Determining the best strategy for changing the configuration of a football team

This paper proposes a dynamic programming (DP) approach to find the optimal substitution strategy for a football match, which maximises the probability of winning or the expected number of league points, supported by real data of the English Premier League. We use a Markov process model to evaluate the offensive and defensive strengths of teams by means of maximum likelihood estimators. We develop a DP formulation to derive quantitatively the optimal substitution strategy of a team, in relation to the number required of each type of outfield player. We demonstrate how this approach may help to determine how many of each type of player should start a match and be substituted during a match. We also show how the expected league points would increase if the optimal strategy were followed.