Department of Economics and International Development, University of Bath, Bath,
†
BA2 7AY, UK, Tel: 44 (0)1225 383074, Email: [email protected]
Nottingham Trent University
††
IASE/NAASE Working Paper Series, Paper No. 08-09
The Influence of Social Pressure and Nationality on Individual
Decisions: Evidence from the Behaviour of Referees
Peter Dawson and Stephen Dobson
†††
August 2008
Abstract
This study considers the influences on agents’ decisions in an international context.
Using data from five seasons of European cup matches it is found that football referees favour
home teams when awarding yellow and red cards. Previous research on referee decisions in
national leagues has identified social pressure as a key reason for favouritism. While social
pressure is also found to be an important influence in this study, the international context reveals
that referee decisions are also influenced by the nationality of the referee and club, and the
reputation of the league.
JEL Classification Codes: D81, L83
Keywords: social pressure, decision-making, referee behaviour, home bias, football
The Influence of Social Pressure and Nationality on Individual Decisions: Evidence from
the Behaviour of Referees
1. Introduction
Team sports are (almost) unique in that the final stage of production (contest between two
teams) is observed. This feature presents numerous opportunities for studying the behaviour of
agents in sporting contests. One aspect that has received attention is managerial decision making
in the form of team selection, substitutions or interchanges (Clement and McCormick, 1989).
Another area of interest is the testing of economic hypotheses concerning strategic behaviour by
players. In the case of penalty-kicks in football (soccer) for example, a number of studies have
found evidence that goalkeepers and penalty-takers adopt mixed strategies (Chiappori et al. 2002;
Palacios-Huerta, 2003; Coloma, 2007).
Attention has also focused on the behaviour of match officials (referees). Referees are
assigned the task of implementing the laws of the game and ensuring that players abide by the
regulations. Research based on match analysis from the European Football Championship in
2000 suggests that a top official makes 137 observable interventions on average during a game,
including awarding free-kicks, penalties, corners, throw-ins, and halting play for serious injury
(Helsen and Bultynck, 2004). In the case of free-kicks and penalties, the referee has the discretion
to decide whether a foul merits a caution, in the form of a yellow or red card. Since some of this
decision making is guided by subjective judgment, football referees are often accused of being
inconsistent and biased in their decision making (Dawson et al., 2007, Buraimo et al., 2007,
Boyko et al., 2007).
Studies of referee decision making in football tend to focus on two decisions: the decision
to add on time at the end of matches and/or the decision to award red and yellow cards. Research
on a number of domestic European leagues suggests a home team bias in referee decision making
2
and identifies social pressure (influence of the crowd) as one of the main reasons for the bias. In
contrast, research on North American sports has recently focused on (racial) discrimination in
decision making by match officials (see, for example, Price and Wolfers, 2007).
Though referee behaviour has received attention from academics in recent years, little is
known about the influences on decisions in an international context
1
. This paper seeks to fill this
gap by analysing the decision to award yellow and red cards in European cup football (UEFA
Cup and UEFA Champions League). In particular, the study addresses the extent to which social
pressure influences the award of red and yellow cards (incidence of disciplinary sanction). In
doing this, the roles played by absolute and relative size of the crowd, and the architecture of the
stadium (in terms of running tracks and fencing) are considered. The study’s international
dimension is also exploited by examining the role of nationality in the incidence of disciplinary
sanction. To the best of our knowledge, this is the first study to examine the influence of
nationality on individual decisions.
The reminder of the paper is structured as follows. Section 2 reviews the previous
academic literature. Section 3 describes the data and considers the empirical methodology.
Section 4 provides the results and Section 5 concludes.
2. Literature Review
Evidence of inconsistency and bias in decision making by referees has been found in a
number of European domestic leagues. Garicano et al. (2005), using Spanish data, find a
tendency for referees to add on more time at the end of matches when the home team is trailing
by one goal compared to when the home team is leading, particularly when contests are close.
1
In a study of the FIFA World Cup, Torgler (2004) observes that a team’s probability of winning is increased when
a referee is from the same (football) region. However, the impact is only marginally significant and appears to be
non-robust.
3
Similar findings have been demonstrated for the German premier league (1
st
Bundesliga) by
Sutter and Kocher (2004) and Dohmen (2008), and for the Italian league by Scoppa (2007).
One potential source of bias by referees is social pressure (influence of the crowd).
Dohmen (2008) finds that architectural conditions play a key role in the refereeing bias observed,
namely: the size of the crowd (absolute size), the attendance-to-capacity ratio (relative size) and
the proximity of supporters to the pitch (the presence of a running track). He finds that there is
more added time in close matches when the crowd is physically close to the field of play. Also,
home teams are significantly more likely to be awarded a disputed penalty, with the physical
distance between the crowd and the playing field important to this decision. Petersson-Lidbom
and Priks (2007) find similar results for Italian football following the Italian government’s
decision to enforce clubs with sub-standard stadiums to play home games behind closed doors.
Buraimo et al. (2007) and Dawson et al. (2007) consider the impact of social pressure on
disciplinary sanction. Buraimo et al. (2007) find the size of the stadium has no statistically
significant effect on sanctions awarded to either the home or away team in the English Premier
League or in the German Bundesliga. In contrast, Dawson et al. (2007) show that home teams
playing in front of larger crowds incur more disciplinary sanctions. Buraimo et al. (2007), in the
context of the German Bundesliga, find the presence of a running track increases the number of
yellow and red cards awarded to the home team. Neither study, however, considers the impact of
relative crowd size.
