Fun with Probabilities, Wild Card Edition

ATLANTA, GA - SEPTEMBER 26: Dan Uggla #26 of the Atlanta Braves sits in the dugout after their 4-2 loss to the Philadelphia Phillies at Turner Field on September 26, 2011 in Atlanta, Georgia. (Photo by Kevin C. Cox/Getty Images)

Last night, the Tampa Bay Rays pulled even with the Red Sox in the AL Wild Card standings. The Rays have played .610 baseball since August 18th when they stood 8.5 games behind the Red Sox in the Wild Card standings. In contrast, the Red Sox have played .380 ball over the same stretch, allowing the Rays to catch up.

It got me thinking, what were the odds of both these teams playing to those levels over the past month and a half?

On August 18th, the Red Sox were 75-48 (.610), while the Rays were 66-56 (.541). Let's assume those records reflected the true talent levels for both teams.

Over their last 37 games, the Red Sox have gone 14-23. The probability of a .610 club winning less than or equal to 14 out of 37 games is .3%. The Rays have gone 23-15 over their last 38 games. The probability of a .540 team winning greater than or equal to 23 out of 38 games is 26%. So while the Rays recent stretch was reasonable to expect, the Red Sox collapse looks absolutely fluky.

Add it all up, and the probability of Boston playing that bad while the Rays played that well was .078%

What about the Braves and Cardinals?

As late as August 25th, Atlanta held a 9.5 game lead over San Francisco and a 10.5 game led over St. Louis. At the time, Atlanta was playing .598 ball, while the Cardinals were plodding along at .519.

Since then, Atlanta has gone 10-18 (.357). The probability of Atlanta winning 10 or fewer games out of 28 is .8%.Meanwhile, St. Louis has gone 20-9 (.690). The probability of the Cardinals winning 20 or more games out of 29 is 4.7%.

Altogether, there was a .038% chance of these two teams playing to these levels since August 25th.

Now, to be fair, these calculations don't take into account the records of the opponents each team faced during these stretches, nor do they take into account that in many cases the talent of these teams did change over time (e.g. injuries, call-ups, etc.). However, it's hard to imagine the probabilities changing all that drastically. Some change, sure. But overall the chances would still have been quite low.

Suffice it to say that these incredible races have only become incredible due in large part to some good old fashion luck. And that's one of the things that makes the game so much fun to watch and analyze.

The next two days should be a blast.


For another, less back-of-the-envelope analysis of the Red Sox collapse check out some guy named Nate Silver at The New York Times. I hear he used to write a little about baseball back in the day.

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