Standard Deviation From The Spread In NFL

**pedro803** · 09-26-10, 07:11 PM

I am not sure what you mean, could you explain a little more about what you are trying to do. I think a standard deviation would be something you would get from looking at a sample of results, so for example, you could have a bunch of spreads and the actual results of the games and then compute the standard deviation of the distance between the spreads and the actual results, but if I understand the concept of standard deviations correctly you can't compute, or look up on a chart, the standard deviation of a single number -- a standard deviation is something you would use to describe a sample.

I'm not completely sure about this, but I think I have stated it correctly -- hopefully someone will jump in and clear it up. In the meantime, Sportslover it might help if you would describe for us exactly what you are trying to do.

**Sean81** · 09-26-10, 10:32 PM

A standard deviation assumption of 13 is very accurate for the NFL.

**Sportslover** · 09-27-10, 12:21 AM

Ok let me explain a little further, Pedro.

I am using a Normal Distribution (not sure if this is accurate or not) to predict if a team will beat the spread. So the point spread is "x", the "mean" is my model's estimation of how much the team will win by and now I need to find "sigma" which is the standard deviation from the spread (historically).

I will use the last 5 years of NFL results to find the historical standard deviation from the spread to input into my Normal Distribution for this season. Should I be using the standard deviation from the spreads generated by my model for the past 5 years or should I be using the standard deviation from the spreads from Pinnacle in the last 5 years?

**Sportslover** · 09-27-10, 12:22 AM

Originally posted by Sean81

A standard deviation assumption of 13 is very accurate for the NFL.

Is that based on the margin of difference from the Sportsbook spreads?

**Peregrine Stoop** · 09-27-10, 01:02 AM

Originally posted by Sportslover

Ok let me explain a little further, Pedro. I am using a Normal Distribution (not sure if this is accurate or not) to predict if a team will beat the spread. So the point spread is "x", the "mean" is my model's estimation of how much the team will win by and now I need to find "sigma" which is the standard deviation from the spread (historically). I will use the last 5 years of NFL results to find the historical standard deviation from the spread to input into my Normal Distribution for this season. Should I be using the standard deviation from the spreads generated by my model for the past 5 years or should I be using the standard deviation from the spreads from Pinnacle in the last 5 years?

you should chuck out your model and start over. Points aren't scored nicely in the NFL. They chunk with 3s and 7s. This puts the normal curve out to pasture of the short run of a football game.

**Sean81** · 09-27-10, 01:45 AM

Originally posted by Sportslover

Is that based on the margin of difference from the Sportsbook spreads?

Yes in aggregate. Point spreads that are low or unusually high will have different risk profiles. I imagine the total also has an impact but I'm not completely sure.

Peregrine brings up a good point in that scoring is not continuous, so using standard normal distribution tables to determine probability would be accurate.

**Sportslover** · 09-27-10, 01:52 AM

Originally posted by Sean81

Yes in aggregate. Point spreads that are low or unusually high will have different risk profiles. I imagine the total also has an impact but I'm not completely sure. Peregrine brings up a good point in that scoring is not continuous, so using standard normal distribution tables to determine probability would be accurate.

I think you meant to say inaccurate, judging by what you said before that.

So I guess my next question would be, what is a more accurate method to use to determine probability if a normal distribution is not workable?

**Sean81** · 09-27-10, 02:34 AM

Thanks I meant to say inaccurate.

I have no experience with modeling, so I am not the best person to answer your question. However, if I were trying to do what you do what you are, I would come up with data for every point spread. For instance, for every game with a closing line of 3, the mean of the difference of final margin and 3 is 0 with a standard deviation of s (lets say 10). I would guess that the data is normally distributed when isolating a single point spread.

Lets say New England is -3 and you have them capped at -13 the probability of a cover is 66%.

This is probably wrong but someone else on here will have more experience with it.

**Sportslover** · 09-27-10, 02:44 AM

Originally posted by Sean81

Thanks I meant to say inaccurate. I have no experience with modeling, so I am not the best person to answer your question. However, if I were trying to do what you do what you are, I would come up with data for every point spread. For instance, for every game with a closing line of 3, the mean of the difference of final margin and 3 is 0 with a standard deviation of s (lets say 10). I would guess that the data is normally distributed when isolating a single point spread. Lets say New England is -3 and you have them capped at -13 the probability of a cover is 66%. This is probably wrong but someone else on here will have more experience with it.

Thanks for the input, I think I understand what you're saying, although I got 84% probability of covering for the same example...

**Sean81** · 09-27-10, 02:59 AM

84% is right, I thought my number looked too low.

**That Foreign Guy** · 09-27-10, 04:48 AM

Originally posted by Sean81

A standard deviation assumption of 13 is very accurate for the NFL.

13.87 for the last three seasons.

However it is really really lumpy. I don't know how to format it nicely but the numbers are below:

Score vs Closing Spread Count -41.5 1 -40.5 1 -37.5 1 -36.5 1 -36 1 -35.5 1 -31 1 -30 1 -29.5 1 -29 3 -28.5 1 -28 1 -27.5 1 -27 2 -26.5 5 -26 1 -25.5 2 -25 3 -24.5 2 -24 1 -23.5 1 -23 3 -22.5 1 -22 2 -21.5 5 -21 1 -20.5 2 -20 3 -19.5 3 -19 2 -18.5 3 -18 9 -17 9 -16.5 4 -16 4 -15.5 3 -15 5 -14.5 8 -14 3 -13.5 8 -13 11 -12.5 10 -12 3 -11.5 3 -11 8 -10.5 11 -10 15 -9.5 11 -9 11 -8.5 11 -8 7 -7.5 5 -7 20 -6.5 14 -6 20 -5.5 3 -5 6 -4.5 7 -4 14 -3.5 12 -3 6 -2.5 6 -2 14 -1.5 8 -1 18 -0.5 10 0 20 0.5 7 1 18 1.5 7 2 9 2.5 9 3 12 3.5 11 4 20 4.5 8 5 10 5.5 6 6 10 6.5 6 7 12 7.5 8 8 9 8.5 4 9 12 9.5 3 10 7 10.5 4 11 6 11.5 3 12 11 12.5 7 13 5 13.5 5 14 10 14.5 6 15 6 15.5 9 16 4 16.5 3 17 2 17.5 11 18 7 18.5 4 19 5 19.5 3 20 9 20.5 4 21 5 21.5 3 22 5 22.5 2 23 3 23.5 1 24 6 24.5 3 25 2 25.5 3 26 3 26.5 1 27 3 27.5 2 28 1 28.5 1 29 2 29.5 1 30 2 30.5 2 31 2 31.5 1 32 2 34 1 34.5 1 36 1 37 1 39.5 1 50 1 Grand Total 768