The optimal layout of football players: A case study for AC Milan

This paper attempts to find the optimal formation of three midfielders and three forward football players on ground, using the classic Quadratic Assignment Problem or Facility Layout problem. Players are treated as “machines”, their positions as locations, and the flow of materials between machines as “flow of passes” and “flow of markings”. Based on detailed statistics from four matches of AC Milan, and formulated the problem as minimum (quick strategy), maximum (slow strategy), and mixed or balanced strategies, a number of various layouts emerged. Compared to the initial formation of players, the efficiency time gains in the unconditioned layouts are between 3 and 6.8%. Also, when the manager claims that his three forwards shouldn’t shift positions with the midfielders, the efficiency gains in these restricted layouts is about 14´´ to 74´´, which is about 1 to 3% of the approximately 40´ effective time spent into passes and markings from both teams.