Another Math Question (NHL Grand Salami)

calmB4storm · #1 10-04-2007, 11:49 AM

Pinny has the total at o45.5 (-115), u45.5 (+105).

Is it possible to figure out the probability of the total going 45, with just this information? If yes, how? Thanks.

TomCowley · #2 10-04-2007, 11:58 AM

No.

TomG · #3 10-04-2007, 01:01 PM

Nope. Pinny doesn't use a drop-down menu for any NHL bets. You'll have to figure out the "push percentage" of the Grand Salami bets on your own.

calmB4storm · #4 10-04-2007, 02:12 PM

So something like this won't work, because it's an infinite series instead of a distinct number of possible outcomes?

TomG · #5 10-04-2007, 02:31 PM

[ QUOTE ]
So something like this won't work, because it's an infinite series instead of a distinct number of possible outcomes?

[/ QUOTE ]
The thread you linked to uses the binomial distribution to approximate the distribution of a NFL team's regular season win distribution. It is a decent approximation not because there is a definite number of possible outcomes but because of the shape of the distribution of possible outcomes. Visualize how a NFL team's regular season win distribution should look (Hint: think bell curve). The question you then have to ask yourself, does the NHL Grand Salami distribution look similar? If so, you may also be able to model it using binomial distribution.

TomCowley · #6 10-04-2007, 02:33 PM

The Grand Salami distribution is the combination of individual (unique) distributions in each game.

Imagine rolling 3 6-sided dice. The fair O/U is 10.5 +100. The odds of getting exactly 10 are 12.5%

Now imagine rolling a 20-sided die. The fair O/U is 10.5 +100, but the odds of getting exactly 10 are 5%.

Without knowing at least something about the underlying distributions (the likelihood of each total for each individual game), you can't evaluate the distribution of the Grand Salami total.

Thremp · #7 10-04-2007, 02:38 PM

Tom,

Couldn't you just Poisson it for a quick and dirty approx?

calmB4storm · #8 10-04-2007, 02:50 PM

[ QUOTE ]
Tom,

Couldn't you just Poisson it for a quick and dirty approx?

[/ QUOTE ]
I tried this calculator, putting in 45.5 and 45, and it told me that the total would hit exactly 45 ~5.9197% of the time, which sounds reasonable. I wasn't sure how to account for the fact that each of the 8 games must have at least one goal scored, or the fact that the total was actually leaning -115/+105 toward the over, but I figure neither one of those facts would have much impact.

BTW it's a moot point now, since BetJam moved their line up to 45.5.

TomG · #9 10-04-2007, 03:09 PM

Thremp,

The Poisson distribution can be derived as a limiting case of the binomial distribution.

calmB4storm · #10 10-04-2007, 03:11 PM

Holy Sh*t! Can someone check this?

Using the 5.9197% chance of a push, and assuming Pinny's line is efficient:
<ul type="square">[*]Chance of 46 or More = 110 / 210 = 52.38%[*]Chance of Exactly 45 = 5.9197%[*]Chance of 44 or Less = 1 - (.5238 + .059197) = 41.70%[*]True Line on over 45 = -126[*]Betting on a -110 line, the optimum full kelly stake = 6.93% of bankroll, and expected ROI = 6.3%[/list]Is this right?