Quote:
Originally Posted by Ether
You can't find the per-match scores for Coop, Auto, RC, Tote, and Litter from the data FIRST provides.
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Hmm, it looks like that's correct: the system of equations I provided is (in most circumstances) underdetermined.
However, it looks like in many instances (specifically, when the number of matches is at most twice the number of teams) we should be able to differentiate between coopertition points and points scored through totes, litter, and recycling. We can do so with the following system of equations:
M_(r,i) = a_(r,i) + p_(r,i) + t_(r,i) + c_i
M_(b,i) = a_(b,i) + p_(b,i) + t_(b,i) + c_i
T_(j,c) = sum c_i (P_(r,j,i)+P_(b,j,i))
T_(j,t) = sum (t_(r,i) P_(r,j,i) + t_(b,i)P_(b,j,i))
where M_(r,i) (respectively, M_(b,i)) is final score of the red (respectively, blue) alliance, the a and p represent the autonomous and foul points (each of which is given), t represents the non-coopertition points (Tote, Litter, and Containter), c represents the coopertition points (since these are shared between the red and blue alliance, there is no need to distinguish between c_(r,i) and c_(b,i)), and P(r,j,i) (respectively, P_(b,j,i)) is 1 if team j was a non-surrogate, non-disqualified member of the red (respectively, blue) alliance in the ith match. Altogether, for 2M half-matches, we are estimating 3M parameters (1 t value per half-match, and 1 c value per pair of half-matches) from 2M+2T data points (the score data from M matches, plus 2 pieces of ranking data about the total coop and non-coop points scored by a team), where M is the number of half-matches and T is the number of teams. We have an over- (or exactly) determined system provided 3M <= 2M + 2T, or if M <= 2T.