Social pressure and biased refereeing in Italian soccer 

 I recently came across  a paper  by Per Pettersson-Lidbom and Mikael Priks that uses a neat natural experiment in Italian soccer to estimate the effect of stadium crowds on referees' decisions. After a bout of hooliganism in early February, 2007, the Italian government began requiring soccer stadiums to fulfill certain security regulations; those stadiums that did not meet the requirements would have to hold their games without spectators. As a result, 25 games were played in empty stadiums that month allowing Petterson-Lidbom and Priks to examine game stats (like  this ) and see whether referees were more disposed toward the home team when the bleachers were filled with fans than when the stadium was empty. Looking at fouls, yellow cards, and read cards, the authors find that referees were indeed more likely to penalize the home team (and less likely to penalize the away team) in an empty stadium. There does not appear to be any effect of the crowd on players' performance, which suggests that fans were reacting to the crowd and not the players (and that fans should save their energy for haranguing the refs).  

 One of the interesting things in the results is that refs showed no favoritism toward the home team in games with spectators -- they handed out about the same number of fouls and cards to the home and away teams in those games. The bias shows up in games without spectators, where they hand out more fouls and cards to the home team. (The difference is not statistically significant in games with spectators but is in games with spectators.) If we are to interpret the empty stadium games as indicative of what refs would do if not subjected to social pressure, then we should conclude from the data that refs are fundamentally biased against the home team and only referee in a balanced way when their bias is balanced by crowd pressure. This would indeed be evidence that social pressure matters, but it seems unlikely that refs would be so disposed against the home team. A perhaps more plausible interpretation of the findings is that Italian refs are generally pretty balanced and not affected by crowds, but in the "empty stadium" games they punished the home team for not following the rules on stadium security. This interpretation of course makes the finding less generally applicable. In the end the example highlights the difficulty of finding "natural experiments" that really do what you want them to do -- in this case, illustrate what would happen if, quite randomly, no fans showed up for the game.