Social Pressure or Rational Reactions to Incentives? A Historical Analysis of Reasons for Referee Bias in the Spanish Football

A relevant question in social science is whether cognitive bias can be instigated by social pressure or is it just a rational reaction to incentives in place. Sport, and association football in particular, offers settings in which to gain insights into this question. In this paper we estimate the determinants of the length of time between referee appointments in Spanish soccer as a function of referee decisions in favour of the home and away team in the most recent match by means of a deep-learning model. This approach allows us to capture all interactions among a high-dimensional set of variables without the necessity of specifying them beforehand. Furthermore, deep-learning models are nowadays the state of the art among the predicting models which are needed and here used for estimating effects of a cause. We do not find strong evidence of an incentive scheme that counteracts well-known home referee biases. Our results also suggest that referees are incentivised to deliver a moderate amount of surprise in the outcome of the game what is consistent with the objective function of consumers and tournament organisers.