In my last post, What’chu Talkin’ ‘Bout Willis?, I suggested a framework for a new Candidates Cycle. It was partly based on the current model, with a series of qualifying events and then one-on-one matches. The big proposal was to solve some of the problems I saw in the current match cycle by incorporating draw-odds for the higher-seeded player, along with an extra-white for the lower-seeded player. (It’s explained in more detail in the original post, but the series of qualifying events would provide the top half of the seeds.)
In the comments section there, Dan Schmidt suggested that using the draw-odds/extra-white might not combine to create a scenario in which the draw-odds advantage was not overly large. Someone posted a link to that entry on the ChessPub forums, and “Symslov_Fan” responded along similar lines, saying that the draw-odds advantage is too large.
At the time of my first post, I hadn’t done any simulations to figure out what sample odds might be in such a scenario, but I began doing that last week. Then David Krantz (a statistics professor at Columbia) had an article published on ChessVibes that looked in more detail at some stuff I was just doing myself. His article can be seen here.
I had assumed some different result-probabilities, but one basic conclusion is the same – matches of 4 games aren’t markedly different than matches of 6 or 8 games when it comes to the odds of having a clear winner in the classical portion.
(I used a model where the chances for each player were the same with white, namely 24% win, 64% draw, and 12% loss. At least in my somewhat-outdated database, these were the average statistics for all classical games where both players were 2700+ FIDE.)
Anyways, here’s the summary table for “short” match lengths:
So longer matches help, but there are diminishing returns. Certainly 6 game matches are more likely than 4-gamers to produce a decisive match, but 27% still seems quite high to me. As explained in the last post, I’d rather avoid quickplay tiebreaks for the classical title, while promoting more fighting chess. Completely risk-averse play from both players (a la Kramnik-Radjabov) can be seen in an 8-game match too after all.
Using the same result-probabilities, here are the simulated results for matches where one player has draw-odds while the other has an extra white:
Pretty much all 3 lengths give the higher-seed near a 60% chance of advancing. Of course, this assumes that both players are identical in terms of their result-probabilities, so in the real world, the odds would probably be different. For example, if the lower-seed is relatively better than that with white, while the higher-seed is relatively weaker with black, the draw-odds advantage decreases. From a quick look, this is a few percentage points more than what home-field advantage usually confers in major sports.
In his article, Krantz breaks down the complaints into five categories:
“(i) Uninteresting: the large number of short draws detract from spectator and subsequent reader and historical interest.
(ii) Unsporting: the short draws suggest lack of serious effort.
(iii) Excessive role for luck: the ‘best’ challenger has a poor chance of winning, because too much depends on luck in short matches.
(iv) Excessive reward for ultra-cautious play by the weaker player: In longer matches, an ultra-cautious strategy, such as the one I attributed to Grischuk, would have little chance of success, and therefore would not be used.
(v) Departure from ‘classical’ chess: the winners are determined by methods that are not valid indicators of superiority in slow-play chess; just as in point (iii), the “best” challenger may not win.”
He suggests slightly longer matches to try and reduce (iv), and thereby possibly reduce the other four complaints. My suggested 5- and 7-game matches would actually feature the same number of black games for the higher-seeded player as 6- and 8-game matches, while further ameliorating the other four complaints in my view.
It was also suggested in the comments to give the higher-seed the option of draw-odds or extra-white, but it’d be a very strange scenario where the higher-seed would want to take the extra white over draw-odds. Just spot-checking a few of the Candidates in this cycle, nobody would have come close to flipping these results around.
Radjabov as a 2700, against other 2700s for example, is heavily inclined to draw: with white, he wins about 18% of the time, draws 77% of the time, and loses 5% of the time. Meanwhile, as black, he wins 20% of the time, draws 63% of the time, and loses 17% of the time. His drawing percentage was the highest of any of the candidates, and frankly, the boring nature of Kramnik-Radjabov should’ve been expected, as besides Radjabov, Kramnik was next in line with the highest drawing percentages (31%, 63%, 6% as white; 17%, 73%, 10% as black).
If I understand correctly, these analyses implicitly treat each game of a match as an independent event. That is not a correct assumption. In particular, the first win by either side will significantly change the dynamics of play, throwing off all the math.
If it’s this difficult to get matches to work – not to mention the challenge of finding Western sponsors – perhaps the answer is staring us in the face: sayonara, elimination matches! Let’s join the rest of the sporting world and embrace World Championship tournaments, once and for all.
Yup, both my numbers and the ones in Krantz’s article assume independence (and stationarity). I guess you could use a Markov chain to model the changes along the way, but that’s a lot more work and this wasn’t meant to be that rigorous.
Doesn’t the sporting world use matches as well? The 4 major American sports all have head-to-head playoffs, and generally use the regular season results to determine home-field advantage. The Champions League is round-robin followed by match play. Same with the ATP Tour Finals in tennis.
I think that a match in which every game is decisive (baseball teams, for instance, play for a win in every game) is fundamentally different from a (chess) match in which draws are relatively easily attainable.
In a fixed length chess match, if you’re up by one game, to say nothing of two or three, you can draw your way to victory. If you’re up 3-0 in the World Series, well, you still need to win another game.
Hmm, that’s true that a draw is much more likely. I’m not sure about just drawing your way to victory though. If both players are fine with a draw, then they can choose an opening and a variation that is conducive to that. I’m not sure it’s necessarily so simple to draw otherwise. I’m sure there are many examples, but one that comes to mind is from Leko-Kramnik, where Kramnik was down 1 with 2 to go. He played the Benoni and had serious winning chances, although he didn’t make the most of them and only drew.
In any case, if you’re ahead by enough points, the same strategy comes into play in tournaments too. After Topalov’s 6.5/7 start, he drew all 7 games in the second half of the San Luis WCh tournament. He could afford to do so (and nobody was strong enough to bother him there after round 1) because he showed some amazing play in the first half. If you’re so much better that nobody can touch you or catch you, that’s fine by me.
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