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A few days ago I published my own pre-tournament odds (based on statistical analysis) for all of the participants in the FIDE World Championship tournament in Tripoli, Libya. The first of seven rounds is now complete. Although there were not many notable first-round upsets, the odds of winning the tournament have nevertheless changed significantly, due to several factors.
For one thing, the last-minute withdrawal of #2 seed Alexander Morozevich definitely skews the odds. Several players have a clearer path to the semifinals now that Morozevich is out of the picture. The withdrawal of #13 seed Vadim Milov, and the first-round upset of #24 seed Krishnan Sasikiran, also have an impact (though less severe).
In addition, the July FIDE ratings were released last week in preliminary format, providing some additional clues about which tournament participants might be under-rated or over-rated, since the seedings were derived from the April rating list. By investigating the various rating lists, including the June list of Professional Ratings (an alternative rating list known to be more sensitive to recent results than the FIDE ratings) it is possible to identify several players who probably deserved a different tournament seeding from what they actually received.
Taking the various rating lists into consideration, and adjusting for the Round 1 results, here are the updated tournament-winning chances, going into Round 2:
You might notice that #7 seed Vladimir Malakhov is missing from the list of tournament favorites, although he has not been eliminated. Malakhov received a considerable rating penalty in my calculations, due to his low placement in the Professional Ratings (#35 in the world) and the latest FIDE list (#30 in the world). Based upon those lists, he probably merited a tournament seed somewhere between #15 and #20, rather than #7, and so my calculations only give him one chance in sixty to win the tournament.
Also worth mentioning is Etienne Bacrot, who has vaulted to fourteenth in the world on the latest (preliminary) FIDE list, going from a rating of 2675 to 2712! This 37-point gain almost looks like a calculation error to me. Normally such a large increase would be accompanied by an even larger jump in the player's Professional rating (since Professional ratings tend to be more dynamic). However, Bacrot's Professional rating has only increased by 11 points since the start of the year, despite his (preliminary) FIDE rating increasing by almost 50 points over that same time. Seems kind of odd. Nevertheless, when you combine this new rating for Bacrot with the absence of Morozevich, who was Bacrot's likely 4th round opponent (assuming no upsets), then we find that Bacrot's chances of winning the tournament have nearly tripled since I wrote my original pre-tournament article (back when I was using the older FIDE ratings and assuming that Morozevich would be playing).
The main beneficiary of the first-round upset of Sasikiran appears to be #9 seed Ivan Sokolov, who would have faced Sasikiran in the 3rd round (assuming no upsets) and instead will face a much lower-rated opponent if he does make it to the 3rd round. Sokolov now seems to have one chance in twenty-five to win the tournament, just barely the best chances of anyone rated below 2700.
Moving further down the rating list, you might be looking for a long shot to bet on, perhaps on a website like betsson.com. Although I would caution you that my odds are strictly statistical and contain very few subjective factors, I would like to point out that there is exactly one player rated below 2650 who has better than a 1% chance to win the tournament: #34 Levon Aronian, with odds of 42-to-1 against.
Aronian has several considerations in his favor. For one thing, he does quite well on the latest rating lists, showing up with the 20th-best Professional rating among all Tripoli participants, and he is projected to gain 26 points on the next FIDE rating list. As the #34 seed, he was already benefiting from the absence of Morozevich (since Morozevich's most likely opponents in the third round would be the #31 seed or the #34 seed) but the Round 1 results were even more kind to Aronian: one of the highest-rated players to lose was #31 seed Giovanni Vescovi, who would have been Aronian's Round 2 opponent. Normally the #34 seed would face a higher-rated opponent in all rounds after the first one, but now Aronian is guaranteed to be the favorite in both his 2nd round and 3rd round matchups (assuming he gets that far).
With Morozevich not playing, the 2700+ crowd is now down to five: Topalov, Adams, Grischuk, Ivanchuk, and Short. Of the five players, Short's chances seem to be the least promising, because he has dropped down on the latest rating lists that I have used in my own calculations. There was a large gap between #6 Short and the sub-2700 participants on the original pre-tournament FIDE rating list, but he has fallen out of the top-twenty on the latest FIDE list, and the Professional ratings tell a similar story.
Clearly, this tournament could realistically be won by any of a large group of players. At this point, it appears that the tournament outcomes can be roughly split into three different possibilities, each of which has approximately equal chances to happen. You can see this on the pie-chart, where the dark gray slice takes up about a third of the area, and the combination of blue+red+yellow+white takes up about a third, and the other nine colors take up the remaining third.
(Group 1) There is a 36% chance that the tournament will be won by one of the four top seeds: Veselin Topalov, Michael Adams, Alexander Grischuk, and Vassily Ivanchuk. According to the latest rating lists, those players all have an estimated strength between 2710 and 2750. I don't mean anything particularly fancy by "estimated strength". I'm just talking about their latest FIDE rating, averaged with their Professional Rating if available (although you have to add 55 to a Professional rating to align it properly with the FIDE list).
