While we have listed odds for every player to actually win the World Cup (or reach the finals and earn a Candidates Tournament berth) on our main page, we realize that this doesn’t serve quite as well as it could to explain how the players paths look. Towards that end, we now present the bracket (divided into 8 sections, as it is on Wikipedia, which we shamelessly screen shot the brackets from.) Above or below each open spot in rounds 2, 3, and 4 we have listed all players with at least a 0.1% chance of reaching that position, along with their odds of doing so. Hopefully this will allow you to more easily visualize the most likely results in the first three rounds, and most likely matchups in rounds two through four:
Chess by the Numbers 
Fascinating work! I like how the first round opponents of Topalov, Nakamura, Caruana and Giri aren’t even given a chance to survive round 2.
By the way, all the Chinese names are reversed (e.g. Hou Yifan surname is HOU).
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Yeah, I realized I was doing that (the names) halfway through, felt bad about it, but decided it was easier to keep messing it up than to go back and fix it (since I’d already saved the files as images, so would have had to do a lot of re-typing to fix them all). Ultimately as long as it’s clear who I’m referring to, I figured it was good enough for this purpose.
I’ll place a renewed emphasis on not making this same classic “Westerner” mistake in the future; it’s easier when it’s in text and if I mess it up I can edit easily.
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Very nice indeed! An elegant way to show the big picture and still give detailed information.
I was surprised at first that 4th seed Giri’s chances to reach round 4 were so much bigger that 5th seed So (68.2% vs 52.5%). But then I realized that the seeding was made before St. Louis and that the rating difference between those two is now almost 40 Elo points, and of course your predictions are based on live ratings.
Which got me thinking: I guess you will also be using live ratings for future predictions as the World Cup progresses. Obviously, those ratings will depend on the exact results of the two classical games in each match and not just on who wins the match. But still, the underdogs cannot progress without gaining Elo points, as they would have to at least tie the classical games. Have you considered building these “partly predictable” Elo gains into the model? If Adu were to eliminate Topalov in round 1, I guess we would consider his chances against Bukavshin or Zhigalko to be bigger than we do now, and that would to some extent be reflected by his increased rating.
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My argument for using live ratings has always been that it includes the most data, and is therefore the best available number to represent a player’s current strength.
If Adu defeats Topalov he’ll gain rating points, yes, but not (theoretically) become inherently stronger in the process. The win will be due to the innate uncertainty of life. His 1/1000 chance exists based on our CURRENT estimates of his and Topalov’s strengths. As a theoretical exercise, we’re considering both the one time he does win and the 999 times he doesn’t, so his current live rating remains appropriate to use for predictions of his later round results.
It will be a different scenario entirely if he actually achieves that win in the real world. Then we have an actual data point by which to adjust his rating, and we’ll do so.
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