Soccer as a Markov process: modelling and estimation of the zonal variation of team strengths

Abstract

This study models soccer as a Markov process. We discretize the pitch into nine zones, and define the states of the Markov process according to the zone of the pitch in which the ball is located, the team in possession and the score. Log-linear models are used to represent state transitions. Using the log-linear models, we estimate team strengths not only with respect to scoring or conceding, but also with respect to gaining or losing possession, while considering the discretized zones in which the ball is located. We use play-by-play data from Japan League Division 1 games in the 2015 season to illustrate our approach, and characterize the strengths of teams in this league. Sanfrecce Hiroshima is used as a particular example. We determine the goodness-of-fit of the log-linear models. Additionally, we introduce random effects into the log-linear models and discuss the complexity of the state transition process. We demonstrate that our Markov model, at the nine-zone level, provides estimates of teams’ strengths to a good approximation.