2014 Sinquefield Cup - Round 5

It's not over yet, even though Caruana's 5-0 puts him 2.5 points above his nearest competitor. Carlsen still has some residual chances to catch up.

Since multiple players can tie for first, the first column sums to more than 100%.

2014 Sinquefield Cup - Round 4

The Sinquefield Cup is billed as the strongest tournament in history - and Caruana is leading with a very impressive 4-0. He hasn't guaranteed himself first place, as there are still 6 rounds to go, but victory is looking very likely.

Since many players can tie for first, the first column adds up to more than 100%. Standings:

2014 Sinquefield Cup - Round 3

Caruana defeated the World Champion and now leads by 1.5 points. Due to his fantastic 3/3 start, he has excellent chances to win the tournament.

Since more than one player can tie for 1st, the percentages in the first column add up to more than 100%.

2014 Sinquefield Cup Round 2

Caruana seized the lead with victories over Topalov and Vachier-Lagrave in the first two rounds. Aronian saw his chances improve in the second round as he beat Topalov. Meanwhile the World Champion is off to a slow start with two draws, though he is still the favorite in the latest forecast. As usual, the fact that multiple players can tie for first means that the numbers in the first column will sum to more than 100%, while the total in the second column will be less than 100%.

The previous post mentioned Nakamura's poor score against Carlsen: 15 draws, 10 losses, and 0 wins. Today he improved that record with a draw in round 2. A statistical test resoundingly rejects the hypothesis that the players are equal. If they were, then there is less than a 0.5% chance of seeing a score this lopsided over their 26-game history. There can be little doubt that Carlsen is the stronger player. But this was never in dispute; the typical claim is that Carlsen is an especially difficult opponent for Nakamura, so he performs worse than would be expected given his rating. However, the disparity in their ratings seems to explain much, if not all, of Carlsen's success against Nakamura. Based on the ratings in their previous games, Elo's formula would predict that Carlsen would have a slight plus score: 15-11. The actual score of 18-8 is not radically different; such a mismatch between the actual and expected scores will occur about 10.7% of the time. Hence, we can't dismiss the simple explanation that Nakamura's struggles against Carlsen are driven entirely by the difference in their ratings. He doesn't necessarily have any special difficulties when playing against the World Champion.

2014 Sinquefield Cup

The Sinquefield Cup starts today with a star-studded lineup: Carlsen, Aronian, Caruana, Nakamura, Topalov, and Vachier-Lagrave. The forecast, based on 30,000 simulations:

As usual, the fact that multiple players can tie for first implies that the numbers in the first column sum to more than 100% while the second column will be less than 100%.

It is well known that Nakamura struggles against Carlsen; at classical time controls, he has 15 draws, 10 losses, and 0 wins. This could be because Carlsen has been consistently higher rated, but at first glance the disparity seems too large for that to be the sole explanation. By tomorrow I should have results from a statistical test that will determine if Carlsen significantly outperforms his rating when playing against Nakamura.

Meanwhile, I found that there is no clear trend in the draw rate over the years. If chess were being "played out," we would see the draw rate rise over time, but there is no evidence of that. More details to come later, as well as analysis of whether 1.e4 or 1.d4 has a higher draw rate once everything else is accounted for.

The chess Olympiad, draws, and the 2014 Lindau Meeting on Economic Sciences

No forecast for the Olympiad. Why? First of all, each match has 4 games even though all the teams have more than 4 players. Due to this, I don't know who will be playing whom; it is unclear whose ratings should be plugged into the model. The second difficulty is related to computing power. It takes a couple of minutes to run 40,000 simulations for a typical elite round robin. But in the Olympiad there are more than 170 teams playing 4 games each round. Even if I scaled down to a more modest 10,000 simulations and made the code more efficient, this would take a long time.

Nevertheless, I should be able to release a forecast for the last 2 or 3 rounds of the Olympiad. That is because the objections above don't apply to the final rounds: only a handful of teams will be in contention, so the rest of the results can be discarded. The computation problems vanish. In these critical rounds, it seems safe to assume that each country will only use its top players, thus resolving the uncertainty over who is playing whom.

Looking ahead, the Sinquefield Cup begins on August 27. It is a double round robin with a star studded field: Carlsen, Aronian, Caruana, Nakamura, Topalov, and Vachier-Lagrave. It will also be the debut of the long awaited draw rate model. Over the last week, my research stalled, so I had enough time to nearly complete the project. Most likely, there won't be any noticeable difference in the forecasts, but it does feel better to give the model a better empirical foundation. But this project has implications beyond just tweaking forecasts; it will shed light on the debate over whether chess is being "played out" - i.e., originality is being exhausted and more games will end in a draw. The data includes the ratings of both players and the year that the game was played. If chess really was being played out, then the draw rate should increase as year increases, all else equal. The preliminary results are very clear: the year that a game was played in definitely impacts the probability of a draw. At the moment, it isn't obvious if the draw rate is increasing or decreasing over time; the coefficients on interaction terms in probit models are notoriously difficult to interpret. It is entirely possible that there is no clear-cut answer: perhaps the draw rate has been rising for 2500-players during 1976-1987 but then draws declined for 2600s during the 1990s - this can't be ruled out at the moment. When the results are ready, I'll try to get them published in a major chess magazine or website. My earlier essay, "1.e4 - 'Best by Test'?", touched on this subject. I found that White's percentage score was dropping by 0.01% per year, all else equal. This passed tests of statistical significance, but was hardly a cause for concern: we are very far from the day where Black can completely nullify White's edge just by reciting opening theory.

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I'm honored to be able to attend the 2014 Lindau Meeting on Economic Sciences and even more honored that they published a media summary of my research: The Economic Impact of Beliefs. Don't worry: it's short and written in plain English. They even inserted a neat (and relevant) picture of a solar eclipse. Look for more on Twitter under #LindauEcon14