[James Kuszmaul]

I'm not sure if there is a good clean method which produces some sort of statistical standard deviation or the such, although I would be happy to be proven wrong.
However, I believe that the following method should give a useful result:

If you start out with the standard OPR calculations, with the matrix equation A * x = b, where x is a n x 1 matrix containing all the OPRs, A is the matrix describing which teams a given team has played with and b has the sum of the scores from the matches a team played in, then in order to compute a useful error value we would do the following:
1) Calculate the expected score from each match (using OPR), storing the result in a matrix exp, which is m x 1. Also, store all the actual scores in another m x 1 matrix, act.
2) Calculate the square of the error for each match, in the matrix err = (act - exp)^2 (using the squared notation to refer to squaring individual elements). You could also try taking the absolute value of each element, which would result in a similar distinction as that between the L1 and L2 norm.
3) Sum up the squared err for each match into the matrix errsum, which will replace the b from the original OPR calculation.
4) Solve for y in A * y = errsum (obviously, this would be over-determined, just like the original OPR calculation). In order to get things into the right units, you should then take the square root of every element of y and that will give a team's typical variance.

This should give each team's typical contribution to the change in their match scores.

added-in note:
I'm not sure what statistical meaning the values generated by this method would have, but I do believe that they would have some useful meaning, unlike the values generated by just directly computing the total least-squared error of the original calculation (ie, (A*x - b)^2). If no one else does, I may implement this method just to see how it performs.