Evaluating player relevance in football teams through cooperative game theory

This paper develops a cooperative game-theoretic methodology to measure a footballer's relevance to team play by combining structural information-the network of completed passes-with individual performance data. This integration is the core of our methodological contribution. Using this information and the Shapley value concept from game theory, we propose four relevance measures (based on the Shapley value) that quantify each player's relevance in a given match. We then apply the methodology to Argentina's seven matches at the 2022 FIFA World Cup in Qatar. Our results illustrate how the method can reveal players whose structural importance may not be captured by standard performance metrics (such as individual ratings) or standard centrality measures, providing complementary insights. Furthermore, the methodology is flexible, allowing analysts to tailor it to emphasize alternative tactical hypotheses and making it adaptable for team self-analysis, opponent preparation, and scouting.