The impact of referees on match outcomes in professional sports: Evidence from the German Football Bundesliga

Transcription

1 The impact of referees on match outcomes in professional sports: Evidence from the German Football Bundesliga Stefanie Pohlkamp Economics Department University of Hamburg hamburg.de December 18, 2013 Abstract Using data from German 1 st Bundesliga from season 1993/94 until season 2007/08 we examine whether referees in football have significant individual influence on match results or outcomes like goals, penalties, yellow and red cards. This study contributes research on referee bias in football. Here, we show that not only a significant individual effect from referees exists, but also that these referees have different referee styles and that there are differences in their behavior for home and away teams. Further, we use referee characteristics like age and experience as well as a referee s profession to explain these individual effects. Keywords: fixed effects, referees in football, referee bias, decision making I would like to thank Gerd Mühlheußer, Thomas Siedler, Berno Büchel, Thomas Peeters, Sandra Hentschel and Kathrin Thiemann, as well as the participants of the 5 th ESEA Conference for helpful comments. 1

2 1 Introduction This paper investigates whether there is a significant individual influence of football referees on match outcomes in 1 st Bundesliga in Germany and ontributes research on referee bias in football. Although it is assumed that referees act as a neutral and impartial observer it often happens that referees make decisions which suggest that these referees are biased or do not act as this neutral monitor. Frequently, a referee from 1 st Bundesliga is in the focus of reporting after a matchday. Articles in sports magazines are full of discussions on wrong awarded or not awarded goals, decisions on offside as well as eligible or not eligible penalties. Even coaches or managers from professional football clubs often mention that their teams are systematically discriminated by referees. In the season 2011/12, the chairman (Karl-Heinz Rummenigge) and the president (Uli Hoeneß) from F.C. Bayern Munich claimed that referees always decide against Bayern Munich. 1 A similar assertion was made by Fredi Bobic in the season 2010/11. Here, the head of sports of the VFB Stuttgart suspects systematical disadvantages against his team. He even argued that his team lost six points caused by wrong decisions from referees. 2 Another example, that more football teams believe that referees are biased to the detriment of their teams, is a letter of protest from Hertha BSC Berlin in the season 2009/10 where the management claim that the club is disadvantaged by referees and even referee appointments in matches of Hertha BSC Berlin. 3 One highlight of the referee discussion might be the circumstance that it was decided by the German Football Association (DFB) that the German referee Wolfgang Stark is not appointed for matches from Borussia Dortmund in season 2012/13. Reason for this decision was the suspicion that this referee is biased, because there were too many dubious decisions from Wolfgang Stark to the detriment of Borussia Dortmund. 4 In the light of this public discussion, the aim of this paper is to analyze whether these statements are only a hint for a bad day of the referee because referees are also just humans and make errors or whether referees and their decisions systematically influence the result of a football match. Thus, it is asked whether referees deliberately treat home and away teams in different ways, although someone would assume that German referees 1 c.f html and last access: May 27th, c.f. http : // b undesliga/artikel html, last access: May 27th, c.f html, last access: May 27th, c.f. last access: May 27th,

3 have no incentives to make biased decisions. Until a referee is on the list for matches of 1. and 2. Bundesliga he gained practical experiences in matches from lower divisions and is promoted on the basis of good monitoring results as a referee from the German Football Association. Good reports are also necessary to stay on that list or even to be promoted as a Fifa referee. Another reason why German referees have no incentives to be partial are financial compensations, even though referees in Germany do not work as professionals. 5 Another hint for the quality of German referees might be the fact that in total ten German referees and ten referee-assistants are listed on the Fifa list. 6 Thus, Germany has the most referees on that international Fifa list. 7 Hence, to avoid substantial wrong decisions as well as discussions on referees performance, it is always attempted to improve decision making of referees. Recent examples are the goal-line referees in matches from Champions and Europa League as well as the introduction of a a goal-line technology during the Fifa World Championships in the year Previous studies, as discussed in detail below, find evidence for a home advantage 8 and later this advantage is explained with biased decisions from officials 9 in favor of home teams. Therefore the extra time at the end of the second half and referee decisions like goals, penalties or bookings are used to indicate whether referees systematically favor home teams. One explanation for this bias is often the social pressure which is caused by the crowd in the stadium. This psychological argument was developed for example by Nevill et al. (2002) and it says that referees are influenced by fans and/or players in the stadium. Another strand of literature follows the argument that referees work in a principal-agent relationship as the agents and the football governing body (e.g. German Football Association / Deutscher Fuball Bund (DFB)) acts as their principal. Thus, it is assumed that referees act like an impartial to satisfy their principal and simultaneously 5 Further information on training, monitoring and rewards are given in section 3. 6 c.f. last access: March 4th, The Fifa annually decide about the maximum number of referees from each association. Among other factors, the following three points are take into account: First, the level of refereeing of each association. Second, the level of competitions of each association and third, the professional level of each association s competitions. (c.f. last access: May 28th, 2013) A detailed overview was done by Courneya and Carron (1992). 9 A so called referee bias is found in different famous European football leagues like in England, Spain and Germany. 3

