Quote:
Originally Posted by JewishDan18
I'm toying around with calculating OPR, but I'm running into something of a road block. The matrix of team pairs is supposed to be diagonally dominant, and thus invertible, but I don't see how this is. If Team A played with two other teams in only one match, the diagonal element would be 1 and there would be two other 1's in Team A's row. This row alone would violate the conditions for diagonal dominance. I know I'm missing something simple, does anyone have any pointers?
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For the OPR equation Ax ~= b where:
A is a match-team matrix where the rows of A are half-matchs, the columns of A are teams, a 1 indicates that the team represented in that column participated in the half match indicated by the row, and a 0 indicates that the team represented in that column did not participate in the half match indicated by the row.
x is the column vector where the values in each row indicate a unique team's OPR, arranged in the same order as are the columns in A.
b is a column vector which represents the half-match scores at the event.
A is not generally square, so the idea of diagonal dominance is generally meaningless.