September 29, 2005
Crunching Baseball's Numbers (Carl Bialik, September 29, 2005, Wall Street Journal)
The Oakland A's are a very good baseball team that nonetheless will miss the playoffs, thanks in large part to a stretch of bad play at home late this season.
Just how much of a fluke was that stretch from August 12 to September 7, in which the A's lost five straight three-game series at home? A's manager Ken Macha hazarded a guess last week in a chat with Sacramento Bee sports columnist Mark Kreidler: a 512-to-1 shot. "It sounds high, but since Macha studied civil engineering in college and I studied journalism ethics (or did I only audit that course?), we'll go with his version," Mr. Kreidler wrote.
It seems Mr. Kreidler should have trusted his instincts, because Mr. Macha's calculations appear to misstate the odds against his team's poor play. But examining the numbers more deeply provides an interesting illustration of probability theory, and demonstrates why many statistics and math professors like to use baseball in their lesson plans.
Let's start by assuming the A's have a 50% chance of losing each home game. The games in question were played as a best-of-three series. Each game of that series had two possible outcomes, so for the three-game set, there are eight (2*2*2) possible outcomes. One such outcome is that the A's sweep; another is that their opponent wins the first and third games but loses the middle game, for instance.
In four of the eight possible outcomes, the A's lose the series, because they lost at least two of the three games. Each outcome has an equal probability in this scenario. So the A's have a 4 in 8 (or 1 in 2) chance of losing any particular series.
There were five series, and we've already seen that the A's had a 1 in 2 chance of losing any individual series. To come up with their odds of losing all five series, you multiply the probabilities together (1/2 * 1/2 * 1/2 * 1/2 * 1/2) to get 1/32. In other words, using this method, the odds of the A's losing all five series is 1 in 32 -- far more likely than the 1 in 512 that Mr. Macha estimated.
Whahappen? Posted by Orrin Judd at September 29, 2005 12:00 AM