## Saturday, April 6, 2013

### The likelihood of a sweep.

Question:   In a particular championship series, both teams have a 0.5 victory probability in each independent and identically distributed game.  What is the probability of a sweep in a best-of-five game series?  What is the probability for a sweep in a best-of-seven game series?

Answer: Since outcomes are binary (win/loss), independent, and identically distributed, the probability of a series lasting k games is binomially distributed.  There are two possible ways a sweep could occur.   Either team A sweeps or team B sweeps.  The probability of a sweep in a best-of-five series is 2x0.53 or 0.250.  The probability of a sweep in a best of seven series is 2x0.54 or 0.125.

Note this analysis assumes that the teams are evenly matched, that each team has a 50/50 shot in each game.   In reality some teams are much better than others.  Also a team with a dominant starting or relief pitcher is more likely to win certain games.   I suspect that the likelihood of a sweep is larger than these theoretical estimates.

I am working on the second edition of my book.  The now dated but still useful first-edition could be borrowed on Kindle.