"standard error" of OPR values

[wgardner]

Originally Posted by Citrus Dad

The OPR measures the expected contribution per MATCH. We usually compute it for a tournament as representing the average contribution per match. So if we run the same match over and over, we would expect to see a similar OPR. The SE tells us the probability range that we expect the OPR to fall in if we kept running that match over and over. Confidence intervals (e.g. 95%) tell us that we have 95% confidence that the OPR will fall into this set range if we ran the same match (with complete amnesia by the participants) over and over.

OPR is not computed per match, it is computed per tournament (or at least based on a large number of matches).

We use OPR to estimate the score of an alliance in a match. Or to be even more precise, we compute the OPR values as the ones that result in the best linear prediction of the match results.

If we have an alliance run the same match over and over, we will see a variability in the match results and a variability in the prediction error we get when we subtract the actual match results from the OPR-based prediction. We can compute the standard error of this prediction error. This SE tells us the probability range that we would expect the match result to fall in, but doesn't tell us anything about the range that we would expect OPR estimates to fall in over a full tournament.

I'm confused by this sentence: "So if we run the same match over and over, we would expect to see a similar OPR." ???