Mathematical Modeling of Sports Club Squad Rotation

In this work, we consider a sports club as a mathematical object and describe the phenomenon of squad rotation. Currently, the level of competition in sports is extremely high, and for the achievement of significant results it is important to allocate resources of the club, i.e. players. We build a mathematical model which allows us to plan a team lineups for every match in order to maximize the chances of the club winning the tournament. To obtain the goal, we apply graph theory and describe the algorithm that can effectively distribute the participation of players in matches throughout the whole season. In our model, we consider a linear utility function of a sports team. Additionally, we assume that the head coach has perfect information about the players, i.e. each player's fatigue function, playing skills in different positions and all the previous matches' statistics are known to the head coach. The study of sports enables sport clubs to allocate resources more effectively and, as consequence, to achieve high results. Nowadays, every sport organization has analysts. By learning and modelling the sport team life, scientists discover new methods of preparation and training which can improve a club performance.