Hi guys! I'm doing it again. Tracking the qualifying process for the next Candidates Tournament as events occur, like I did for the 2014 Candidates. Hope you enjoy!

The next scheduled World Championship Match will be between reigning champion Magnus Carlsen and a challenger to be determined in a Candidates Tournament. The Candidates Tournament will be held in 2016, with the winner facing Carlsen in a match later in the year. The field for the Candidates Tournament will be determined through a series of events in 2014/2015, and on this page we will track those events as they occur, and keep a running projection of the most likely field.

THE FIELD (Players listed in bold are officially in, others mentioned are “potential” winners of the given spot):

Viswanathan Anand – 2014 World Championship Runner-up

FIDE Grand Prix 1st Place – Current leader after 2 of 4 events: Fabiano Caruana (estimated 58% chance of finishing top-2)

FIDE Grand Prix 2nd Place – Currently after 2 of 4 events: Hikaru Nakamura (estimated 3% chance of finishing top-2); Note that while not currently in the top-two, Alexander Grischuk has an estimated 40% chance of finishing there.

2015 World Cup 1st Place – Way too early to predict winners for this event

2015 World Cup 2nd Place – Way too early to predict winners for this event

Highest Average Rating – Currently Fabiano Caruana

Second Highest Average Rating – Currently Alexander Grischuk (Note, in case Caruana and/or Grischuk qualifies via the Grand Prix or World Cup, that #3 is Veselin Topalov and #4 is Anish Giri)

Organizer’s Nominee – Must be rated 2725 or higher in the July 2015 rating list

I figured I should get this thread up today, since round one of the third leg of the Grand Prix starts tomorrow. As of right now, here are my estimated chances of each of the 16 Grand Prix participants ultimately finishing top-two and qualifying (this will change drastically over the next two weeks, as the Tbilisi event progresses, of course):

Player ODDS (PRE-TBILISI)
Fabiano Caruana (ITA) 58%
Alexander Grischuk (RUS) 40%
Hikaru Nakamura (USA) 39%
Maxime Vachier-Lagrave (FRA) 15%
Anish Giri (NED) 14%
Dmitry Andreikin (RUS) 10%
Shakhriyar Mamedyarov (AZE) 6%
Boris Gelfand (ISR) 6%
Sergey Karjakin (RUS) 5%
Peter Svidler (RUS) 5%
Evgeny Tomashevsky (RUS) 2%
Dmitry Jakovenko (RUS) 1%
Baadur Jobava (GEO) 0%
Leinier Dominguez (CUB) 0%
Teimour Radjabov (AZE) 0%
Rustam Kasimdzhanov (UZB) 0%

EDIT: Oops, had one major error in my spreadsheet! Fixed it and re-ran the sim.

Pretty interesting to see how important one game is. Picking up round 1 wins (with black) improved Grischuk and Giri's odds a lot - from 40% and 14% up to 49% and 20% respectively. Part of it of course is that the full point is higher than whatever their expected score for the game was, so their projected score in the event improves that way. The other part of it is that the gain in live rating improves their projected result in all future games! They would have seen smaller gains if they weren't both also playing in leg 4.

For a noob, can you tell me what the Candidates cycle is? I can google it but you may enjoy telling me about it.

The Wikipedia article about the 2016 championship and related ones are your friends, as usual. The official site of the FIDE Grand Prix series (one of the ways to qualify for the Candidates tournament) is here.

The two top rating qualifiers will be determined on the basis of the average of the 12 published ratings from August 2014 to July 2015.

Yes, yes I would enjoy that

As concisely as reasonably possible (given my aversion to brevity), the "Candidates Cycle" is the process of choosing who will become the challenger in the 2016 World Championship Match, to compete against Magnus Carlsen.

And now I'll set aside brevity, and go into all the detail. Through a combination of a few different methods, beginning as early as 2014 but mostly occurring this year, eight "Candidates" are identified. These eight will play a "Candidates Tournament" in early 2016, and the winner of that tournament will play a match against Magnus later that year with the World Championship at stake.

