Referee Bias in Professional Soccer: Evidence from Colombia

Transcription

1 Referee Bias in Professional Soccer: Evidence from Colombia Septiembre 2013 JUAN MENDOZA* Department of Economics, Universidad del Pacífico, Av. Salaverry 2020, Lima 11, Perú. ANDRÉS ROSAS Department of Economics, Pontificia Universidad Javeriana, Calle 40, No. 6-23, Piso 7, Bogotá, Colombia. * Corresponding author. 1

2 ABSTRACT This paper measures the magnitude of referee bias using data from the Colombian professional soccer league. Our dataset contains more than 1,600 observations encompassing all first-division games played between 2005 and We use both OLS and Poisson regressions to estimate the effect of the score difference on the length of injury time added at the end of both the first and second halves of each game. Our main result is that there is statistically-significant referee bias favoring home teams. In particular, we find that referees extend injury time by approximately a quarter of a minute if the home team is trailing the half or the game by one goal. We also find that referees tend to end injury time half a minute earlier if the home team is winning by one goal. Our estimation controls for various determinants of injury time such as the number of player substitutions, the number of yellow and red cards, the occurrence of penalties or other unusual events during the game. We also consider fixed effects at the team and referee levels. We study how the size of the referee bias might depend on variables such as attendance, ranking difference, previous performance in the tournament, homicide rates in the city of the home team, as well as a measure of historical performance of each team. Our results are consistent with the hypotheses that social pressure or psychological motives, either conscious or unconscious, exert a significant influence on referees decisions. Keywords: Soccer, Referee Bias, Favoritism. JEL: M50, L83, Z13. 2

3 I. Introduction In this paper we study the presence of referee bias in the Colombian professional soccer league. In particular, using more than 1,600 observations, encompassing all games played between 2005 and 2010, we estimate whether or not the length of injury time depends on the relative position of the home team in the match. We control for various sources of variability on the length of injury time such as the number of red and yellow cards, the number of goals scored, the number of penalty kicks, and the number of substitutions. We also consider fixed effects for teams and referees. Soccer is arguably the most important sport in the world. Billions of spectators follow the sport s professional leagues with intense interest as the business of soccer continues to grow every year. During some games of the FIFA World Cup, which rivals in advertising revenue with the Olympics, productive activities in many countries are temporarily halted. But the worldwide fascination with the sport crucially rests on the assumption that the decisions of the referees are fair. For if match outcomes are not fair or if they can be somehow anticipated, then much of the thrill and suspense of the sport will be gone. As in other sports, the referee plays a fundamental role in soccer. Because the sport does not use technological aides in a systematic manner, the referee has to make subjective decisions throughout the game. In effect, the referee is the final authority in the match and his or her calls over-rule any calls made by the two assistant referees. Among the various decisions made by the referee, the length of injury time should be the least subjective. The game has two halves of forty-five minutes. The purpose of injury time is to compensate for the number of substitutions as well as by any possible development that might have caused an unforeseen halt to the play such as unusually serious injuries or penalty kicks. Further, to eliminate suspicion over the objectivity of the referee as regards to injury time, in 1998 the Fédération Internationale de Football Association (FIFA) stipulated that referees should post the number of minutes of extra time added at the forty-fifth-minute mark of each 3

