Who will be the next FIDE world champion?

Libya World Championship Statistics

Alexander Morozevich and Veselin Topalov appear to be the two favorites to win the FIDE championship knockout tournament, which starts in a few days in Tripoli, Libya. Although they are the "favorites", that is definitely a relative term, considering that each has only a 13% chance to win the tournament (based upon my own statistical analysis). Next in line are the other four participants rated above 2700: Michael Adams (9% chance to win), Alexander Grischuk (7%), Vassily Ivanchuk (6%), and Nigel Short (4%). Those six players have a combined 52% chance to win the tournament, leaving an overall 48% tournament winning chance for the remaining 122 players, all of whom are rated below 2700.

In the above chart, the number after the "#" sign tells you the tournament seeding of the player, based upon their FIDE rating. One of the things you'll notice is that the players are not quite listed in FIDE rating order. Most prominently, you'll see that there are actually eleven different players given a better chance to win the tournament than #7 seed Vladimir Malakhov, and that only seven players are given a better chance than #14 seed Zurab Azmaiparashvili. Why is this? It's because the tournament placement of the players is based directly upon their current FIDE ratings, whereas in my estimates of everyone's playing strength, I am using a combination of FIDE and Professional ratings, the two most widely published rating lists.

I have analyzed the differences between FIDE and Professional ratings in various other articles in the past, but for now let me just say that although the FIDE ratings are known to be too conservative, the Professional ratings seem to be too dynamic; in other words, they can overreact to variations in a player's recent results, even when the player's strength has probably not changed significantly. I have found that a simple average of the FIDE and Professional ratings is more effective at predicting future results than using either rating by itself. Normally in this kind of analysis, I would be using my own Chessmetrics ratings (which are even more accurate), but they are currently undergoing renovation and so I am using the published rating lists.

There will always be certain players who have done unusually well recently, although their FIDE rating may not have had time yet to catch up. Those players will be relatively high on the Professional list, and so my calculations award them a rating bonus. For instance, #14 seed Azmaiparashvili (with the 5th best Professional rating among all Tripoli participants) is given an extra 16-point rating bonus on top of his existing FIDE rating. The reverse is true for #7 seed Malakhov (14-point penalty) and #13 seed Vadim Milov (25-point penalty), based on their inferior recent results. There are also indirect effects upon the odds that result from these adjustments; someone who is likely to face Malakhov or Milov would end up with better prospects than someone who is likely to face other players with the same FIDE ratings.

You may have noticed that the two top seeds Topalov and Morozevich each have a 13% chance to win, compared to #3 seed Michael Adams with only a 9% chance, despite all three players having FIDE ratings between 2731 and 2737. Why is this? Well, Topalov and Morozevich already have the two highest FIDE ratings among Tripoli participants, but in addition my methodology also gives both players special rating bonuses thanks to their Professional ratings, which are even more impressive: on the June list Morozevich is #4 in the world and Topalov is #5 in the world. This means their recent results have been better than those of Adams, and the FIDE ratings are slow to catch up with this. Added to the fact that Adams is reasonably likely to face Azmaiparashvili in the fourth round, that is why you see such a large dropoff from 13% down to 9%.

According to the ChessNinja website, Garry Kasparov recently said that there was a 99% chance that the tournament would be won by one of the top 6 seeds (the 2700+ crowd). If you're looking for such a strong level of certainty, all I can say from my statistical perspective is that there's a 99% chance that the tournament will be won by one of the top-64 seeds (the 2600+ crowd), and only about a 50-50 chance that it will be won by one of those top six seeds.

Nevertheless, I should point out that I actually love the knockout format as a qualifying event, which is what it theoretically is this time around. In theory, the winner will play Garry Kasparov in a FIDE world championship match. In theory, the winner of that match will play the winner of the match between Vladimir Kramnik and Peter Leko, and the world chess championship will be "unified". It is very likely that the player who faces Kasparov will have a significantly lower FIDE rating than Kasparov, Kramnik, or Leko. However, it is my contention that the Tripoli winner will NOT be significantly weaker than those three players, even if he does have a lower FIDE rating.

The key thing to realize here is that the published FIDE ratings are uncertain. They are not the precise measurements of playing strength that we would like them to be. They are merely estimates, and most of them are incorrect, in varying amounts. There is an important distinction to make, which many people overlook, between "published" rating/strength and "true" rating/strength.

