Nah, It Couldn’t Happen, Could It?
Posted by Steve L. on September 27th, 2010 · Comments (2)
The Yankees just lost to the Blue Jays. And, in Chicago, the Red Sox lead the White Sox, 6-1, in the top of the 9th inning. Say, that Boston hangs on for the win…
There’s no chance that the Yankees lose their next two game in Toronto and that Boston sweeps Chicago in their series, is there?
I knew this post was coming.
Well, in the infinite monkeys + infinite typewrtiters + random typing = infinitesmal chance of reproducing Shakespeare, yes.
As a practical matter, no, not really.
Before tonight’s loss/win, Baseball Prospectus had the odds against at roughly 1500 to 1.
Well, heck, do it mathematically. At the extreme end, the Sox can’t be rated any higher than 0.6 to beat the White Sox in an individual game (on average). The Yanks can’t be rated any lower than 0.4 to lose a game to the Jays. The Sox can’t be any higher than 0.6 to take an individual game from the Yanks over the weekend (again, on average).
To TIE the Yanks for the Wild Card, forcing a 1 game playoff:
(0.6)^4 * (0.6) ^ 3 * (0.6) * 3 = 0.6 ^ 10 = .0060466, or 164 to 1 against.
To win the Wild Card, multiply by 0.6 again: 275 to 1 against.