Paired comparison models with tie probabilities that depend on competitor strength

Paired comparison models, such as the Bradley–Terry model for win–loss outcomes and the Davidson extension that incorporates ties, provide a foundation for modeling head-to-head competition and order effects. Recent developments allow the probability of a tie to depend on the average strength of the competitors, reflecting the tendency for stronger players to draw more frequently. In this talk, I introduce a semiparametric extension of this framework in which the draw probability is modeled as a non-linear function of the competitors' average strength using a spline basis. This approach generalizes earlier linear specifications, providing a flexible yet interpretable means of capturing nonlinear relationships between strength and tie propensity while preserving the model's invariance properties. The framework is applied to game outcomes from the US Chess Open tournaments from 2006 to 2019, though it is broadly applicable to other paired comparison contexts where ties are common and may depend on absolute strength.