Dynamic Bradley-Terry modelling of sports tournaments

• Published in: Applied statistics Vol. 62; no. 1; pp. 135 - 150
• Main Authors: Cattelan, Manuela, Varin, Cristiano, Firth, David
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.01.2013; Wiley-Blackwell; Oxford University Press
• Subjects: Ability; Applications; Applied statistics; Ball games; Basketball; Bradley; Combinatorics; Combinatorics. Ordered structures; Cumulative logit model; Data smoothing; Dynamic modeling; Dynamics; Exact sciences and technology; Exponentially weighted moving average process; Football; Forecasting models; Graph theory; Italy; League of Nations; Linear inference, regression; Mathematics; Modeling; Modelling; Multivariate analysis; Overtime; Paired comparisons; Parametric models; Predictive modeling; Probabilities; Probability and statistics; Professional sports; Sciences and techniques of general use; Seasons; Soccer; Sport games; Sports; Sports tournaments; Statistical analysis; Statistics; Studies; Summaries; Teams; Terry model; Time series; Tournaments; Tournaments & championships; Cumulative logit model; Sports tournaments; Paired comparison; Exponentially weighted moving average process; Bradley-Terry model; Statistical association; Moving average processes; Multiple comparison; Multivariate analysis; Statistical regression; Paired comparisons; Logit model; Tournament
• ISSN: 0035-9254; 1467-9876; 1467-9876
• DOI: 10.1111/j.1467-9876.2012.01046.x

In the course of national sports tournaments, usually lasting several months, it is expected that the abilities of teams taking part in the tournament will change over time. A dynamic extension of the Bradley—Terry model for paired comparison data is introduced to model the outcomes of sporting contests, allowing for time varying abilities. It is assumed that teams' home and away abilities depend on past results through exponentially weighted moving average processes. The model proposed is applied to sports data with and without tied contests, namely the 2009—2010 regular season of the National Basketball Association tournament and the 2008—2009 Italian Serie A football season.