All

The ELO topic stirred memories from Linear Algrbra, hence, the **DOMINATION MATRIX**: *used to rank competitors from the strongest to the weakest within a competition group* using the following scheme:

ALL competitiors compete against each other in such a way that each one is pitted against the others **exactly once**.

D = n x n Matrix {where n = number of competitors}

d = the row/column element(s) where d*i,j* = 1 if competitor i beats competitior j, 0 of this is NOT true

The strength of competitior i is the sum of the entries of the i'th row of D + D^2, ie mesures how many competitors i has beaten either directly or thru another competitior.

A domination matrix is useful to rank the strength of competitors where each competitior matches up one time against every other competitior. The domination matrix is a square matrix, where each element d(i,j)==1 IF competitior i beats competitior j, ELSE == 0, so the sum of row i gives the # of wins by competitior j.

The strength of the schedule is accounted for by squaring the matrix (D * D) and row i of this result sums all the wins by all the opponents that player i beats & the attendant RANK is the summ of row i of D + D*D.

This method gives greater reward for beating competitors that also did well without penalizing for losing to competitors that did poorly.

Curious how this compares to the ELO algorithim.

*Edited: 22 June 2013, 3:46 p.m. *