"Backgammon" is not mostly luck, or there would not be players with ratings as high as yours! An individual game of backgammon can be determined by the dice, but a player's overall success -- such as is shown by his rating -- is determined entirely by skill. In other words, since in the long run luck is the same for everyone, a player's RELATIVE degree of overall success has nothing to do with luck and everything to do with his or her ability.

right, in the long run it will tend to show the better players, though the luck aspect will mean the ratings will fluctuate more than a game like chess (my rating fluctuates between 1900 and 2100, whereas in chess versions it is relatively stable).

I'm sure you two guys are right about the luck aspect. The cream will always rise to the top eventually. The more games used for calculating the rating the better.