Team-Bounded DEA Efficiency Scores: The Case of UEFA Champions League Players

Abstract

Measuring the efficiency of a football player is an interesting task. Every player invests time and energy to produce an outcome during the game that can lead to a better score for the team. However, football is a team sport, thus the synergy of the entire team is an invisible factor that influences the outcomes a player produces. In this paper, we introduce a novel efficiency estimation model based on the data envelopment analysis that incorporates the team effect in the efficiency score. To achieve this effect, we presented data envelopment analysis models using a single mathematical model. This allows us to define lower and upper bounds on the team efficiency score. More specifically, we introduce a novel type of assurance region constraint around the team performance such that the efficiency score cannot exceed γ times the average team efciency score. The results of the proposed mathematical model on the UEFA Champions League 2021/22 season show that efficiency scores can be heavily affected by inefficient teammates. However, if the entire team performed well, the drop in efficiency scores is insignificant.