An Empirical Bayes Approach for Estimating Skill Models for Professional Darts Players

TL;DR

This paper develops an empirical Bayesian method using Dirichlet-Multinomial models to estimate player skills in professional darts, improving predictive accuracy and analyzing real match situations.

Contribution

It introduces two novel DM-based skill models that borrow strength across players and regions, outperforming benchmarks in predictive scoring.

Findings

DM models outperform benchmarks in Brier and Spherical scores

DM models show practical significance in zero-sum game settings

Application to 2019 darts matches provides real-world insights

Abstract

We perform an exploratory data analysis on a data-set for the top 16 professional darts players from the 2019 season. We use this data-set to fit player skill models which can then be used in dynamic zero-sum games (ZSGs) that model real-world matches between players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial (DM) model that overcomes limitations in the data. Specifically we introduce two DM-based skill models where the first model borrows strength from other darts players and the second model borrows strength from other regions of the dartboard. We find these DM-based models outperform simpler benchmark models with respect to Brier and Spherical scores, both of which are proper scoring rules. We also show in ZSGs settings that the difference between DM-based skill models and the simpler benchmark models is practically significant. Finally, we use our DM-model to analyze specific situations that arose in real-world darts matches during the 2019 season.