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#1
06-01-2007, 04:58 PM
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OT: Sports 7 Game Playoff Probabilities
Hey guys,
This isn't poker, but I figured this would be the best place to ask this question. I haven't taken probability in forever, but I'd like some help with the formula for figuring out what the probability of a team winning a 7 game series is at any point if I were to assign them a certain chance to win each game? Probably as the best example of what I want relates to the current NHL Finals. Anaheim is up 2-0. Ottawa needs to win 4 out of the next 5 to win the Cup. They have 3 home games and 2 road games left. If I say Ottawa has a 60% chance to win at home and a 40% chance to win on the road, what's the formula to get the probability of them winning 4 out of 5 games? If I remember correctly, the formula for 4 out of 4 would be just multiplying the probabilities together (.6*.4*.6*.4=.058). I'm just not sure how to factor in being able to lose one game...or even 2 or 3. Thanks in advance for your help. I truly appreciate it. 
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#2
06-01-2007, 07:16 PM
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Re: OT: Sports 7 Game Playoff Probabilities
With only 5 games left, you can really just count up the cases where they can win. So the chance of them winning 4 straight is X, the chance of them losing the first but winning the next 3 is Y, the chance of them winning the first, losing the second, but winning the next three is Z, etc etc. In this case you should only have 5 cases, so it should be easy.
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#3
06-01-2007, 07:28 PM
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Re: OT: Sports 7 Game Playoff Probabilities
So, the 5 cases are...
WWWW: .6*.6*.4*.6=8.6% LWWWW: .6*.4*.6*.4=5.8% WLWWW: .6*.4*.6*.4=5.8% WWLWW: .6*.6*.6*.4=8.6% WWWLW: .6*.6*.4*.4=5.8% Now how do I combine them into one percentage? It should be something between 5.8% and 8.6% I beleive, but how can I get to that number? Hmmm, on second thought I'm guessing it's a weighted total with 20% to each, assuming each situation has an equal chance to happen (i.e. winning 4 in a row isn't any harder than winning 2 or 3 in a row)... (3*.2*5.8%)+(2*.2*8.6%)=6.9% Correct? Or maybe I screwed this up altogether and those 5 percentages are addditive.
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#4
06-02-2007, 04:22 AM
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Re: OT: Sports 7 Game Playoff Probabilities
I don't know the order the games would go in so I assume HAHAH, it makes an insignificant difference
.6x.4x.6.x4 .0576 .4 .4 .6 .4 .6 .02304 .6 .6 .6 .4 .6 .05184 .6 .4 .4 .4 .6 .02304 .6 .4 .6 .6 .6 .05184 they do add so the I believe that Ottawa would have a .21 chance of winning the series.
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