# Paired comparison models with strength-dependent ties and order effects

arXiv: https://arxiv.org/abs/2505.24783 · HTML: https://mlsanity.com/paper/2505.24783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2025.

## Built on by (most cited first, 2 of 2)

- [Score-Driven Rating System for Sports](https://mlsanity.com/paper/2604.09143/) (2026)
- [Bradley-Terry Rankings for Recommender Systems Across Dataset Taxonomies](https://mlsanity.com/paper/2606.07492/) (2026)

## Abstract (arXiv)

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.