The rating gap is still quite wide; Carlsen has a spectacular Elo of 2863 while Anand is at 2792. Since the model is based on the Elo ratings, Carlsen is once again the favorite by a large margin. I ran 40,000 simulations of the match:
Carlsen wins: 79.875%
Anand wins: 10.4325%
Match drawn: 9.6925%
The draw rate in the forecast comes from the new model I discussed in some of my earlier posts. It projects that there is a 51% chance of a draw in each game. This is well below the 66% rate observed in modern World Championship matches ("Are the World Champions Just Lucky" Part 1). The reason? The large rating gap again. Draws are more likely when the ratings are close than when they are far apart. If it were 2800 vs. 2800, then the draw rate would be about 58.2%. However, even this seems to be a bit low. Perhaps draws occur more frequently in the World Championship because the incentives are different. In a regular tournament, you have to win several games in order to take first place. But in a match, it suffices to win one game more than your opponent does. Unfortunately, there is no clear way to test for and, if necessary, correct for this increased draw rate in matches. There are not many matches at a high level featuring a wide gap in the ratings. The amount of data that we need just isn't there. But if you believe that the draw rate should be higher, then Carlsen's chances should be revised upwards.
Sagar Shah on ChessBase.com provides a fine summary of Anand and Carlsen's play since their previous match. I'll only touch on a pattern I noticed. Most recently, Anand has been trending upwards and Carlsen downwards. After losing his crown, Anand won the Candidates Tournament and Bilbao with impressive performances. His rating is on the rise and he is playing excellently. Earlier, I called Carlsen's 2863 rating "spectacular" - which it certainly is - but it is also below his record. His highest official rating, 2881, was attained this year, as was his highest live rating (2889.2). If we compare his peak live rating to his current rating, then he has shed 26 points in 6 months. However, we should be cautious when interpreting these results. It is easy to "find" patterns in small samples when none exist; when there is only a handful of observations, then luck can play a big role. And even if there was a significant trend, it may not be enough to overcome the large gap in the ratings. In the Candidates Tournament, Anand's performance rating was about 2850. He would still be the underdog if he maintained that level of play.
In short, it is unclear if the draw rate is too low or if there should be some adjustment for the trend in the ratings. There isn't enough evidence either way. Raising the draw rate would improve Carlsen's chances while adjusting for trend would improve Anand's prospects. Thus, the errors (again, only if they exist, and they might not) will probably cancel out. The forecast can be trusted.
Now what happens if the match is drawn? According to the rules, there will be a 4 game tiebreaker played at rapid time controls. Fortunately, we can turn to FIDE's rapid ratings to form a new forecast. Last year, there were very few rated games played at rapid time controls, so my concern was that the rapid ratings reflected performance at classical time controls instead. By now, both players have more than 30 rapid games in FIDE's records. Carlsen is rated 2855 while Anand stands at 2809. To estimate the draw rate, I took rapid games played this year between players rated 2700+. Again, since rapid ratings are relatively new, using older games could be inaccurate. The draw rate is still around 52% based on a logit model. I was surprised that it was so close to the draw rate for the classical games. In general however, there were fewer draws in rapid games. In this case, the rating gap is smaller in their rapid ratings than in classical. This raises the chance of a draw, offsetting the effect of faster time controls. If the match is drawn, then Anand's chances greatly improve in the tiebreaks:
Chances in 4-game rapid tiebreak match
Carlsen wins: 51.1075%
Anand wins: 22.6175%
Draw: 26.275%
This can be combined with the original forecast for the 12-game classical match:
Chances in 12-game classical match with 4-game rapid tiebreaker
Carlsen wins: 84.83%
Anand wins: 12.62%
Draw: 2.55%
In the unlikely event that the match is still drawn, then a blitz match begins. No forecast for that is available at this time.
Once the match begins, I'll have a model ready that can estimate the effect of having an extra White or extra Black. Of course, both players will have 6 Whites and 6 Blacks. But after game 1, one will have 6 Whites and 5 Blacks, while the reverse will be true for his opponent. This color correction is not easy to estimate, as discussed in my other ChessBase article ("1.e4 - 'Best by Test'?" Part 2). However, I have found a way to do it for the draw rate, and the same idea can be applied to predicting the expected scores.
In addition to updating the probability models, there will also be some chess to enjoy. Looking forward to that.
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