A Bayesian Mixture Model Approach to Expected Possession Values in Rugby League

TL;DR

This paper introduces a Bayesian Mixture Model to estimate expected possession values in rugby league, providing a flexible, smooth pitch surface for outcome probabilities and EPV, even with limited data.

Contribution

It presents a novel Bayesian Mixture Model approach that improves EPV estimation in low-data sports like rugby league, surpassing previous zonal methods.

Findings

Produced a smooth, detailed EPV surface across the pitch.

Enabled visualization of team attacking and defensive strengths.

Developed an actual vs. expected player rating system.

Abstract

The aim of this study was to improve previous zonal approaches to expected possession value (EPV) models in low data availability sports by introducing a Bayesian Mixture Model approach to an EPV model in rugby league. 99,966 observations from the 2021 Super League season were used. A set of 33 centres (30 in the field of play, 3 in the try area) were located across the pitch. Each centre held the probability of five possession outcomes occurring (converted/unconverted try, penalty, drop goal and no points). Weights for the model were provided for each location on the pitch using linear and bilinear interpolation techniques. Probabilities at each centre were estimated using a Bayesian approach and extrapolated to all locations on the pitch. An EPV measure was derived from the possession outcome probabilities and their points value. The model produced a smooth pitch surface, which was able to provide different possession outcome probabilities and EPVs for every location on the pitch. Differences between team attacking and defensive plots were visualised and an actual vs expected player rating system was developed. The model provides significantly more flexibility than previous approaches and could be adapted to other sports where data is similarly sparse.