Here are the September run differentials from the 44 teams that made post-season after 2000. The bars shaded in black are those of teams that lost in the first round:

Perhaps unsurprisingly, most playoff teams played well in September. This is not because "that's when it counts" so much as good teams usually play well. What really stands out is that the losers (in black) are clustered towards the left. In particular, teams that fell apart in September (say, the 2008 Cubs, Brewers and ChiSox) and post negative run-differentials tend to lose.
Of course, the game is not played in a vacuum: and if you have a hot team with a +60 run differential (RD) playing a hotter team with a +80 RD, well, then you might think that the +80 team has the better shot. (This has not happened in the last 11 years, but you get the idea!)
So, here's what we get when we look at the difference in September Run Differentials between the winner and the loser.

I've added the 3 Cubs series because, well, this is a Cubs site! The Cubs do not stand out in the slightest: the 2003, 2007 and 2008 LDS all were won by the team with the better September.
This is the only breakdown I can find that predicts significantly more than 50% of the winners. Basically, half the time the team with the most wins or greatest rund-differential for the entire season takes the series. Slightly more than half the time, the team with the best actual won-loss record wins: but the run differential (which predicts W-L with some error) does a much better job.
So, as a rule of thumb, bet on the team that had a better run-differential in September. Such teams win about 3 times in 4. Last year was a good example: the Cards, Tigers and Rangers won but the DBacks lost. Now, you say, what good is this if you cannot tell me which 3? Well, tough: probability does not work that way!
I will add this caveat: the new 1-game WC playoff might very well alter this by making a "hot" September team use up their Ace and thus getting him for only one of the LDS games. At this point, I'm not sure that the managers have decided how they will handle this game: it probably will take a few years before any tactic emerges as superior.
Any way, food for thought....

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