I have noticed several times that the winner gains more points than the loser loses. Every time this happens, more ratings points get "fed" into the system, so to speak, so that there should be a direct correlation between average rating and overall number of games played, in that game.

Even at that, the average backgammon rating cited below strikes me as high. A rating of 2219 would rank you #14 out of 902 established backgammon players right now, and I am playing #451 (at the moment), so essentially, the median rating, and that individual is rated 2012. You're saying the average backgammon rating is 200 points higher than the median? There aren't that many people that are over 2200.

Are you counting every ridiculously high provisional rating into that average? That will skew your figures. Better to average just established ratings or to weight each average according to number of games played. Not that I would take that much time figuring all this out, but that would tell you more about the big picture.