Error bar of OPR in Stronghold

[Whatever]

Stronghold was my first year as a mentor in FRC. I have been interested in the OPR statistic. One thing I have noticed is it commonly gets quoted to 2 decimal places which seems like way too much accuracy. So the question I have been asking myself is what is the error bar on OPR (at least for Stronghold)?


As a starting point I looked at the Einstein alliances. My thought process being those alliances have a bunch of matches together and their qual OPR would have the least oddities. I looked at division and Einstein matches where the 2nd pick of the alliance was on field and there were no red cards in the match (either side). I also assumed the alliance would breach and capture so the expected score for an alliance was the sum of the 3 OPRs plus 45.

The standard deviations of the actual scores averaged 24.6 for those alliances (min 18.2, max 34.3). The swing (max score-min score) of scores for each alliance averaged 77.9 points (min 55, max 107). 7 of the 8 alliances had an average score higher than their expected. 2 of the 8 alliances had an average score more than 30 points greater than their expected.


For a thought experiment, I created a spreadsheet that would calculate the OPRs of a small scale event. The event has 6 teams and each would play 10 matches. This meant every possible lineup is included. The match scores were the sum of 3 alliance OPRs plus a random +-25 points (roughly the average stdev of scores from the Einstein alliances). The true OPRs of the 6 teams was fixed at 60,50,40,30,20,10. After 126 events, the average OPRs for each team was under 1 away from their true OPR. The max error was just a shade over 17. Out of the 126 events, OPR had all 6 teams in the correct order 59 times. In 4 cases a team was above the team 2 places above them in true OPR.

I did sanity check the +-25 against the early week regional winning alliances. Backing out the breach/capture points, those alliances showed swings of 50 for those alliances over 6 to 8 matches. It should be noted, I used the random function in excel so the distribution of the randoms is flat and not gaussian.

So I would estimate the error bar on OPR (for Stronghold) at around 15.

Does that seem to align to other people's thoughts?
Has anyone tried to do an analysis on this?