4 referees want to quieten the crowd in the stadium (e.g. Sutter and Kocher (2004),Dohmen (2003)). In this paper, we examine whether referees have individual effects on match outcomes or possible match-winning decisions like goals, penalties and also not match-winning decisions like bookings. For that reason, a data set from season 1993/94 until 2007/08 containing 4,590 matches and 70 referees is generated. Following the innovative approach from Bertrand and Schoar (2003), a new method to estimate a referees influence is applied within this study. Thus, our strategy is described in the following way: First, the dependent variables like result, goal difference, goals, penalties and bookings are estimated by regression analysis. The right hand side from this regression equation is independent from referees and only describe the two playing teams of a match (e.g. performance, budget). Afterwards this regression equation is enhanced by referee fixed effects. A significant individual influence is found if the explanatory power of this regression model increases after we include referee fixed effects, and if the F-test for jointly significance of these referee dummy variables is significant. Following this, the estimated referee fixed effects from this first stage are used to describe different referee styles while the correlation between the significant fixed effects is examined. Here, we want to figure out, if for example referees with significant effects on result also have significant impacts on their fixed effects for other decisions like goals or cards. Last but not least, in a second stage regression we use observable properties from the referees (e.g. age, experience, Fifa, professional job) instead of the referee fixed effects, to explain which referee characteristics are responsible for the significant individual referee effects. One central conclusion from this study is that referees have a significant individual influence on match outcome. Moreover, the significant individual effects slightly vary between home and away teams and it follows that referees treat home and away teams in different ways. Furthermore, we estimate the correlation between the significant individual referee effects to find referee styles. Here, referees with significant individual effects for match outcome also have high positive and significant effects for other referee fixed effects like awarded yellow, yellow-red, red cards and goals as well as not awarded red cards in home matches. In away matches, referees with a significant effect on match outcome have different and especially smaller impacts on the other referee effects. Thus, there are positive effects from match outcome on not awarded goals and awarded penalties but negative effects on awarded yellow cards and yellow-red cards. 4

5 Last but not least, we use observable referee properties to explain the significant individual effects. Here, we suppose that referees may follow career concerns and that they are interested in a good reputation at the beginning of their career. That would be in line with the behavior of judges (e.g. Levy (2005)) or managers (e.g. Frank and Goyal (2007)) where empirical evidence is found that a good reputation causes better performance. Here, reputation is described with the opportunity to be a Fifa referee and the chance to referee matches in international competitions (e.g. Champions League, Europa League, World and European championships). Referring to the career concerns model from Holmström (1982a) (and Holmström (1982b)) we suppose that a referees experience (age) has first a decreasing effect on the individual effects but this only holds until a special turning point is reached. Further, we also use the professional jobs of the referees, their national football association and height as well as a variable for their last performance to describe the significant individual referee effects. However, if we use these referee characteristics instead of the referee fixed effects we do not find huge empirical evidence for our assumptions on the individual effects. Especially, we find no significant effects from the Fifa dummy-variable as well as in home and away matches. Further, there is only small empirical support that referees follow career concerns in home matches. In away matches, the coefficients for age and experience are always insignificant. Concerning the referee s profession we find some empirical power in away matches but not in home matches. Thus, it seems that observable referee characteristics are not adequate to explain the significant individual effects from referees on match outcome and further referee decisions. The remainder of this paper is organized as follows: Section 2 provides an overview on the literature concerning referee bias. Section 3 describes the system for referees in German Bundesliga. In section 4 the data set is described and summarized statistics are presented. Section 5 presents the empirical results and section 6 concludes. 2 Literature On Referee Bias In Football There are many studies which try to explain the behavior of football referees and how they favor home teams (e.g. Nevill et al. (2002), Dohmen (2003), Sutter and Kocher (2004), Garicano et al. (2005)). One main result about favoritism is that referees are influenced by spectators. Another findings in these studies are, that increasing years of experience would decrease favoritism but also that referees follow career concerns which result again in an increasing referee bias if referees are older or at the end of their referees career. As 5

