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，我们拟合了选手技能模型，这些模型可进一步应用于模拟选手间实际比赛的动态零和博弈（ZSG）。针对数据中的局限性，我们提出了一种基于狄利克雷-多项分布（DM）模型的经验贝叶斯方法。具体而言，我们引入了两种基于DM的技能模型：第一个模型借用其他飞镖选手的信息增强估计能力，第二个模型则借用镖盘不同区域的数据。研究发现，在布莱尔评分和球面评分（两者均为适当评分规则）上，这两种DM模型优于简单的基准模型。我们进一步表明，在ZSG环境下，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，我们利用所提出的DM模型分析了2019赛季实际飞镖比赛中出现的特定场景。