World Chess Championship - Game 11

"Draw" is now the favorite in the match. Carlsen gets one last shot with the White pieces; if it is a draw, then there will be a 4 game rapid tiebreaker.

World Chess Championship - Game 10

Carlsen wins, and his chances rebound in the forecast. In the next few days, I will be at a chess tournament and away from my work computer, which has the software for running the simulations. After Game 11, there will be just one game left, so I can work out the probabilities manually. I'm planning on posting the numbers, but there won't be a nice graph until later.

World Chess Championship - Game 9

Carlsen certainly took risks, but he was the only one who seemed to be in danger. After this draw, Karjakin's chances continue to improve. The model gives a lot of respect to Carlsen's rating, but this will be a daunting challenge even for him; he trails by 1 point with 3 games to go.

World Chess Championship - Game 8

This was a game-changer: Carlsen lost with White. There are still 4 games left, so he has opportunities to close the gap. But his chances are more in doubt then ever before.

World Chess Championship - Game 7

At this point, draws with White no longer help Karjakin's chances. It's now a 5-game match in which Carlsen has an extra White.

World Chess Championship - Game 6

A short draw.

World Chess Championship - Game 5

Each time Karjakin draws with Black, his chances improve.

World Chess Championship - Game 4

Another long game ended in a draw, so Karjakin's chanced ticked upwards.

Every time Karjakin holds a draw, his chances improve. They grow by a larger amount when he draws with Black. In a shorter match, an upset is more likely. Here's why. In a long match, the underdog has to beat the odds several times in order to win the title. Beating the odds in a single game may suffice in a short match. After 4 draws, the World Championship is now effectively an 8-game match. And every game in which Karjakin maintains a tied score effectively shortens the match.

World Chess Championship - Game 3

Karjakin was under heavy pressure, but he managed to defend and hold a draw.

World Chess Championship - Round 2

Karjakin's chances inched upwards after he drew Game 2.

What happens if the World Championship match is drawn?

The short answer: a 4-game rapid match. However, it becomes more difficult to forecast the results. As I mentioned earlier, there are far fewer rapid games in most databases. When I was looking at the Anand - Carlsen rematch, I assembled a small database and attempted to make a forecast. Bear in mind that there is substantial uncertainty here. Carlsen and Karjakin have established rapid ratings of 2894 and 2818, respectively. I estimated their chances in each game using an ordered logit. The forecast for the rapid tiebreaks (if they become necessary):

Carlsen wins: 64.5675%
Drawn: 21.35%
Karjakin wins: 14.0825%

Carlsen is still the clear favorite; a gap of 76 Elo is not easily overcome. If the match is still tied, then they will play a blitz match. I don't have a forecast for that.

The original forecast for the entire match, including rapid tiebreaks if necessary (new model):
Carlsen wins: 85.10%
Drawn: 2.1%
Karjakin wins: 12.80%

We know that the first game of the match ended in a draw, so after revising the above forecast, we get:

Carlsen wins: 83.52%
Drawn: 2.37%
Karjakin wins: 14.11%

2016 World Chess Championship - Game 1

Carlsen drew with White, unsuccessfully trying to squeeze something out of nothing in the endgame. A strength of the new statistical model is that it adjusts for whether a player had Black or White. Drawing with Black boosts Karjakin's chances.

Carlsen wins: 76.385%
Drawn match: 11.0575%
Karjakin wins: 12.5575%

2016 World Chess Championship

The World Chess Championship begins tomorrow in New York City. Magnus Carlsen (2853) and Sergey Karjakin (2772) will face off in a 12-game match. The Norwegian is the favorite due to his extraordinary rating; 81 Elo points separate him from the challenger. However, short matches are prone to upsets. I'll spare you from my usual rant that the match is not long enough.

I ran 40,000 simulations in my standard statistical model. The methodology link below explains how it works. Basically, I estimated the probability of a draw from a large database. Then I plugged that into Elo's formulas to find the probability of a win. Repeat for 12 games:

Carlsen wins: 82.795%
Draw: 8.595%
Karjakin wins: 8.61%

Methodology

Drawn matches are resolved by rapid games. These are hard to predict since (1) there is not such an abundance of data on rapid games. There is a handful of top rapid tournaments each year, but that is nothing compared to my 1 million+ game database of classical games. The second reason? Because rapid tournaments are fairly scarce, the rapid ratings from FIDE might not be entirely reliable.

We are very excited to introduce a new statistical model. The older one relied in part on Elo's theoretical formulas; this one is entirely data-driven. (It's an ordered logit in which the independent variables are a 10th degree polynomial of year, white's rating, and black's rating, in case you were wondering. Not entirely sure how to express that in plain English). The results after 40,000 simulations:

Carlsen wins: 78.74%
Draw: 9.8425%
Karjakin wins: 11.4175%

Karjakin's chances are slightly better here. The probability of a draw in each game is nearly the same in both models (Old: 48% New: 46%). The main factor is Carlsen's expected score, i.e., how many points per game he will score on average. Elo's formula yields an expected score of 64%. In the data, it seems to be closer to 60%. In either case, Carlsen is heavily favored to win. It's hard being the underdog when you're rating is 81 points less - even in a short match.

Showdown in St. Louis Chess Forecast

Tomorrow the Showdown in St. Louis begins. The first part of the tournament is a 4-player double round robin. The average rating is only slightly lower than the World Championship; the players are Nakamura, Caruana, and two former world champions: Anand and Topalov. Caruana's 2823 rating makes him the favorite. One caveat: the "classical" 4-player round robin has a time control of G/60 with a 5 second delay. This is more like a blend of classical and rapid in my view. The model can't account for this since there are hardly any games played at this time control at the top levels. I don't have a forecast for the rapid or the blitz tournaments. The vast majority of the games in my database were played at classical time controls, so forecasting blitz or rapid involves making predictions with little data to guide you.

Methodology

My forecast for the World Championship match will be up soon.