6 an indicator for referee bias the extra time at the end of the second half is often used. Further, awarded goals and penalties or not awarded penalties and bookings are mentioned as hints for favoritism, too. But how a referee affects the result of a match is not often examined, yet. However, most studies on referee bias have in common that public data on football matches were analyzed. Indeed one exception was done by Nevill et al. (2002). They follow the hypotheses that there is a relation between the experience of a referee and the referee bias. Therefore they ask a group of 40 referees. Some of them had only just begun their careers and others had 43 years work experience as a referee. The referees judge about 47 incidents in a game between Liverpool and Leicester City which they watch on a video tape. One group of these referees watch this video with crowd noise and the other group without. Finally, their empirical findings from the experiment are a significant influence from the crowd noise as well as a significant non-linear influence between the experience of a referee and the amount of fouls caused by the home team which are recognized by the referees. Dohmen (2003) studies the behavior of referees in German professional soccer and assumes a principal agent relationship between the governing body and the referees. He finds that a special social atmosphere, like in a football arena, can persuade agents to make decisions, that are neither in the interest of their principal 10 nor in the agent s own interest. He uses information about injury time at the end of a half, awarded and not awarded penalty kicks as well as the power of the teams and other decisive data like yellow or red cards. After analyzing this data the following four main results are figured out by Dohmen (2003). First, the length of injury time in the second half is much longer the closer the match. Dohmen (2003) supposes that fans influence a referee s decision and that there are differences between a stadium with and without racetrack. Therefore, a second result of this study is that a high attendance to capacity ratio reduces the home bias in stadiums without a racetrack around the field and the bias increases in stadiums with a track. Because he find no direct influence on the outcome of a match through injury time, Dohmen (2003) controls for penalty kicks, too. He figures out that home teams receive penalty kicks twice as often as away teams. Based on his results, Dohmen (2003) concludes that special social pressure can affect the behavior of agents in a way that they make decisions which do not follow their private interests. In another study, Dohmen (2008) uses, besides the length of injury time, wrong and right referee decisions on goals, penalties as well as yellow and red cards. Regarding the referee decisions, Dohmen (2008) find empirical evidence for a referee bias again. First, 10 In Germany it is the German Soccer Association (DFB). 6

7 the probability for a wrong awarded goal for home teams or penalty depends on the match score. Thus, the probability for such a wrong decision increases if the home team is behind. Another point is, that away teams are more often penalized by the referee while more often a legitimate penalty is denied. Again, Dohmen (2008) find significant differences between stadiums with and without a racetrack and he even find evidence that the referee bias depends on the structure of the crowd (fans). Another study on referee bias shows the existence of a home team bias on referee decisions in Italian (Serie A) and United States (MLS) professional football leagues. Lucey and Power (2004) assume that referees tend to act in a way that favors a home team. The authors consider that referees act in a principal agent relationship with their national football federation and that leads to two aims of their study. First, they analyze whether the decisions 11 of football referees are really systematically biased and second they figure out if the decision to allow more extra time is influenced by the social environment that is created from the crowd in the stadium. With respect to the referees it is interesting that they examine two different reward systems. On the one hand there are the Italian referees. Here exists a similar reward system as in Germany. 12 But in the US system, the rewards of referees are linked to their performance, because the wage per game is based on their past performance. Therefore, Lucey and Power (2004) mention two factors which influence the decisions of referees. First, referees are interested in being impartial because their aim is to be reappointed and/or promoted and secondly, referees are in an endeavor to satisfy the crowd in the stadium. Boyko et al. (2007) do research on home advantage in sports. They examine among others if referees are biased and whether this bias has an influence on the outcome of a match. A new aspect of this study is that Boyko et al. (2007) are interested in the question if referees have any effects on match outcomes. Second, they figure out if the influence from the crowd really forces the behavior of referees or whether the players are influenced by crowd noise. They figure out that favoritism of referees is an individual characteristic and that more experienced referees show lesser home advantage. Buraimo et al. (2007) use another approach and underline the importance of withingame dynamics. Their unit of observation is the minute within the game and not the whole match as in the studies before. They model the probability of a yellow card or a dismissal within a specific minute of the match. Furthermore, Buraimo et al. (2007) use 11 The decision which is examined is the amount of injury time after the end of the second period in a game. 12 The referees get a fixed salary for every match they judge. 7

