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BGonline.org Forums
ELO for a multiplayer game
Posted By: Bob Koca
Date: Thursday, 4 October 2012, at 9:27 p.m.
I am in a group of about 12 people who play Settlers of Catan. In this game from 3 to 6 players can play. My guess is that the skill/luck ratio is roughly comparable to backgammon 9 point match but probably a litle more to the luck side(whatever that might mean).
Each player has a rating Ri (starting at 1500). Define Qi = 10^(Ri/400)
The expected points won in any contest for player i is Qi/ SUM(Q)
The ratings change is given as Ra' = Ra + k(Sa - Ea) where Sa is actual result from a game (or series of games) and Ea is the predicted result based on the expected points won equation.
I am thinking about k = 12 with a linear multiplier based on first 100 points of experience with k = 24 initially down to 12 after 100 experience. This means that a win in a 4 player game against equally rated opponents wuold gain one 9 points and the losers would lose 3 points.
I am wondering about a few things. 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? ii) Not sure how long a ramp period to have or how much it should be elevated initially. iii) Should the ratings be updated after every game or after every session or something else? I am not sure but I think that most local clubs that use an ELO system update after every match. I think it is better to update after each tournament though instead. My plan for now is to wait until several sessions (usually we play 2 games per session) before doing the first update.
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