In a laboratory style setting, Nevill et al. (2002) showed videotapes of tackles to referees
who, having been told the identities of the home and away teams, were asked to classify the
tackles as legal or illegal. One group of referees viewed the tape with the soundtrack (including
the crowd’s reaction) switched on, while a second group viewed silently. The first group was
4
more likely to rule in favour of the home team (calling, on average, 15.5% fewer fouls). The first
group’s decisions were also more in line with those of the original match referee.
Recent research also suggests that match officials respond to incentives. Rickman and
Witt (2008) apply a natural experiment to assess the introduction of professional referees in the
English Premier League. They find that home team bias in adding on time at the end of matches
essentially disappears following the introduction of professionalism. This is explained in terms of
the higher remuneration associated with professional status, which, together with increased
monitoring, acts as a disincentive to show (implicit) favouritism.
A popular notion of refereeing inconsistency is the same offence being treated differently
by different referees. The fact this occurs suggests officials use prior information to inform the
decisions they make. Research has found this to be important both prior to contests taking place
and as contests unfold. Plessner and Betsch (2001) observe that officials are less likely to award a
penalty to a team if they have previously awarded the same team a penalty but are more likely to
award a penalty if they have awarded a penalty to the opposing team. Jones et al. (2002) suggest
that a player’s aggressive reputation can influence the number of red and yellow cards awarded.
For example, on observing a bad challenge by a player with an aggressive reputation, the referee
may be more inclined to dismiss that player because he interprets the challenge as a deliberate
attempt to injure an opponent. In contrast, a similar challenge made by a player with little or no
aggressive reputation may only lead to a caution because the referee believes in this instance, and
based on prior knowledge of the player, the tackle was mis-timed rather than intentional
2
.
2
The reputation of athletes has also been found to influence the behaviour of judges in individual sports such as
boxing (Balmer et al., 2005), ice skating (Findlay and Ste-Marie, 2004) and gymnastics (Ste-Marie and Valiquette,
1996).
5
3. Data and Empirical Methodology
The empirical analysis relates to matches played in the UEFA Champions League and the
UEFA Cup over the period 2002-03 to 2006-07
3
. Match data on home (away) club name, home
(away) club nationality, number of yellow and red cards, referee name, referee nationality, date
and time of contest, and attendance was provided by UEFA and the UEFA Documentation
Center. Data was also gathered for the construction of team rankings (details of which are
described below)
4
and for stadium information pertaining to ground capacity and architecture
5
.
In the analysis, all matches played at neutral venues (including finals) are excluded
6
. Following
the removal of missing values, there are 1,720 useable observations.
Figures 1 and 2 present frequency graphs of the number of yellow cards incurred by the
home and away team by competition. The distributions show that away teams are less likely to
incur zero yellow cards compared to home teams and are more likely to incur three or more
yellow cards. The pattern is similar across both competitions.
Figures 1 and 2 about here
Tables 1 and 2 show the distribution of yellow and red cards by home and away team. In
only 4.63% of Champions League matches and 3.78% of UEFA Cup matches were no yellow
cards issued to either team. More significantly, in only 24.3% of Champions League and 26.67%
3
Both tournaments have undergone a number of format changes in recent times. Currently, both competitions adopt
a mix of elimination rounds and round-robin group stage matches, with both using a seeding system to protect the
stronger teams from being eliminated in earlier rounds. The total number of teams and the total number of matches
played in these competitions has also grown considerably. Prior to 1992, 32 teams competed and a total of 73
matches were played in the European Cup (former name of the Champions League). The corresponding figures for
the UEFA Cup were 64 and 126, respectively. By the start of the 2006-07 season, the number of teams competing in
the Champions League had more than doubled (to 76 teams) and the total number of games nearly trebled (to 213
games). The number of teams (157) competing and the number of matches played (353) in the UEFA Cup has also
increased, although part of this increase is the result of the amalgamation of the UEFA Cup with the European Cup
Winners’ Cup in 1999.
4
http://www.xs4all.nl/~kassiesa/bert/uefa/data
5
http://www.worldstadiums.com/europe/maps/europe.shtml
6
Examples of matches played at neutral venues include a number of matches involving Israeli teams in 2002-03 and
2006-07. A number of other matches were played in empty stadiums as punishment for crowd trouble. These
matches remain in the sample.
6
of UEFA Cup matches did the home team incur more yellow cards than the away team. It is also
notable that the number of yellow cards tends to be higher in the UEFA Cup. Red cards, in
contrast, are observed less frequently: less than 20% of matches in either competition generated
one or more red card.
Tables 1 and 2 about here
Measurement of the dependent variable follows the approach of Dawson et al. (2007). In
the estimations below, the dependent variables are the total numbers of disciplinary “points”
incurred by the home and away teams in each match, calculated by awarding one point for a
yellow card and two points for a red card. Two points are also awarded when a player is
dismissed as a result of two cautionable (yellow card) offences in the same match.