8 data from two leagues (Premier League and 1 st Bundesliga) over the same time period and compare their results. Again, in this study it is distinguished between stadiums with and without a racetrack around the football field. The matches that are examined are differentiated in matches with teams which are favorite or underdog. Their results do not differ from other studies and they find a home referee bias, too. But with their method Buraimo et al. (2007) have further implications on favoritism. First, they figure out that home teams which play in stadiums without a racetrack have lesser probability in receiving yellow and red cards. Further, they find out that home teams which are not very successful and are considered as the underdog of the match, will benefit from the referee bias. Rickman and Witt (2008) analyze whether financial incentives help to control favoritism in hierarchical principal agent settings and consider that principals can use a combination of financial rewards and imperfect monitoring to incite their agents. Therefore Rickman and Witt (2008) use data from football and study if a governing body in soccer (the higher principal) can influence favoritism displayed by referees (the principal) towards players/teams (the agents). Rickman and Witt (2008) pursue a similar approach like in the other studies mentioned above. The authors distinguish their data 13 between a Premier League with referees acting as amateurs (the pre-professional English Premier League) and a League where referees acting as professionals with more financial incentives (post-professional Premier League) for their analysis. 14 The results show that favoritism disappears after professionalisation of the English referees and that financial incentives for referees have a decreasing effect on the amount of extra time. Page and Page (2010) find evidence that referees are influenced by social pressure, too. They analyze the home advantage effect and if varying effects depend on which referee leads the match. Therefore, Page and Page (2010) examine 37,380 matches with 872 referees from 58 different competitions (national club matches and international matches). Using a random effects as well as a fixed effects approach Page and Page (2010) figure out that the home advantage effect differs significantly between referees. They conclude that increasing effects on home advantage are caused by social pressure from spectators and that varieties in these effects are evidence for significant individual differences between the referees. 13 Rickman and Witt (2008) compared professional referees from Premier League and referees acting as amateurs in First Division. They used data from the seasons and So, they examine 760 Premier League Matches and 1,104 First Division games. 14 At the beginning of season 2001/02 there was a reform for referees in English professional football. Referees from the Premier League were not amateurs anymore and were treated as professionals. This resulted in higher wages per match and a better training and education. 8

9 Once more, Dawson (2012) examine whether a referees experience influence his performance if it is controlled (among others) for social pressure. He uses data from European Cup competitions like the UEFA Champions League and the UEFA Cup 15 for the years 2002/03 to 2006/07. Within this data Dawson (2012) control for the quality of the two teams, period of the competition, number of spectators and a variable for racetrack. The dependent variable is designed by a weighted average of yellow and red cards. As a first result Dawson (2012) find out that there is a negative correlation between the years of referees experience and the number of sanctions. Further, he control for an interaction between experience and crowd size. Again there is a negative effect from more experienced referees on the number of sanctions. Within these studies the extra time at the end of second half, goals, penalties, yellow cards and dismissals are often used as the dependent variables for regression analysis. Then, it is controlled for number of spectators, racetrack, team abilities or age and years of experience from referees. variables for the length of extra time, too. Further, awarded yellow cards are often used as control In contrast, we also use yellow cards and yellow-red as well as red cards as dependent variables, because we suppose that awarding a yellow card etc. is driven by the rules of the games and should be independent from the individual referee. Like Page and Page (2010) and Boyko et al. (2007) we are interested in the individual differences in referee bias, especially whether there are any effects on match outcome. For the purposes of this study the main focus lies on the number of points that are won (0,1,3) within a match. Therefore regression analysis is used too, but here the main interest lies in the referee fixed effects. In the studies discussed above, the referee fixed effects are only used to control for specific referees. Now, we try to describe the magnitude of these fixed effects and if they have a significant influence on match outcome, although it is assumed that there should be no significant effects from referees. Notwithstanding from the studies mentioned above, it is not controlled for number of spectators, racetrack, capacity ratio or if a match is very close. The main focus lies on the two playing teams of a match and the known circumstances of match Since 2009 this competition is known as the Europa League. 16 Further information on this regression analysis is given in section

10 3 German Referees The following section outlines some information about the referee system in Germany. It is presented, how in refereeing interested people will become a referee, how they are educated as well as some information about the reward system, monitoring and their possibilities to be promoted and relegated within the German Football Association. Training of German Referees As Ebersberger et al. (1989) describe, a successful referee has to comply the following expectations: A German referee is believed to referee a game impartial, be fair, does not make any differences in the judgment of similar processes of the match or events, treat every player equal, make clear decisions, be as close to match events as possible, show players understanding (does not react sensitive on criticism), be consequent and be unbiased. The aim of a referee is to avoid any disturbance on the football ground by players and spectators. But to execute these expectations it is very important that a referee is physically fit and a good referee has to bring along a mental flexibility. Furthermore, for top class referees it is really important, that they arrange their working time in a flexible way because the professional job career has to be subordinate to the activities of a referee (Strigel, 1999). The organization of the German referees is similar to the structure of the German football association (Ebersberger and Pohler, 1997). Thus, there exist different national associations 17 and the allocation of the referees into the different associations happens geographically. These associations are managed by an elected committee. The activities and the functions of the committee and their chairman are defined by the referee acts of the current state associations. The most important functions of these associations are education, mentoring, further training and qualification of the referees. The nomination of the referees for the matches is also a task of these referee groups. After passing the exam, the referees only know the basics, hence it is expected from new referees, that they participate in further education. 18 Additional, they are requested to train their own personal condition because only referees with a relative strong physical fitness are able to handle tough matches without any problems. Thus, ambitious referees must, besides the participations at further training, they have to spend a lot of time for private studies (Teipel et al., 1999). 17 c.f. section These are organized by the local district chairman for two evenings in a month. Here the focus lies on single rules for refereeing in soccer and the behavior of the referees on the pitch. 10