4 half. Because the number of substitutions, penalty kicks or any unusual development should be uncorrelated with the location of the game, one should not expect any relationship between the length of injury time and the score at the forty-five-minute mark. Because impartial referees are essential to the game, there is wide agreement that scandals over match fixings have caused great damage to the reputation of the sport. A case in point is the discovery of widespread corruption among some Italian professional clubs in 2006 which colluded with some referees to rig match results over several years. Soccer authorities enacted harsh punishments, including the relegation to Serie B of Juventus which had won two consecutive Serie A titles, in an effort to defuse further suspicion among the fans. Similar episodes in Brazil and Germany in 2005 generated considerable turmoil in the soccer community. However, not only the discovery of match fixings has been a source of concern regarding the fairness of the game. There is increasing statistical evidence that referee bias mars the sport in some of the most important professional leagues. In effect, several authors have found that the length of injury time in close matches tends to favor the home team. Examples include most notably Garicano et al. (2005) for the Spanish La Liga, Scoppa (2008) for the Italian Serie A, and Sutter and Kocher (2004) and Dohman (2004) for the German Bundesliga. All these studies report that if the home team is trailing the match by one goal then injury time tends to be longer whereas if the home team is winning by one goal then injury time tends to end sooner. 1 Of course, the existence of referee bias in extending or shortening injury time does not necessarily imply corruption in soccer. 2 Such bias might be also a consequence of social pressure exerted by the crowd which, either consciously or unconsciously, affects the decisions of the referee. In this vein, Garicano et al. (2005) find that the bias is increasing on attendance, by approximately one standard 1 Referee bias has also been found in other sports such as boxing, see Balmer et al. (2005), and basketball, see Anderson and Pierce (2009). 2 Duggan and Levitt (2002) find much evidence that the behavior of sumo wrestlers is consistent with the exchange of economic favors among them. These authors are able to identify this behavioral pattern because of nonlinearities in the rewards of sumo wrestlers. In contrast, the findings of referee bias in soccer have not been linked, to our knowledge, to payments to the referees. 4

5 deviation, as well as on the ratio of attendance to stadium capacity in Spain. Dohmen (2005) as well as Lucey and Power (2009) provide similar conclusions for the German Bundesliga and Major League Soccer in the United States. Scoppa (2008) reports that, in the Italian Serie A, crowd proximity, measured by whether or not there is a running track in the field, tends to increase the magnitude of the bias. Referee bias because of social pressure is consistent with primal fears triggered by crowd stimuli. 3 For example, Greer (1983) detects substantial changes in referee decisions after episodes of intense spectator booing, whistling and shouting in American basketball. The experiment of Nevill et al. (2002) concludes that crowd noise affects whether or not tackles against home-team players are ruled as irregular even among seasoned referees in soccer. Pettersson-Lidbom and Priks (2009) tell us that referees are much less likely to favor the home team with favorable rulings when the match is played before an empty stadium in Italian soccer. According to these studies, referees might make biased rulings in an unconscious effort to appease the crowd. Furthermore, referee bias might contribute to the presence of home advantage, a well-established stylized fact in professional sports. 4 Nonetheless, it is noteworthy that not all empirical investigations have concluded that there is referee bias in professional soccer. For example, Rickman and Witt (2008) fail to find any evidence of bias in the English Premier League after the introduction of professional referees in Interestingly, these authors report referee bias prior to the 2001 institutional change in English soccer. Our paper attempts to ascertain whether or not there is referee bias in the Colombian professional soccer league, one of the most important leagues in the Americas. We replicate the methodology 3 Social pressure has been identified as a fundamental explanation of a wide array of human behavior. Reysen (2007), for example, provides evidence of the significant effect of social pressure on eliciting false memories. Stutzer and Lalive (2001) explore the relationship between social pressure and the intensity of job searching. Huck and Kubler (2000) relate social pressure to cooperation in psychological games. 4 Crowd involvement might also affect performance by improving the performance of home players. Neave and Wolfson (2003), for example, find that testosterone levels are higher among players of the home team. The analysis of Nevill et al. (2001) implies that crowd noise might serve as a cue, albeit biased, to the decisions of the referee. See Schwartz and Barsky (1977) and Nevill and Holder (1999) for more on the importance of home advantage in sports. 5

