ELO - Domination Matrix
Message #1 Posted by Kimberly Thompson on 21 June 2013, 5:34 p.m.
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 di,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.
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