11 The opportunities to be promoted as a referee are different. A young eighteen year old referee has the possibility to be promoted 19 into the German Bundesliga within six years with the help of a special program of the DFB. This means for such a young talent, that he has to decide for a career as a referee very early. On the other side the referee board of the district and association have to worry about the young referee in time. That means he often has to be monitored to realize the qualification and to identify the strengths and weaknesses. Responsible for further training are the respective referee groups (Teipel et al., 1999). At the beginning of a referees career they have to start in matches in lower leagues (county level). But it is annually possible to be promoted in higher leagues whereby successful referees have to hurdle the admission into the promotion squad of the German Football Association. Referees who are promoted as official DFB referees are subordinated to the DFB referee board. The functions of this referee board are to classify, assist and educate the referees. A last and important step in the career of a successful referee is the nomination as a Fifa referee with the chance to umpire matches in international competitions (Artium and Rimkus, 2001). 20 During their career it will become more difficult to fulfill these hard performance requirements with increasing age. Therefore age limits are defined on national and international level. The national age limit of the DFB lies on 47 years and for referees on the Fifa list exist an age limit of 45 years. As it is shown, referees receive specific education and training and if a referee is promoted to 1 st Bundesliga he has to shown an excellent performance over time. That means, that referees are highly selected in German football. Further, because referees can be relegated too, they have high incentives to be neutral and perform well. Therefore, it is assumed that no significant effects from referees on match outcomes should be found. Remuneration for German Referees In Germany referees are remunerated according to their league in which they referee. Matches in the third league are waged by e 750, in the second league referees received e 1,800 per match and in the first division they get e 3,800 for every match that they umpire (DFB, 2009). According to this compensation, referees from 1 st Bundesliga are on second place compared to other European leagues. The Primera División is the only league where referees earn with e 6,000 more than in 19 Promotion or relegation happens in annual frequency. 20 Although the performance requirements change within professional leagues, a really good referee will only need six till eight years to be promoted to a DFB referee and another two years to become a Fifa referee. Only these ones, who became referee at an early age have a viable chance to be nominated for the Fifa list (Strigel, 1999). 11

12 Germany. In England, the professional referees earn e 1,170 per match but receive a base salary of e 38,500 per season. 21 Although there are such high allowances for referees, it is not planned to introduce the professional referee in Germany. Reasons are not clarified questions about consequences after a relegation or injury. However, since 2012/13 the DFB honors their professional work and pay an additional compensation. For example the five Fifa referees who are Fifa referees for the longest time get additional e 40,000 within this season. The two referees who promoted from 2 nd to the 1 st Bundesliga even get e 20, Monitoring German Referees Promotion or relegation of a referee depends on one hand of performance tests which referees should pass four times in a year, and on the other hand on their results of monitoring. Four criteria are relevant to evaluate the performance of referees: (1) physical fitness, (2) involvement outside the soccer field, (3) personality and (4) results of referee monitoring. The members of the referee committee must evaluate the performance of the referees to get a right appraisal of a referee. In higher leagues this is done by former referees who use a detailed observation form. This observation is essential for referees of the DFB, too. The observation form of the DFB not only deals with the performance of the referee, but also regard the performance of the referee assistants in a specific match. Employing interior and external factors a match is classified in a definite ranking (c.f. table 1): c.f. last access: June 11th, Another incentive for referees to provide a good performance is the possibility to umpire international matches. For example, Herbert Fandel, one of the most famous referees in Germany, talks about the special honor to referee in a Champions League Final (DFB, 2007a). Furthermore there are still more potential earnings for really good or famous referees after the personal end of the referee career. For example, the Swiss Fifa referee Urs Meier appear as an expert for referee decisions in German television. Besides the media, even the economy indicate their interests for successful ex-referees. The former world referee Dr. Markus Merk appears as a referent since he finished his referee career and is so successful with it, that he must abandoned his dental clinic. 23 Besides the external and interior factor it is also possible that a match becomes very heavy because of a weak referee performance (BFV, 2001). 12

