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FIDE Championship odds after round three

6/26/2004 – The favorites are still the favorites, says Jeff Sonas. He has calculated the odds of each player in the sweet sixteen winning the event. Nakamura's 122 to 1 doesn't look so good, unless you placed your bet back when he was at 785 to 1! Plus, what is the best qualifying tournament system for a world championship?
 

Place your bets

Although there have been plenty of high-rated casualties in the first three rounds of the FIDE championship tournament in Tripoli, the two tournament favorites have continued to advance. Going into the previous round, #3 seed Michael Adams had pulled into a statistical tie with #1 seed Veselin Topalov, with each player having a 16% chance to win the tournament. This was partially because Topalov had a much tougher Round 3 opponent than did Adams. But by defeating Movsesian, Topalov has once again pulled in front, with a 19% chance to win the tournament, compared to 17% for Adams. Topalov's chances were also given a boost when #4 seed Vassily Ivanchuk, a likely semifinal opponent, was eliminated. Here are the current odds for all sixteen players, as of the end of Round 3:

I have been calculating these FIDE knockout tournament odds for years, going back to Alexander Khalifman's win in Las Vegas in 1999. Back then, I was naively trusting that the FIDE ratings were perfectly accurate. That led to some embarrassing predictions over the years. Most memorable for me, due to the amount of nasty emails I got during the tournament, was the fantastic performance by Alexander Grischuk in 2000. He had a relatively low pre-tournament FIDE rating, and as the tournament progressed, I kept calling him the heavy underdog each round, ignoring the recent evidence of the tournament itself. And he kept winning, and I kept getting email from Grischuk fans saying "I told you so!" By the time the next FIDE championship tournament rolled around, I had learned my lesson, and kept adjusting #19 seed Ruslan Ponomariov's "estimated strength" higher and higher as he kept advancing through the tournament.

Similarly, the lower-rated players who are still in the Tripoli tournament have shown clear evidence that they are underrated by the FIDE list. For instance, before the tournament started, #83 seed Hikaru Nakamura looked to be at least 150 points weaker than #3 seed Michael Adams. By now it looks more like a 100-point gap, based on Nakamura's apparent current form. Similarly, the estimated gap in strength between #1 seed Veselin Topalov and #49 seed Zdenko Kozul was 100 points before the tournament, and now it's down to 70 points. I'm not saying that the FIDE list will immediately show the gap closing so rapidly, because I'm sure it won't. I'm talking more about my "best guess" statistical estimate of each player's current strength. When we acknowledge that ratings are not the super-accurate measurements we would like them to be, we have to place less emphasis on the original rating list, and correspondingly more emphasis on the recent evidence of the tournament results themselves. This is also what we would witness if the rating mechanism were more dynamic.

Nevertheless, Topalov and Adams remain the clear favorites, even though their Round 4 opponents have also done well thus far. There is a good reason why Topalov and Adams are rated so high, and even giving Nakamura and Kozul considerable credit for what they've done in the first three rounds, my calculations still give Adams an 80% chance to eliminate Nakamura, and Topalov a 70% chance to eliminate Kozul.

Knock-outs, good or evil?

While I have your attention, I would like to return to the general topic of knockout tournaments, because I believe we can make substantial practical improvements to the current format. Some of you may recall an article I wrote a couple of years ago, as a follow-up to Yasser Seirawan's "Fresh Start" proposal for unifying the world chess championship. In that article, I evaluated thousands of different formats for determining the world champion, including various combinations of knockout or Swiss or round-robin qualifying tournaments, followed by candidates matches of various lengths. At the time, my conclusion was that FIDE's 128-player knockout tournament was an extremely poor way to determine a world champion, whereas Yasser's suggestion (a Swiss qualifier leading to a series of long candidate matches) was in fact a fantastic way to determine a world champion. In fact, it was almost the ideal format, mathematically speaking.

However, Yasser told me later that he was surprised by the negative reaction from top players regarding his suggestion of a Swiss qualifier. But when you think about it from a top player's perspective, it really makes sense. In a Swiss tournament, or even a round-robin tournament, it is very difficult to "force" your way into first place on your own. Almost invariably, you need indirect help from the other players (who can either defeat your top challengers or at least hold them to a draw). Because of this interdependence, in such an important and lucrative event, it is inevitable that there will be accusations of collusion: either an out-of-contention player not trying their hardest, or two players agreeing to a mutually beneficial "grandmaster draw".

According to Yasser, the top players much preferred the idea of a knockout, where neither of those collusion scenarios is relevant. In a knockout, all players are equally "in contention" until the moment they are eliminated, so nobody would choose to intentionally lose a game, and even if they did, it doesn't really hurt anyone else's chances very much. And two players in a knockout might agree to a brief draw for short-term tactical reasons, but that will only make their own match last even longer, to their own detriment in the long term. So, from a sporting perspective, the knockout tournament is very appealing to the top players, who feel more in control of their own destiny. Plus, knockouts are simply more fun to follow. Every game matters.

Well, what's wrong with the knockout format? Easy: with so many participants, and so little time, there is just not enough room to identify the single strongest player in the field. It is very easy for the strongest player to falter in one game and suddenly become eliminated. We expect that an effective championship cycle will allow the strongest player (whoever that might be) a real chance to demonstrate their superiority by winning the cycle, and this clearly isn't the case when a minus-one score over a stretch of two games can eliminate you from the whole cycle, however much success you had in the previous games during the tournament.

Thus a knockout tournament should not be the final championship event, merely a preliminary qualifying event. And there needs to be a way for a truly strong player to lose a match and nevertheless ultimately qualify for the championship, either through the use of a double-elimination format, or by there being additional knockout tournament(s) where players eliminated from the first tournament can have at least one more chance to qualify.

