Buraimo, B and Forrest, D and Simmons, R (2010) The 12th man? Refereeing bias in English and German soccer. Journal of the Royal Statistical Society Series A, 173 (2). pp. 431-449. ISSN 0964-1998
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The paper investigates potential bias in awards of player disciplinary sanctions, in the form of cautions (yellow cards) and dismissals (red cards) by referees in the English Premier League and the German Bundesliga. Previous studies of behaviour of soccer referees have not adequately incorporated within-game information. Descriptive statistics from our samples clearly show that home teams receive fewer yellow and red cards than away teams. These differences may be wrongly interpreted as evidence of bias where the modeller has failed to include within-game events such as goals scored and recent cards issued. What appears as referee favouritism may actually be excessive and illegal aggressive behaviour by players in teams that are behind in score. We deal with these issues by using a minute-by-minute bivariate probit analysis of yellow and red cards issued in games over six seasons in the two leagues. The significance of a variable to denote the difference in score at the time of sanction suggests that foul play that is induced by a losing position is an important influence on the award of yellow and red cards. Controlling for various pre-game and within-game variables, we find evidence that is indicative of home team favouritism induced by crowd pressure: in Germany home teams with running tracks in their stadia attract more yellow and red cards than teams playing in stadia with less distance between the crowd and the pitch. Separating the competing teams in matches by favourite and underdog status, as perceived by the betting market, yields further evidence, this time for both leagues, that the source of home teams receiving fewer cards is not just that they are disproportionately often the favoured team and disproportionately ahead in score. Thus there is evidence that is consistent with pure referee bias in relative treatments of home and away teams.
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