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

Abstract

Soccer referees are required to make instant decisions during the game under non-optimal conditions such as imperfect view of the incident and substantial pressure from the crowd, the teams, and the media. Some of the decisions can be subjective, such as a yellow card decision after a foul is called, where different referees might make different decisions. Here we perform quantitative analysis of factors related to the reputation of the team such as the team's rank, budget, and crowd attendance in home games, and correlate these factors with 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 Pearson correlation is not statistically significant. For budget, or audience in home games. On the other hand, a significant Pearson correlation has been identified between the chance of a foul call to result in a yellow card and the rank or budget of the team 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 team.