In order to establish whether there is systematic bias in either the distribution or incidence
of disciplinary sanction, it is necessary to control for relative team quality. In this study, a team
quality measure is constructed using historical match data and follows the method of UEFA in
the seeding and drawing procedures of the two cup competitions. A team coefficient is calculated
as the sum of the number of points of each individual team plus 33% of the country coefficient
7
.
The average coefficient (hereafter referred to as the coefficient index) from the previous five
years is used as a measure of team quality.
One weakness of this method is that it does not weight performance according to
competition. Further, it is less sophisticated than forecasting models, including ones based on
betting data (e.g. Buraimo et al. 2007). Whilst a detailed evaluation of forecasting models is
7
For details on the precise calculations can be found at http://www.xs4all.nl/~kassiesa/bert/uefa/.
7
beyond the scope of this study, preliminary analysis found that the team coefficient index does a
reasonably good job at predicting match outcomes
8
.
In addition to team quality, a variety of other controls are also included, based on the
discussion in Sections 1 and 2. These include variables relating to crowd size, crowd density
(attendance to capacity ratio) and stadium architecture (i.e. presence of a running track and/or
fencing), competition (Champions League or UEFA Cup) and stage of competition. The
nationality of the referee and the nationality of the club are also used as controls. Definitions of
the variables used in this study are provided in the Appendix.
The number of disciplinary points per match takes the form of count data, which suggests
the use of a count data regression model
9
. However, it is also possible to model count data using
discrete choice methods that recognise the sequential nature of the data (Cameron and Trivedi,
2005). One such candidate is the ordered probit model, hence:
aaa
hhh
y
y
εβX
εβX
+
′
=
+
′
=
*
*
(1)
Where the subscripts “h” and “a” refer to the home team and away team, respectively.
are constructed according to the following criteria:
**
and
ah
yy
8
Binary probit and ordered probit models were constructed with the team coefficient index as the explanatory
variable. In the majority of cases it was found that a one unit increase in rank difference is predicted to increase the
probability of a home win by approximately 2%, which seems intuitively plausible. Also, with the exception of
Dawson et al. (2007) and Buraimo et al. (2007), previous studies have used relatively simple measures to capture
team quality.
9
For example, Dawson et al. (2007) use zero-inflated Poisson and negative binomial regression models.
8
(2)
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
≥
=
=
=
=
=
=
5 if 5
4 if 4
3 if 3
2 if 2
1 if 1
0 if 0
*
*
*
*
*
*
h
h
h
h
h
h
h
y
y
y
y
y
y
y
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
≥
=
=
=
=
=
=
5 if 5
4 if 4
3 if 3
2 if 2
1 if 1
0 if 0
*
*
*
*
*
*
a
a
a
a
a
a
a
y
y
y
y
y
y
y
Each endogenous discrete variable is associated with X exogenous variables and coefficients β
h
β
a
as described above. If ε
h
and ε
a
are assumed to be independent and normally distributed, (1)
can be estimated using a univariate ordered probit model. A bivariate ordered probit model is
required if ε
h
and ε
a
are assumed to be joint normal
10
and
ρ
ε
ε
=
),( Cov
ah
. Thus, the univariate
model can be considered a special case of the bivariate model, where ρ=0. Both univariate and
bivariate models are estimated using the method of maximum likelihood.
4. Results
Table 3 presents results for the determinants of disciplinary points based on univariate
and bivariate ordered probit models. In the univariate model, the home team equation shows that
the difference in the team coefficient index (home coefficient index minus away coefficient
index) is negative and statistically significant. This implies that a strong home team will incur
fewer disciplinary points. For the away team, the coefficient is correctly signed (positive) but is
not statistically significant. In both the home and away equations it appears that, on average and
10
1)(Var)Var( ,0)()(
=
===
ahah
EE
ε
ε
ε
ε
9
other things unchanged, the number of disciplinary points is lower in the Champions League.
However, there is also evidence, for both teams, that the number of disciplinary points increases
as the competitions enter the final phases. In terms of the influence of the crowd and the
architecture of the stadium, it appears that relative size of the crowd matters more than the
absolute size: the away team is likely to incur more disciplinary points the closer the stadium is to
capacity. The presence of a running track has the effect of increasing the number of disciplinary
points awarded to the home team.
Table 3 about here
The findings associated with the impact of the crowd and the architecture of the stadium
are consistent with previous research. The presence of a running track increases the distance
between the pitch and the crowd. This works to increase the number of disciplinary points
awarded to the home team, implying less implicit favouritism towards the home team when the
influence of social pressure is weaker. On the other hand, the relative size of the crowd appears to
work in the opposite way, by increasing the number of disciplinary points awarded to the away
team. The absolute size of the crowd and the presence of fencing have no impact.
One criticism of the univariate approach is that it assumes no correlation between the
home and away team equations. Buraimo et al. (2007), in their study of the German Bundesliga
and the English Premier League, find that a yellow card previously awarded to the home (away)
team increases the probability of the away (home) team receiving a similar sanction. As the
authors suggest, this could reflect retaliation by players or the tendency for referees to “even-up”
decisions. To allow for this possibility, a bivariate ordered probit model is also estimated. The
significance of the ρ statistic and the LR test of independent equations provide strong evidence
10
that the error terms in the two equations are correlated, and justifies the use of a bivariate model.
