Letter to the Editor

by Rick Abts

A recent puzzle in MAAM asked what are the chances of a World Series going 4, 5, 6 or 7 games. To answer questions such as these statisticians use something known as the “negative geometric distribution”. Here’s how it works. Call the chance of winning a game p, losing q. Assume we win the last game (because otherwise the series would have ended sooner). For a series to go 7 games means that the first six would have been split 3-3, therefore the percent would be described by (6 choose 3) p^4 q^3. For it to go 6 games would be (5 choose 3) p^4 q^2 and so on. The critical insight in this is to realize that when we decide who won the series and in how many games, then we know who won the last game, this allows us to find the coefficient. I’ve deliberately decided not to go into what (n choose k) means, that’s a whole topic in itself.