Sagarin says

[thebootfitter]

You kind of touched on it a bit, but does Sagarin (or can it be extrapolated from there) explore the % chance of a certain spread happening? For example, and looking specifically at NDSU vs. UNI, there is a 9% chance NDSU wins by 24+, 19% NDSU wins by 17+, 38% chance NDSU wins by 11+, etc. I guess you would just have to pick some point breaks in the spread, say +1, +5, +10, +15, +20, -1, -5, -10, -15, -20.

Does my question make sense? I may have confused myself.

Audit can probably answer this more clearly, but the short answer is yes. Audit's last paragraph gives the basis for making these calculations using Sagarin's standard deviation of roughly 14 points.

NDSU's rating is 79.93. UNI's is 67.22. They get a 3.17 point bump for home field advantage, so we are favored by 9.54 points. Statistically, there is roughly 2/3 chance that the actual margin of victory is within 14 points either way of the 9.54 points in our favor. (Between a 4.5 pt victory for UNI and a 23.5 pt victory for NDSU.) There's a 1/6 chance that we have greater than a 23.5 pt victory and a 1/6 chance that UNI beats us by more than 4.5 pts.

The specific percentages for each point differential can be calculated as well, rather than just using the rough calculations from the full standard deviations of a normal distribution. Since it would take me a little bit of digging to make sure I got the calculations right, I'll be lazy and see if Audit whips something up first.

Edited to add: You weren't too far off in your example above, RTO, but you aren't giving the Bison enough credit. There's a roughly 16% chance that we win by 24+, and roughly 25% chance that we win by 19+. There's even a 2.5% chance that we win by 37+. But also a 2.5% chance that we lose by 18+.

[runtheoption]

Audit can probably answer this more clearly, but the short answer is yes. Audit's last paragraph gives the basis for making these calculations using Sagarin's standard deviation of roughly 14 points.

NDSU's rating is 79.93. UNI's is 67.22. They get a 3.17 point bump for home field advantage, so we are favored by 9.54 points. Statistically, there is roughly 2/3 chance that the actual margin of victory is within 14 points either way of the 9.54 points in our favor. (Between a 4.5 pt victory for UNI and a 23.5 pt victory for NDSU.) There's a 1/6 chance that we have greater than a 23.5 pt victory and a 1/6 chance that UNI beats us by more than 4.5 pts.

The specific percentages for each point differential can be calculated as well, rather than just using the rough calculations from the full standard deviations of a normal distribution. Since it would take me a little bit of digging to make sure I got the calculations right, I'll be lazy and see if Audit whips something up first.

Thanks to you for taking over during Hammersmith's hiatus, and for Audit as he continues his # crunching ways. BTW, did you know Hammersmith and I have the same last name? Esplaines his brainz.

[bisonaudit]

You kind of touched on it a bit, but does Sagarin (or can it be extrapolated from there) explore the % chance of a certain spread happening? For example, and looking specifically at NDSU vs. UNI, there is a 9% chance NDSU wins by 24+, 19% NDSU wins by 17+, 38% chance NDSU wins by 11+, etc. I guess you would just have to pick some point breaks in the spread, say +1, +5, +10, +15, +20, -1, -5, -10, -15, -20.

Does my question make sense? I may have confused myself.

Yes, it can be extrapolated. For entertainment purposes only, that's almost entirely the point. The fact that the variances are normally distributed around the model's estimate of the point spread with a standard deviation of about 14, allows an interested person to determine, based on the lines and prices offered, how much of an edge they may have and therefore how much to wager.

If the UNI line is NDSU -9 1/2 (which is what Sagarin model thinks it is) there's a 50% chance NDSU wins by 9 1/2 or more (I know it's a little funky with the non continuous variable). There's about a 16% chance NDSU wins by 23 1/2 or more. There's 76% chance NDSU wins. There's about a 16% chance UNI wins by 4 1/2 or more.

Just in general regarding distance from the predicted spread about 67% of the results should fall within 14 points on either side of the predicted result (evenly distributed above and below the prediction) and about 95% of the results should fall within 28 points on either side of the predicted result.

[thebootfitter]

Thanks to you for taking over during Hammersmith's hiatus, and for Audit as he continues his # crunching ways. BTW, did you know Hammersmith and I have the same last name? Esplaines his brainz.

Ha ha! I just noticed that, actually. He gotz all the brainz with that name, eh? That DOES make sense!

[Bison bison]

Because everyone knows that scores follow a normal distribution...

[thebootfitter]

Because everyone knows that scores follow a normal distribution...

They pretty much do, though. There's just a little bumpiness to the distribution because of the way points are scored, as Audit pointed out.

[bisonboone11]

You kind of touched on it a bit, but does Sagarin (or can it be extrapolated from there) explore the % chance of a certain spread happening? For example, and looking specifically at NDSU vs. UNI, there is a 9% chance NDSU wins by 24+, 19% NDSU wins by 17+, 38% chance NDSU wins by 11+, etc. I guess you would just have to pick some point breaks in the spread, say +1, +5, +10, +15, +20, -1, -5, -10, -15, -20.

Does my question make sense? I may have confused myself.

Audit, correct me if I'm wrong, but I believe you can use this calculator:

http://stattrek.com/online-calculator/normal.aspx

"Mean" = Sagarin's projected point spread (9.54 for the UNI game).
"Standard deviation" = Sagarin's standard deviation (13.86 or 14 if you want to round).
"Normal random variable" would be the desired spread that you want to check.
Leave "Cumulative probability" blank, as the calculator will give that as an output.
The way the website calculates it, the "Cumulative probability" that is given as an output is the probability that NDSU wins by the point spread or less or loses (multiply by 100 to get %). If you want the probability that NDSU wins by more than the point spread you input, take 1 minus "Cumulative probability" (multiply by 100 to get %).

[thebootfitter]

Audit, correct me if I'm wrong, but I believe you can use this calculator:

http://stattrek.com/online-calculator/normal.aspx

Yep, that's pretty handy! Works beautifully.

[EndZoneQB]

You won't regret the time away. I've disconnected a few times and it's not the worst thing.

[stevdock]

So I find it interesting that NDSU is only 5-4 against the spread. But the more interesting thing to me is how the standard deviation is calculated. At plus or minus 14 points, our games have been within the standard deviation 6 out of the 9 times (which is what's supposed to happen). The rest of them are within 2 st. dev's (which is also supposed to happen), but they are all on the low side (meaning -14 to -28 of the mean). Do you think that is normal?? Is it simply a product of our average just being too high to be able to cover by 2+ TD's??