2016 Candidates Tournament - Round 13

Nakamura beat Topalov, while the rest of the games were drawn. Caruana and Karjakin continue to lead.

Methodology

The key games in the last round will be Karjakin - Caruana and Svidler - Anand. The winner of Karjakin - Caruana will certainly win the tournament. If they draw, then the first tiebreak is head to head score, and the second tiebreak is most wins. Thus,

Karjakin - Caruana draw + Anand draws or loses -> Karjakin wins the tournament. He will have an equal score in his mini-match with Caruana, but more wins.

Karjakin - Caruana draw + Anand wins -> Caruana wins the tournament. Karjakin, Caruana, and Anand will all have an equal number of points. However, Caruana has a plus score against Anand and an equal score with Karjakin, while Karjakin has an equal score against both. Therefore, Caruana has the best head to head score, so he wins based on that tiebreak.

Therefore, the probabilities for becoming the winner of the tournament are

Karjakin: 61.585%

Caruana: 38.415%

2016 Candidates Tournament - Round 12

Karjakin rebounded with a win over Topalov. Meanwhile, Anand lost to Nakamura, so Caruana and Karjakin share the lead.

There is roughly a 35% chance of a tie for first. Most likely, that will be a 2-way tie between Caruana and Karjakin. In that case, Karjakin will probably have the better tiebreaks. The first tiebreak is the head-to-head score between the players. That will likely be a tie, since they drew their earlier game. The second tiebreaker is number of wins, which favors Karjakin.

I have to say that number of wins is a ridiculous tiebreaker. If 2 players have the same score, then the player with more wins is also the player with more losses. Picking the player with more losses doesn't make any sense. More thought should have been given to the tiebreak rules, since the stakes are so high and there is a good chance of tie. At the beginning of the tournament, you can see that the model predicted a 23.5% chance of a tie for first (to calculate this, note that the probability of a tie = 1 - probability that one player wins). This also indicates that we should find a new format for picking the challenger to the World Championship; the double-round robin will so frequently fails to select a winner. This is a project I would like to explore later.

Methodology

2016 Candidates - Round 11

Aronian lost to Svidler. But the big news is that Anand defeated Karjakin, so now he is tied with Caruana for first place. If tiebreaks are necessary, then Caruana will be ahead of Anand, since Caruana won their individual match 1.5 - 0.5.

Methodology

2016 Candidates - Round 10

Caruana defeated Anand, tying with Karjakin for the lead.

Methodology

2016 Candidates - Round 9

The big news in the last 3 rounds is Anand's victory over Aronian. Meanwhile, Caruana beat Nakamura, so he is well within striking distance of the leaders, Anand and Karjakin.

Methodology

2016 Candidates Tournament - Round 6

Anand bounced back impressively, winning a miniature against Svidler. Meanwhile, Aronian defeated Nakamura to join Karjakin in first place.

Methodology

Meanwhile on ChessBase, there is another set of predictions using computer simulations (http://en.chessbase.com/post/computer-simulates-and-predicts-candidates-winner). Our methods differ a bit, though the predictions are fairly similar. They estimated the draw rates using a database of recent games between the players. This is a smaller sample than in my model, and there is the difficulty of deciding how recent the games have to be in order to be relevant for this tournament. However, it might be able to approximate the effect of different styles. For example, even when Giri and Topalov have similar ratings and face similar opponents, they may still have different draw rates. Is it better to estimate this effect with a small sample (knowing that small samples can be unreliable) than it is to ignore it, as my model does? At the moment, it's hard to say. Once the university upgrades my computer, I might be able to get an answer. Their model also uses deep learning, which is something I don't know very much about.

I have not tried to estimate the results of the tiebreaks. For many tournaments, the tiebreak rules seem to be complicated or arbitrary. If it comes down to rapid and blitz games, the databases don't have a lot of reliable data on that yet.

2016 Candidates Tournament - Round 5

Karjakin defeated Anand in Round 4. All the other games in that round and in Round 5 ended in draws.

Notably, after Anand's loss, he is no longer the #1 player in India. According to the Live Ratings, Harikrishna is slightly ahead. Another big change in the Live Ratings: Topalov is no longer in the top 10.

Methodology

2016 Candidates Tournament - Round 3

Anand managed to win his first round game, echoing his performance in the previous Candidates Tournament. In rounds 2 and 3, Karjakin and Aronian caught up.

Methodology

2016 Candidates Tournament

The 2016 Candidates Tournament starts in about a week. It is a double round robin with a very strong field, even though World #2 Kramnik is missing. That leaves Caruana as the favorite, though his chances are only slightly better than those of his closest rivals.

Methodology