13 1. External factors 2. Interior factors Teams Foul play (local derby, promotion/relegation, (many fouls, neighbors in table) unsportsmanlike behavior, dives) Match ground and weather (slippy canvas) Attendance (large spectators setting, noisy fanatics, frantic trainer or substitute) Table 1: External and interior factors Monitoring the referees is essential for the German referees, hence they are still trying to increase efficiency. In the first and second division a so-called coach is implemented, who also look after the referees. This coach shall review the match with the referee team and prepare the active referees for their next match administration by video analysis. Observers and coaches are supposed to evaluate the whole match and assess match-winning mistakes negatively. Monitoring is essential to ensure a fair rating of performance and discover talents to promote them further (DFB, 2007b). 4 Data The data to estimate the individual effects were mostly collected from the company Impire AG. 24 Among others, Impire is specialized in statistics on football matches and provides data for example for TV broadcasts and Bundesliga football teams. From Impire, we use data about football matches like match day, home and away team, goals and referee decisions (e.g. yellow, yellow-red and red cards, not awarded goals or red cards etc.). But in principle, these data are all public available and it would be possible to collect them per hand from different football websites. One of these websites is from the German football magazine Kicker From Kicker, data about the referees like age, date of the first match in Bundesliga 27, height and in some cases their professions 28 are collected. In total, this data-set contains 4,590 matches from 1 st Bundesliga in Germany from season 1993/94 until 2007/08. Within these data there are 67 referees with up to 20 years of ex Other possible data sources are or 27 With this date years of referee s experience is calculated. 28 Remember, in Germany football referees do not work as professionals, therefore the DFB claim that all DFB referees must work in a regular occupation. 13

14 perience and at least two matches in the data-set. Table 2 provides an overview about the average number of matches per season that were umpired by a referee in 1 st Bundesliga between season 1993/94 and 2007/08. As it is shown, the average number of matches increases from 9.13 in 1993/94 to in season 2007/08. Even the maximum number of matches for a single referee increases from 12 to 24. One reason for this rise in the number of matches for referees is that the DFB reduced the total amount of referees in 1 st Bundesliga. In the season 1993/94 in total 32 referees were appointed in matches of 1 st Bundesliga but in the season 2007/08 only 19 referees were nominated to referee in 1 st Bundesliga. Thus, it is more difficult to promote to 1 st Bundesliga. Year Mean S.D. Min Max Table 2: Number of matches per season and referee Table 3 describes how often a referee has to umpire the same team within a season. As it is shown, there is a huge variation between referees and teams. Within 18 teams and 34 match days, the same referee and the same team meet each other only 1.34 to 1.82 times on average. Even the maximum lies at only 4 to 5 encounters. That implies that there is enough variation between referees and teams within a season, to examine individual referee effects in a next step (in the next section). 14

15 Season Mean S.D. Min Max Table 3: Distribution of referees and teams per season Figure 1 describes the distribution between a referee and the same teams in a referees tenure. Figure 1 should help to answer the question how often a referee meet the same team within his career as a referee from 1 st Bundesliga. Only a few referees referee more than thirty times the same team during their tenure. The peak in this distribution is about eight times, that is due to the fact that a referees career does not persist for a long time. As it is discussed later in section 5.4 a referee on average stays in 1 st Bundesliga only for seven years. 15

16 Density Matches/Team Figure 1: Distribution of referees on teams Table 4 shows descriptive statistics on referee decisions taking into account the whole sample and the referee characteristics sample. 29 That sample only includes observations of matches with a referee where some further information like profession, height and football association is found. Although there is a data loss of about 26% if only the referee characteristics subsample is applied, the descriptive statistics of both samples show no huge differences. That implies that there should be no problems if we use referee characteristics instead of referee fixed effects. Table 4 displays that on average the goal difference between home and away teams amount to 0.5 goals per match. On average, three goals are awarded in a match whereby one match exist with even eleven awarded goals. The number of not awarded goals 30 and awarded penalties are very similar. On average, there are 0.7 not awarded penalties per match and even one match exists with six not awarded penalties. As table 4 reveals, on average referees brandish four yellow cards, but the yellow-red and red cards were only drawn 0.1 times per match on average. Lastly, table 4 shows that the number of not awarded red cards is 0.3 on average. 29 Later on, this referee characteristics subsample is used to examine which properties influence the individual referee effects. 30 Not awarded goals, penalties and red card are the respective sum from wrong and disputable referee decisions. 16

