At Decision Science News, Dan Goldstein asks the question, looks at the data, and finds a surprising result.
If a team wins on one day, what’s the probability they’ll win against the same opponent when they play the very next day?
We asked two colleagues knowledgeable in baseball and the mathematics of forecasting. The answers came in between 65% and 70%.
The true answer: 51.3%, a little better than a coin toss.
That’s right. When you win in baseball, there’s only a 51% chance you’ll win again in more or less identical circumstances. The careful reader might notice that the answer is visible in the already mentioned chart. The reversals of size 0, (meaning no reversal, meaning the same team won twice) occur 51,296 times per 100,000 pairs of consecutive games.
Statistician Andrew Gelman is not surprised and explains why.
I have to say, I’m surprised his colleagues gave such extreme guesses. I was guessing something like 50%, myself, based on the following very crude reasoning:
Suppose two unequal teams are playing, and the chance of team A beating team B is 55%. (This seems like a reasonable average of all matchups, which will include some more extreme disparities but also many more equal contests.) Then the chance of the same team winning both games is .55^2 + .45^2 = .505. Even .6^2 + .4^2 is only .52.
Two interesting posts, worth reading. Thanks to Jonathan for the pointer.