[Ether]

Here is how I processed the data:

Step1

Create 2 whitespace-delimited text files for each event: one for the Rankings data and one for the Qualification Match Results data.

Step2

Run an AWK script which reads the Match Results data and creates the alliances design matrix [A], the alliance scores vector [b], and a vector [T] which maps the team numbers to consecutive integers. [A] is a 2MxT binary matrix (each element either 1 or 0), where M is the number of matches and T is the number of teams.

Step3

Run an AWK script which reads the Rankings data and the [T] vector, and creates a matrix [dr] whose columns correspond to the component scores and whose rows are ordered to correspond to the columns of the design matrix [A]

Step4

Run an Octave script which reads [A], [b], [T], and [dr], and does the following computations:

- [N]=[A']*[A] ....N will be a square symmetric positive definite TxT matrix
- [dm]=[A']*[b]
- [d]=[dm,dr]
- [x]=[N]\[d] .... "left division" solves for [x]
- [Tx]=[T,x]
- sort Tx by team and by OPR

... and writes the sorted [Tx] matrices containing the components scores, sorted by team and sorted by final score OPR