[Bean]

Bodog had an interesting prop bet this weekend:

2011 NFL Playoffs - How Many Wild Card Teams will Win in Round 1 of the Playoffs? (Jets, Ravens, Saints, Packers)
0 +2500
1 +400
2 +140
3 +175
4 +700

Using Bodog's Saturday morning spreads for the four games, I came up with these winning probabilities for each of the four WC teams: Saints 84%, Jets 42.6%, Ravens 63.23%, Packers 44.4%. So, the predicted number of WC winners should have been: .84 + .426 + .632 + .444 = 2.342

Plugged this into the Poisson calculator, which spit out:
0 winner +940 9.6%
1 winner +361 22.51%
2 winner +279
3 winner +386
4 winner +728
Which means that "0" was a great value at +2500 and "1" a good value at +400. So naturally, I took these two bets (and "0" is already dead, thank you Antonio Cromartie and Nick Folk!). It just occurred to me that this logic might be completely flawed, because the 4 events are not identical like interceptions, rushing yards, or pass completions might be. The right way to think about it might be as a sum of 4-way parleys, in which case "0" and "1" were probably horrible bets (haven't done the math). Or maybe the two approaches amount to the same thing???

[durito]

Yes.

Take the no vig ml at pinny and then calculate:

odds of 0 winners = P Colts Win * P Seattle Win * P KC Win * P Phi Win
odds of 4 winners = P Jets W * P Ravens W * P Saints W * P GB W

odds of 1,2,3 winner have multiple possibilities compute the probabilities and add them

[Justin7]

Poisson doesn't work very well when you have this few trials. If you have only 4, I would use a Binomial (or do each outcome manually).

Consider this problem: You have one wild-card team that is 67% likely to win. What answer does Poison give you for 1 wild-card win, with one trial at 0.67? 0.488, when it should obviously be 0.67.

A general rule I use on Poissons... You normally want at at least 20 trials with odds of 0.1 or less per trial. Or, N/p >200. So if you have lots of trials, it is ok for higher p's.

[Bean]

Interesting, thanks Justin! You da man!

[Peregrine Stoop]

giving the poisson calculator to these fools that don't know what the distribution is or how to use it is like giving the crack pipe to Whitney Houston

[Bean]

Thanks for the complement Peregrine Stoop! I'm just an average Joe, win some/lose some, trying to learn something every day. And look on the bright side: if it wasn't for fools like me to take the wrong side of bets, how would the elites like yourself get rich???

Namaste!

[jackpot269]

wow wish i had seen this when looking at bodog yesterday

[jackpot269]

Thanks for the complement Peregrine Stoop! I'm just an average Joe, win some/lose some, trying to learn something every day. And look on the bright side: if it wasn't for fools like me to take the wrong side of bets, how would the elites like yourself get rich???

Namaste!

Hey , I'm not the only one, after all for years I thought everyone on here was a great betting mind except for myself glad to know there are others out there!!!!

Now you know I meant in each ones opinion of there self !!!!!!!!!!!!

[subs]

stattrek maybe can help with the binomial distribution...

namaste baba

[That Foreign Guy]

When accurate odds are available for each constituent event, attempting to approximate it by (mis)using a generalised distribution is foolish.

Durito's method is optimal IMO.

[uva3021]

Poisson distributions are reserved for events that are mutually exclusive, extremely rare, and more or less randomly associated with its cause. Such as the weather, the mutation rate of genes, or the gait of a drunkard. Football outcomes scarcely qualify as following a Poisson Distribution.

In this case, either calculate the odds manually or use BINOMDIST in excel: [insert "=BINOMDIST(ROW()-1,4,2.34/4,FALSE)" in cell A1 and copy to A5]

0 - 2.97% 3271
1 - 16.72% 498
2 - 35.36% 183
3 - 33.23% 201
4 - 11.71% 754

[simplydusty]

A general rule I use on Poissons... You normally want at at least 20 trials with odds of 0.1 or less per trial. Or, N/p >200. So if you have lots of trials, it is ok for higher p's.

Just finished reading this in the props chapter of Conquering Risk. Great read