Runs scored/allowed per inning

I’ve been looking at the distribution of runs scored and allowed per inning for the Red Sox and for all (or AL and NL) teams.  (See also: Has the Evolution of Bullpens Made Grinding Out At-Bats Less Effective?) My hypothesis was that the early-2000s Sox would score a relatively high percentage of their runs in the middle innings, while the modern (futile) Sox would not.  I don’t really see that, and no obvious patterns related to success or the lack thereof are jumping out at me.

I downloaded data from (as well as analyzing equivalent date from and from PITCHf/x data).  Numbers are percent of total runs, per inning, normalized to the same number of innings (thus reducing the problem of rainouts, not to mention that in about half the games the home team doesn’t bat in the 9th).  Blue represents all AL teams, red is the Red Sox.  The vertical arrows show the years in which the Sox won World Series.  Conversely, they have been very poor teams in 2012, 2014, and 2015, but I don’t see obvious differences in the scoring distributions.  Each chart shows one inning (innings 1-3 on the top row, 4-6 on the middle, and 7-9 at the bottom).

Red Sox runs scored per inning as a percent of total runs

Red Sox runs scored per inning as a percent of total runs

Red Sox runs allowed per inning as a percent of total runs

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