  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.
