of interesting statistics are presented to the viewers. The most obvious one is the score, but the percentage of first serves in, the number of aces, and a few other statistics are also regularly reported on TV. These statistics are then discussed by the commentators to provide a deeper insight into various aspects of the match. However, a... [Show full abstract]