The reigning World Chess Champion Magnus Carlsen squares off against Sergey Karjakin int The World Chess Championship Match in New York City starting on Friday, November 11. As I did in 2014, I have tried to model the probable outcomes of this year’s match.
First a bit about methodology. Last time there were two different models; one based on rating alone, and one that was adjusted for the match situation. This year there will only be one model, which merges two different sets of analyses. Namely one that is based on the ratings of the two players, and one that is based on analysis of previous championships.
First the rating based part. Currently, Magnus Carlsen has a rating of 2853 while Sergey Karjakin has 2772. That is a difference of 81 points, which means that over 12 games, Carlsen should be expected to score 7.38. However, since the model simulates each individual game, I needed to find the probabilities when Carlsen has the white pieces as well as when he has the black. The first thing I wanted to examine was the draw rate, and investigate whether there is a difference depending on which color the highest rated player has. To do this, I analyzed approximately 800 games in which both players were rated at least 2700 and where the difference in rating was between 70 and 90. This revealed two different draw rates, if the highest rated player was white, the draw rate was 44.5%, while it was 56.5% when the lower rated player was white. This was then set as the probable draw rate based on rating, and then each players win chances were calculated based on their respective ratings after adjusting for white’s first move advantage (equivalent to about 35 points). That would yield the following probabilities per game, which alone would give Carlsen an 88% chance of keeping the title.
|Karjakin White||Carlsen White|
|Carlsen Win||28.3 %||43.9 %|
|Draw||56.5 %||44.5 %|
|Karjakin Win||15.2 %||11.6 %|
However, match situations are different and World Championship Matches especially so. That’s why I further analyzed the 269 games in the same matches used to build the alternate model two years ago. Again, I split the games based on on whether the highest rated player had the white or the black pieces. That produced the following probabilities per game, which alone would give the generic higher rated player a 56% chance of winning the title, a 19% chance of tie break, and a 25% chance of the lower rated player winning. (which is how it has played out historically over those 16 matches analyzed).
|Lower ELO White||Higher ELO White|
|Higher ELO Win||12.0 %||27.9 %|
|Draw||69.2 %||64.0 %|
|Lower ELO Win||18.8 %||8.1 %|
As can be seen, the draw rates are much higher in the championship games. Further, white has somewhat of an advantage regardless of who starts with white. If the lower rated player has white, white scores 0.534 equivalent to a 24 rating difference, while white scores 0.599 when white is higher ranked, equivalent to a rating difference of 70.
From here, I simply took the average of each of those scenarios to create the assumption for each game. Which means that this year’s model uses the following probabilities for simulating each game:
|Karjakin White||Carlsen White|
|Carlsen Win||20,2 %||35,9 %|
|Draw||62,8 %||54,2 %|
|Karjakin Win||17,0 %||9,9 %|
This means that the model assumes that there will be a higher chance of a draw if Karjakin is white, and that Carlsen is a slight favorite, while the draw rate drops and Carlsen becomes a much bigger favorite to win when he has the white pieces. Overall, the model assigns Carlsen an expected score of 0.573, which is equivalent to a rating difference of 51 points.
Overall, that gives Carlsen a 72.5% chance of winning outright, a 13.4% chance of a tie break, and the chance of a Karjakin upset within the regular 12 games being 14.1%. The distribution of expected outcomes are as follows:
Expected match outcomes.
This makes Magnus Carlsen a heavy favorite to retain the title, and is somewhat on par with betting markets. However, being an 80% favorite is by no means certain, and things that have a 20% chance of happening occur on average one out of five times. Rating wise, the historic match lineup that is closest to this year’s is the 2000 match between Kasparov (2849) and Kramnik (2772). Kramnik won.
Edit: The post was edited to reflect that Magnus Carlsen starts with the white pieces.