Sorry, the Yankee 10-run comeback the other day inspired me. I've been busy ever since then trying to incorporate Retrosheet's game log data into my own little data
stores. The first results of this data merger are in, and I hope are interesting. As far as the greatest comebacks of all time, the best was from a 12-run deficit, but that's fodder for another day.
I decomposed the linescore information and was able to determine the average results per inning. On average, the home team outscores the visiting team .491 to .475.
The first inning is the highest scoring (.523 runs for the visitors and .615 for the home team). The home team as a matter of fact outscores the visitors in every inning until the ninth, when they destroy the homeys, .460 to .236 (though this does include games in which the home team leads and therefore, does not bat). Then in extra innings, the visitors have an advantage in every frame until small sample size overwhelms them in the 24th inning.
Here's a table of the average score per inning with the lead between innings and at the end of each inning, the number of lead changes expected per each inning, and the total (and percentage) of games for which the given inning is reached: