I’ve heard multiple discussions about what an atrocity it is for the first round of the baseball playoffs to be only five games. That after an eternal 6-month, decadently large 162-game sample size to decide who makes it, it’s unfair for the best teams to be subjected to such a crapshoot as a 5-game opening round. But is a 7-game series really that much better?
Let’s assume that the “better” team has some (> 0.5) probability of winning each game (Game WP). What then is the probability that the “better” team will win a playoff series? As a function of single Game WP, with the curves representing a series of length 1, 3, 5, 7, and 9 games (bottom to top):
The bottom curve (1-game series) is obviously a straight line with Game WP = Series WP. As the series gets longer, the sample size increases and eventually the curves would all converge to Series WP = 1 for all Game WP > 0.5.
In a series “mismatch,” say, a matchup between a 102-win team and an 85-win team, then using the log5 method, Game WP = 0.606 for the 102-win team. For this value of Game WP we can plot Series WP vs. the Series Length:
Even with a series mismatch like this one, you’d have to play a 15 game series just to get 80% certainty that the best team won.
And what about a 7-game series compared to just 5? The better team’s Series WP improves to 72.2% from 69.3%. So 7 games isn’t exactly worlds better than 5.
There’s a lot of luck in postseason baseball.