This thread is intended for tracking the various methods by which Candidates will be chosen, and attempting to predict the eventual eight players as the field is filled in. Most immediately relevant is the FIDE Grand Prix, a series of four tournaments (two of which were held last year, and the third of which started today). 16 players are participating, and each of the four "legs" is a round robin played among 12 of the 16 (each player sits out one leg). Players are awarded "Grand Prix Points" for their finish in each leg they compete in, and at the end the two players with the most total Grand Prix Points earn two of the eight spots in the 2016 Candidates Tournament.

I've built a Monte Carlo simulator in Excel that covers both the unplayed portion of leg 3, and the entirety of leg 4, and spits out odds that each of the 16 players will end up in one of those top two spots. As additional games are played, I'm updating those odds to account for changes in players' live ratings (because the simulator predicts game results based on rating) and of course the results that directly affect the standings, aka games in Grand Prix tournaments.

After the first two legs, Fabiano Caruana was in the lead and Hikaru Nakamura #2 in the standings, but of course they had a temporary advantage over players who had already taken their one bye. My numbers showed that while Caruana is in fact the most likely of anyone to qualify for the Candidates by finishing top two, Alexander Grischuk (by virtue of being the second highest rated player in the world, and having a solid leg 1 score) actually was a slight favorite over Nakamura for the second spot, going into leg 3 (which Caruana and Nakamura are both sitting out). Grischuk won his game in round one of that third leg today (it's being played in Tbilisi), and helped solidify that #2 spot in the "most likely to eventually finish top two" race, improving his chances from 40% to 49%. That gain was partially at Naka and Caruana's expenses, Naka has dropped from 39% to 38%, and Caruana from 58% to 56%. They remain the top three most likely to earn those berths, though. Noone else has better than a 20% chance of finishing top two.

Cool, thanks guys. So the championship is challenged every other year and not every year?

In fact, it's challenged as often as FIDE can find enough sponsors

Yeah, there were championship matches in 2012, 2013, and 2014, but the next one will be in 2016. After that, who knows? I'm suspecting the shift to every-other-year will hold, and the 2016 winner won't defend until 2018, but as cooon74 said, it definitely depends on FIDE finding sponsors.

Every year seems like it might be too often anyway. It doesn't seem like there is much change in chess at the top of the ranks.

BJJ, thanks for putting this together. I enjoy knowing how the process works as opposed to just finding out who the candidates are when it's tournament time. Much appreciated.

https://twitter.com/bennedik/status/568094413819383808

lol, what a noob, he's not even doing Monte Carlo sims.

Definite noob. He should be cranking out 1200 word posts on all the nitty gritty stats, for the rest day. That's what a real chess blogger would do.

Update: his numbers now DO include the results of Monte Carlo sims. That he borrowed (with credit) from elsewhere on the internet. You'll never guess where!!!

You're in the big leagues now.

Jobava's 2.5 in his last three games is a welcome change of pace from his 3.5/17 streak. Was on an approx 50-point slider.

One more win and he'll be back up over 2700. Agreed, it's nice to see. He's so entertaining to watch, that as a fan I really want his results/rating to stay high enough for him to continue playing in top level tournaments.

Jobava wins again. V-L–Tomashevsky has a pretty crazy material balance -- R+4P against N+2B.

Quite an interesting endgame in the game MVL-Tomashevsky, even after all the pawns were eliminated.

That R+4P vs NBB endgame was fascinating, and an excellent practical demonstration for beginners of where "point count" isn't the end-all be-all of material evaluation (not that it isn't a good starting point... better than nothing, certainly.)

Interesting game indeed. What's the tablebase answer? I remember this game:

http://www.chessgames.com/perl/chessgame?gid=1067317

from the KID. Karpov couldn't win with BNN vs R, but BBN is obv a lot stronger.

tablebase says basically every position is won. It makes it look simple enough that you can probably win even against a computer holding out for the 50-move rule

Where do we find this 10-man tablebase that has an answer to KRPPPP vs. KNBB?

Or are you saying that it's won in basically every position after all the pawns are corralled?

Yeah that's what I suspected as well (both he and I meant the KNBB vs KR I think). The 3 pieces just synergize so well together (like Q+N, R+N+B or just 2B). Obviously with 4 pawns it depends a lot on if he can set up a fortress.

Yeah I meant without the pawns. Obviously depends where the pawns are, I suspect black can win them by force in the game position