A 2-1 result in a best-of-3 is rarely more likely than a 2-0

This is just a minor thing that bothers me when hearing predictions.  It comes up a lot with League of Legends casters; I hear a fair number of 2-1 predictions for a best of 3 that the casters feel is pretty evenly matched.

In the case of the teams being exactly evenly matched and there being nothing like home-field advantage (or side advantage in League), you get a 2-0 result 50% of the time and a 2-1 result 50% of the time.  Making the teams uneven of course makes a 2-0 result more common.

If there is a home-field/side advantage, such that the team that is more likely to win game 1 is less likely to win game 2, then it is true that with two very closely matched teams a 2-1 is actually very slightly more likely than a 2-0.

Of course what the casters really mean is they just think the teams are close to even.  But you should not be surprised when teams that are evenly matched go 2-0 in a series, unless you have some reason to believe that winning the first game makes you less likely to win the second game.

 

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