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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