A statisticians view of the FIDE World Championship

By Jeff Sonas

With only two rounds remaining in the FIDE world championship tournament in San Luis, it seems extremely likely that Veselin Topalov will shortly be crowned the new FIDE world champion. After winning six of his first seven games, Topalov has drawn five games in a row to remain at +6. Two others (Viswanathan Anand and Peter Svidler) are still barely within striking distance at +3, but this tournament is effectively over. My calculations give Topalov a 96% chance to win the tournament at this point, with Anand having slightly less than a 4% chance and Svidler slightly less than a 0.4% chance.

Despite being tied with Anand, Svidler has much less of a chance than Anand to catch Topalov, because of the classical tiebreaking criteria. Topalov defeated Svidler in Round 5 and they drew their Round 12 game, and so Topalov wins out in any shared first place with Svidler thanks to their head-to-head results. This means that Svidler must finish ahead of Topalov in order to win the title, and thus Svidler must win his last two games to finish at +5, while Topalov must lose his last two games to finish at +4. That is a very unlikely scenario (the odds are 273-to-1 against it happening), so for Peter it is really a question of whether he finishes in second or third place.

For Viswanathan Anand, on the other hand, the prospects are relatively better (though still gloomy). If he can make up the 1.5 point difference on Topalov over the final two games, then he probably wins the title. If Anand wins both games, and Topalov loses one game and draws the other, then Anand has seven wins, compared to Topalov's six wins, and so Anand wins the title based on the second tiebreaking criterion (number of wins).

In the unlikely scenario that Topalov loses both of his last two games, and Anand wins one and draws the other, then they both have six wins and so it would go to a rapid tiebreak (and I should remind you that Anand is rated well over 100 points higher than Topalov on Stefan Fischl's unofficial rapid rating list). So there are multiple scenarios where Anand wins the title, but overall the odds are still remote (26-to-1) against that outcome.

All Topalov needs to do is win one more game, or draw both of his games, and he wins the title and the real battle comes down to Svidler's game against Anand in the final round, to determine who finishes in second place. Independent of the prize money, second place is much more preferable than third place because the second place winner automatically qualifies for the quarterfinals of the next FIDE cycle of candidates' matches, whereas the third and fourth place winners have to win a first-round match in order to reach the quarterfinals. According to my calculations, Anand has a 58% chance to finish in second place, compared to a 37% chance for Svidler. This is mostly because of the fact that Anand currently has one more win than Svidler and thus would win out on tiebreaks, although if their final round game is decisive then it doesn't matter what happens in Round 13, the winner of that game gets second place.

The fourth-place winner will very likely be Alexander Morozevich, whose late surge has put him a full point ahead of both Peter Leko and Rustam Kasimjanov, and Morozevich wins out over either or both in a tiebreak due to his +1 score against Leko and his +1 score against Kasimjanov. Morozevich is the only player other than the front-runners who could still theoretically finish in third place, but that is a remote (8%) chance. At this point he has a 79% chance of finishing in fourth place and thus automatically qualifying for the first round of the next FIDE cycle of planned candidates' matches. The only other players with a chance to catch Morozevich and finish in fourth place are Leko (6% chance) and Kasimjanov (4% chance), but just as with the situation for first place, they would have to make up 1.5 points in two rounds, a very difficult task. So in all likelihood, we will see Topalov finish first, Morozevich finish fourth, and the battle for second place will come down to the final game between Anand and Svidler, with Svidler probably needing to win it with White in order to finish in second place.

Links

• Short challenges Kasparov: who will win?
• Sonas: San Luis World Championship – who will win?
• San Luis: Anand's chances after round four
• San Luis: Topalov and other historical performance records