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ELO for a multiplayer game

Posted By: Maik Stiebler
Date: Friday, 5 October 2012, at 11:38 a.m.

In Response To: ELO for a multiplayer game (Bob Koca)

i) A game takes about 50 - 100 minutes so about same as a 9 pointer in backgammon in which k is 12. that is why I chose k = 12 but not sure what is an ideal choice. If I think Settlers has more luck I think that means a smaller k should be used but is 12 the "right" value for 9 point backgammon in some sense?

Inspired by Zare's and Stock's article, I'd say:

12 is not the "right" value, but one that is time-proven on backgammon servers. There used to be at least one backgammon server that used k=15 instead. I think that works well, too. The larger the k, the larger the ratings fluctuation (bad!) but the stronger the restoring force once you're rating is not in equilibrium (good! And that's why ramps exist, of course.) So every choice of a particular k is guided by a trade-off between those two arguments.

I don't think "more luck" should have anything to do with it. If approximately equally strong opponents meet, I'm not even sure what "more luck" means. What should matter is the variance of the possible results. I used to track my backgammon server rating using variance reduced results with k=20*sqrt(N) and that worked very well. Lower variance should come with larger k. Due to the multiplayer property of Settlers, the variance of the results is slightly reduced compared to backgammon matches.

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