However, the coefficients are virtually indistinguishable.
A unique feature of this study is the opportunity to test for the influence of nationality on
decisions. In European cup football, referees are assigned to matches according to Article 19.02
of the Regulations of the Champions League and UEFA Cup
11
. Generally, referees cannot be
from the same football association as the two teams competing in the contest. Given this, home
nation bias should be of limited concern. However, this does not preclude the possibility of
variation in referee behaviour by nationality. Nor does it preclude the possibility that referees
form judgements about teams and nations
12
.
Table 4 reports bivariate ordered probit estimates under a variety of different
specifications. Model (1) includes club nationality fixed effects alongside referee nationality
effects. The inclusion of club nationality results in the team coefficient index becoming
insignificant, so it appears that club effects are capturing some (most) of the impact of team
quality. The stage of the competition becomes insignificant in the home team equation and less
significant in the away team equation. Champions League matches (home equation and away
equation), the presence of a running track (home equation only), and the relative size of the
crowd (away equation only) remain important determinants of the incidence of disciplinary
sanction.
11
The Referees Committee, in cooperation with the UEFA administration, appoints a referee, two assistant referees
and a fourth official for each match. Only referees whose names appear on the official FIFA list of referees are
eligible. The fourth official and assistant referees are, in principle, proposed by the national association of the
referee, in accordance with criteria established by the Referees Committee.
12
In the 2006 World Cup Finals there were numerous complaints and allegations of referee bias in favour of the
larger, well-established teams. During the 2002 tournament, held jointly by South Korea (Korea Republic) and
Japan, there were allegations of favouritism towards the host nations - specifically when South Korea played, and
subsequently defeated, Italy in the Second Round. During the European 2004 Championship the Portuguese media
criticised the appointment of the German referee Merkus Merk for a game involving Portugal and Greece, claiming
that he would favour Greece because they were coached by a German national. The Romanian Football Association
has also claimed discrimination against their national team (and other Eastern European countries) when involved in
games against teams from more established associations.
11
In Model (2) club nationality fixed effects are replaced with variables denoting whether
the home or away teams (or both) is from one of the “big five” leagues (England, Italy, Germany,
Spain and France). This is designed to capture possible “league reputation” effects, whereby a
team from one of the big five leagues is likely to incur fewer disciplinary points. As expected, a
home team from the “big five” incurs fewer disciplinary points if playing a team from outside the
“big five” but the coefficient is not statistically significant. The effect is significant for an away
team from one of the big five leagues. Also, more disciplinary points are awarded to the home
team and away team if they are both drawn from one of the big five leagues. It would appear
therefore that these variables are also capturing the quality of the teams involved in the contest.
Table 4 about here
A dummy variable, capturing whether the referee officiated at the 2004 European
Championships (defined here as an “elite” referee), is included in Model (3). A positive impact is
found in both the home and away team equations (Models (3) and (4)) but there is no significant
difference. A possible interpretation is that elite referees compensate for inherent (implicit)
favouritism by issuing more disciplinary sanctions to the home team, though this conclusion must
be tentative as there may be problems associated with sample selection effects.
A sensitivity analysis, in the form of a separate analysis for yellow cards, is provided in
Table 5. In general, the coefficients are less significant compared to the disciplinary points
models. However, it is possible to control for an additional feature in these specifications, namely
the extent to which red card offences relate to yellow card offences. Here evidence is found of
simultaneity between the award of red cards and yellow cards: teams that are punished for red
card offences also tend to incur more yellow cards.
Table 5 also provides a further sensitivity test through the inclusion of within game
parameters for Champions League matches only. A series of variables are included relating to
12
possession, shots on goal and number of fouls committed. With the exception of number of fouls,
none of these factors are significant. Moreover, previous variables remain reasonably robust to
the inclusion of these additional variables.
Table 5 about here
Finally, the marginal effect of referee nationality is presented in Table 6. A priori, and
given the above discussions, it might be expected that referees from the more prominent
associations (England, France, Germany, Italy and Spain) will be less prone to implicit
favouritism compared to referees from other associations. There appears to be some evidence to
support this since officials from Belgium, Holland, Norway, Russia and Sweden tend to award
fewer disciplinary points to the home team. However, Belgian, Dutch, Russian and Swedish
referees also tend to issue fewer disciplinary points to the away team. There are also some
interesting anomalies in the data. Portuguese officials issue more disciplinary points to the away
team. On the other hand, Greek officials tend to issue more sanctions (to both the home and away
teams) compared to anyone else.
Table 6 about here
The precise role of nationality in influencing referee decisions is difficult to identify not
least because of the interplay between referee and team nationality, and team reputation. Akerlof
(1997) and Akerlof and Kranton (2000) suggest that individual decisions are influenced by one’s
own identity and the perception of others. This notion seems particularly relevant in the present
context since football referees, much like officials in many other sports, are required to make
split-second decisions under uncertainty. Faced with a key (and possibly contentious) decision,
the results of this study suggest a referee is likely to be influenced not only by the crowd but also
by his perception of the quality, and nationality, of the teams involved in the contest.
13
5. Conclusion
This study has considered the influences on agents’ decisions in an international context.
