RMS of OPR residuals at MSC

*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.

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

WAMOU had only 28 teams and there were 56 Qual matches.

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Any chance you could do the same, but leave out the residuals of the previous matches? I doubt it would differ very much, but it’s the real life situation: after X matches, how far off are the rest of the predictions going to be.

*Attached is a chart for MSC that shows the average of the absolute deviation of the partial OPR vectors (based on the first N qual matches) compared to the final OPR vector.

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After posting the first 2 graphs, I decided that a more intuitive way to see what’s going on (for FRC purposes) might be to compare the partial OPRs (based on the first N matches) to the final OPR. This way it’s easier to see how the partial OPRs are converging to the final OPR.

*WAMOU average of the absolute deviation of the partial OPR vectors (based on the first N qual matches) compared to the final OPR vector.

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*SCMB average of the absolute deviation of the partial OPR vectors (based on the first N qual matches) compared to the final OPR vector.