# Bayesian inferences on uncertain ranks and orderings: Application to ranking players and lineups

## TL;DR

This paper introduces a Bayesian method to quantify uncertainty in rankings of entities, demonstrated by ranking NBA players, addressing the issue of misleading single-point estimates due to similar latent abilities.

## Contribution

It develops a Bayesian framework that accounts for uncertainty in orderings, especially when many entities have similar abilities, improving interpretability of rankings.

## Key findings

- Many NBA players have similar latent abilities.
- The Bayesian approach provides more conservative, uncertainty-aware rankings.
- Application to NBA data demonstrates improved interpretability.

## 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. In this paper, we are particularly interested in 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 uncertainty. Motivated by this, we propose a Bayesian 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.