World Cup Odds – First Four Rounds

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:

Group1 Group2 Group3 Group4 Group5 Group6 Group7 Group8


World Cup Upset Predictions!

Sports fans are notoriously fond of underdog stories. Outside of games or matches involving our personally beloved teams or individuals, we almost always tend to root against the favorite. We love to see upsets! Knockout tournaments are excellent for this, especially in the early rounds. They set up lots of matches simultaneously, and even if each underdog has, individually, less than a 50% chance of winning (by the definition of “underdog”), probability dictates that several of them will likely still win. This is why basketball fans look forward to “March Madness” (the NCAA Tournament) all year, and it’s why chess fans should love watching the World Cup.

In the 2013 World Cup, out of 64 first round matchups, the lower seeded player advanced in 13 of those. The lowest seeded player to advance was some kid you’ve probably never heard of, just 14 years old, rated only 2557. What was his name again? Oh yeah, Wei Yi, and come to think of it maybe you have heard of him after all. We do enjoy writing about him here! Not only did he upset Nepomniachti in round one, he went on to knock of Shirov in round two, before finally falling to Mamedyarov in rapid tie breaks in round three. Elsewhere in the bracket we saw the #102 seed (Adhiban) and the #91 seed (Fier) face each other in round two, after both achieving upset victories over their first round foes. Adhiban won the privilege of advancing to the third round, where he was promptly dispatched by Nakamura. #75 seed Daniil Dubov and #89 seed Jon Ludvig Hammer also both reached the third round, scoring two upset victories to get there. And the #50 seed, Julio Granda, scored upsets over Leko and Giri in rounds two and three to reach the round of 16!

The point here is that upsets will inevitably occur this time around as well. We can’t predict any specific upset as likely, every underdog (by rating) is by definition expected to win less than 50% of the time, as we said before. We’re not going to highlight any individuals as more likely to overperform than any other underdogs. However we can estimate how MANY upsets are likely to occur, and what the biggest upset might be.

We used our model’s odds on each round 1 matchup to simulate the first round 10,000 times, counting how many upsets occurred each time. For these purposes we defined an upset as “the higher rated player loses”, so in a few cases this means the higher seeded player winning is considered an upset, as ratings did shift a little after seeds were determined.

Overall we saw an average of 15 first round upsets (median and mode of 14) across our simulations, and one crazy run through gave us as many as 27! We also saw one boring first round with only 3 upsets, but don’t worry, 95% of the time we saw at least 10 upsets in the round, with a 26% chance of 17 or more upsets occurring!

Now yes, some of these are less interesting than others. When the 64 and 65 seed play, it hardly matters if Zhigalko (2656) beats Bukavshin (2657), even though that counts in our simulation as an “upset”. Don’t fear, though, we also saw an average of 6 upsets where the weaker player was outrated by at least 50 ELO, with an 18% chance of 9 or more of these “real” upsets coming to pass.

We have a 95% chance of at least one 100+ rating point upset (and a 14% chance of five or more, with 10 occurring in a single simulation once out of the 10,000 run throughs).

Can we go higher? Sure! There is a 65% chance that we’ll see at least one upset of 150 rating points or more (remember that our largest upset in 2013 was 160 points, and fell in this category). There’s even a 34% chance that we might see someone advance ahead of an opponent rated 200 or more ELO higher, and a 250+ point upset comes in as a 20% likelihood.

The latter (a 250+ point upset) would mean one of the top 12 seeds losing in round 1. Parham Maghsoodloo, an untitled player from Iran, only has a 2% chance of knocking of Wesley So (his superior by 313 rating points), and GM Ziaur Rahman of Bangladesh gets a 4% shot at beating Tomashevsky (overcoming a 258 point rating gap), and these are more likely than some of the others in this group of 12. Individually they’re extraordinarily unlikely, but the chance that just one of the 12 might succeed aggregates to 20%! Still unlikely, but certainly not implausible!

Overall, the largest upset averages out to be 187 rating points (median 182). The mode (single most common value) for our biggest upset comes out at 124 rating points, which is probably because there are two chances for this to happen: #28 seed Vitiugov and #24 seed Wei Yi both outrate their first round opponents by exactly that amount. How ironic would it be if the biggest upset of the tournament this time around were Wei Yi losing to GM Saleh Salem? Salem has a 17% chance of winning, according to our model, although most of the time he does so it isn’t the biggest upset of the tournament!