(Group 2) There is a 31% chance that the tournament will be won by one of the remaining nine players shown in the graph above. To recap, those nine are: Ivan Sokolov, Liviu-Dieter Nisipeanu, Etienne Bacrot, Vladimir Akopian, Zurab Azmaiparashvili, Nigel Short, Alexey Dreev, Ye Jiangchuan, and Alexander Beliavsky. Each of those players has odds (against winning the tournament) that are somewhere between 25-to-1 and 40-to-1. Each of those players also has an estimated strength (based on the latest rating lists) somewhere between 2680 and 2695.
(Group 3) There is a 33% chance that it will be won by one of the other 51 players still in the tournament. About a third of them have an estimated strength between 2640 and 2680, a third are between 2600 and 2640, and a third are below 2600. None of those individuals has more than one chance in forty to win the tournament, but because there are so many of them, they all add up to a reasonably likely outcome.
I know that some of the claims I made in my last article, about statistics and playing strength, were somewhat controversial, and certainly unsubstantiated. In my defense, I can only claim that it is tricky to provide evidence that would be meaningful to very many people. But I will need to revisit that topic briefly, because I do have a simple question to ask. Out of those three groups of players I just listed, which group contains the strongest player in the tournament?
Perhaps you believe that the FIDE ratings are perfectly accurate, and that they exactly measure the performance rating that people would show in the near future, if only they could quickly play enough games to be statistically significant. If you do believe that, then you would say that the strongest player in the tournament must be #1 seed Veselin Topalov, because he has the highest rating. And so you would say that obviously the strongest player in the tournament is in Group 1, and thus it would be embarrassing if this championship were won by a less-deserving player in Group 2 or Group 3.
I don't think it's that simple. Chess ratings are not devoid of meaning, but they are unquestionably imprecise. As I said last time, we need to keep in mind that FIDE ratings are not the precise measurements we would like them to be. In fact, nobody really knows just how effective the FIDE ratings are at measuring the "true strength" of a player. However, based upon the research that I performed a few years ago in developing my Chessmetrics historical ratings, I don't think it's too far off the mark to say that the estimation error in an Elo rating is normally distributed, with a standard deviation of 50 rating points. That means if somebody has a 2550 rating, we can only be about 70% sure that their "true strength" or "current form" is somewhere between 2500 and 2600. And we can only be 99% sure that their "true strength" is between 2400 and 2700.
I'm sorry about this; I really am. I wish I could tell you that ratings are nice and accurate. I wish I could wave a magic wand and tell you that I have a super-magical rating formula in my bag of tricks, but I don't. In all honesty, I simply don't know who the strongest player in the tournament is. They haven't played enough recent games to let me figure that out with any certainty. All I know is that it's too simplistic to say that it MUST be one of the four players with a 2700+ rating.
Here's what I can tell you. If we believe that ratings have zero error, then we are 100% sure that Group 1 contains at least one player whose true strength is 2700+, and of course Group 2 and Group 3 contain no players whose true strength is 2700+. That much is clear.
However, if we accept my "standard deviation is 50" claim, then we are only 99.2% sure that Group 1 contains at least one player of 2700+ strength. It's not 100% sure, because maybe all four players (Topalov, Adams, Grischuk, and Ivanchuk) are significantly overrated right now. Pretty unlikely, but at least it's conceivable.
But if you run the numbers, assuming you're willing to take the time to enter all of this into a spreadsheet, it turns out that we're also 99.2% sure that Group 2 contains at least one player of 2700+ strength. Because there are nine of them, it's very likely that at least one of those players is significantly underrated (and remember that their ratings are already pretty close to 2700). And believe it or not, if we accept the "standard deviation is 50" claim, then we are 99.6% sure that Group 3 contains at least one player of 2700+ strength, out of those bottom 51 players still in the tournament. We're even slightly more than 50% sure that there is a player of 2750+ strength somewhere in Group 3.
What do all these numbers mean? It means that we can't just trust the ratings to tell us who deserves to play in a championship match. We have to actually hold a competition and give the lower-rated players a reasonable opportunity to demonstrate how good they are. As a final world championship event, a 128-player knockout tournament is a disaster. But I do think there is a real place for it as a qualifying event in an effective championship cycle.
Somewhere out there is a diamond in the rough, maybe even among the lower-rated players. The trick is how to distinguish a true diamond from someone who just looks kind of glittery for a few games, especially if the actual diamond overlooks a tactic in severe time trouble and gets eliminated in a rapid tiebreak by a block of granite! I have gone into great detail in the past about the "effectiveness" of various types of tournaments, and I have much more to say on the subject, including some interesting feedback I got from Yasser Seirawan. But not just yet…
Please feel free to send me email at jeff(at)chessmetrics.com if you have any questions, comments, or suggestions.
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Jeff Sonas is a statistical chess analyst who has written dozens of articles since 1999 for several chess websites. He has invented a new rating system and used it to generate 150 years of historical chess ratings for thousands of players. You can explore these ratings on his Chessmetrics website. Jeff is also Chief Architect for Ninaza, providing web-based medical software for clinical trials. Previous articles:
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