After 5 rounds of the 2010 London Chess Classic, 3 players share the lead. Anand and McShane have 2 wins, and 3 draws, while Carlsen has 3 wins and 2 losses. Of course the fact that they share the lead is a result of the 3-1-0 scoring system, which has provoked a degree of discussion in the chess world.
While this may seem to be a new debate, in a sense it is a topic that has been around for quite a while. Not in the direct sense of how many points should a win be worth compared to 2 draws, but in the indirect sense of what is a win worth when discussed in connection with tie-break systems.
In the Sonnenborn-Berger system the tie-break score is sum of the scores of the opponents you beat plus half the scores of the players you draw with. What of course is missing from this total is the scores of the players you lose to. It turns out that you get a better tie-break by losing to weaker players and beating stronger ones, meaning that losing to strong players has a bigger impact than beating weak ones. This has never seemed quite right to me, but I've never seen a way of fixing it up (if S-B does need fixing at all).
Of course 1-0.5-0 or 3-1-0 aren't the only way to score results. One suggestion is a 5-2-0 system, which if used in London would have Anand and McShane a point in front of Carlsen (which some people think is fair). However if you look at such proposals properly you will soon discover that scoring systems using 2n+1 - n - 0 points are the same as 1-0.5-0 if n becomes large enough. So if you travel down this road you may as well not travel at all.
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3 comments:
"It turns out that you get a better tie-break by losing to weaker players and beating stronger ones, meaning that losing to strong players has a bigger impact than beating weak ones. This has never seemed quite right to me, but I've never seen a way of fixing it up"
I wonder whether using "performance rating" as a tie-breaker would work, as that seems similar to what you're describing. (I.e., let Elo sort it out?)
I think performance rating isn't meaningful in a round robin (which is what Shaun is discussing) as two tied players have an identical score against an identical field except that the higher rated of the two has played the lower rated and vice versa - hence the lower rated always comes out on top by virtue of having the lower rating.
You could use performance rating against players who score over 50% as a tiebreak system.
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