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-- Dylan Thomas
One of the services IAGO will seek to provide is a central location to record games played (providing this information for statistical analysis and perhaps providing our own) and a central authority for game ratings/rankings. This would allow for pan-clubhouse ladders and tournaments. This document attempts to outline requirements for such a service.
Everybody's ratings would be regenerated for a particular game whenever a new game record is added. The total regeneration allows for auditors to modify any record in the system and have the ratings reflect that. Such a generation could be done on a daily basis if processing time became an issue. The system would simply take each record for a specific game in “Game End” order and calculate ratings. This would also allow us to completely change or add new rating systems accurately.
I propose the following ranking system as the default. (See old revisions of this document for a different approach.)
The rating system should allow for more than 2 players. While Microsoft's TrueSkill is pretty interesting, I am personally not in a place to figure out how to implement it. I think ELO can be extended to allow for more than 2 participants. A game with 4 players, for example, would be processed as a 6 separate duels (A over B, C, and D; B over C and D; C over D). The resulting ratings are then averaged and posted. Here are some 4-player examples:
Start: --- - 1200 - 1200 - 1200 - 1200 Final: --- - 1216 - 1205.33333333333 - 1194.66666666667 - 1184 Deltas: --- - 16 - 5.33333333333326 - -5.33333333333326 - -16
Start: --- - 1200 - 1400 - 1400 - 1150 Final: --- - 1220.77899451613 - 1399.27397760856 - 1388.60731094189 - 1141.33971693341 Deltas: --- - 20.7789945161337 - -0.726022391439074 - -11.3926890581058 - -8.66028306658882
Discussion
Can we break this up into phases doing the rankings first, and so on?
I'm not sure how. All the math depends on having game records, and once you have the game records, the rest is quite trivial. The first part is the hardest.