Let's take Michael Adams as an example. His current FIDE rating is 2731. What does that mean? If we somehow could magically make Adams play 10,000 games right away, against opposition with an average rating of 2731, would he necessarily score very close to 50%? No, not necessarily. His rating of 2731 is an estimate. We are guessing from his past results that his current "true strength" is 2731, but that estimate is uncertain. Perhaps he was lucky in several recent games, or now he has health problems, or he has finally cured himself of some bad habits, or he has developed a mental block which impedes his results, or he has dramatically improved his opening repertoire. Who knows? Despite the evidence of his recent games, perhaps today's Michael Adams would score 43% in that long match (and I would say his "true strength" is 2680) or perhaps he would score 57% (and I would say his "true strength" is 2780). Or maybe he would really score 50% and I would say his true strength is indeed 2731.

Of course this is hypothetical nonsense. I'm not trying to prove anything by this example; I am trying to illustrate what I mean by "true strength". There's no way we could make Michael Adams play 10,000 games, and even if we could do that, he would learn from the games, and his opponents would learn from the games, and he would get sick and tired of this ridiculous experiment, and so on. We cannot possibly measure somebody's "true strength" exactly, but we can describe it statistically. If Teimour Radjabov has a FIDE rating of 2670, that doesn't mean that we know exactly how strong a player he is. We are more confident that his strength is in the 2640-2700 range, than in the 2700-2760 range, or the 2400-2500 range, but we are not certain about it. Well, at least I am not certain about it, and you shouldn't be, either.

Although those six top seeds (Topalov, Morozevich, Adams, Grischuk, Ivanchuk, and Short) are unquestionably the highest-rated players in the tournament, we actually don't know for sure whether any of them is the "strongest" participant. We can be sure that many players right now are stronger than their FIDE rating would indicate, and we can be sure that many players right now are weaker than their rating would indicate. There are even many players for whom the FIDE rating is very accurate right now.

We don't know which player is in which group, but we should acknowledge that ratings are uncertain estimates, and we should try to account for that in our calculations. I do it by using thousands or millions of iterations. Each iteration, I will randomly calculate a "true rating" for each player, based on a standard error of 50 points around their "published rating", and then I use that "true rating" in my tournament simulation during that iteration. Taking the uncertainty of rating estimates into consideration, and considering how many players are in the tournament, my calculations show that we can only be 60-70% sure that the strongest player in the tournament field is actually one of those top six seeds.

However ineffective such a knockout tournament may be at identifying the one single strongest player in the field (even the strongest player can easily be upset in a two-game match), it is extremely difficult to win such a tournament without being a truly strong player, whatever your published FIDE rating may be. Flukes can happen, in one or two rounds, but my analysis shows that to actually win the event, your "true strength" must be quite high. You can look at the excellent post-FIDE-championship results by Alexander Khalifman at Linares 2000, or Ruslan Ponomariov at Linares 2002, as further evidence that an unexpected win by a low-rated player in one of these FIDE knockout tournaments is probably a very strong indication that the player was significantly underrated before the tournament.

My analysis shows that if the Tripoli event is won by one of the top six seeds, that player's "true strength" is probably at least 2770, and such a strength would clearly entitle the player to be in the same category as Kasparov, Kramnik, and Leko. I have already said that there is about a 50% chance of one of those top seeds winning. And even if the tournament is won by one of the seeds between #7 and #30, with a current FIDE rating somewhere between 2650 and 2700, then that winner's "true strength" is probably at least 2740, which would make him a clear underdog in a match against Kasparov, but still deserving of a place in the final four. There is about a 40% chance of the tournament being won by a player whose tournament seeding is between #7 and #30.

In case you're wondering about the winning chances of one particular player whom I haven't already mentioned, I am including my calculated odds against winning the tournament, for all 128 participants, in ascending order. I have also specified everyone's FIDE rating and (where available) their "adjusted" rating estimate thanks to the additional evidence from the Professional ratings. With no clear favorite, the odds will probably start shifting around wildly as the tournament progresses, top seeds get eliminated, and various players start to have easier-looking paths to the final. I will try to provide updated odds as frequently as possible.

Please feel free to send me email at jeff(at)chessmetrics.com if you have any questions, comments, or suggestions.

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: Championship Chessmetrics Analysis The Sonas Rating Formula – Better than Elo? How strong are the top chess programs? Have chess computers surpassed the strongest grandmasters? Are chess computers improving faster than grandmasters? What does the future hold for grandmasters against computers? How (not) to play chess against computers… Are you a betting man (or machine)?