6 used by previous researchers by controlling for various determinants of injury time, such as the number of substitutions, yellow and red cards, the number of goals scored and whether or not there were penalty kicks during the game. Because of possible changes in team strategy, we also investigate referee bias in injury time at the end of the first half. Further, we attempt to identify the dependence of the bias on various factors such as attendance, the relative importance of the game, the stage of the championship, and the inherent violence of the home city. This paper is, to our knowledge, the first effort to study referee bias outside of the European leagues or of Major League Soccer in the United States. In this sense, this paper aims to contribute to a better understanding of the worldwide prevalence and cross-country variation in the determinants of referee bias. In the next section we describe the data and comment on some characteristics of the Colombian soccer league. In section III we discuss our identification strategy and present the results of the estimation. Section IV relates our findings to the existing literature and concludes. II. The Data We use data of first-division soccer games played in Colombia between 2005 and We collected the data from referee reports of each game to which we had access via the statistical division of the Colombian Professional League, DIMAYOR, and from the website The Colombian first-division soccer league is among the top tournaments in Latin America, ranked 3 rd in South America between 2001 and 2010 by the International Federation of Football History and Statistics ( Many world-class talents in soccer, such as Alfredo Di Stefano and Carlos Valderrama, have played in the Colombian league. In the Colombian first-division soccer league 18 teams play two tournaments each year. The first tournament runs from February to June and is called Apertura. The second tournament lasts from July to December and is called Finalización. Each tournament consists of two stages. In the first stage there is a single round-robin round plus an additional game against each team local rival for a 6

7 total of 18 games played by each team. The top 8 teams of the first stage advance to the second stage or the playoffs. In the second stage, the remaining teams are divided into two groups. The winners of each group play two final matches against each other for the tournament championship. At the end of each calendar year, the tournament champions and teams at the top of the standings play international tournaments while the teams at the bottom either lose or have the option of losing their first-division status. 5 We have gathered the following information on each game: the length of injury time both at the end of the first and second halves, the score difference, the number of player substitutions, yellow and red cards, the number of penalties and the number of goals scored. We also have data on the identity of each referee. Our data runs from the Apertura tournament of 2005 to the Apertura tournament of In Figures 1 and 2 we plot the average length of injury time, both at the end of the first and second halves, as a function of the score difference. Our measure of the score difference goes from having the home team behind by three or more goals to the home team being three or more goals ahead. Figure 1 appears to indicate a negative relationship between injury time and score difference at the end of the first half. According to Figure 2, injury time appears to be shorter when the home team is either behind or ahead by three or more goals. However, because both Figures do not control for the possible determinants of injury time, we cannot reach any definitive conclusions. 5 A team plays in international competitions if is among the top seven teams of the combined ranking of both tournaments during each calendar year. Whether or not a team loses its first-division status depends on its standing in a ranking based on the average number of points per game obtained during the last five tournaments. The 18 th team in the ranking drops to the second division tournament while the 17 th team plays against the 2 nd team of the second division teams to decide whether or not they will remain in first division. 7

8 FIGURE 1 Average Injury Time First Period 3 or more behind 2 behind 1 behind draw 1 ahead 2 ahead 3 or more ahead 0.5 mean of injuryfp FIGURE 2 Average Injury Time Second Period 3 or more behind 2 behind 1 behind draw 1 ahead 2 ahead 3 or more ahead mean of injurysp

9 III. Estimation and Results In order to estimate the presence of referee bias in awarding injury time we would like to estimate the following equation: (1) Injury time = β0 + β1 Score difference + β2 Controls + ε In other words, our identification assumption is that once we control for all measurable sources of variability on the length of injury time, the estimated value of the coefficient on score difference should reveal whether or not there is referee bias. In particular, if the estimated value of β1 is zero, then there is not referee bias while a positive estimate of β1 would indicate otherwise. We begin in Tables 1 and 2 by estimating regressions of the length of injury time on six measures of score difference: Homebehind1: Dummy variable which takes the value of 1 if the home team is trailing by 1 goal and 0 otherwise. Homebehind2: Dummy variable which takes the value of 1 if the home team is trailing by 2 goals and 0 otherwise. Homebehindm: Dummy variable which takes the value of 1 if the home team is trailing by 2 or more goals and 0 otherwise. Homeahead1: Dummy variable which takes the value of 1 if the home team is winning by 1 goal and 0 otherwise. Homeahead2: Dummy variable which takes the value of 1 if the home team is winning by 2 goals and 0 otherwise. Homeaheadm: Dummy variable which takes the value of 1 if the home team is winning by 2 or more goals and 0 otherwise. 9

