Optimal selection of the starting lineup for a football team

Abstract: The success of a football team depends on various individual skills and performances of the selected players as well as how cohesively they perform. We propose a two-stage process for selecting optimal playing eleven of a football team from its pool of available players. In the first stage a LASSO-induced modified multinomial logistic regression model is derived to analyse the probabilities of the three possible outcomes. The model considers strengths of the players in the team as well as those of the opponent, home advantage, and also the effects of individual players and player combinations beyond the recorded performances of these players. In the second stage, a GRASP-type meta-heuristic is implemented for the team selection which maximises its probability of winning. The work is illustrated with English Premier League data from 2008/09 to 2015/16. The application demonstrates that the model in the first stage furnishes valuable insights about the deciding factors for different teams whereas the optimisation steps can be effectively used to determine the best possible starting lineup under various circumstances. We propose a measure of efficiency in team selection by the team management and analyse the performance of the teams on this front.