Candidates Qualifying: Average Rating

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%

Khanty-Mansiysk Round 10 Update

With just one round left in the FIDE Grand Prix series, we have the same favorites we’ve had for a while. However things are not yet entirely final! While Fabiano Caruana and Hikaru Nakamura each have roughly a 90% chance of emerging from this final round in the top two of the overall Grand Prix standings, which would earn them berths in the 2016 Candidates Tournament, they both still face some danger. Jakovenko picked up a critical win in round 10, setting up a huge showdown with Nakamura in the final round, and keeping his chances alive. There are also a few crazy scenarios where Tomashevsky remains alive as well… and believe it or not it’s even possibility where Jakovenko and Tomashevsky both qualify, ahead of Caruana or Nakamura.

Confused yet? Let’s look at some tables of projected standings, and then we’ll dive into the scenarios. Here are what the Grand Prix standings would look like based on the current Khanty-Mansisyk standings (so this would match the final result if all six games tomorrow are drawn), along with each of the four remaining contenders’ odds of finishing in the top two:

Player Live Rating Baku Tashkent Tbilisi Khanty-Mansiysk CURRENT TOTAL ODDS (PRE K-M) ODDS (CURRENT)
 Fabiano Caruana (ITA) 2805.3 155 75 140 370 71% 92.6%
 Hikaru Nakamura (USA) 2802.9 82 125 140 347 49% 87.6%
 Dmitry Jakovenko (RUS) 2758.4 30 140 140 310 9% 19.5%
 Evgeny Tomashevsky (RUS) 2745.0 82 170 35 287 52% 0.3%
 Boris Gelfand (ISR) 2750.8 155 15 85 255 7% 0%
 Shakhriyar Mamedyarov (AZE) 2735.0 35 125 75 235 0% 0%
 Sergey Karjakin (RUS) 2753.3 82 75 60 217 8% 0%
 Teimour Radjabov (AZE) 2738.0 50 50 110 210 0% 0%
 Dmitry Andreikin (RUS) 2717.9 20 170 10 200 0% 0%
 Alexander Grischuk (RUS) 2781.1 82 40 60 182 3% 0%
 Anish Giri (NED) 2772.2 40 75 60 175 1% 0%
 Leinier Dominguez (CUB) 2745.0 10 75 85 170 0% 0%
 Peter Svidler (RUS) 2735.3 82 20 35 137 0.1% 0%
 Baadur Jobava (GEO) 2697.8 75 40 20 135 0.2% 0%
 Maxime Vachier-Lagrave (FRA) 2723.0 75 40 10 125 1% 0%
 Rustam Kasimdzhanov (UZB) 2703.8 35 15 75 125 0% 0%

At this point it seems likely that we will see two or more players tie for first place in the Khanty-Mansiysk leg, but if someone does win outright, here are each player’s odds of being that someone, along with each player’s expected average Grand Prix points earned from the leg:

Player K-M Expected Score Score Today Odds of Clear 1st (Pre-Event Odds)
 Hikaru Nakamura (USA) 142 140 29% 14%
 Fabiano Caruana (ITA) 131 140 10% 17%
 Leinier Dominguez (CUB) 90 85 0% 2%
 Sergey Karjakin (RUS) 63 60 0% 5%
 Dmitry Jakovenko (RUS) 123 140 10% 3%
 Boris Gelfand (ISR) 85 85 0% 3%
 Peter Svidler (RUS) 41 35 0% 2%
 Alexander Grischuk (RUS) 60 60 0% 11%
 Anish Giri (NED) 61 60 0% 7%
 Baadur Jobava (GEO) 22 20 0% 1%
 Evgeny Tomashevsky (RUS) 41 35 0% 3%
 Maxime Vachier-Lagrave (FRA) 10 10 0% 3%

So then, let’s talk scenarios. First we’ll look at the most critical game, Nakamura-Jakovenko. If this game ends decisively, things are (mostly) clear. Should Nakamura win (which we expect to happen 36% of the time), then Nakamura and Caruana will be the top two. Order will depend on Caruana’s result, but they will be the two Candidates. On the other hand, if Jakovenko pulls the upset with the black pieces (which we expect to happen 12% of the time), then Jakovenko and Caruana will be the two qualifiers, except in one crazy absurd scenario we’ll discuss later.

