Although the Pythagorean expectation formula does well at predicting win percentage, the shape of the run distribution can also be a factor. Given two baseball teams with the same average runs per game, the team with the narrower run distribution tends to win more games. Modified formulas that take into account both the runs per game and the shape of the run distributions are presented. Also, slugging percentage has an inverse correlation with the width of the run distribution. A team slugging percentage .080 above average is worth about one extra win compared to the simple prediction using only runs scored and runs allowed.
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