Factors influencing the penalty cards in soccer

Abstract

A compound Poisson distribution is used to study factors that motivate the fact of showing yellow and red cards in a football competition such as a national league, the FIFA World Cup or the UEFA Champions League. The resulting model is applied to the outcomes in the Spanish Football League during the season 2013\14, studying the partial and total effects on the home and away teams. It is shown that various factors, such as the victory of the guest team, goal difference in the game, total of fouls committed, attacking play of the home team, whether or not the match is a derby, round when the game is played, level of fair play, age of the referee, whether or not the referee has international experience, may infuence the number of cards. The model introduced in this paper is simple and it works well, providing a useful tool that can be applied in different sport settings.