[Ether]

Originally Posted by Nathan Streeter

OPR (Offensive Power Rating) is an approximation at how many points your team scores in the average match.

Mathematically speaking, it's an exact (and unique) solution to a least-squares problem.

I believe two equations exist for each match, one for the red alliance (A + B + C = X) and one for the blue alliance (D + E + F = Y)... in which A, B, C, D, E, and F are the teams on each alliance and X and Y are the match scores. If A and D competed with each other in a later match, two more equations might exist: A + D + G = R and H + I + J = S.

Good description, but replace the phrase "match scores" with whatever alliance metric is being analyzed.

I believe these equations are then approximated incrementally until values are determined for each team.

No iteration is necessary since the set of simultaneous equations is linear in the parameters. It can be solved directly without iteration by forming the normal equations for the system and then using matrix methods (this is how all the solvers I have seen here on CD do it). It can also be solved by using matrix methods directly on the design matrix without forming the normal equations. This latter method is numerically more stable and provides greater precision, but it is more computation-intensive and is overkill for this application.

For those interested in the math, a short explanation of the matrix math required to solve the normal equations is given here.