17 Match-Referee-Sample Referee-Characteristics-Sample Mean S.D. Min Max N Mean S.D. Min Max N Goal difference , ,383 Goals , ,383 Not awarded goals , ,615 Penalties , ,383 Not awarded penalties , ,559 Yellow cards , ,202 Yellow-red cards , ,202 Red cards , ,202 Not awarded red cards , ,559 Table 4: Descriptive statistics Table 5 displays the frequency of the match outcome variable result 31 in favor of home teams. That means, that home teams win 3 points in 48% of the matches. In 26% of the matches, a match ends up with a draw and home teams only lose 26% of their matches between the seasons 1993/94 and 2007/08. Thus, home teams more often win three or at least one point than lose their matches. 32 Again, table 5 shows no huge differences in frequencies between the whole sample and the referee characteristic subsample. Match-Referee-Sample Referee-Characteristics-Sample Result Abs. % Abs. % 0 1, , , , Table 5: Frequencies of result 31 Result is equal to three points if the home team win the match and zero if it loss. Does a match end up with a draw both teams receive one point. 32 This could be a small hint for home advantage. Evidence for home advantage was often examined in literature. For example Clarke and Norman (1995) find a home ground effect for teams in English football from 1980/81 until 1990/91. Another work was done by Koyama and Reade (2008) and they find evidence for home advantage in English football and that this phenomenon changes over time. Assuming that there is a home advantage in sports, many other studies have examined reasons for this phenomenon. As it is mentioned above (c.f. section 2) one explanation for this home advantage might be that referees are influenced by crowd noise and due to this social pressure they often decide in favor of home teams (c.f. Nevill et al. (2002), Dohmen (2003), Garicano et al. (2005), Boyko et al. (2007), Dawson et al. (2007) etc.). 17

18 5 Individual Effects The following section describes the empirical results on individual effects from referees. First, we estimate whether referees really have an individual effect on match outcome or referee decisions. With respect to selection criteria, education and evaluation of DFB, it is assumed that there are no individual effects from referees. But as we demonstrate in the next section there is substantial empirical evidence for the joint significance of referee fixed effects. In a next step, the estimated referee fixed effects are used to examine and describe different referee styles (c.f. section 5.3). Afterwards, we use referee characteristics instead of the fixed effects to explain which properties might influence the individual referee effects. (c.f. section 5.4). This empirical approach refers to the literature on individual effects of managers (CEO, CFO etc.). Therefore, this section starts with a brief literature review on the most important studies on estimating individual effects from managers on firm performance. Pioneer in estimating individual effects were Abowd et al. (1999). They first attempt to measure individual worker effects and firm fixed effects on wage. That means, they examine the variation in personal wage rates holding firm effects constant and variation in firm wage rates holding person effects constant. Bertrand and Schoar (2003) enhanced this approach and tried to answer the question: whether and how do individual managers affect corporate behavior and performance?. Particularly they find out how manager personalities contrary to firm, industry or market factors, explain unobserved differences in firm s success. Bertrand and Schoar (2003) are interested to quantify how much of the observed variation in firm performance can be explained by manager fixed effects. Therefore, they only use data on managers who change their jobs and work at least for two firms. Their variables of interest are different firm policy variables like Investment, Cash Flow etc. In a first step, the authors run a regression without manager fixed effects (CEO, CFO, other). Next, they include CEO fixed effects at first and then CEO, CFO and other fixed effects. An individual effect from a manager is found if the p-value from the F-test for joint significance of the manager fixed effects is significant and the explanatory power increases, after the manager fixed effects are included. In a next step, Bertrand and Schoar (2003) estimate different management styles while they interpret the correlation between the manager fixed effects for the different policy variables. Lastly, they repeat their first regression on corporate policy variables. But instead of manager fixed effects, they now control for manager properties like birth cohort, tenure and if managers have an MBA. In the end, besides 18

19 the joint significance of managers in firms and different management styles, Bertrand and Schoar (2003) conclude that these manager effects are referable to observable individual characteristics like education or age. One problem of these results is that the estimated manager effects could be due to a selection bias. That means, that successful firms select successful managers. These possible endogeneity problems were revisited by Fee et al. (2010) and Graham et al. (2012). Fee et al. (2010) capture the problem that most of CEO turnovers are endogenous and that it is difficult to isolate manager effects. It is ambiguous whether varieties in firm performance are the result of a special manager style or rather if there is a firm policy change which is accompanied with a CEO change. So, Fee et al. (2010) use in their study exogenous (death, health problems) as well as endogenous CEO turnovers and replicate the results from Bertrand and Schoar (2003). One result of their analysis is that it is uncertain if varieties in firm performance are referable to individual manager effects or if it is the effect from an underlying endogenous process. Even their alternative test for the joint-significance that account for serial correlation and endogeneity is non-significant. Graham et al. (2012) examine the role of unobservable time-invariant firm and manager effects. As dependent variable they use variation in executive pay and answer the question how the inclusion of fixed effects impact the interpretation and contribution of traditional explanatory variables?. In total, Graham et al. (2012) use three methods and therewith they want to isolate and quantify how much of the variation in executive pay is traceable to observable time-variant firm and manager fixed effects, as well as timeinvariant firm and manager fixed effects and year effects. Bennedsen et al. (2007) search for evidence that managers have notable effects on firm performance, too. But afterwards they are not interested in personal characteristics of CEOs like age or MBA but rather if deaths from these CEOs or deaths from immediate family members (children, parents, mother-in-law) will affect firm performance. Bennedsen et al. (2007) mention two advantages from this unusual approach. First, the above mentioned shocks will definitively impinge on the firm performance. Either because of their own death or they are diverted because of the death of a family member. Second, it is assumed that these shocks will only influence the managers but have no direct effect on firm performance. This unusual approach was chosen to solve again possible endogeneity problems because firms often do not fire or appoint managers randomly. Bennedsen et al. (2007) find that CEOs with large positive investment fixed effects are correlated with large declines in firm profitability after one of these external shocks. An external 19

