Modeling Baseball Outcomes as Higher-Order Markov Chains
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Baseball is one of the few sports in which each team plays a game nearly everyday. For instance, in the baseball league in South Korea, namely the KBO (Korea Baseball Organization) league, every team has a game everyday except for Mondays. This consecutiveness of the KBO league schedule could make a team's match outcome be associated to the results of recent games. This paper deals with modeling the match outcomes of each of the ten teams in the KBO league as a higher-order Markov chain, where the possible states are win ("W"), draw ("D"), and loss ("L"). For each team, the value of k in which the k^th order Markov chain model best describes the match outcome sequence is computed. Further, whether there are any patterns between such a value of k and the team's overall performance in the league is examined. We find that for the top three teams in the league, lower values of k tend to have the k^th order Markov chain to better model their outcome, but the other teams don't reveal such patterns.
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