I agree with Alan that Hyper is different enough in the game itself to be excluded from the average from certain aspects (eg, that it doesn't have the structural game play of the other variants) but for completeness and ease I think it should be included in any group measurement. Otherwise we'd have to examine each game to see whether it belonged with its fellows or was an outsider within its own clan. Which chess variants are not quite truly chess? The only exceptions I'd have are the anti- games which I think are almost an abomination under the eyes of Great Bunny.

Hauling out the old stats that I posted a while back...

Game ........... #1 ........... #20 ....... Average ....... Range ...... Players
Hyper ........ 2188 .......... 2120 ..........1960 ..........160 ........... 536
Back .......... 2431 ..........2210 ..........2002 ..........210 ........... 882
Nack ......... 2011 ...........1881 ..........1696 ..........185 ........... 257
Crowded .... 2081 .......... 1853 ..........1690 ..........163 ........... 202
Race .......... 2026 ..........1911 ..........1688 ..........223 ........... 234

You can see from the ratings of the #20 and the average rating that Nack, Crowded and Race are somwhat similar but not in terms of the range. Backgammon and Hyper are in their own camps. any average which was only an average would be skewed by the Backgammon rating. The only meaningful ways to produce a representative value are the ones that normalise the raw ratings before combining them, for example calculating the standard deviations of a player's ratings, averaging them and then multiplying by some factor to make it look like a rating again. I don't know the maths well enough to know whether that can be done incrementally after each match. It could be difficult keeping them up to date.


Just out of interest, here are the same figures now that we're two weeks into the new BKRs. The range for Hypergammon has shrunk by 7.5% and those for Crowded and Race expanded by about 6%, and Nack has expanded by over 8%.

Hyper ........ 2313 .......... 2122 ......... 1974 ......... 148 ........... 532
Back .......... 2441 ......... 2216 ......... 2008 ......... 208 ........... 898
Nack ......... 2108 .......... 1893 ......... 1693 ......... 200 ........... 252
Crowded .... 2086 .......... 1865 ......... 1693 ......... 172 ........... 198
Race .......... 2043 ......... 1932 ......... 1696 ......... 236 ........... 233