My vote is for the double-elimination knockout format, which was originally suggested by Khalifman. In this scenario, losing a match does not eliminate you from the tournament; you simply drop down to the losers' bracket, where you keep playing elimination matches against other players who have also lost once. You aren't eliminated until you lose one of those matches. This is an ideal way to allow multiple players to qualify, and it lends itself to all kinds of variations if a specific number of qualifiers is desired. Unless you've thought a little bit about it, you may not be aware that there are many ways to structure a double-elimination tournament. It's not as simple as a single-elimination tournament would be, and there can be pitfalls. However, it turns out that there are very clean ways to design a 128-player double-elimination knockout tournament so that it generates one, two, three, four, five, six, seven, or eight people who qualify into a championship cycle.

My favorite approach is to have all winners' bracket matches last four games (starting with Round 3), while all losers' bracket matches last two games. This leaves room for two rounds of losers' bracket matches to be played simultaneously with each round of winners' bracket matches. In addition to the obvious benefit of having longer matches among the top players, I like this approach because it preserves the "power of two" numbers (128, 64, 16, etc.) that are so prevalent in typical knockout tournaments. Otherwise you can easily fall into a situation where one bracket reduces down to an odd number of players, and you have to give one of them a late-round bye, and it's very ugly.

I know this is somewhat complicated, so I want to provide an illustrative example. As always, we would start with 128 players, and Round 1 consists of two-game-matches. Instead of going home, the 64 players who lose in Round 1 will drop down to the losers' bracket, where they get to face other players who have also lost one match. Thus, at the start of Round 2 we have 64 players in the winners' bracket, and 64 players in the losers' bracket.

The Round 2 matches would again be two games long, and so at the end of Round 2 there would be 32 players still in the winners' bracket, and 32 players who just dropped down from the winners' bracket to the losers' bracket, and 32 players who just won their losers' bracket match. So now we have twice as many players in the losers' bracket as in the winners' bracket. The key is to preserve that 2:1 ratio until the end.

To continue the example, and to show how we preserve that 2:1 ratio, let me go through one more round. We start Round 3 with 32 undefeated players (in the winners' bracket) and 64 players with one loss (in the losers' bracket). This round lasts four days, rather than two. In the winners' bracket, you have the usual 16 four-game matches involving undefeated players. Meanwhile, during the first two days of this round, down in the losers' bracket there are 32 normal two-game matches between players with one loss. That gets it down to 32 players left in the losers' bracket, and those 32 players immediately play another set of two-game matches (across days three and four of the round), getting us down to 16 players still in the losers' bracket. At the end of the four days, there are 16 undefeated players in the winners' bracket, 16 players who just dropped down to the losers' bracket, and 16 players who just won the last set of losers' bracket matches. That leaves us with 16 undefeated players in the winners' bracket, and 32 players with one loss in the losers' bracket. As you can see, the 2:1 ratio is preserved, and subsequent rounds work the same way.

Ultimately, after Round 7, we are left with one player in the winners' bracket, and two players in the losers' bracket. If we had wanted only one player to qualify into the Candidates cycle, then the two players in the losers' bracket could play each other as the only Round 8 match, and the survivor faces the undefeated player, who gets draw odds in the Round 9 championship match. This has the wonderful benefit that the tournament championship can't be decided by tiebreak games (remember the FIDE Championship final between Anatoly Karpov and Viswanathan Anand which went to a rapid tiebreak?). If we had wanted two qualifiers, then we could simply take the undefeated player and the winner of that Round 8 match. And if we had wanted three qualifiers, then we would have just taken the original three players who were still around after Round 7, without bothering about the Round 8 or Round 9 matches, unless they were needed for prize money considerations or seeding into candidate matches.

The really neat part is that if you want a few more people to qualify, you can control the number of qualifiers by deciding at what point you switch over to having only one set of losers' bracket matches per round (instead of two). By controlling which round this happens in, you can make the tournament generate four, five, six, seven, or even eight qualifiers. This makes the double-elimination knockout tournament perfectly suited to whatever type of championship cycle is proposed. Presumably there would be some kind of plan where there is a series of final matches, including the defending champion and maybe others, plus a specific number of qualifiers from the knockout tournament.

Everyone would love to have the knockout tournament include matches of four games, instead of two. Everyone, that is, except the sponsor, who has to support a much longer event, and that eats up a lot of money. So, although it pains me, I feel compelled to point out that we could do that whole format I just described, except in half the time, by having the winners' bracket matches last two days each, and the losers' bracket matches last ONE day each.

In fact, it really wouldn't look too different from the current Tripoli tournament. The main difference is that the first time you lose a match, you aren't eliminated yet. Instead, you come back tomorrow and play a single-day match against someone else in the losers' bracket, maybe following the same time controls as a typical tiebreak. If you win, you come back the next day and do the same thing again, while the undefeated players are conducting their own tiebreak matches. If you survive long enough, to the round where once again there is only one losers' bracket match per round, then you're back to one game per day at regular time controls, with tiebreaks every other day. It's grueling for the players, but I'm sure they would prefer it to the current alternative of a single-elimination tournament, where they just go home if they lose one match.

It is very easy to criticize the current knockout format and call it a lottery, without suggesting a truly practical alternative. It needs to have the support of the top players, and it needs to be perceived as a more effective structure that will be won by a more deserving player. I hope you agree that my suggested changes to the current format would be both superior and quite feasible. I also hope that you have enjoyed my articles and my statistical analysis of the odds, throughout the Tripoli tournament. The updated odds will continue to appear as the tournament progresses, in the ChessBase reports at the end of each round.

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:

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