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Mirror MLB Games

Heath K-W Atomstramm
Organization: WhoWins(tm)
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In the game of baseball, the inning-by-inning road/home team line score denotes which team scored how many runs in what innings. Given a final score, and given the nature of whether the home team bats in its ninth inning, the question of how many possible combinations of road/home team line scores correspond to that final score is a question of combinatorics. This notebook addresses that question, presenting formulas for determining how many different road/home team line scores correspond to a given final score. This notebook also examines the phenomenon of "mirror games" -- baseball games with identical road/home team line scores. Retrosheet data from 1978 through 2000 are used to identify the occurrence of mirror games. These historical data are combined with theoretical results from the combinatorics realm, to provide a first- order analysis of how frequently such mirror games should be expected.

*Mathematics > Discrete Mathematics > Combinatorics
*Mathematics > Recreational Mathematics

combinatorics, baseball, line scores, Retrosheet
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mirrorgames.nb (313.4 KB) - Mathematica Notebook