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I am not really that interested in averages. I've encountered players that will maintain a high average, but still move slowly. Some people play games of one type rapidly, and of another type only when they're about to run out. Or they find the time to play 5 anti-backgammon matches in a day against their friend, and don't bother moving at their other games. High averages, but you don't really want to play them.
I propose the following statistic: given a game G a player has to move on, let TG the time it has been the players turn. (So, if today is Dec 27, and his opponent has last moved on Dec 24, TG is 3 days). Then let Tmax the maximum of all TG's of a player. A high Tmax means the person is moving slowly in at least one game at the moment. If his Tmax is close to when he last made any move, he's probably on vacation, or otherwise unable to play. If there's much difference between Tmax and when he was last active, he has too many games running then he can manage.
AbigailII: Such a single datum isn't really an improvement over an average. Consider our chess player with a 30-days chess game but who loves a quick game of backgammon.
I do think a time per match metric is better than a time per move one. Those 5 anti-backgammons with the friend would only be 5 matches rather than 500 moves and would therefore distort the average much less.
All: One think I'm not clear on, where is the information to be displayed and how and when is it to be used?
No offense to everybody, but this will never happen. Fencer does what he wants and he'd never take the time to study the math to do all that's involved here. I'm not speaking for him, of course, I've just been here long enough to know how he operates.
A better strategy would be to ask Fencer to give us access to player statistics (but no personal information) and then someone could program up any stats we want. You could have any or all of the ideas mentioned below. Since all the info relating to past moves and current games and such is already public (except for private games), Fencer would not be giving anyone access to information that isn't already available, so it shouldn't be a problem.
(gem) Hvis du vil spille et spil med en modspiller som er på omtrent samme niveau kan du lave en invitation med et ønsket BKR-område. Da kan kun de spillere med den BKR se og acceptere invitationen. (Katechka) (vis alle tips)