Sports organizations often want to estimate athlete strengths. For games with scored outcomes, a common approach is to assume observed game scores follow a normal distribution conditional on athletes' latent abilities, which may change over time. In many games, however, this assumption of conditional normality does not hold. To estimate athletes' time-varying latent abilities using non-normal game score data, we propose a Bayesian dynamic linear model with flexible monotone response transformations. Our model learns nonlinear monotone transformations to address non-normality in athlete scores and can be easily fit using standard regression and optimization routines, which we implement in the dlmt package in R. We demonstrate our method on data from several Olympic sports, including biathlon, diving, rugby, and fencing.

翻译：体育组织常需评估运动员实力。对于具有得分结果的比赛，常见方法假设观察到的比赛得分在运动员潜在能力（可能随时间变化）条件下服从正态分布。然而，许多比赛并不满足这一条件正态性假设。为利用非正态比赛得分数据估计运动员时变潜在能力，我们提出了一种采用灵活单调响应变换的贝叶斯动态线性模型。该模型通过学习非线性单调变换来应对运动员得分的非正态性，并可通过标准回归和优化程序轻松拟合，我们已将其实现为R语言的dlmt包。我们通过冬季两项、跳水、橄榄球和击剑等多项奥运体育项目的实际数据验证了该方法的有效性。