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Data Clustering for Fitting Parameters of a Markov Chain Model of Multi-Game Playoff Series

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  • Rump Christopher M

    (Bowling Green State University)

Abstract

We propose a Markov chain model of a best-of-7 game playoff series that involves game-to-game dependence on the current status of the series. To create a relatively parsimonious model, we seek to group transition probabilities of the Markov chain into clusters of similar game-winning frequency. To do so, we formulate a binary optimization problem to minimize several measures of cluster dissimilarity. We apply these techniques on Major League Baseball (MLB) data and test the goodness of fit to historical playoff outcomes. These state-dependent Markov models improve significantly on probability models based solely on home-away game dependence. It turns out that a better two-parameter model ignores where the games are played and instead focuses simply on, for each possible series status, whether or not the team with home-field advantage in the series has been the historical favorite - the more likely winner - in the next game of the series.

Suggested Citation

  • Rump Christopher M, 2008. "Data Clustering for Fitting Parameters of a Markov Chain Model of Multi-Game Playoff Series," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(1), pages 1-19, January.
    • Handle: RePEc:bpj:jqsprt:v:4:y:2008:i:1:n:2
    DOI: 10.2202/1559-0410.1087
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    References listed on IDEAS

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    1. Anito Joseph & Noel Bryson, 1997. "W-efficient partitions and the solution of the sequential clustering problem," Annals of Operations Research, Springer, vol. 74(0), pages 305-319, November.
    2. Rump Christopher M, 2006. "The Effects of Home-Away Sequencing on the Length of Best-of-Seven Game Playoff Series," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 2(1), pages 1-18, January.
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    Cited by:

    1. Pettigrew Stephen, 2014. "How the West will be won: using Monte Carlo simulations to estimate the effects of NHL realignment," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(3), pages 1-11, September.
    2. Chia-Hao Chang, 2021. "Construction of a Predictive Model for MLB Matches," Forecasting, MDPI, vol. 3(1), pages 1-11, February.

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