San Luis: Anand's chances after round four

10/3/2005 – Just before the start of the World Championship in San Luis chess statistician Jeff Sonas gave Anand a 31% chance of winning. Topalov got 17%. After four rounds the latter has a one-point lead, while Anand suffered a serious setback. What are the Indian's chances of winning now? And what about Topalov? Try to guess before you read Jeff's latest figures.

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A statisticians view of the FIDE World Championship

By Jeff Sonas

With four rounds completed, and ten rounds still left to play, Veselin Topalov has become the clear favorite to win the FIDE World Championship tournament. He is currently alone in first place with a +3 score, half a point ahead of Peter Svidler and a full point ahead of Viswanathan Anand. Nobody else has a plus score, and the chances for anyone else to win the tournament are rapidly dwindling; currently my calculations show a 92% chance that one of those three leaders will eventually win the title.

Veselin Topalov, initially given a 17% chance to win the tournament, has enhanced his own prospects greatly by starting with three wins and a draw. His first-round game with the black pieces against Peter Leko was supposedly the one game out of the tournament that Topalov was least likely to win, given his historical problems against Leko as well as Leko’s very conservative tendencies with White. But Topalov got off to a great start by winning that game, and currently is given a 44% chance to win the tournament.

Although Viswanathan Anand is already a full point behind Topalov, it should be pointed out that Anand has only had the white pieces once out of his four games, and his most likely score at the end of the tournament is still +3, while Topalov’s current projection is to finish at either +3 or +4. Anand’s chances to win the tournament are still about 30%; it’s just that most of the scenarios where Anand doesn’t win are looking like they’ll be won by either Topalov or Svidler, rather than being more evenly spread out among the others.

The other player with a plus score at this point is Peter Svidler. Although he is currently a half point ahead of Anand, the most likely result for Svidler at this point is to manage an even score over the last ten rounds and to finish at +2, which is why Anand is still considered statistically more likely than Svidler to win the tournament. Before the tournament started, my Chessmetrics ratings identified Anand, Topalov, and Svidler as the three players most likely to win the tournament, and that still appears to be the case. The FIDE July rating list did have Leko 25 points above Svidler, but I explained in my pre-tournament preview why I thought Svidler was indeed more likely than Leko to win the tournament. Even after defeating Judit Polgar in the fourth round, Leko nevertheless has barely a 1% chance to win the tournament at this point, wheras Svidler has almost a 20% chance.

The Chessmetrics chances at the start of the event

In my pre-tournament article, I also predicted that fewer than half of the games would be drawn, which was perhaps a surprise, considering how often the elite tournaments are full of draws. However, the presence of Topalov, Judit Polgar, Alexander Morozevich, and Rustam Kasimdzhanov (all of whom play unusually many decisive games) suggested that we would see relatively few draws. And that has surely proven to be true so far, with only six draws out of the first sixteen games. Incredibly, everyone has already played at least two decisive games, after only four rounds!

In addition to satisfying the bloodthirsty fans around the world, this also makes a rapid tiebreak quite unlikely. Because there will be a lot of variability in the head-to-head results as well as in the total number of wins for each player, the tiebreaker criteria (provided for in the rules) will probably resolve any shared first places without resorting to rapid or blitz games. There is still only one chance in forty that rapid tiebreaks will be required in order to determine the champion, another fact that should please chess fans everywhere.

The new favourite in San Luis: Bulgarian champion Veselin Topalov

I also noticed one other interesting thing when investigating the potential tiebreakers. If Anand does manage to draw even with the leaders and share first place, then he once again turns into the favorite, for several reasons. Topalov has three wins already, but none of those three opponents (Leko, Morozevich, and Michael Adams) is likely to finish with a share of first place. And the same thing is true for Anand’s loss to Kasimdzhanov, and Svidler’s wins over Leko and Morozevich. So nobody has an early edge in the head-to-head tiebreaker, and if Anand catches up then it may be via wins against the leaders. Finally, if it does come down to rapid games, then Anand is king. According to Stefan Fischl’s unofficial rapid ratings, Anand is more than 100 points stronger in rapid chess than either Topalov or Svidler, and at least 60 points stronger than anyone else in the tournament field.

So far it’s been a great show, and everyone still has chances to contend. After the end of the eighth round (the next rest day) I will return with another statistical update, and we will see what the numbers look like at that point. If the next four rounds are anything like the first four rounds, it should be a great week of chess!


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