ELO - Domination Matrix - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: ELO - Domination Matrix (/thread-245402.html) ELO - Domination Matrix - Kimberly Thompson - 06-21-2013 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.