Paired Comparison Models with Tie Probabilities and Order Effects as a Function of Strength

• Activity Number: 329
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Mark E. Glickman*+
• Companies: Boston University School of Public Health
• Keywords: tournament ; chess ; DIC ; Bayesian

Abstract

Paired comparison models, such as the Bradley-Terry 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 2006 US Chess Open, a large tournament with players of wide-ranging strengths, and to the Vienna 1898 chess tournament, a double-round robin tournament consisting of 20 of the world's top players.