Paired comparison models with age effects modeled as piecewise quadratic splines

We propose new models for analyzing pairwise comparison data, such as that relating to sports. We focus on changes in players’ strengths and the prediction of future results. Our models are based on the Thurstone-Mosteller and Bradley–Terry models, and make use of the time variation in the parameters. Furthermore, we apply our models to data from the Japanese traditional sport sumo, and analyze this data. The proposed models perform better than the standard Thurstone-Mosteller and Bradley–Terry models according to both the Akaike information criterion and the Brier score. We compare the proposed models in detail by focusing on individual sumo wrestlers.