What was the highest OPR possible?
Who had the highest OPR recorded?
What was the highest OPR possible?
1323 - 48.75 (Newton)
2910 - 46.99 (Newton)
1114 - 45.91 (Curie)
5460 - 45.15 (Archimedes)
Those are who broke 45 at Champs. Likely the highest.
Highest possible would be if you (1) finished all the tasks as an alliance every match (max score) and (2) all your alliance partners scored zero points in every other match. In that case, your OPR = max score.
I was guessing 50-60 as being an upper limit in this game based on reasonable expectations.
2056 had 52.64 at McMaster University
I used 16 cycles as a high water mark and came up with 60.
there was no upper bound this year because there is no max score (you can always get more penalties).
For a single event, 2056 at McMaster with 52.64 tops the list.
OPR represents the points a robot is expected to contribute to an alliance each match. So if a strong offense robot draws defense nearly every match, their OPR will be less than their maximum scoring capabilities.
ZPR (Zebra Power Rating) takes into account defense and offense under defense to calculate how much a robot would score with no interference. ZPR requires special UWB sensors on all robots, and we only have data from a handful of events. Consistent with your intuition, 2056 had a ZPR of 61.2 at IRI.
So, not sure how much others care, but the question of what the max OPR would be if there was a hard score cap (and no negative scores) is pretty interesting to me, here are my thoughts on it:
The max OPR is unbounded even if there is a hard score cap assuming a schedule has twice or more as many teams as matches (because the system of equations will be underdetermined). After that point, I think the cap is schedule dependant, but will roughly follow this shape (assuming a fair scheduling algorithm, it might be unbounded forever if you can construct ridiculous schedules):
All I know for sure is that there is a vertical asymptote at teams/2 and a horizontal asymptote at the max score. The chart above uses a power function of -1 but the actual max OPR is likely derived with a different power, or possibly not even a power function. Whatever the max is, it is certainly dependent on the number of teams, the number of matches, and the schedule. My hypothesis would be that in all cases where # of matches is not an integer multiple of (((# teams) choose 3)/2) then the max OPR will be greater than the max score, but that sounds like it needs a proof.
If you had every possible combination of teams play in a match ((40 choose 3)/2) matches = 4940 matches in a 40 team event, then the max OPR would be equivalent to the max score. This would be assuming your team scores the max in all of their matches and all other matches score 0 points.
If team X plays with every other team at the event, their max OPR is the max score (they score max points in all their matches, every other alliance scores 0).
If all matches either include team X or one of their alliance partners, their max OPR is also the max score (same scenario).
If there are matches in which neither team X nor any of their alliance partners play, their max OPR is higher than the max score (team X scores the max points in all their matches, other alliances that includes their alliance partners scores 0, other alliances that don’t scores the max points)
I haven’t thought of a mathematical proof for this, but I think it makes sense intuitively.
I disagree with both of these, I’ll see if I can construct a counterexample.
I can easily construct a counter-example for the second point. At Big Bang, team 5 or one of their partners plays in every match. Using the fake scores below, which are hard capped at 154, I can get team 5 to an OPR of 154.04. The boost is due to the blue score of 10 in match 4.
Big Bang fake schedule and scores
|match||blue 1||blue 2||blue 3||red 1||red 2||red 3||blue score||red score|
It’s going to be more difficult to construct a counter-example to the first claim because there are almost no events in which a team is partnered with all other teams. I think I may need to use the cheesy arena schedules.
It would be an amazing feat for 3604 to play in all of their 29 matches (sometimes playing against themselves).
Ugh, darn B teams at off-seasons. I’ll go find another counter-example.
Alright, I’ve got a much better counter-example now that covers both cases described by Rachel (and there’s no B teams to mess it up). Here is the schedule for the Mid-Mitten Roborodeo along with fake scores. Team 703 is partnered with every team at this competition, which covers scenario 1, and as such all matches must contain either team 703 or one of their partners, covering case 2. With these scores, team 703 has an OPR of 154.04, even though all scores are between 0 and 154.
mimm schedule and fake scores
|Match||Blue 1||Blue 2||Blue 3||Red 1||Red 2||Red 3||blue score||red score|
The additional 0.04 comes from the 10 points scored in match 4 by red.
An even simpler counterexample I found is the following 5 team 5 match “event” which disproved my first scenario, which I think can be extended to disprove them all:
Match 1 - teams 1/2/5 - 1pt
Match 2 - teams 1/3/5 - 1pt
Match 3 - teams 1/4/5 - 1pt
Match 4 - teams 2/3/4 - 1pt
Match 5 - teams 2/3/5 - 0pt
Which yields the following OPRs, which in this scenario is also the exact solution to the equations:
Team 1 OPR = 1.33
Team 2/3/4 OPR = 0.33
Team 5 OPR = -0.67
I think this occurs whenever the sum of alliance partners’ OPRs multiplied by the times the team plays with them is negative? That was definitely true when I randomly generated two team alliances, I’m not sure about three team. Also still not sure how to extend this to find the max possible OPR.
I wrote up a detailed answer to this question in my Blog Post. Short answer is that the maximum possible unpenalized OPR in 2019 was 269.4.