algorithm - Elo rating system without order of game played -

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i looking rating system similar elo rating system in chess. problem have elo system depends on order games played. eg. player starting elo 1000 player b starting elo 1000

if player b wins on have lets 1015 points , 985.

if keeps on playing , wins against other people, have higher ranking b, if b stops playing. don't want that. b should still stronger a.

how can realise that?

there number of schemes amount writing down win/lose/draw record matrix , typically calculating largest eigenvalue of matrix related this. 1 summary @ http://java.dzone.com/articles/ranking-systems-what-ive, points more technical papers including https://umdrive.memphis.edu/ccrousse/public/math%207375/perron.pdf - "the perron-frobenius theorem , ranking of football teams".

if can more information out of game win/lose/draw might better using this. work on soccer has used number of goals , against @ each match try , work out strengths of each team's offense , defense separately (and realise soccer doesn't have separate offensive , defensive teams). in soccer reasonable model number of goals scored poisson process. 1 deduction this, way, soccer inherently pretty uncertain game, , predicting score draws, required in gambles, uncertain. try , remember inevitable uncertainty every time england play game :-).


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