The Pirates were lucky to win the 1971 World Series, but how lucky?

This came up on one of the SABR bulletin boards.

Their OPS differential for the whole season was .073. That translates into a winning pct of .592 using my equation Pct = .5 + 1.26*OPSDIFF. The Orioles had a differential of .096, good for a pct of .621. That means that the Orioles would have 53% chance of winning any given game using Bill James' Log 5 method. I came up with the Orioles having about a 56.5% chance of winning the series, taking into account all the different ways they could win a series of a given length. They also had home field advantage, which should have increased things about 2% (2% more than 55.7% so about 58%)

7.9% of the time it is an Orioles sweep

14.8% of the time the O's win in 5

17.4% of the time they win in 6

16.4% of the time they win in 7

So the Pirates had a 42% chance of winning