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.

翻译：我们对2019赛季排名前16位的职业飞镖选手数据集进行了探索性数据分析。利用该数据集拟合选手技能模型，该模型可应用于模拟选手间真实比赛的动态零和博弈。我们提出了一种基于狄利克雷-多项分布模型的经验贝叶斯方法，以克服数据中的局限性。具体而言，我们引入了两种基于DM的技能模型：第一种模型从其他飞镖选手处借力，第二种模型从飞镖盘其他区域借力。研究发现，在布里尔评分和球形评分（两者均为恰当的评分规则）方面，这些基于DM的模型优于简单的基准模型。我们还证明，在动态零和博弈场景中，基于DM的技能模型与简单基准模型之间的差异具有实际显著性。最后，我们利用DM模型分析了2019赛季真实飞镖比赛中出现的特定情境。