03 October 2009

Chess Ratings as a Predictor of Chess960 Skill

After writing the short post on Chess960 @ Chess.com, I spent some time reading relevant threads on Chess.com's chess960 forum. A few of them touched on points that I hadn't encountered before, and immediately caught my interest.

The first post that interested me was "Rating too low to accept this match!" Are you kidding me!?. The initial point of the thread was a complaint about how Chess.com uses ratings to match players who have requested a game with upper/lower limits on the ratings of potential opponents. It seems that traditional chess ratings are used in the algorithm for chess960 games. I assume this is done because the chess960 service was introduced on the site a few months ago and there were no chess960 ratings.

If that were the only point in the thread, I wouldn't bring it up here. More relevant were the following comments by ReLentLess5150, who was also the originator of the thread.

'I sincerely doubt that the so-called "higher rated players" in chess 960 have as huge an advantage as the might in standard chess.' • 'Do you HONESTLY believe that ratings play that much of a role in 960!?' • 'Chess 960 is basically a free for all, and I would hazard a guess and say that the odds of a low rated versus highly rated player [at traditional chess] are probably pretty low, 1400 versus a 2200. Who would you put your money on? On the other hand, I would give the 1400 at least even money in 960.'

Despite ReLentLess's apparent unfamiliarity with the rating system -- a 1400 has almost zero chance of winning a traditional game against a 2200 (see the table 'Rating expectancies vs. differences' at the end of Chess Ratings for the odds at different rating spreads) -- the writer raises some good points.

If we're talking about chess960 ratings that have been computed only on the results of chess960 games, then the chess960 rating will be just as good a predictor of future chess960 results as the chess rating is for traditional chess results. This has nothing to do with skill at chess; it's a result of the statistical and mathematical foundation of the rating system. As Elo pointed out, his rating system is valid for any two-player competition, whether fencing, boxing, or cribbage.

Of course, cribbage ratings have no predictive value for a chess game between the same pair of adversaries, just as chess ratings have no predictive value for a boxing match. The more pertinent question is whether traditional chess ratings have any predictive value for a chess960 game. I am certain that they do.

Suppose our 1400 player survives into an endgame against the 2200 player. As I pointed out in Differences Between Chess and Chess960, a chess960 endgame is 'usually indistinguishable' from a chess endgame. I said 'usually' because we can imagine some chess960 endgames where a Bishop might be in the corner, still blocked on the diagonal by a Pawn of the same color. That is obviously the result of a chess960 opening.

What chance does the 1400 player have against the 2200 in the endgame? A little better than in the earlier phases, because the position might peter into a theoretical draw (assuming the 1400 recognizes the opportunity and steers for it), but in general, the 2200 will win due to a better grasp of endgame principles and general superiority in accurately calculating long variations.

Now suppose the 1400 player reaches a middle game against the 2200. It is very unlikely that the 1400 is going to survive that phase. The 2200 has a superior ability to calculate tactics, a better understanding of positional play, a greater familiarity with combinations, and a wider knowledge of stock positions. One, if not several, of those advantages will result in a win for the 2200.

If the 1400 is totally outclassed in both the endgame and the middle game, that leaves the opening. Unlike the 'free for all' that ReLentLess imagines, the opening is exactly the phase where the 2200's superior knowledge of positional play is likely to swamp the 1400 even before the pieces are fully developed. The choice of castling (less obvious in chess960 than it is in chess), the effective deployment of the minor pieces, and, above all, the choice of a game plan are going to leave the 1400 hopelessly confused.

The example of a 1400 against a 2200 is just that: an example. The statistical advantage of the higher rated player is the same across the entire rating scale. The example might have been a 2200 against a 2700, where the same table of 'Rating expectancies vs. differences' predicts a 96% winning chance for the higher rated player.

I'll go even further in my claim that chess ratings are good predictors of chess960 results. In chess960 the lower rated player can no longer hide behind the shield of memorized opening variations and will make a mistake even earlier than in a traditional chess game. That means the higher rated player has a greater statistical chance of winning the game, meaning that the chess960 rating difference between the two players will be even greater than the difference in their chess ratings. Chess is, after all, a game of skill rather than a game of chance, and so is chess960.

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