Next spring the 2016 Candidates Tournament will be held, with eight players vying for the right to face off against Magnus Carlsen later in the year in a match for the world championship. These eight Candidates will be selected through a variety of criteria, which we have been tracking here, and we offer a closer look at one particular criteria (average rating) as well. However things have begun to grow clearer as we move into the last few months of the year, so now let’s look even more closely at the ratings, and see if we can’t pin down specific odds of various players qualifying. Here are a series of key points to be aware of:

**There are only four serious contenders**

Let’s start here. The top six in our projected average ratings are Topalov, Giri, Grischuk, Kramnik, Aronian, and So. It is basically guaranteed that the two ratings qualification spots will go to two of these six players, with the last two themselves being extremely unlikely, and nobody else has a chance worth considering.

7th place Ding Liren could see his rating rise to 2832 tomorrow, and stay there for all three of the remaining lists, and if Wesley So’s rating didn’t change So would still finish ahead of Liren in the final average ratings (by a tenth of a point). The gap is just too big for Liren to have much chance of bridging, and that’s just to get into sixth place in the race, which won’t be good enough to actually qualify. So, currently in sixth place, is only in our list of “serious contenders” because if HE makes huge gains he could climb as high as fourth, and have a shot if two of the players ahead of him reach the finals of the World Cup, removing themselves from contention as qualifiers by rating by qualifying in a higher precedence way. For Liren to get to fourth place, without anyone else’s ratings changing, he would need to post a published rating of 2854(!) in all three remaining lists. Obviously this won’t happen. There are at most six contenders, and Aronian and So are huge longshots themselves (relying on huge rating changes AND two of their competitors to qualify at the World Cup). We will address their path, but each of them has well under a 1% chance of qualifying, it’s over 99% that both qualifiers will be from the top four: Topalov, Giri, Grischuk, and Kramnik.

**October ratings are probably already known**

The only tournament that any of the six possible contenders are scheduled to play in September (as far as we know) is the World Cup, and since that event doesn’t end until after the October rating list is published it will not impact the ratings on that list. World Cup results will only be included for the first time on the November list. The October list, therefore, will almost certainly be the same as the current live ratings for all the players that matter in this analysis. Maybe one of them will play an event we’re not currently aware of that will sneak in before the end of the month, but because of the World Cup none are likely to have anything planned. We expect the live ratings to turn into published ratings for October. This means that there are really only going to be two, not three, remaining opportunities for players to

**Topalov will qualify if he doesn’t withdraw from the World Cup**

Veselin Topalov has a live rating of 2813. If this is his published rating in each of the remaining three rating lists, his average rating through the year would end up at 2806.6, while third place Grischuk projects to finish at just 2783.7 with no rating changes. Maybe there is a small chance that Giri could pass Topalov, but even that isn’t likely. For TWO people to pass him, and prevent him from qualifying, would take an impossibly absurd collapse. Let us say, despite the previous point, that he somehow plays a couple rated games in September and his rating falls to 2800 in the October supplement (0/2 against a 2700 opponent would do it). Then let us say he goes into a complete tailspin between the World Cup and the European Club Cup (October 18-24) and sheds 50 more rating points, dropping to a published rating of 2750 on the November list. Then let’s say he somehow loses 50 MORE rating points in November, and finishes with a published 2700 rating in the December list. His average rating for the year would still finish at 2790.8 – better than we project for Giri! Of course he isn’t going to lose over 100 rating points in the next two months, but the fact that even if he did he would probably still qualify by average rating should convince you that he’s a lock.

There is only one catch: to qualify by rating a player must compete in either the Grand Prix or the World Cup. He skipped the Grand Prix, so the latter is mandatory. Now he has said that he will, and is listed as the #1 seed in the bracket, for this tournament that begins in a week, so our assumption is that he has clinched a spot in the Candidates Tournament. Technically though it’s not official until he actually plays his World Cup games. If for some unforeseen reason he withdrew without playing a game, our understanding of the rules is that he would not be eligible for the ratings qualification. So he has to compete to qualify. If he does, he’s in, and that’s all there is to it.

**Giri is extremely likely to qualify as well**

A solid performance at the Sinquefield Cup might have come close to clinching the second qualifying spot for Anish Giri. Through September (the first nine rating lists, out of twelve, that will be averaged together), Giri’s average rating is 2787.4, just barely ahead of Grischuk (2786.9). This would be a minuscule lead, except that Giri is now rated 2798, and Grischuk just 2774. The Sinquefield Cup was Grischuk’s last good chance to close this gap in time to remain in contention, and while he played well (gaining 3 rating points), he did not make the extraordinary move he needed to catch up, nor did Giri stumble (gaining 5 rating points of his own). Now we expect these ratings to be published for October, as we’ve discussed, and one more month of this large rating gap will create a big deficit for Grischuk to try to bridge in the final two months.

To catch up, assuming the October ratings match current live ratings as we expect, Grischuk’s November and December ratings would have to EXCEED Giri’s by a total of 29 for a tie, or 30 to actually surpass the Dutchman. If all the gains were to be made in November, this could mean “just” a 15 point rating edge, published twice (November and December), but to achieve this (given his current rating deficit) Grischuk would need to gain (and/or see Giri lose) 39 rating points net before the end of November. If Giri gets knocked out of the World Cup early (and preferably for Grischuk fans it would be by losing classical games, not losing on rapid/blitz tiebreaks) while Grischuk makes a deep run, then this could still be in play, but right now it’s pretty unlikely. We’ll certainly keep an eye on their World Cup results, and see if there’s hope for Grischuk, but really he probably should just focus on reaching the World Cup final and qualifying that way, because anything less probably won’t be enough to close the rating gap anyway.

