Paired comparison models with strength-dependent ties and order effects

TL;DR

This paper introduces a new paired comparison model that accounts for strength-dependent ties and order effects, improving the fit for tournament chess data with diverse player strengths.

Contribution

The paper proposes a novel paired comparison model that incorporates strength-dependent ties and order effects, addressing limitations of existing models in real-world data.

Findings

Model better fits chess tournament data from 2006-2019

Captures increased tie probability among stronger players

Reflects more pronounced order effects for stronger competitors

Abstract

Paired comparison models, such as the Bradley-Terry (1952) model and its variants, are commonly used to measure competitor strength in games and sports. Extensions have been proposed to account for order effects (e.g., home-field advantage) as well as the possibility of a tie as a separate outcome, but such models are rarely adopted in practice due to poor fit with actual data. We propose a novel paired comparison model that accounts not only for ties and order effects, but recognizes two phenomena that are not addressed with commonly used models. First, the probability of a tie may be greater for stronger pairs of competitors. Second, order effects may be more pronounced for stronger competitors. This model is motivated in the context of tournament chess game outcomes. The models are demonstrated on the results of US Chess Open game outcomes from 2006 to 2019, large tournaments consisting of players of wide-ranging strengths.