The Football Team Composition Problem: A Stochastic Programming approach

Abstract

Most professional European football clubs are well-structured businesses. Therefore, the financial performance of investments in players becomes crucial. In this paper, after the problem is discussed and formalized, an optimization model with the objective of maximizing the expected value of the team is presented. The model ensures that the team has the required mix of skills, that competition regulations are met, and that budget limits are respected. The model explicitly takes into account the uncertainty in the career development of football players. A case study based on the English Premier League is presented. Our results show that the model has significant potential to improve current decisions ensuring a steady growth of the value of the team. The team value growth reported is particularly driven by investments in young prospects.