Last week a commentator on a game (I think it was on TBS) said that the White Sox might have problems in the playoffs since they rely on HRs so much and pitchers in the playoffs are good at preventing HRs. So I looked at all the playoff teams in both leagues over the last three years and compared their HR rate allowed (HRs divided by batters faced) to the league average. Over that time, the NL playoff teams allowed about 1.5% fewer HRs than average. The AL teams allowed about 5.3% fewer HRs than average.
How might this impact the White Sox if they make it to the post-season this year? Suppose their season rate of hitting HRs is 1.5 per game (it is not quite that high, but close). Then even if that goes down 5.3% in the playoffs, that still leaves them with about 1.42 HRs per game. If a typical HR is worth 1.4 runs (using the linear weights value from Pete Palmer), the White Sox would lose about .112 runs per game (since .08*1.4 = .112). If a typical playoff team hit 1 HR per game, then that goes down to .947 a game in the playoffs. That would cost them about .074 runs per game.
Now the difference between what the White Sox lose and what the typical team loses is less than .04. Not very big. And the other teams will probably see something that they do better go down more than for the Sox and suffer bigger loss (like in stealing or walking or just plain hits-remember that the pitching staffs of playoff bound teams are probably better than average at other things than just preventing HRs). Then that brings the two teams even closer togther. The Sox reliance on the HR is not a big deal.