Printer-friendly

October 19, 2005

Lies, Damned Lies

Running the Odds

by Nate Silver

A thousand-to-one shot. That was my first reaction when the Cardinals rallied to beat the Astros on Monday night, down to their last strike with a two run-deficit against one of the scariest one-inning pitcher in baseball.

Actually, that was my second reaction. My first reaction was something that would have made Andy Pettitte blush. And my third reaction, after a few moments of reflection about Donnie Moore, Grady Little, and Steve Bartman, was that we might have just witnessed the most unlikely comeback in postseason history.

We don’t have a comprehensive way to test that proposition. There is probably some long-forgotten game from the early days of baseball when the Boston Pilgrims scored 13 times in the bottom of the ninth to shock the Cincinnati Red Stockings. But we can at least compare Monday’s events against some other recent postseason comebacks, by estimating the odds against the trailing team coming back to win the game when facing a seemingly dire situation. These estimates will be based on three things:

1. The Expected Wins Matrix. This gives us the empirical probabilities of a team winning the game given a particular inning, score differential, number of outs and number of baserunners. We will use 10 years worth of data to come up with our estimates, since these things are subject to sample-size considerations, particularly for things like the probability of an unlikely victory.

2. The opposing pitcher. The most important thing for a team to do when down to its last few outs is to extend the inning. Thus, we’ll look at the opposing pitcher’s OBP against for the season in question. We’ll assume that an "average" pitcher allows a OBP of .300. This is deliberately lower than the actual league OBP, which usually runs in the .330 range. The Expected Wins statistics are compiled from historical gameplay, and a team down in the late innings will usually be facing the closer, another good relief pitcher, or an ace starter who has stayed in the game because he’s throwing effectively. We’ll multiply the raw win probability by the ratio of the opposing pitcher’s OBP to the “league average” of .300 to come up with an adjusted figure. For example, if a team would ordinarily have a 6% probability of coming back to win the game, but they’re facing a tough pitcher with an OBP allowed of .250, the modified figure will be (6% * (.250/.300)), or 5%.

3. The count. Historical ball-strike records are hard to come by, but we’ll make a further adjustment for the count in the two games in which it was most important: Dave Henderson's home run against Moore, which came after an 0-2 count, and the Cards’ comeback on Monday.

   The rest of this article is restricted to Baseball Prospectus Subscribers. Not a subscriber? Click here for more information on Baseball Prospectus subscriptions or use the buttons to the right to subscribe and get access to the best baseball content on the web.

   Cancel anytime. That's a 33% savings over the monthly price! That's a 33% savings over the monthly price! Already a subscriber? Click here and use the blue login bar to log in.