Using data from European cup matches, it is found that football referees tend to favour home
teams when disciplining players. Consistent with previous work, social pressure is an important
influence on behaviour, with crowd density and stadium architecture playing important roles. The
incidence of disciplinary sanction is also influenced by the type and stage of the competition. The
international context for this study allows a further dimension to referee decisions to be
investigated, namely the role played by nationality. Of particular interest is the finding that
nationality influences individual decisions.
Referees are required to make split-second decisions. Faced with significant time
pressure, individuals tend to focus on salient cues in forming a decision. Dohmen (2008) and
Sutter and Kocher (2004) argue that in the case of football referees, crowd noise is the salient
cue. This analysis confirms that crowd noise is important but also suggests that in an international
context decisions are also influenced by referee nationality, team nationality and league
reputation.
14
Acknowledgements
The authors gratefully acknowledge UEFA and the UEFA Documentation Center in particular for
providing the data. The views expressed here represent the views of the authors and not the views
of UEFA or any of its employees. We would also like to thank Christos Papahristodoulou for
providing the match-play statistics from the Champions League tournament and the research
assistance of Joseph Birch. The usual disclaimer applies.
15
References
Akerlof, G.A (1997). Social distance and social decisions. Econometrica 65, 1005-1027.
Akerlof, G.A. and Kranton, R. (2000). Economics and identity. Quarterly Journal of Economics
115, 715-753.
Balmer, N.J., Nevill, A.M. and Lane, A.M. (2005). Do judges enhance home advantage in
European Championship Boxing? Journal of Sports Sciences 23, 409-416.
Boyko, R.H., Boyko, A.R. and Boyko, M.G. (2007). Referee bias contributes to home advantage
in English Premiership football. Journal of Sports Sciences 25, 1185-1194.
Buraimo, B., Forrest, D. and Simmons, R. (2007). The twelfth man? Refereeing bias in England
and German soccer. International Association of Sports Economists Working Paper 0707.
Cameron, A.C. and Trivedi, P.K. (2005). Microeconometrics: Methods and Applications.
Cambridge University Press, New York.
Chiappori, P.-A., Levitt, S., and Groseclose, T. (2002). Testing mixed-strategy equilibria when
players are heterogeneous: The case of penalty kicks in soccer. American Economic Review 92,
1138-1151.
Clement, R.C. and McCormick, R.E. (1989). Coaching team production. Economic Inquiry 27,
287-304.
16
Coloma, G. (2007). Penalty kicks in soccer. An alternative methodology for testing mixed-
strategy equilibria. Journal of Sports Economics 8, 530-545.
Dawson, P., Dobson, S., Goddard, J. and Wilson, J. (2007). Are football referees really biased
and inconsistent? Evidence from the English Premier League. Journal of the Royal Statistical
Society, Series A 170, 231-250.
Dohmen, T.J. (2008). The influence of social forces: Evidence from the behavior of football
referees. Forthcoming in Economic Inquiry. Published online January 2008.
Findlay, L.C. and Ste-Marie, D.M. (2004). A reputation bias in figure skating judging. Journal of
Sport and Exercise Psychology 26, 154-166.
Garicano, L., I. Palacios-Huerta, and C. Prendergast (2005). Favoritism under social pressure.
Review of Economics and Statistics 87, 208-216.
Helsen, W., & Bultynck, J. B. (2004). Physical and perceptual cognitive demands of top-class
refereeing in association football. Journal of Sports Sciences 22, 179-189.
Jones, M.V., Paull, G.C. and Erskine, J. (2002). The impact of a team’s aggressive reputation on
the decisions of association football referees. Journal of Sports Sciences 20, 991-1000.
17
Nevill, A.M., Balmer, N.J. and Williams, A.M. (2002). The influence of crowd noise and
experience upon refereeing decisions in football. Psychology of Sport and Exercise 3, 261-272.
Palacios-Huerta, I. (2003). Professionals play minimax. Review of Economic Studies 70, 395-415.
Pettersson-Lidbom, P. and Priks, M. (2007). Behavior under social pressure: empty Italian
stadiums and referee bias. CESifo Working Paper 1960.
Plessner, H. and Betsch, T. (2001). Sequential effects in important referee decisions: the case of
penalties in soccer. Journal of Sport and Exercise Psychology 23, 254-259.
Price, J. and Wolfers, J. (2007). Racial discrimination among NBA referees. National Bureau of
Economic Research, Working Paper No.13206.
Rickman, N. and Witt, R. (2008). Favouritism and financial incentives: a natural experiment.
Economica 75, 296-309.
Scoppa (2007). Are subjective evaluations biased by social factors or connections? An
econometric analysis of soccer referee decisions. Empirical Economics (forthcoming). Published
online June 2007.
Ste-Marie, D.M., & Valiquette, S.M. (1996). Enduring memory-induced biases in gymnastic
judging. Journal of Experimental Psychology: Learning, Memory, and Cognition 22, 1498-1502.
18
Sutter, M. and Kocher, M.G. (2004). Favoritism of agents – the case of referees’ home bias.
Journal of Economic Psychology 25, 461-469.
Torgler, B. (2004). The economics of the FIFA football World Cup. Kyklos 57, 287-300.
