Hi everyone! I am desperate for some help on a complex probability problem I am trying to tackle. Here's the scenario:
A team has 5 games, and in each game they have an independent win probability. The result of one game has no effect on the next game, or any game the rest of the year. Here are the team's win probabilities by game:
What I am looking for is the probability they will finish the season with a given record, for all possible records. 5-0 and 0-5 are easy.
0-5 record = .7 *.3 *.85 *.1 *.45 = 0.8%
5-0 record = .3 * .7 * .15 * .9 * .55 = 1.55%
Now the hard question: What are the chances the team finishes exactly 1-4, 2-3, 3-2 or 4-1? And how is that calculated?
Ideally I would like to expand this a larger list of probabilities, but I figured I would start with something "simple" like a 5-game series.
A team has 5 games, and in each game they have an independent win probability. The result of one game has no effect on the next game, or any game the rest of the year. Here are the team's win probabilities by game:
| Game # | Win Probability |
| #1 | 30% |
| #2 | 70% |
| #3 | 15% |
| #4 | 90% |
| #5 | 55% |
What I am looking for is the probability they will finish the season with a given record, for all possible records. 5-0 and 0-5 are easy.
0-5 record = .7 *.3 *.85 *.1 *.45 = 0.8%
5-0 record = .3 * .7 * .15 * .9 * .55 = 1.55%
Now the hard question: What are the chances the team finishes exactly 1-4, 2-3, 3-2 or 4-1? And how is that calculated?
Ideally I would like to expand this a larger list of probabilities, but I figured I would start with something "simple" like a 5-game series.