Social pressure in the stadiums: do agents change behavior without crowd support?

Social pressure may have relevant consequences in many contexts but it is hard to evaluate it empirically. In this paper we exploit a natural experiment in soccer to provide clear evidence of its effects. We aim to study how social pressure from the crowd in a stadium affects both players and referees. While in normal matches crowd support may be correlated to a host of variables affecting the outcome of interest, we exploit the fact that after the health emergency for the Covid-19 pandemic in 2020, soccer matches in top European Leagues have been allowed only behind closed doors, that is, without spectators in the stadiums. We use data of first and second division of 5 major European Leagues (Germany, Spain, England, Italy and Portugal) for the last 10 championships and compare several outcomes (determined by players' performance and referees' decisions) of matches played with crowd support to the same outcomes when matches were played without crowd. We find considerable effects of the pressure from the crowd: while with the support of the crowd a considerable home advantage emerges in various measures of performance (points, goals, shots, etc.), this advantage is almost halved when matches are behind closed doors. Similar effects are found for the behavior of referees: decisions of fouls, yellow cards, red cards and penalties that tend to favor home teams in normal matches, are much more balanced without crowd pressing on referees. The evidence we provide strongly supports the idea that social pressure has intense effects on agents' behavior.