19
Figure 1: Frequency Distribution of Home Yellow Cards by Competition
Champions League
403020100
0 5 10 0 5
UEFA Cup
Frequency Percentage
Number of Yellow Cards (Home Team)
10
Figure 2: Frequency Distribution of Away Yellow Cards by Competition
Champions League
3020100
0 5 10 0 5
UEFA Cup
Frequency Percentage
Number of Yellow Cards (Away Team)
10
20
Table 1: Cross-Tabulation of Yellow Cards Issued to Home and Away Teams (by
Competition)
Home
Yellow
Away Yellow
Total
0 1 2 3 4 5 6
0 4.63 6.52 5.67 2.27 0.95 0.76 0
20.79
1 3.59 9.64 11.15 6.52 3.31 0.38 0.19
34.78
2 2.46 6.43 8.98 5.48 1.98 1.13 0.09
26.65
3 1.23 2.74 3.12 3.40 1.13 0.38 0.09
12.10
4 0.66 0.76 0.95 0.95 0.57 0.19 0
4.16
5 0 0.09 0.38 0.09 0.19 0.28 0
1.04
6 0 0 0.19 0 0.19 0 0
0.38
7 0 0 0 0 0 0 0
0
8 0 0 0 0.09 0 0 0
0.09
Total 12.57 26.18 30.43 18.81 8.32 3.12 0.57 100.00
Panel (a): Champions League
Home
Yellow
Away Yellow
Total
0 1 2 3 4 5 6 7 8
0 3.78 6.10 5.35 2.52 0.94 0.25 0.06 0 0
19.01
1 3.84 9.88 7.17 5.98 2.83 0.88 0.13 0.06 0.06
30.84
2 2.45 7.05 8.75 6.23 2.83 1.13 0.31 0.06 0.06
28.89
3 0.63 3.65 4.47 3.52 2.14 0.94 0.19 0.06 0.06
15.67
4 0.25 0.76 1.83 0.88 0.44 0.38 0.19 0 0
4.72
5 0 0.25 0.25 0.13 0.06 0.06 0 0 0
0.76
6 0 0 0.13 0 0 0 0 0 0
0.13
Total 10.95 27.69 27.94 19.26 9.25 3.65 0.88 0.19 0.19 100.00
Panel (b): UEFA Cup
Table 2: Cross-Tabulation of Red Cards Issued to Home and Away Teams (by
Competition)
Champions League UEFA Cup
Red
Card
Home
Red Card Away Red Card Away
0 1 2
Total
0 1 2
Total
0 82.89 9.74 0.95
93.57
81.31 9.13 0.82
91.25
1 5.10 0.85 0
5.95
6.54 1.57 0.13
8.24
2 0.19 0.28 0
0.47
0.13 0.25 0.06
0.44
3 0 0 0
0
0.06 0 0
0.06
Total 88.19 10.87 0.95 100.00 88.04 10.95 1.01 100.00
22
Table 3: Univariate and Bivariate Ordered Probit Estimates
Univariate Ordered Probit Bivariate Ordered Probit
Home Team Away Team Home Team Away Team
Variables
Difference in
Team Coefficient
Index
-0.008** (0.003) 0.002 (0.003) -0.008** (0.003) 0.002 (0.003)
Stage of
Competition
0.113* (0.060) 0.150** (0.060) 0.114* (0.060) 0.149** (0.060)
Champions
League
-0.199*** (0.069) -0.187*** (0.068) -0.199*** (0.069) -0.188*** (0.068)
Attendance / 1000 0.0003 (0.002) 0.002 (0.002) 0.0003 (0.002) 0.002 (0.002)
Attendance to
Capacity Ratio
0.072 (0.093) 0.232** (0.093) 0.073 (0.093) 0.231** (0.093)
Track 0.185*** (0.059) 0.019 (0.059) 0.185*** (0.059) 0.019 (0.059)
Fence 0.101 (0.066) -0.013 (0.065) 0.101 (0.066) -0.012 (0.065)
Referee
Nationality Fixed
Effects
INCLUDED INCLUDED INCLUDED INCLUDED
Rho (ρ)
0.241*** (0.025)
Thresholds
Cut1 -0.924*** (0.077) -1.174*** (0.079) -0.924*** (0.077) -1.176*** (0.079)
Cut2 -0.031 (0.075) -0.316*** (0.075) -0.028 (0.075) -0.314*** (0.075)
Cut3 0.727*** (0.076) 0.384*** (0.075) 0.728*** (0.076) 0.388*** (0.075)
Cut4 1.366*** (0.081) 0.963*** (0.077) 1.363*** (0.081) 0.964*** (0.077)
Cut5 1.847*** (0.090) 1.484*** (0.081) 1.840*** (0.090) 1.481*** (0.081)
Pseudo-R
2
0.013 0.013
LR test (joint
significance of
covariates)
69.68 75.63 69.57
LR test
(independent
equations)
87.34
N 1720 1720 1720
Notes: Standard errors in parentheses. ***, **, *, significant at 1%, 5% and 10% levels, respectively (two-
tailed tests.
