Modelling Penalty Cards in Football with Applications

A compound Poisson distribution is used to study factors which can affect the showing of yellow and red cards in a football competition such as a national league, the FIFA World Cup or the UEFA Champi-ons League. The resulting model is applied to 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 away team, the goal difference be-tween the teams, the total number of fouls committed, the attacking play of the home team, whether the match is a derby or not, the stage reached in the league competition, the level of fair play, the age of the referee and his international experience or lack of it, can all influence the use of cards. The model works well, providing a simple tool which can be applied in this and other sports settings.