Quote:
Originally Posted by T3_1565
what numbers were you using, if you don't mind me asking
and I am amazed we made the list haha!! not that we shouldn't be there....  |
Basically, it's what's called a least-squares estimation (also known as maximum likelihood). You apply a basic optimization technique to determine what set of numbers fits the data (all the alliance scores, in qualifiers, for a given competition) the best. "The best" means it gives the lowest sum of the squares of the errors. (Hey - I call my self
"Optimizer" for a reason!
).
For an example of an "error" from today's scores, in Q46 247, 1305, and 1565 were teamed up. From previous competitions, I had calculated ratings of 17.41, 10.04, and 25.55, respectively. So I would have expected you folks to score in the neighborhood of 17.41+10.04+25.55 = 53.00 points. You actually scored 88, so I'd say you had a great game. The "error" was 88-53=35 points (which is a fair amount larger than usual - usually, I think 20 is kinda big).
Anyway, if you think in terms of not having those ratings to start with, and SOLVING for them, so as to minimize the sum of the squares of these errors you would get for all the alliances in each qualifying match in the competition, that's what the method does. I know - it's complicated. You end up solving N linear equations in N unknowns, where N is the number of teams (66, in this case). I think it probably gives you a decent
guideline for how good a team is, to within (I'm guessing) maybe 3 pts, even though you can come up with all kinds of (legitimate) criticisms - for example, it doesn't account for the value of defense, or how well certain teams might work together.
Like I've said, though - at least it's objective, and it entertains a math guy like myself.
Unfortunately for me, I can't run today's results because I never did manage to install the software I need to run my code on this laptop, it seems like some of the teams have gotten significantly better, and there are 30 teams for which I have no previous ratings at all. I have to settle for seeing the results after the fact.
BTW: 1114 came out with 48.82 in Midwest and 73.06 in Waterloo.