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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Mark Glickman PhD

4 Issues per year

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Models for Third Down Conversion in the National Football League

Ryan Cafarelli
  • Southern Illinois University Edwardsville
/ Christopher J. Rigdon
  • Southern Illinois UniversityEdwardsville
/ Steven E. Rigdon
  • Saint Louis University
Published Online: 2012-10-09 | DOI: https://doi.org/10.1515/1559-0410.1383


Several models are proposed for the probability of converting a third down attempt in the National Football League. The probability, which can depend on the number of yards to go, the strength of the offense, and the strength of the defense, leads to a logistic regression. We approach the problem through a hierarchical Bayes model and estimate parameters by using Markov chain Monte Carlo (MCMC). This MCMC estimation in the context of a hierarchical Bayes model may be relevant in other sports situations where a probability depends on the difference of strengths of the two teams. We find that the statistic "third-down conversion rate" to be a nearly meaningless measure of the efficiency of an offense. Even when this is adjusted for yards to go for a first down, there is little evidence that teams differ in their ability to achieve a first down on a third down conversion.

Keywords: hierarchical Bayes; Markov chain Monte Carlo

Published Online: 2012-10-09

Citation Information: Journal of Quantitative Analysis in Sports. Volume 8, Issue 3, ISSN (Online) 1559-0410, DOI: https://doi.org/10.1515/1559-0410.1383, October 2012

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