Towards interpretable expected goals modelling using Bayesian mixed models

Loïc Iapteff ¹ Sebastian Le Coz ¹ Maxime Rioland ¹ Titouan Houde ^1,2 Christopher Carling ³ Frank Imbach ^1,4*

• ¹ Seenovate, Montpellier, Occitanie, France
• ² Université de Lyon, Lyon2, Bron 69676, France
• ³ EA7370 Laboratoire Sport, Expertise et Performance, Institut National du Sport, de l'Expertise et de la Performance, Paris, France
• ⁴ DMEM, Univ Montpellier, INRAE, Montpellier, France

Empowered by technological progress, sports teams and bookmakers strive to understand relationships between player and team activity and match outcomes. For this purpose, the probability of an event to succeed (e.g. the probability of a goal to be scored, namely xG for eXpected Goals) brings insightful information on team and player performance and helps statistical and machine learning approaches to predict match outcomes. However, recent approaches come with powerful but complex models that need more inherent interpretability for practitioners. This study uses a Bayesian generalized linear mixed effects model to introduce a simple and interpretable xG modelling approach. The model provided similar performances when compared to the StatsBomb model (property of StatsBomB company) using only seven variables relating to shot type and position, and surrounding opponents (AUC = 0.781 and AUC = 0.801, respectively). Pre-trained models through transfer learning are suitable for identifying teams’ strengths and weaknesses using small sample sizes and enable interpretation of the model’s predictions.