[Ed Law]

I would like to spend some time to clarify regarding the different rankings OPR, DPR, CCWM and PMR (plus/minus ranking). I tried to explain this in another post but I was rushing and didn't explain fully.

If we look at the system of equations to calculate OPR, it is

A * OPR = B(opr)

B(opr) is assembled by adding the scores of every match each team was involved in

and the system of equations to calculate DPR is

A * DPR = B(dpr)

B(dpr) is assembled by adding the scores of the opposing alliance of every match each team was involved in.

The way I solve for CCWM is

A * CCWM = B(wm) = B(opr)-B(dpr)

A is the same matrix for all 3 systems of equations. I put the winning margin into vector B which is the same as vector B for OPR minus vector B for DPR.

The way PMR is calculated is to first calculate OPR and DPR separately. Then PMR = OPR - DPR

I don't remember the proper name of the math theory but since this is a linear system, you can do some kind of superposition such that

A * PWR = A * (OPR-DPR) = A * OPR - A * DPR = B(opr) - B(dpr)

Hence CCWM and PWR are identical numerically. This was confirmed by Jesse Knight. Having said that, once I have OPR and CCWM which is what my spreadsheet calculates, I can get DPR simply by

DPR = OPR - CCWM

Isn't math great? I learned all that and more when I was in college and there is some use for it afterall.

Ed Law