Bayesian multivariate rank regression models for the analysis of sports data

Abstract

Rank data arise when multiple raters express preferences by ordering a set of items. Such data are often multivariate, with raters providing rankings across multiple criteria or time points. For instance, in the field of sports analytics, media outlets rank players or teams across several years. However, these rankings substantially deviate from one another – both across raters and across time – and may not even rank the same set of players. We introduce Bayesian Multivariate Rank Regression (BMRR) to address these challenges. Using latent hierarchical regression models, BMRR pools information across raters and criteria, incorporates covariates and rater expertise, and constructs an aggregate ranking. Crucially, BMRR provides full posterior uncertainty quantification for this aggregate ranking and all model parameters, and readily handles partial (i.e., incomplete) rankings and ties. We apply BMRR to analyze annual rankings of Major League Baseball players published by sports media outlets, where we identify the consensus leading players each year and overall, conduct pairwise comparisons between players, and assess the impact of key covariates, in each case accompanied by posterior uncertainty quantification. On simulated data, BMRR offers robust performance across a range of rank data scenarios and consistently outperforms competing methods.