So Caruana should be rooting for a decisive result – he wants to see fireworks on the board between his two rivals. If either of them wins, then Fabiano is almost guaranteed a top-two finish and Candidates berth (even if he loses his own game). On the other hand, if Nakamura and Tomashevsky draw (which, sadly for Caruana, is the most likely possibility at 52%) then things are murkier.

The draw would be good for Nakamura, who would qualify 99.8% of the time. His only danger is if Caruana, Tomashevsky, Gelfand, and Dominguez all win their games. Credit to Colin McGourty at for identifying that scenario. With a draw between Naka and Jakovenko, though, Caruana would drop to an 86.3% chance of a top two finish, Jakovenko would be at 13.4%, and Tomashevsky would be alive at 0.5%.

The second critical game is Giri-Caruana. We give Giri a 21% chance of winning, which is all that really matters. If Caruana wins or draws, he guarantees himself one of the two Candidates berths; all his danger comes in scenarios where he loses. Also in the case of a Nakamura draw, a win or draw by Caruana completely clarifies matters: Nakamura and Caruana would get the two spots. The crazy possibilities come into play in roughly 11% of all cases: when Nakamura and Jakovenko draw and then Caruana also loses!

Those various scenarios are rare enough, and varied enough, that it seems most convenient at this point to start looking at it from each individual player’s perspective. If your mind has melted at all the “if” and “unless” nonsense above, take a moment to refresh and we’ll start over from a new angle.

Fabiano Caruana: 92.6% chance of qualifying.

Caruana has the black pieces against Anish Giri. If he wins or draws his game, he guarantees himself a top-two finish. If he loses, then he should root for a decisive result in Nakamura-Jakovenko, in which case he’ll still qualify 99.8% of the time. His worst case scenario is to lose, and for Nakamura and Jakovenko to draw. Then the other four games would all start to matter, and Caruana would have roughly a 32% chance to qualify, depending on how those games worked out for him.

Hikaru Nakamura: 87.6% chance of qualifying.

Nakamura faces Jakovenko in the most critical game of the day. Any decisive result is clear, as we explained before. If Nakmura wins, he’s in (and Caruana is too). If Nakamura loses he’s out. With a draw, he’s also basically safe, except for one weird (and very unlikely) scenario we talked about earlier. Basically, he controls his own destiny and will have no real need to worry about other games. Just don’t lose, and he qualifies for the Candidates.

Dmitry Jakovenko: 19.5% chance of qualifying.

Jakovenko is on the flip side of the key game. He also has a simple “win and in” spot, but beating the 4th highest rated player in the world is always a tough task – especially with the black pieces. The good news is that even if he doesn’t manage to win, a draw still leaves him alive (his chances only drop to around 13.5% if he fails to win). He would need Caruana to lose, and then would also need some additional help in the other games. Ultimately if Jakovenko draws but then Caruana loses, Dmitry will qualify about 67% of the time.

Evgeny “I’m Not Dead Yet” Tomashevsky: 0.3% chance of qualifying.

And then we have the dark horse. First of all, to have any hope of earning a Candidates berth, Tomashevsky must of course win his game (with white, against last place Vachiere-Lagrave). Even with a win, Tomashevsky needs a ton of help. Interestingly the results of Caruana’s game and the huge Nakamura-Jakovenko game make little difference to him. If Tomashevsky wins his own game, his rooting interest lies with Gelfand and Dominguez. In fact both of those players must win their games to keep Tomashevsky alive at all! The reason it matters is that by moving up in the standings, those two players would be able to limit the points earned by the other contenders near the top of the field. A loss, or even a draw, from any of Tomashevsky, Gelfand, or Dominguez is enough to eliminate Tomashevsky’s slim hopes. If all three of them win, though, his chances jump up to the 29% range!

There is one particularly crazy scenario we need to look closely at, now. We’ve hinted at it a few times already. It requires specific results in all 6 games of the round, but there is a way for Jakovenko and Tomashevsky both to qualify, while leaving Caruana and Nakamura both outside of the top two. What is this madness?