10 Hence, the coefficients on these dummy variables should are relative to the half or the match being tied. In Table 1 we consider the score at the end of the first half. Table 2 uses the score at the end of the second half. Some authors, Scoppa (2008) for example, argue that the score at the end of the first half is inconsequential for the match. However, as the theoretical contribution of Carrillo and Brocas (2004) shows, teams might change their strategy in the second half if they find that they are winning or losing the match at the end of the first half. As control variables for the length of injury time we include: Goalsfp: Number of goals scored in the half/match. Yellowfp: Number of yellow cards in the half/match. Redfp: Number of red cards in the half/match. Penaltyfp: Number of penalties in the half/match. Subsfp: Number of substitutions in the half/match. Further, we include in some of our regressions dummy variables for each team in each tournament. We consider these fixed effects to control for sources of variability in performance originated by team characteristics that remain constant during each tournament, such as its organizational culture, popular support or the identity of the owner. Also, these fixed effects account for possible heterogeneity in the competitiveness or difficulty of particular tournaments. A tournament might be more or less competitive because of business cycle fluctuations or because of the occurrence of international competitions at the national level, such as World Cup or the South American championship, during the same calendar year, all of which are likely to affect attendance, advertising revenue as well as the availability of international players. We also consider fixed effects in some regressions as bias might be explained by the individual referees. We compute robust standard errors in all the estimations. 10

11 According to Table 1, the length of injury time increases by about a quarter of a minute if the home team is behind by one goal at the end of the first half at the 99% level of confidence. Also, injury time appears to be up to 20 seconds shorter if the home team is ahead by 2 or more goals at the end of the first half at the 90% level of confidence. All other measures of the score difference are not statistically-significant determinants of the length of injury time. In contrast, Table 2 tells us that the coefficients of all measures of the score difference but the home team being ahead by one goal are statistically significant. The general finding of Table 2 is that injury time tends to be shorter when the home team is winning and longer when the home team is losing the match and the end of regulation. For example, when the home team is winning by two or more goals the match tends to end up 48 seconds sooner than when it is tied. Also, when the home team is behind by one goal injury time appears to be extended by 12 seconds. 11

12 TABLE 1 OLS ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Homeahead ( ) ( ) ( ) ( ) ( ) ( ) hombehind ( ) ( ) ( ) ( ) ( ) ( ) homeahead ( ) ( ) ( ) ( ) ( ) ( ) homebehind452m ( ) ( ) ( ) ( ) ( ) ( ) homeahead452m ( )** ( )* ( )** ( )* ( )** ( )* Goalsfp ( ) ( ) ( ) ( ) ( ) ( ) Yellowfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( ) ( ) ( ) ( ) ( ) ( ) Subsfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Observations R-squared

13 TABLE 2 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )*** ( )*** ( )** ( )*** ( )** ( )*** Homeahead ( ) ( ) ( ) ( ) ( ) ( ) Hombehind ( )* ( )* ( )** ( ) ( )** ( )* Homeahead ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Homebehind902m ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Homeahead902m ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( )* ( )* ( )* ( )* ( )* ( )* Observations R-squared

