I'm very in to Sports analysis and am keen to look at finessing my analysis models that I have worked up  (I don't have a great maths background, I've just done a little bit of reading).

Standard deviation of Game Results about prediction from a Ratings system (in this case least squares regression with a few tweaks) equals the stochastic element in a normal distribution function where:

x = the margin of victory that you are trying to get a % against (e.g. it could be a point spread e.g. % to cover)
the mean = the predicted margin of victory derived in this case from my least squares regression to create power ratings for teams
sigma = standard deviation of error on the difference between the predicted margin of victory and actual margin of victory based on past results.

Based on the above I would treat in Excel terms a win % for team A as:

1-NORMDIST(0.5,mean,sigma,true) - with the mean and sigma having values obviously.

Based on Stern "The Probability of Winning an American Football Game" American Statistician (August 1991) - the sigma value (stochastic element? - sorry this isn't my usual thing) is approximately 13.86. How would you go about refining this for other sports? - e.g. Australian Rules Football. I said this could be done for any sport (and I believe it can within reason unless the results or the sport doesn't lend itself to this type of analysis).

Looking at past AFL results from the end of the season point of view the standard deviations are as follows (have only started looking at these in the last two days):

2009: 31.34 (150+ results)
2010: 33.44 (150+ results
2011: 34.91 (150+ results)
2012: 25.62 (only approximately 70 results so far as it is mid season)

As you feed more data into the model for 2012 it will build up a more accurate picture but looking at past data I'm putting the sigma value for AFL at around 33.5 (above the 25.62 value). Is there anyway of defining a best fit value? Where I don't have a great background in this kind of thing, if someone could give me some gentle nudges in the right direction in terms of where I should be looking or what I could be applying I would be grateful.

I believe this can definitely be applied to other sports as well e.g.:

English Premiership:

2008/2009: 1.45 (Season with over 300+ results)
2009/2010: 1.52
2010/2011: 1.54
2011/2012: 1.64 (but when looking over the last 100 results around the 1.50 mark)

I've also looked at the percentages that this then gives for home wins, away wins and draws and they are virtually identical to the percentages for bookmakers odds (except they work to 105-106% instead of 100% so they have an edge which accounts for the small differences).

NBA:

2008/2009: 11.30 (Season with 1000+ results)
2009/2010: 11.56
2010/2011: 10.88
2011/2012: 11.36

Thanks in advance for any advice,