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Modeling the Evolution of Distributions: An Application to Major League Baseball

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Abstract

In this paper, we develop Bayesian techniques for modeling 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 modeling 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.

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  • Gary Koop, 2001. "Modeling the Evolution of Distributions: An Application to Major League Baseball," Edinburgh School of Economics Discussion Paper Series 71, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:71
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    1. Jeroen Schokkaert & Johan Swinnen, 2016. "Uncertainty of Outcome Is Higher in the Champions League Than in the European Cup," Journal of Sports Economics, , vol. 17(2), pages 115-147, February.
    2. Richard Evans, 2014. "A review of measures of competitive balance in the ‘analysis of competitive balance’ literature," Birkbeck Sports Business Centre Working Papers 9, Birkbeck College, Department of Management.
    3. Hamrick Jeff & Rasp John, 2011. "Using Local Correlation to Explain Success in Baseball," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-29, October.
    4. Martin Schmidt, 2006. "On the evolution of competition: an application of nonlinear tests," Applied Economics, Taylor & Francis Journals, vol. 38(1), pages 1-12.

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    Keywords

    Bayesian; Gibbs samples; ordered probit; Damn Yankees;
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