LamKram
Joined: May 27, 2010
• Posts: 3
May 27th, 2010 at 6:28:12 AM permalink
I was just wondering this morning (although this hasn't happened YET...)

What is the probability that two teams from the same city (say a basketball team and a hockey team) in the same year will both be eliminated from their respective playoffs in a 7 game series by going up 3 games to zero and then losing 4 games in a row? Each sport's playoff format is best of seven for each round and each has a maximum of 4 rounds. For simplicity, I'm assuming that all teams are equally matched without home court/ice advantage.

I put it at 0.000215 (4659-to-1 against) for any two prior identified teams. Can the Wizard (or anyone else) confirm this?
miplet
Joined: Dec 1, 2009
• Posts: 1930
May 27th, 2010 at 8:11:13 AM permalink
Quote: LamKram

I was just wondering this morning (although this hasn't happened YET...)

What is the probability that two teams from the same city (say a basketball team and a hockey team) in the same year will both be eliminated from their respective playoffs in a 7 game series by going up 3 games to zero and then losing 4 games in a row? Each sport's playoff format is best of seven for each round and each has a maximum of 4 rounds. For simplicity, I'm assuming that all teams are equally matched without home court/ice advantage.

I put it at 0.000215 (4659-to-1 against) for any two prior identified teams. Can the Wizard (or anyone else) confirm this?

Looks good to me.
A team will win the first 3 games and lose the next 4 games 1 in 128 rounds. (.5)^7
A team can lose round 1 in the above way. (.5)^7
A team can win round 1 and lose round 2 in the above way. (.5)^8
A team can win round 1 and 2 and lose round 3 in the above way. (.5)^9
A team can win round 1,2 and 3 and lose round 4 in the above way. (.5)^10
Add them up and we get 15/1024
We need this to happen twice so we square it (15/1024)^2 = 225/1048576 = apx. 0.000214576721191 or 1 in about 4660 (4659-to-1 against)
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