Magnus Carlsen’s Probability of Defending the World Chess Championship Crown

When Magnus Carlsen won the World Chess Championship in 2013, he was expected to keep the throne for a long time. As the 2014 Championship Match starts on Saturday he will get his first chance at defending his crown, and he will try to do it against the man he dethroned last year, Viswanathan Anand.

Carlsen is favored to win, even if he has had some sub-par tournaments lately. However, it is important to keep in mind that he reached the highest ever rating by a chess player on April 21st, and his current rating of 2863 is higher than any other player has ever reached. Anand currently has a rating of 2792, which is on par with his average score over the last 14 years (2784).

Which begs the question, what is their chances of winning?

And there are a lot of ways to try to predict this, and an excellent summary is posted at fivethirtyeight.com and the estimates of Carlsen’s chances are somewhere between 75% to 95%.

We wanted to give it a shot of our own, and try to estimate each player’s chance of winning the championship. There are several ways of estimating this based on the assumptions that you use. What is each player’s chance of winning any given game? What is the expected draw rate? Do you adjust for who plays with the white pieces? Do you adjust for in-game psychology?

For our calculation, we decided to use the probability calculator at chess-db.com for our initial assumptions. And that states that with the current ratings of the two players, Magnus Carlsen is expected to win 35.2% of the games, Viswanathan Anand 15.2% of the games, while 49.6% of the games are expected to end in a draw. Given this, we can ignore who plays with the white pieces and simply simulate each game with the =RAND() function in Excel. We then added up each player’s match score to see who won, then ran the simulation 10,000 times to calculate each player’s chance of winning the match.

This gives Magnus Carlsen a 78.8% chance of winning the match outright, while Viswanathan Anand has an 11.5% probability of re-claiming the throne. That leaves a 9.7% chance that the game will end in a tie-break. If we estimate that they have an even chance of winning the tie-break (a likely probability given that they tied the match), then Magnus Carlsen’s overall chance of remaining the champion increases to 83.7%.

But these are just simulations and probabilities, the real match will be decided at the chess board. And we are looking forward to it.

Update: The breakdown of the win percentages is posted here.