What about other contenders? Who else might catch Giri with big gains at the World Cup? Kramnik trails Giri by a lot more, and would need to be rated 40(!) points higher than Giri by the end of November to catch up. Given that he’s currently 21 points lower rated, this seems highly improbable to say the least. Aronian is rated higher than Kramnik or Grischuk, but trails Giri by even more through the first 10 months, and would need to gain an absurd 82 points on Giri by the end of November to catch him in December. Wesley So would need to gain 94 rating points. The point is: only Grischuk can catch Giri, and it will take a strong effort before the end of October (for the November rating list).

**The World Cup could make a big difference**

If Grischuk is the only player with a realistic chance to catch Giri, then why are we mentioning Kramnik, Aronian, and So? Because it might not be necessary to catch Giri in order to end up with one of the two open Candidates berths by average rating. If either of the top two contenders (Topalov or Giri) reaches the finals of the World Cup, and earns a spot in the Candidates Tournament that way, what used to be a battle for third place suddenly turns into a battle for second place. Kramnik is alive for this reason: he does have chances at catching Grischuk.

While Grischuk’s average rating so far is higher than Kramnik’s, his current live rating is three points lower. That’s not enough; in order to actually finish with a higher average rating Kramnik will need to be rated 25 points higher than Grischuk on each of the last two lists (for the tie). This is a tall task, but not so unlikely as to discount entirely. He’s already ahead, so he only needs a net gain of 22 points based on results over the next two months to get there.

It’s worth noting, here, that we carefully referred to the possibility of Topalov OR Giri reaching the World Cup final. They are on the same half of the bracket (seeded #1 and #4, and slated to potentially face each other in the semifinals if they make it that far), so it’s impossible for both of them to qualify. What are the odds of at least one of them reaching the World Cup final, and opening a window for Grischuk (or maybe for Kramnik)? Our latest World Cup odds say that Topalov should reach the finals 24% of the time and Giri 18.6%. Since their chances are mutually exclusive, this is the rare situation in probability where we can just add two numbers together and get a valid result, so assuming Grischuk holds on to the #3 rating spot, he has a 43% chance of qualifying for the Candidates Tournament by virtue of Topalov or Giri qualifying on World Cup results and turning Grischuk into the #2 average rating among eligible players.

None of this yet addresses Aronian or So. Their odds of catching Grischuk for the #3 spot are lower than Grischuk’s chances of catching Giri were, as they would need to gain 43.5 and 55 net rating points (respectively) worth of ground to catch Grischuk. Unlikely. However there’s still another scenario. While Topalov and Giri can’t both reach the finals, Grischuk himself could, he is seeded #7 putting him on the other half of the bracket. And our calculations say he has about a 10% chance of reaching the final himself.

Aronian and So are in trouble, but not completely eliminated. Their hopes rest on a series of unlikely events. First they must root for Grischuk to reach the final, and for his opponent to be either Topalov or Giri. There’s slightly better than a 4% chance of this happening, but that’s about what Aronian’s odds of winning the Sinquefield Cup were when the event began! This is just the beginning though, if two of the top three players in the current average rating standings remove themselves from the pool by both making the World Cup finals, that still only improves Aronian and So to 3rd/4th in the standings themselves. They would ALSO have to catch and pass Kramnik to ultimately get in. Looking at it the same way we’ve looked at other deficits, Aronian would have to gain 22 net rating points on Kramnik to pass him, and So would need to gain 33. These are large deficits, but not completely insurmountable. It’s as likely for Aronian to pass Kramnik as it is for Kramnik to pass Grischuk, and it’s more likely for So to pass Kramnik than it is for Grischuk to pass Giri. All of these look unlikely, but none of them can be completely ruled out as impossible at this juncture.

**What if there is a tie?**

Right now the gaps between each player are large enough that it seems extremely unlikely to come down to a tie. Average ratings are rounded to two decimal places, so two players would have to have EXACTLY the same average rating over the 12 months for it to matter. For the record, though, if two players do tie for second place the tie break is number of standard rated games played in 2015. If anyone wants to go compile game counts for the players in the hunt and post it in the comments, that would be welcome! If after the October and November lists are published (and World Cup finalists are known) a tie begins to look more likely, we’ll drill down more closely on tie break possibilities, but right now it appears irrelevant.

**What about games played in November?**

All the numbers we gave above for how many rating points a player must gain (or the person they’re chasing must lose) before the November rating list is published, in order to pass someone ahead of them, naively assumed that the November and December rating lists would be the same. Of course this is not the case, the European Team Championships are played in November, and likely all of these players will compete, so December ratings will differ from November ratings. It’s just that rating changes that only apply on the December list are only counted once, while rating changes that impact the November list are counted twice, so it takes more effort to catch up in the final month.

Of course, though, when we said (for example) that Grischuk needs to gain 39 points (net) on Giri before the November list is published, he could alternatively achieve the same result by gaining 33 points (net) before the November list, then gaining 12 more before the December list is published. However far short of a goal someone falls on the November list, they have to gain twice the difference in that final month.

**So what are the actual odds?**

Topalov is 100% in the Candidates Tournament, but we don’t know if it will be by virtue of rating or by reaching the World Cup final. Making sure we’re clear on that point, here are each player’s estimated chances of qualifying ON RATINGS for the 2016 Candidates Tournament. These are a little bit intuitive and rough, we did not do detailed simulations of how many rating points can be made up in the last two months, we’re pretty much just guessing. Remember that since two spots are open, the odds must add to 200%:

Player |
Odds |

Topalov | 76% |

Giri | 75% |

Grischuk | 44% |

Kramnik | 4% |

Aronian | <1% |

So | <1% |