coan.net: It is very true that the BKR system is not accurate when applied to backgammon, but it is a common mistake to think that it is because of the luck factor. In fact, as alanback stated, it is because of the multi-game matches (cubed or not) that are counted like if they were one game.

There is no such thing as an absolute measure for skill. What the rating system can calculate is the "winning expectation", and that defines the skill difference. If I win more than 50% of the games against someone, then I am defined as stronger. If I win 90% of the games, I am defined as much stronger.

Now, and in a non quantifiable way, in some games the weaker player has more chances to win ; but these are not necessarily the ones where pure luck (e.g. dices) are involved. These are usually the short games, and the games that have a lot of forced moves. Less moves to think about mean less occasion to make mistakes for the weaker player. Of course the luck factor plays a role too, but it is one factor amongst others.

What will happen in games which offer good chances to the lesser player is not that ratings will be inaccurate, but that the rating scale will be shrinked. For instance, instead of scaling for 400 BKR to 2400 BKR, it could scale from 1200 BKR to 1600 BKR. The only undesirable effect is that as one game still carries the same BKR change, there will be more variation of the positions of the players. E.g., if I lose 10 points, I will lose 10 positions in the ranking list, because the players are all very close to each other.

If wished, this can be corrected as there is a "rating scale" constant in the BKR formula. But you can see that it is definitely not the problem in backgammon, where top players do have a lot more than 1600 BKR !

The real problem in backgammon is that matches count the same as single games. But if player A beats player B 60% of the time in single games, he may beat him 90% of the time in a 5-point match. Or whatever, I didn't do the math :-) Hence, rating-wise the matches favour the better player and the single games favour the lesser player. This is a real distorsion in the rating system, and you can indeed see that good players who play a lot of single games are considerably underrated - AlliumCepa comes to my mind, although he plays matches as well. On the other hand, people who play only matches are overrated. For example, me (but not for rating reasons, I just don't like playing without the cube).

The good news is that one knows a very simple way to adjust the BKR formula in order to take the length of the match into account. Basically, in a n-length match, one should just multiply the rating difference by the square root of n. As you can notice, this changes nothing to the way single games are counted.

This is not a specific backgammon formula, because it is not perfect for taking cubed matches into account, but perfect for taking "first to n points" matches of any game into account. In fact it should be applied to all games. If I start a rated 10-games chess match against a lower rated player, I am just getting some undue rating points. Of course, this is much more often done in backgammon than in chess, because the doubling cube can be used only in matches.

The bad news is that I told Fencer about that quite some time ago and while he didn't say no, he did not sound too hot about updating the rating system. Indeed I understand pretty well there are more important issues to settle first. After all, rating are just numbers, what is important here are the games !