Twelve eyes see more than eight. Referee bias and the introduction of additional assistant referees in soccer

We are the first to investigate whether the introduction of additional assistant referees in the UEFA Europa League (in season 2009-2010) and the UEFA Champions League (in season 2010-2011) was associated with lower referee bias. To this end, we analyse a unique database with pre- and within-game characteristics of all games in seven recent seasons in these leagues by means of bivariate probit regression models. We find evidence for substantial referee bias before the introduction of additional referees, while no such evidence is found after the introduction. Furthermore, additional assistants go hand in hand with more yellow cards for both home and away teams. We show that these findings are robust to multiple operationalisations of referee bias and that they are not just picking up a general time evolution towards less referee bias or the effect of parallel reforms.