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.

Sandro Radovanović

Assistant Professor at University of Belgrade

My research interests include machine learning, development and design of decision support systems, decision theory, and fairness and justice concepts in algorithmic decision making.