Quantitative Analysis of Penalty Kicks and Yellow Card Referee Decisions in Soccer

Abstract

Soccer referees are required to make instant decisions critical to the game's outcome under non-optimal conditions. The nearly instinctive fashion in which these decisions are made can lead to errors, often exposing the referee to intensive criticism. Here we perform quantitative analysis to identify factors related to the reputation of the team such as the team's rank, budget, and size of the audience in home games. We compared these factors to referee decisions such as penalty kicks and yellow cards. The calls were normalized by dividing the number of yellow cards by the number of fouls, and the number of penalty kicks by the number of shot attempts from the penalty box. Application of the analysis to the four major soccer leagues shows that certain referee decisions have significant correlation with factors such as the team's rank, budget, and audience in home games, while for other decisions the correlation is not statistically significant. For instance, the results show that referee calls for penalty kicks had no significant correlation with the team's rank, budget, or audience in home games. On the other hand, a significant correlation has been identified between the chance of a foul call to result in a yellow card and the rank or budget of the teams in the Bundesliga. The strongest correlation has been observed between the chance of a tackle to result in a foul call, and the budget and rank of the teams.