In short, I don't have a great maths background but have always mucked about with modelling sports and making predictions (as I enjoy it).
I have always used the Hal Stern "The Probability of Winning an American Football Game" American Statistician (August 1991) - as a basis for this, assuming things were normally distributed (possibly incorrectly) and adding other little modifiers (e.g. homefield advantage) and then solving it in a least squares puzzle in Excel.
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.
This when solved (in Excel - I think you could do it with matrices as well) derives me ratings which can then be broken down further to work out an offensive and defensive component so you can work out scores.
This seems to work OK (as a rough approximation) for sports with no fixed score (e.g. NFL, NBA, Australian Rules Football, Rugby). I have a new interest in Vollyball however which has a fixed maximum score of 3 sets wins the game. I ran this process on the current Italian Volleyball league and whilst I was trusting the ratings that came out the scores didn't make sense (e.g. one game was predicted 1.5 vs 1.8).
Is there a work around that could be applied here (as I believe it is possible e.g. the Ken Massey, Massey ratings site models Volleyball) as I couldn't see anything obvious.
Thanks in advance for any advice or suggestions.