OK, according to rpiforeceast.com, these are the odds that Arizona wins their next 5 games:
rpiforecast.com
60% chance of a win @Wazzu
47% chance of a win @UW
92% chance of a win USC
67% chance of a win UCLA
83% chance of a win @ASU
I want to know what the over all odds are of Arizona winning:
5 games
4 games
3 games
2 games
1 game
Please show your work. Pay for the first correct answer is one million fake internet dollars.
Yeah, I'm so not doing that. There are no shortcuts that I can see, you're going to have to evaluate each possible combination of the 5 games. If the odds were the same for each game, then it would be a relatively simple probability problem.
They aren't going to tourney, so don't even worry about it :P
All 5 is easy.
.6*.47*.92*.67*.83= 14%
To give an outline of how you would get an answer, it's not hard, just tedious. There are 32 possible results, and for each of those 32 results you multiply the probabilities of the 5 events. Use given probabilities if game X is a win in one of those 32 combinations, or 1 - probability if it's a loss. Then sum the products up by the number of wins. I could probably do it in 5-10 minutes in Excel, but frankly it's too boring.
Quote from: DGuller on February 13, 2012, 03:30:49 PM
To give an outline of how you would get an answer, it's not hard, just tedious. There are 32 possible results, and for each of those 32 results you multiply the probabilities of the 5 events. Use given probabilities if game X is a win in one of those 32 combinations, or 1 - probability if it's a loss. Then sum the products up by the number of wins.
:huh:
QuoteI could probably do it in 5-10 minutes in Excel, but frankly it's too boring.
:cry:
Two million fake internet dollars?
5 games = c. 19%
4 games = c. 25%
3 games = c. 31%
2 games = c. 20%
1 game = c. 5%
That's be 2 million internet dollars, please.
Fuck you, Berkut.
Wins Probability
0 0.000951
1 0.019790
2 0.128147
3 0.334805
4 0.372032
5 0.144275
Quote from: grumbler on February 13, 2012, 03:40:10 PM
5 games = c. 19%
4 games = c. 25%
3 games = c. 31%
2 games = c. 20%
1 game = c. 5%
That's be 2 million internet dollars, please.
And fuck you grumbler. Hopefully Berkut requires the answers to be correct in order to claim the price, or I got screwed out of 2 mil. :(
Thanks DG!
(https://languish.org/forums/proxy.php?request=http%3A%2F%2Fboingboing.net%2Fwp-content%2Fuploads%2F2012%2F01%2Fimages__one-million-dollars.jpg&hash=5baded5646e49c54b65358edb72d5f366fdb4442)
(https://languish.org/forums/proxy.php?request=http%3A%2F%2Fboingboing.net%2Fwp-content%2Fuploads%2F2012%2F01%2Fimages__one-million-dollars.jpg&hash=5baded5646e49c54b65358edb72d5f366fdb4442)
Berkut always pays his debts.
DGuller's numbers are right, but only if I get a share of the internet money.
Are you trying to arbitrage the bookies, Berkut? :ph34r:
grumbler tricked Dguller. He knew that Dguller would have to prove him wrong and thus give the answer berk was looking for. Crafty :P
Quote from: grumbler on February 13, 2012, 03:40:10 PM
5 games = c. 19%
4 games = c. 25%
3 games = c. 31%
2 games = c. 20%
1 game = c. 5%
That's be 2 million internet dollars, please.
This seems quite wrong to me. I'm just running this with a random number generator and about a million trials (since its trivial this way), so not an analytical solution. What I get matches DGuller's numbers within the statistical uncertainty.
Games Won | Prob
0 | 0.00092
1 | 0.01985
2 | 0.12834
3 | 0.33430
4 | 0.37231
5 | 0.14429
Since I am an actuary, I have to give one word of caution about the above calculations. We assumed that each game result is independent from the other. Realistically speaking, if Arizona loses the first 4 games, then odds are that they may not be 83% favorites to win the last one. I'd be careful before wagering my kneecaps on these calculations.
True, and I am sure the rpi forecast would change after each game.
And those numbers are mostly bullshit anyway. But thanks for crunching them for me.
