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.
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