Title: Bayesian inferences on uncertain ranks and orderings: Application to ranking players and lineups
Authors: Garritt Page - Brigham Young University (United States) [presenting]
Andres Felipe Barrientos - Florida State University (United States)
David Dunson - Duke University (United States)
Abstract: It is common to be interested in rankings or order relationships among entities. In complex settings where one does not directly measure a univariate statistic upon which to base ranks, such inferences typically rely on statistical models having entity-specific parameters. These can be treated as random effects in hierarchical models characterizing variation among the entities. We are particularly motivated by the problem of ranking basketball players in terms of their contribution to team performance. Using data from the United States National Basketball Association (NBA), we find that many players have similar latent ability levels, making any single estimated ranking highly misleading. The current literature fails to provide summaries of order relationships that adequately account for such uncertainty. Motivated by this, we propose a strategy for characterizing uncertainty in inferences on order relationships among players and lineups. Our approach adapts to scenarios in which uncertainty in ordering is high by producing more conservative results that improve interpretability. This is achieved through a reward function within a decision-theoretic framework. We apply our approach to data from the 2009-10 NBA season.