14 However, it is reasonable to argue that the definition of referee bias should only consider games in which the score is close; namely, games in which the home team is either winning or losing by one goal. Accordingly, we now drop all games in which the score difference is greater than one. Further, we focus our attention on games in which the home team is losing at the end of each half. In Table 3 we estimate a regression of the length of injury time at the end of the first half on Homebehind451, a dummy variable which takes the value of one if the home team is trailing by one goal and 0 otherwise. The estimated coefficient on this measure of the score difference is statistically significant at the 99% level of confidence in all specifications and takes a value of approximately 1/5 of a minute. Thus, our estimation indicates that injury times tends to be 12 seconds longer when the home team is trailing the first half by one goal. TABLE 3 OLS ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Goalsfp ( )* ( )* ( )* ( ) ( ) ( ) Yellowfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( ) ( ) ( ) ( ) ( ) ( ) Subsfp ( )** ( )** ( )** ( )*** ( )** ( )** Observations R-squared

15 Table 4 presents the regression of the length of injury time at the end of the second half on Homebehind901, a dummy variable which takes the value of 1 if the home team is trailing the game by one goal at the ninety-minute mark and 0 otherwise. Across all specifications, our results indicate that injury time tends to be between 1/6 and 1/5 of a minute longer if the home team is losing the game at the end of regulation time. The estimated coefficient implies and extension in injury time of 10 to 12 seconds. TABLE 4 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )** ( )** ( )* ( )** ( )* ( )* Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

16 So far we have established that there is referee bias in the sense that close games, that is games in which the home team is losing either the half or the match by one goal, tend to last up to 12 seconds more. But, is there any dependence of the magnitude of the bias on measures of social pressure identified in the literature? To answer this question we now perform regressions of the length injury time against the score difference, a measure of social pressure as well as an interaction term between the score difference and the measure of social pressure. We continue to use the variables Homebehind451 and Homebeind901 as gauges of the score difference. Our measures of social pressure include the homicide rate in the city, Table 5, crowd attendance, Table 6, whether or not the game is televised, Table 7, a dummy variable which takes the value of 1 if the game is in the playoffs, Table 8, whether or not the referee is affiliated with FIFA, Table 9, a dummy variable which takes the value of 1 if the home team has been among the seven strongest teams in the accumulated historical standings and 0 otherwise, Table 10, a dummy variable which takes the value of 1 if the visiting team has been among the seven strongest teams in the accumulated historical standings and 0 otherwise, Table 11, and the ratio of attendance to stadium capacity, Table 12. We are not able to detect any statistically-significant link between referee bias and our measures of social pressure. 16

17 TABLE 5 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( ) ( ) ( ) ( ) ( ) ( ) Homicide rate ( ) ( ) ( ) ( ) ( ) ( ) Hb901hr ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

18 TABLE 6 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( ) ( ) ( ) ( ) ( ) ( ) Attendance ( ) ( ) ( ) ( ) ( )* ( )** Hb901att ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( )* Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

19 TABLE 7 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )* ( )** ( ) ( )** ( ) ( ) Televisado ( ) ( ) ( ) ( ) ( ) ( )* Hb901tel ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

20 TABLE 8 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )** ( )** ( )* ( )*** ( )* ( )** Semifinal ( ) ( ) ( ) ( ) ( ) ( ) Hb901sem ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( )* ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

21 TABLE 9 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )* ( )** ( ) ( )* ( )* ( ) Fifa ( ) ( ) ( ) ( ) ( ) ( ) Hb901fif ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( )* ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

22 TABLE 10 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )* ( )** ( ) ( )** ( ) ( ) Bthome ( ) ( ) ( )*** ( ) ( )*** ( ) Hb901bt ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Team fixed effects x x x Observations R-squared

23 TABLE 11 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( ( ) ( ) ( )** ( ) ( ) Brvis ( ) ( ) ( ) ( ) ( ) ( ) Hb901brv ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

24 TABLE 12 OLS ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( ) ( ) ( ) ( ) ( ) ( ) Relative attendance ( )* ( )* ( )** ( )*** ( )** ( )*** Hb901ratt ( ) ( ) ( ) ( ) ( ) ( ) Goalssp ( ) ( ) ( ) ( ) ( ) ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( ) ( )* Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations R-squared

