[Ether]

By request, attached is a chart that shows the RMS of the OPR residuals vector vs number of matches N played at MSC Quals.

A is the 256-by-64 binary design matrix of the alliances in Qual match schedule.

b is the 256-by-1 column vector of alliance scores for those Qual matches.

x is the 64-by-1 column vector of OPR values based on the first N matches in the Qual schedule. For MSC, N varies from 32 to 128. For N less than 32, the A matrix is singular.

For each of the 97 OPR vectors (for N=32 to 128), the RMS value of the vector of residuals Ax-b is calculated and plotted vs N.