A Mathematical Analysis of Team Impact and Individual Player Contribution in Football

In this paper, we present an important application of the Hungarian Method - a well-known combinatorial optimization tool for solving assignment problems. For our purposes, we consider the assignment of players to specific roles in a football team. It involves the broad classification of team players as defensive, midfield or attacking, while assigning the main roles associated with each of these positions. This provides insight on specific role of each individual player, thereby facilitating an optimal team selection. To illustrate this method, we utilize the average player statistics per game for two teams from the 2016/2017 Premier League Season. In addition, a team rating index is created by identifying six sub-indices. The first is called team contributions - which includes set piece goals, percentage tackles won, percentage take-ons won, percentage aerial duels won, number of interceptions, number of blocked shots, number of clearances, number of red and yellow cards. To visualize the method, a multiple correlation is carried out on team data for the 2016/2017 Premier League season to generate a correlation coefficient for each contribution. The resulting team index can be a useful tool for measuring the overall strengths of competing teams in a football league. Keywords: Hungarian method, football, team rating index, multiple correlations, team comparisons