25 The appendix tests the robustness of our findings by estimating equation (1) using Poisson-type regressions, which might be more appropriate for count data. We do not detect any change in any of the qualitative conclusions of Tables 1 to 12. Our results are also unchanged to a series of robustness exercises such as changing the sample size or excluding observations two standard deviations away from the mean. These estimations are available upon request. IV. Conclusion This paper has estimated the effect of the score difference on the length of injury time in Colombian professional soccer. Our main conclusion is that the length of injury time is up to 12 seconds longer when the home team is trailing the game at both the forty-five-minute and the ninetyminute marks. We are unable to establish any causal relationship between the magnitude of the bias and the wide array of possible measures of the intensity of social pressure such as attendance, homicide rates in the city, or the level of professionalism of the referee. Our estimation controls for various determinants of injury time such as the number of player substitutions, the number of yellow and red cards, the occurrence of penalties or other unusual events during the game. We also consider fixed effects at the team and referee levels. We study how the size of the referee bias might depend on variables such as attendance, ranking difference, previous performance in the tournament, homicide rates in the city of the home team, as well as a measure of historical performance of each team. Our results are consistent with the hypotheses that social pressure or psychological motives, either conscious or unconscious, exert a significant influence on referees decisions. Our paper confirms the general conclusion of the growing literature on referee bias in professional soccer. However, the magnitude of the bias is considerably lower than in previous studies. For example, Garicano et al. (2005) find that injury time tends to increase by approximately one minute in Spain if the home team is losing the match at the end of regulation. One possible interpretation to account for the smaller bias is that referees might find other ways to favor home team, besides extending injury time, such as awarding penalty kicks to the home team or expelling visiting players. 25

26 We cannot test whether or not this is the case because our identification strategy assumes that such measures, included in our list of controls, are uncorrelated with the score difference. Indeed, it might even be the case that if social pressure is more intense, then the referee might not rely on injury time to please the crowd but, rather, on more effective rulings during regulation time. We leave for future research the importance of referee bias in terms of deciding games and final standings in the tournament as well as to identify sources of variability in the magnitude of the bias. 26

27 REFERENCES Anderson, K.J., Pierce, D.A. (2009). The Effect of Foul Differential on Subsequent Foul Calls in NCAA Basketball. Journal of Sports Sciences, 27: Balmer, N.J.., Nevill, A.M., Lane, A.M. (2005) Do judges enhance home advantage in European championship boxing? Journal of Sports Sciences, 23(4): Carrillo, J., Brocas, I. (2004). Do the `three-point victory' and `golden goal' rules make soccer more exciting? Journal of Sports Economics, 5, Dohmen, T. (2005). Social pressure influences decisions of individuals.evidence from the behavior of football. IZA Discussion Paper, No Duggan, M., Levitt, S. (2002). Winning isn t Everything: Corruption in Sumo Wrestling. American Economic Review, 92(5), Garicano L, Palacios-Huerta I, Prendergast C (2005). Favouritism under social pressure. Review of Economics and Statistics, 87(2), Greer, D. (2003). Spectator Booing and the Home Advantage: A Study of Social Influence in the Basketball Arena. Social Psychology Quarterly, 46(3), Huck, S., Kubler, D. (2000). Social pressure, uncertainty, and cooperation. Economics of Governance, 1, Lucey, B., Power, D. (2009). Do Soccer Referees Display Home Bias? Manuscript. University of Dublin. Neave, N., Wolfson, S. (2003), Testosterone, Territoriality, and the Home Advantage in Soccer. Psychology and Behaviour, 78: Nevill, A.M., Balmer, N.J,Williams, A.M. (2001). The influence of crowd noise and experience upon refereeing decisions in football. Psychology of Sports and Exercise 3, Nevill, A. M., Holder, R. L. (1999). Home advantage in sport. An overview of studies on the advantage of playing at home. Sports Medicine, 28, Pettersson-Lidbom, P., Priks, M. (2009). Behavior under Social Pressure: Empty Italian Stadiums and Referee Bias. Manuscript, Department of Economics, University of Stockholm. Reysen, M.B. (2007). The effects of social pressure on false memories. Memory and Cognition, 2007, 35 (1), Rickman, N. Witt, R. (2008). Favouritism and Financial Incentives: A Natural Experiment. Economica, 75, Schwartz, B., Barsky, S. (1977). The home advantage. Social Forces, 55, Scoppa, V. (2008). Are subjective evaluations biased by social factors or connections? An 27

