Theoretical Explanation
Initially the correlation between the formula and actual winning percentage was simply an experimental observation. In 2003, Hein Hundal provided an inexact derivation of the formula and showed that the Pythagorean exponent was approximately 2/(σ√π) where σ was the standard deviation of runs scored by all teams divided by the average number of runs scored. In 2006, Professor Steven J. Miller provided a statistical derivation of the formula under some assumptions about baseball games: if runs for each team follow a Weibull distribution and the runs scored and allowed per game are statistically independent, then the formula gives the probability of winning.
Read more about this topic: Pythagorean Expectation
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