23
Table 4: Referee Nationality, Club Nationality and “League Reputation” Effects
Bivariate Ordered Probit Estimates
Variables
(1) (2) (3) (4)
Home Team
Difference in Team
Coefficient Index
0.0002 (0.004) -0.0001 (0.003) 0.001 (0.004) 0.0005 (0.004)
Stage of
Competition
0.080 (0.065) 0.098 (0.063) 0.062 (0.066) 0.047 (0.066)
Champions League -0.217*** (0.074) -0.213*** (0.070) -0.259** (0.076) -0.272*** (0.076)
Attendance / 1000 0.0002 (0.002) 0.001 (0.002) -0.0002 (0.002) -0.0002 (0.002)
Attendance to
Capacity Ratio
0.150 (0.100) 0.040 (0.094) 0.158 (0.10) 0.166* (0.100)
Track 0.142** (0.065) 0.177*** (0.059) 0.145*** (0.065) 0.143** (0.065)
Fence 0.022 (0.072) 0.096 (0.066) 0.021 (0.072) 0.022 (0.072)
Big Five Home -0.322*** (0.075) -0.258** (0.122)
Big Five Away 0.089 (0.074) 0.314*** (0.120)
Big Five Home x
Big Five Away
0.296*** (0.103) 0.290*** (0.105)
Elite Referee 0.190** (0.087) 0.173** (0.087)
Away Team
Difference in Team
Coefficient Index
0.0013 (0.004) 0.0001 (0.003) 0.002 (0.004) 0.001 (0.004)
Stage of
Competition
0.121* (0.064) 0.138** (0.063) 0.110* (0.065) 0.097 (0.065)
Champions League -0.207*** (0.073) -0.198*** (0.069) -0.233*** (0.075) -0.244*** (0.075)
Attendance / 1000 0.003 (0.002) 0.002 (0.002) 0.002 (0.002) 0.002 (0.002)
Attendance to
Capacity Ratio
0.273*** (0.099) 0.251*** (0.093) 0.278*** (0.099) 0.285*** (0.099)
Track 0.064 (0.064) 0.017 (0.059) 0.066 (0.064) 0.064 (0.064)
Fence 0.022 (0.071) -0.007 (0.066) 0.021 (0.071) 0.022 (0.071)
Big Five Home -0.053 (0.074) -0.053 (0.121)
Big Five Away -0.169** (0.074) -0.012 (0.120)
Big Five Home x
Big Five Away
0.255** (0.102) 0.272*** (0.104)
Elite Referee 0.116 (0.086) 0.100 (0.086)
Referee Nationality
Fixed Effects
INCLUDED INCLUDED INCLUDED INCLUDED
Team Nationality
Fixed Effects
INCLUDED NOT INCLUDED INCLUDED INCLUDED
Rho (ρ)
0.254*** (0.025) 0.244*** (0.025) 0.252*** (0.025) 0.249*** (0.025)
LR test (joint
significance of
covariates)
167.30 102.67 171.88 179.30
LR test
(independent
equations)
96.40 89.92 95.31 92.84
N 1720 1720 1720 1720
Notes: As Table 3.
24
Table 5: Sensitivity Analysis – Yellow Cards and “Within-Game” Dynamics
Model 1: Yellow Cards
Only
Model 2: “Within Game”
Dynamics
Model 3: “Within Game”
Dynamics
Variables
Home
Equation
Away
Equation
Home
Equation
Away
Equation
Home
Equation
Away
Equation
Difference in Team
Coefficient Index
-0.0004
(0.004)
0.002
(0.004)
0.006
(0.006)
0.007
(0.006)
0.009
(0.006)
0.004
(0.006)
Stage of Competition 0.031
(0.066)
0.099
(0.065)
-0.083
(0.115)
0.010
(0.114)
-0.143
(0.116)
-0.037
(0.115)
Champions League -0.252***
(0.077)
-0.220***
(0.076)
Attendance / 1000 -0.00002
(0.002)
0.002
(0.002)
-0.002
(0.003)
-0.005
(0.003)
-0.003
(0.003)
-0.005
(0.003)
Attendance to Capacity
Ratio
0.142
(0.100)
0.241**
(0.099)
0.370
(0.337)
0.919***
(0.337)
0.281
(0.342)
1.095***
(0.343)
Track 0.100
(0.065)
0.070
(0.065)
0.113
(0.125)
0.223*
(0.125)
0.124
(0.127)
0.194
(0.127)
Fence 0.039
(0.072)
0.008
(0.072)
0.085
(0.130)
-0.190
(0.129)
-0.003
(0.133)
-0.114
(0.132)
Big Five Home -0.298**
(0.123)
-0.034
(0.121)
-0.202
(0.217)
-0.266
(0.216)
-0.154
(0.222)
-0.289
(0.221)
Big Five Away 0.060
(0.113)
-0.366***
(0.112)
0.384*
(0.216)
0.530**
(0.216)
0.292
(0.221)
0.563**
(0.221)
Big Five Home x Big
Five Away
0.339***
(0.106)
0.299***
(0.104)
0.541***
(0.185)
0.195
(0.183)
0.529***
(0.188)
0.085
(0.185)
Elite Referee 0.093
(0.088)
0.058
(0.087)
0.213**
(0.106)
0.185*
(0.106)
0.142
(0.108)
0.840
(0.107)
Home Red 0.317**
(0.128)
0.314**
(0.127)
Away Red 0.040
(0.103)
0.145
(0.102)
Home Red / Yellow -0.135
(0.128)
0.264**
(0.127)
Away Red / Yellow 0.299***
(0.104)
-0.107
(0.103)
Home shots on goal -0.049
(0.055)
0.032
(0.055)
Away shots on goal 0.039*
(0.020)
0.004
(0.020)
Ratio of home possession
to away possession
(HPAP)
0.079
(0.369)
0.153
(0.368)
HPAP x Home shots on
goal
0.029
(0.045)
-0.007
(0.045)
Home fouls 0.086***
(0.010)
0.015
(0.010)
Away fouls 0.017**
(0.009)
0.080***
(0.009)
Referee Nationality Fixed
Effects
INCLUDED INCLUDED INCLUDED
Club Nationality Fixed
Effects
INCLUDED INCLUDED INCLUDED
Rho (ρ)
0.222*** (0.025) 0.239*** (0.042) 0.207*** (0.043)
LR test (joint significance
of covariates)
171.89 89.64 172.84
LR test (independent
equations)
72.40 29.77 21.40
N 1720
Notes: Models 2 and 3 based on Champions League data only.
