Since 1995, home teams have won 53.936 percent of baseball games played in the regular season. Considering that a large portion of home field advantage is, by conventional wisdom, attributed to the effects of home-crowd fans (either on the players, or, more likely, on the umpires), we might reasonably expect the home team to get an even bigger boost during October, when the crowds are bigger, perhaps more partisan, and generally more bananas.
Since 1995, home teams have won 53.986 percent of baseball games played in the postseason. This number is somewhat less reliable because the sample size (552 games) is so much smaller, but if it we conceded it is an accurate representation of the postseason home-field advantage, it would mean that the home teams in the past 18 years of playoffs have won a total of 0.27 more games than they would have won in a regular-season environment. Which is to say, zero games. So, identical.
Surprising and interesting, is all.
(Update: Complicating this is also the fact that "better" teams would probably get to play a few extra home games in October, because of how the playoff rules work. So by a small amount, the home team should be, on average, a bit better than the visiting team in October; in the regular season, the teams are, on average, equal.)
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