Statistically, how much do the odds of winning all five games drop if we lose the first one against Wazzu?
Noticeably.
Even I can figure that one out. ;)
Quote from: DGuller on February 13, 2012, 04:10:27 PM
Since I am an actuary, I have to give one word of caution about the above calculations. We assumed that each game result is independent from the other. Realistically speaking, if Arizona loses the first 4 games, then odds are that they may not be 83% favorites to win the last one. I'd be careful before wagering my kneecaps on these calculations.
What you can say with some confidence is that 3-4 wins is pretty likely, and 2-5 wins is very likely (for statistically normal chances of likely). I don't think you have to worry about 0 wins.
Quote from: Gbeagle on February 13, 2012, 04:03:28 PM
This seems quite wrong to me. I'm just running this with a random number generator and about a million trials (since its trivial this way), so not an analytical solution. What I get matches DGuller's numbers within the statistical uncertainty.
Games Won | Prob
0 | 0.00092
1 | 0.01985
2 | 0.12834
3 | 0.33430
4 | 0.37231
5 | 0.14429
Since my numbers were made up, of course they are wrong. But people like to prove me wrong, so they had to do the calculations Berkut asked for (and the stats guys refused to do because it was too hard) to do so. Berkut wins, and I don't are about being wrong, so this seems like a win to me as well. :P
Quote from: grumbler on February 13, 2012, 05:20:22 PM
Quote from: Gbeagle on February 13, 2012, 04:03:28 PM
This seems quite wrong to me. I'm just running this with a random number generator and about a million trials (since its trivial this way), so not an analytical solution. What I get matches DGuller's numbers within the statistical uncertainty.
Games Won | Prob
0 | 0.00092
1 | 0.01985
2 | 0.12834
3 | 0.33430
4 | 0.37231
5 | 0.14429
Since my numbers were made up, of course they are wrong. But people like to prove me wrong, so they had to do the calculations Berkut asked for (and the stats guys refused to do because it was too hard) to do so. Berkut wins, and I don't are about being wrong, so this seems like a win to me as well. :P
I'm quick, but not that quick. I didn't do those calculations in the 1 minute gap between our posts.
Dont take that away from Grumbler.
Quote from: crazy canuck on February 13, 2012, 05:31:49 PM
Dont take that away from Grumbler.
I didn't even get am honorable mention for coming up with it first :( :P
1 Arizona Sucks
2 Lute Olsen sucks dicks
3 Arizona sucks
4 Arizona football sucks. RICH ROD? BWHAHAHAHA
5 Arizona sucks
Your welcome.
Quote from: Berkut on February 13, 2012, 04:15:53 PM
Statistically, how much do the odds of winning all five games drop if we lose the first one against Wazzu?
Did you mean to ask "how much do the odds change if we lose the first one against Wazzu?". If so:
4 Wins: 0.24045764
3 Wins: 0.45974844
2 Wins: 0.25150884
1 Win: 0.04590644
0 Wins: 0.00237864
If you win the first game just shift the win count up by one. Of course DGuller's warning about non-independent events is well taken, so take these with even more salt then the first set.
Quote from: Berkut on February 13, 2012, 04:15:53 PM
Statistically, how much do the odds of winning all five games drop if we lose the first one against Wazzu?
:lol:
Quote from: fahdiz on February 13, 2012, 07:21:04 PM
Quote from: Berkut on February 13, 2012, 04:15:53 PM
Statistically, how much do the odds of winning all five games drop if we lose the first one against Wazzu?
:lol:
:lol: I didn't notice that the first time I read it.
Quote from: HVC on February 13, 2012, 05:54:19 PM
Quote from: crazy canuck on February 13, 2012, 05:31:49 PM
Dont take that away from Grumbler.
I didn't even get am honorable mention for coming up with it first :( :P
Didn't see you post, sorry. You were correct. How about a dishonorable mention, since it is too late for an honorable one? :D
I'll take my mentions anyway I can get them :D
hmm. when someone requests help from the numbers community, number-folks fall over themselves to provide assistance
...when someone asks a lawyer... :lol: