Tracking Tote/Container/Litter per Match Using API

[Ether]

Originally Posted by Strants

Couldn't you find the per-match Tote/Auto/Litter/Coopertition/Containter/Foul from the system of equations

No. You can't find the per-match scores for Coop, Auto, RC, Tote, and Litter from the data FIRST provides.

You can find an estimate for the OPR for each of those scoring components as follows:

If [A] is the 2MxT binary matrix of the alliances (constructed from the match schedule), and [d] is the Tx5 vector of the Team Rankings component scores Coop, Auto, RC, Tote, and Litter, where M is the number of matches and T is the number of teams, then the OPRs for Coop, Auto, RC, Tote, and Litter can be computed by solving the system of Normal Equations

[A^T][A][OPR] = [d]

... for [OPR]


In fact, that's how it's currently being done this year (with some additional tweaking to account for surrogates and DQ's).

[Strants]

Originally Posted by Ether

You can't find the per-match scores for Coop, Auto, RC, Tote, and Litter from the data FIRST provides.

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.