25
Table 6: Referee Nationality: Marginal Effects
Panel (a): Home Team Equation
Nationality 0 1 2 3 4 5
Austrian N/S N/S N/S N/S N/S N/S
Belgian 0.100 0.036 -0.045 -0.050 -0.024 -0.016
Danish N/S N/S N/S N/S N/S N/S
English N/S N/S N/S N/S N/S N/S
French N/S N/S N/S N/S N/S N/S
German N/S 0.024 N/S -0.028 -0.014 -0.010
Greek -0.065 -0.051 0.018 0.045 0.028 N/S
Italian N/S N/S N/S N/S N/S N/S
Dutch 0.081 0.032 -0.036 -0.042 -0.020 -0.014
Norwegian 0.105 0.037 -0.047 -0.053 -0.024 -0.017
Portuguese N/S N/S N/S N/S N/S N/S
Russian 0.082 0.032 N/S -0.043 -0.021 -0.014
Scottish 0.095 0.035 -0.043 -0.048 -0.023 -0.016
Slovakian N/S N/S N/S N/S N/S N/S
Spanish N/S N/S N/S N/S N/S N/S
Swedish 0.086 0.033 -0.038 -0.044 -0.021 -0.015
Swiss N/S N/S N/S N/S N/S N/S
Panel (b): Away Team Equation
Nationality 0 1 2 3 4 5
Austrian N/S N/S N/S N/S N/S N/S
Belgian 0.073 0.065 N/S -0.047 -0.042 -0.041
Danish N/S 0.045 N/S N/S -0.029 -0.030
English N/S N/S N/S N/S N/S N/S
French N/S N/S N/S N/S N/S N/S
German N/S N/S N/S N/S N/S N/S
Greek -0.042 -0.065 N/S 0.029 0.041 0.058
Italian N/S N/S N/S N/S N/S N/S
Dutch 0.063 0.058 N/S -0.041 -0.037 -0.037
Norwegian N/S N/S N/S N/S N/S N/S
Portuguese -0.044 -0.065 N/S 0.029 0.041 0.058
Russian 0.091 0.075 N/S -0.057 -0.049 -0.047
Scottish N/S N/S N/S N/S N/S N/S
Slovakian N/S N/S N/S N/S N/S N/S
Spanish 0.047 0.046 N/S -0.031 -0.030 -0.031
Swedish N/S 0.047 N/S -0.032 -0.030 -0.031
Swiss N/S N/S N/S N/S N/S N/S
Note: Estimates are significantly different from zero at the 10% level or better. N/S = not significant.
Columns represent the probability of awarding 0,1,2,3,4,5 disciplinary points. For example, the third cell of
column 2 (Panel (a)) indicates that Belgian referees are 10% more likely to issue zero disciplinary points to
the home team. Estimates based on Model 4 (Table 4).
26
Appendix: Variable Definitions
Variables Definition
Difference in Team
Coefficient Index
Team Coefficient Index of Home Team Minus Team
Coefficient Index of the Away Team.
Stage of
Competition
= 1 if Round of 32 onwards (Round of 16 in the case of the
Champions League), 0 otherwise
Champions League = 1 if Champions League Match, 0 otherwise (i.e. UEFA Cup
match)
Attendance / 1000 Attendance scaled by 1000
Attendance to
Capacity Ratio
Attendance divided by stadium capacity
Track = 1 if stadium has a running track, 0 otherwise
Fence = 1 if stadium has fencing, 0 otherwise
Home Cards Total disciplinary “points” issued to the home team
Away Cards Total disciplinary “points” issued to the away team
Referee Nationality Dummy Variables which represent referee nationalities
(minimum of 70 observations required for inclusion).
Home Club
Nationality
Dummy Variables which represent home club nationality
(minimum of 70 observations required for inclusion).
Away Club
Nationality
Dummy Variables which represent the away club nationality
(minimum of 70 observations required for inclusion).
‘Big Five’ Home =1 if home club from one of the “big five” leagues
a
, 0
otherwise
‘Big Five’ Away =1 if away club from one of the “big five” leagues
a
, 0
otherwise.
Elite Referee =1 if match official officiated at the 2004 European
Championship, 0 otherwise.
Notes:
a
Club from England, France, Germany, Italy or Spain.
27
