Hrqls:
Your study is good for the top 100 of all gammon types. But as you know, players of the gammon variants are not in the same quantities. (Click to http://brainking.com/en/Ratings for the latest members quantities.)

For example, today:
Backgammon: 895
Nackgammon: 251
Anti Backgammon: 61
Race Backgammon: 253
Crowded Backgammon: 209
Hyper Gammon: 521

The rating and BKRs self also goes up and down in some periods.

My offer is for the sampling method:

If we get the same percent for these games from their total players and then calculate the ratings and the BKRs for the players; we can get better performance results.

My offer is for the sample percent is: 20% enough good to be able to see the Masters of Gammon variants.

If this offer is acceptable generally, we can begin to calculate the following input numbers:

Backgammon: 895 x 0.2 = 189 players
Nackgammon: 251 x 0.2 = 50 players
Anti Backgammon: 61 x 0.2 = 12 players
Race Backgammon: 253 x 0.2 = 51 players
Crowded Backgammon: 209 x 0.2 = 42 players
Hyper Gammon: 521 x 0.2 = 104 players