20 shock on CEOs with negative investment fixed effect expose no dramatic changes in firm performance. 5.1 Empirical Strategy In contrast to the studies on manager effects, problems with endogeneity and serial correlation do not exist if we analyze the individual effects from referees. An advantage of a study on football data and referees is that the combination between home and away team as well as referee changes every match day. And there is a neutral institution (German Football Association) which is responsible for a referees schedule. 33 Now, for every variable of interest, the following equation is estimated by an ordinary least squares regression: y it = β 0 + α t + γ i + γ j + β 1 χ it + β 2 χ jt + β 3 τ i + β 4 τ j + β 5 µ it + β 6 µ jt (1) + β 7 θ it + β 8 θ jt + λ Referee + ɛ it where y it stands for the variables for match outcome respectively referee decisions (e.g. result, goal difference, awarded yellow, red cards etc.) for every team and it is controlled if this team is the home or away team. α t are season fixed effects, and γ i are team fixed effects and γ j are fixed effects for the opposing team. This equation shall describe which well-known factors before a match might influence the result or the events of a current match. One important aspect is the actual performance of the playing teams that is captured by χ it and χ jt. These are vectors for the playing team and its opponent where time-varying performance variables are included like short-term, middle-term and long-term past performance. A teams long-term performance is measured by the average league position in the last three seasons. Then, as the middle-term performance, it is important to know how well a team performs during the actual season. This type of achievement is measured by the average number of points as well as for home and away matches. observation. Further, the average points are accumulated up to the interesting (actual) The last type of performance measure is an indicator for the short-term performance. Here, we use performance dummy variables that describe the strength of a team in the last four matches. Particularly, for every team a dummy variable for every last four matches exists with the following form: the teams recent performance prior to 33 To capture the problem that the decision which referee is appointed in which match is based on their earlier performance the following regressions are clustered at team level. 20

21 match day t is (y it 1, y it 2, y it 3, y it 4 ) where y it k 3, 1, 0 for k = 1,..., 4 indicates the number of points attained in the match which is played k match days before match day t. The same is done for the opponent which results in 3 4 = 81 of such history dummy variables for each playing team. τ i and τ j are the relative budget within a season for team and opponent. Whereby the relative annual budget is calculated by the fraction of absolute budget and average absolute budget in the league in a given season. µ it and µ jt are variables for the relevance of a match (championship, relegation etc.) for the both playing teams. As it is already discussed (c.f. section 3) it is important to know what kind of match is played. To describe this match type different variables are used to depict the strength and incentives of the two playing teams. First, three performance measures for home and away teams are applied. Second, we control if a match is crucial for one of the both playing teams. Third, we use with θ it and θ jt the number of drives for both teams within a match. The drives are used to capture at least one match specific variable that might influence the match outcome and is independent from the referee. λ Referee are the referee fixed effects. 5.2 Results Before we discuss the results of equation 1, we underline the hypotheses of this study, again: It is assumed that referees in football matches act impartial and do not influence the match outcome. To estimate the individual influence of a referee, equation (1) is first run without the dummy variables for referees. After that, equation (1) is repeated with referee fixed effects. Evidence for influence of referees on match outcome is found if the adjusted R 2 increases after referee fixed effects are included and moreover the F-test for joint significance of these referee dummy variables must be significant. 34 Equation (1) is not only examined for match outcome. Further, it is controlled if referee influence is found on referee decisions, like awarded yellow, yellow-red and red cards, awarded goals and penalties as well as not awarded red cards, goals and penalties, too. Although, these decisions are at the discretion of the individual referee it is expected that these decisions are done neutral and strictly according to the DFB regulations. The results of these estimations are displayed in table 6 for home matches and in table 7 for away 34 Although the dependent variable has only three realizations it is justifiable to use an OLS approach. Because at the end of a match three points are always better than one or zero points (c.f. Angrist and Pischke (2008)). Nevertheless the following results were verified with an ordered probit model and our findings are approved with this model, too. 21