Invited Session

Title: Sports

In paired comparison settings, odds ratio and logistic regression models arise theoretically and as approximations. These models are used to predict winning and other binary events in sports, via estimates of model parameters that measure team and player strengths. Applications include baseball (e.g. Bill James' "Pythagorean" formula), basketball, football, and tennis. Part of this talk is from a paper with Jason Rosenfeld, Dan Adler, and Jake Fisher of the Harvard Sports Analysis Collective) entitled "Predicting Overtime with the Pythagorean Formula", soon to appear in the Journal of Quantitative Analysis in Sports.

We present sophisticated Bayesian methodology for the analysis of fielding performance in major league baseball. Our approach is based upon high- resolution data consisting of on-field location of batted balls. A key issue is the balance between the personal performance of an individual fielder and the shrinkage to the population performance of similar fielders. We combine spatial probit modeling with a hierarchical structure in order to evaluate individual fielders while sharing information between fielders at each position. We present results across seven seasons of MLB data and compare our approach to other fielding evaluation procedures.

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.