Modelling the evolution of distributions: an application to major league baseball

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Abstract

We develop Bayesian techniques for modelling the evolution of entire distributions over time and apply them to the distribution of team performance in Major League baseball for the period 1901-2000. Such models offer insight into many key issues (e.g. competitive balance) in a way that regression-based models cannot. The models involve discretizing the distribution and then modelling the evolution of the bins over time through transition probability matrices. We allow for these matrices to vary over time and across teams. We find that, with one exception, the transition probability matrices (and, hence, competitive balance) have been remarkably constant across time and over teams. The one exception is the Yankees, who have outperformed all other teams.
Original languageEnglish
Pages (from-to)639-656
Number of pages18
JournalJournal of the Royal Statistical Society: Series A
Volume167
Issue number4
DOIs
Publication statusPublished - Nov 2004

Keywords

  • bayesian
  • Gibbs sampler
  • ordered probit
  • sports statistics

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