降级、升级与水球比赛得分构成
Relegation, promotion and the components of scoring in water polo
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- School of Science and Technology, IE University（IE大学科学与技术学院）
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中文总结 AI 辅助
针对欧洲水球联赛降级决策问题，提出首个贝叶斯层次模型，将得分分解为人数均等、以多打少和罚球三部分，基于940场比赛数据，能提前识别降级队并预测附加赛结果。
中文摘要 AI 辅助
在许多欧洲水球联赛中，决定最终结果的并非冠军争夺，而是降级：在意大利、西班牙和匈牙利，近年来每个全国冠军均由同一俱乐部夺得。我们将降级决策作为推断对象。意甲A1联赛将排名垫底的一支俱乐部直接降级，并通过三场保级附加赛确定第二支降级队伍，我们探究在每个阶段，信息在多大程度上以及何时能够被获知。升级俱乐部没有顶级联赛的历史记录，因此我们还比较了四种设定其先验分布的方法。这些分析基于首个贝叶斯层次水球模型，该模型将得分分解为人数均等、以多打少和罚球三个组成部分，分别对机会和转化进行建模，并允许能力在赛季间演化。将各组成部分视为独立被证明是站不住脚的，因为它们竞争共同的控球权预算。该模型拟合了一个包含940场比赛的新数据集，从第九轮起就能识别出直接降级的俱乐部，早于联赛积分榜；对保级附加赛参赛队伍的预测优于积分榜；并显示保级附加赛本身接近抛硬币的随机结果。升级俱乐部在除造成对方被罚出场外的所有组成部分上均低于联赛平均水平：知道俱乐部升级能改善预测；知道其升级方式则不能。
英文摘要
Relegation, not the championship, decides the outcome of many European water polo leagues: one club has won every recent national title in Italy, Spain and Hungary. We make the relegation decision our object of inference. Serie A1 relegates one club for finishing last and a second through a three-match play-out, and we ask at each stage how much can be known and when. Promoted clubs arrive with no top-flight record, so we also compare four ways of setting their prior. These analyses rest on the first Bayesian hierarchical model of water polo, which splits scoring into even-strength, man-up and penalty components, models opportunities and conversions separately, and lets abilities evolve between seasons. Treating the components as independent proves untenable, since they compete for a common budget of possessions. Fitted to a new dataset of 940 matches, the model identifies the directly relegated club from the ninth round, before the league table does, predicts the play-out field better than the table, and shows the play-out itself to be close to a coin toss. Promoted clubs start below the league on every component except drawing exclusions: knowing a club was promoted improves forecasts; knowing how does not.