28 econometric analysis of soccer referee decisions. Empirical Economics, 35, Sutter M, Kocher, M (2004). Favouritism of agents: the case of referees home bias. Journal of Economic Psychology, 25, Stutzer, A. Lalive, R. (2001). The Role of Social Work Norms in Job Searching and Subjective Well- Being. Manuscript. University of Zurich. 28

29 APPENDIX TABLE A.1 POISSON ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Goalsfp ( )* ( )* ( )* ( ) ( ) ( ) Yellowfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( ) ( ) ( ) ( ) ( ) ( ) Subsfp ( )** ( )** ( )** ( )*** ( )** ( )** Observations Pseudo R-squared

30 TABLE A.2 POISSON ESTIMATION OF HOMEBEHIND901 ON INJURYSP Homebehind ( )** ( )** ( )* ( )*** ( )* ( )** Goalssp ( ) ( ) ( ) ( ) ( )* ( ) Yellowsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redsp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltysp ( ) ( ) ( ) ( ) ( )* ( ) Subssp ( ) ( ) ( ) ( ) ( ) ( ) Observations Pseudo R-squared

31 TABLE A.3 OLS ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )*** ( )*** ( )*** ( )*** ( )** ( )*** Homicide rate ( ) ( ) ( ) ( ) ( ) ( ) Hb451hr ( ) ( ) ( ) ( ) ( ) ( ) Goalsfp ( )* ( )* ( )* ( ) ( ) ( ) Yellowfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( ) ( ) ( ) ( ) ( ) ( ) Subsfp ( )** ( )** ( )** ( )*** ( )** ( )** Observations R-squared

32 TABLE A.4 OLS ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )* ( )* ( )* ( )** ( )* ( )** Attendance ( ) ( ) ( ) ( ) ( ) ( ) Hb451att ( ) ( ) ( ) ( ) ( ) ( ) Goalsfp ( ) ( ) ( ) ( ) ( ) ( ) Yellowfp ( ) ( ) ( ) ( )*** ( ) ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( )* ( )* ( )* ( ) ( )* ( ) Subsfp ( )* ( )* ( )* ( )** ( ) ( )* Observations R-squared

33 TABLE A.5 OLS ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )*** ( )*** ( )*** ( )*** ( )** ( )*** Televisado ( ) ( ) ( ) ( ) ( ) ( ) Hb451tel ( ) ( ) ( ) ( ) ( ) ( )* Goalsfp ( )* ( )* ( )* ( ) ( ) ( ) Yellowfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( ) ( ) ( ) ( ) ( ) ( ) Subsfp ( )** ( )** ( )** ( )*** ( )** ( )** Observations R-squared

34 TABLE A.6 OLS ESTIMATION OF HOMEBEHIND451 ON INJURYFP Homebehind ( )*** ( )*** ( )** ( )*** ( )** ( )*** Semifinal ( ) ( ) ( ) ( ) ( ) ( ) Hb451sem ( ) ( ) ( ) ( ) ( ) ( ) Goalsfp ( )* ( )* ( )* ( ) ( ) ( ) Yellowfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Redfp ( )*** ( )*** ( )*** ( )*** ( )*** ( )*** Penaltyfp ( ) ( ) ( ) ( ) ( ) ( ) Subsfp ( )** ( )** ( )** ( )*** ( )** ( )** Observations R-squared