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Bayesian Inferences on Uncertain Ranks and Orderings: Application to Ranking Players and Lineups

Publication ,  Journal Article
Barrientos, AF; Sen, D; Page, GL; Dunson, DB
Published in: Bayesian Analysis
January 1, 2023

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 National Basketball Association (NBA) in the United States, 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 2009–2010 NBA season.

Duke Scholars

Published In

Bayesian Analysis

DOI

EISSN

1931-6690

ISSN

1936-0975

Publication Date

January 1, 2023

Volume

18

Issue

3

Start / End Page

777 / 806

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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Barrientos, A. F., Sen, D., Page, G. L., & Dunson, D. B. (2023). Bayesian Inferences on Uncertain Ranks and Orderings: Application to Ranking Players and Lineups. Bayesian Analysis, 18(3), 777–806. https://doi.org/10.1214/22-BA1324
Barrientos, A. F., D. Sen, G. L. Page, and D. B. Dunson. “Bayesian Inferences on Uncertain Ranks and Orderings: Application to Ranking Players and Lineups.” Bayesian Analysis 18, no. 3 (January 1, 2023): 777–806. https://doi.org/10.1214/22-BA1324.
Barrientos AF, Sen D, Page GL, Dunson DB. Bayesian Inferences on Uncertain Ranks and Orderings: Application to Ranking Players and Lineups. Bayesian Analysis. 2023 Jan 1;18(3):777–806.
Barrientos, A. F., et al. “Bayesian Inferences on Uncertain Ranks and Orderings: Application to Ranking Players and Lineups.” Bayesian Analysis, vol. 18, no. 3, Jan. 2023, pp. 777–806. Scopus, doi:10.1214/22-BA1324.
Barrientos AF, Sen D, Page GL, Dunson DB. Bayesian Inferences on Uncertain Ranks and Orderings: Application to Ranking Players and Lineups. Bayesian Analysis. 2023 Jan 1;18(3):777–806.

Published In

Bayesian Analysis

DOI

EISSN

1931-6690

ISSN

1936-0975

Publication Date

January 1, 2023

Volume

18

Issue

3

Start / End Page

777 / 806

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics