June 2024 Athlete rating in multicompetitor games with scored outcomes via monotone transformations
Jonathan Che, Mark Glickman
Author Affiliations +
Ann. Appl. Stat. 18(2): 1236-1252 (June 2024). DOI: 10.1214/23-AOAS1832


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 nonnormal game score data, we propose a Bayesian dynamic linear model with flexible monotone response transformations. Our model learns nonlinear monotone transformations to address nonnormality 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.

Funding Statement

This research was supported in part by a research contract from the U.S. Olympic and Paralympic Committee and by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1745303.


We thank Dan Webb at the U.S. Olympic and Paralympic Committee for providing the data for this work. We also thank the anonymous referees, an Associate Editor, and the Editor for their constructive comments that improved the quality of this paper.


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Jonathan Che. Mark Glickman. "Athlete rating in multicompetitor games with scored outcomes via monotone transformations." Ann. Appl. Stat. 18 (2) 1236 - 1252, June 2024. https://doi.org/10.1214/23-AOAS1832


Received: 1 June 2022; Revised: 1 August 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1832

Keywords: Dynamic linear model , Kalman filter , monotone spline

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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