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 At least in my somewhat-outdated database, these were the average statistics for all classical games where both players were 2700+ FIDE.)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).