To begin with, Tomashevsky must win and Jakovenko must defeat Nakamura (clinching one of the two Candidates spots for Jakovenko). Of course Caruana would have to lose in order to keep that second spot open. Then Dominguez and Gelfand would each have to win their games, as with any pro Tomashevsky scenario, which would be enough to move those two into a tie for second place, behind Jakovenko but (critically) ahead of Nakamura and Caruana. Nakamura and Caruana would finish tied for 4th-6th place with Giri, and each earn 80 Grand Prix points, putting Caruana’s score at 310. Finally, Jobava would have to win or draw his game against Svidler, so that Tomashevsky manages to finish alone in 7th place (instead of tying with Svidler for 7th-8th), which would get Tomashevsky 60 Grand Prix points bringing his overall total to 312, and sliding him into second place by the slimmest of margins! By our calculations, this result should happen about 1/5500 times (which is to say there is a 0.02% chance).

Wouldn’t that be something? Remember that this final round starts an hour earlier than the previous rounds did: at 14:00 local time, otherwise known as 2 AM for me. Yes, sorry, I’m whining. Time zones are inconvenient when trying to follow events happening on the other side of the world. If you live elsewhere, though, and want to watch all the chaos live, I encourage you to do so! Don’t miss the openings by not knowing the slight change to the schedule, and enjoy!

Khanty-Mansiysk Round 8 Update

Nakamura’s huge run continued today. Not only did he win his second consecutive game (so much for our earlier complaints that he was drawing too much!) but he also benefited from an upset victory by Jakovenko over Caruana. Nakamura is now tied with Caruana and Dominguez for first place at Khanty-Mansiysk, and if the tournament ended today would earn 140 Grand Prix points for his efforts, enough for a comfortable second place finish in the final standings (behind Caruana) and a berth in the 2016 Candidates Tournament.

Despite his loss, Caruana’s odds of a top two finish in the overall Grand Prix standings remain a comfortable 92%, and Nakamura boasts a 76% chance (up from just 31% two days ago). Overall there is more clarity in the race right now, going into tomorrow’s rest day, than at any point so far in this event. Here are how the standings would look if the event ended now, and each player’s current and pre-event odds of qualifying for the Candidates Tournament by finishing in the top two:

Player Live Rating Baku Tashkent Tbilisi Khanty-Mansiysk CURRENT TOTAL ODDS (PRE K-M) ODDS (CURRENT)
 Fabiano Caruana (ITA) 2806.1 155 75 140 370 71% 91.8%
 Hikaru Nakamura (USA) 2803.1 82 125 140 347 49% 75.7%
 Evgeny Tomashevsky (RUS) 2740.3 82 170 25 277 52% 6.2%
 Dmitry Jakovenko (RUS) 2753.1 30 140 80 250 9% 11.1%
 Boris Gelfand (ISR) 2750.8 155 15 80 250 7% 8.7%
 Sergey Karjakin (RUS) 2757.8 82 75 80 237 8% 6.5%
 Shakhriyar Mamedyarov (AZE) 2735.0 35 125 75 235 0% 0%
 Leinier Dominguez (CUB) 2750.2 10 75 140 225 0% 0%
 Teimour Radjabov (AZE) 2738.0 50 50 110 210 0% 0%
 Dmitry Andreikin (RUS) 2717.9 20 170 10 200 0% 0%
 Alexander Grischuk (RUS) 2780.9 82 40 55 177 3% 0.09%
 Peter Svidler (RUS) 2739.8 82 20 55 157 0.1% 0%
 Anish Giri (NED) 2768.2 40 75 40 155 1% 0%
 Baadur Jobava (GEO) 2696.2 75 40 25 140 0.2% 0%
 Maxime Vachier-Lagrave (FRA) 2723.6 75 40 10 125 1% 0%
 Rustam Kasimdzhanov (UZB) 2703.8 35 15 75 125 0% 0%

On the other hand, nothing is decided yet. While the picture is finally clear in the sense of having two obvious favorites, rather than three or more players with similar chances, the number “100%” doesn’t show up in any column. There’s still roughly a one in four chance that Nakamura fails to qualify, and several long shots who could potentially overtake him in the final three rounds. I find it interesting to note that Jakovenko and Gelfand both have better chances of qualifying for the Candidates now than they did when this tournament began. Jakovenko’s 11% chance, for instance, certainly can’t be ignored. Much stranger things have happened.

Here is a map of each player’s most likely final score (in yellow) at this event, and their odds of achieving each possible score. This should emphasize how much remains unclear in the final results – no player in the field has better than a 36% chance of achieving any one specific score:


As for the final standings at this particular event, now that we have a three-way tie with just three rounds left, a clear winner is looking less likely. Here are each player’s expected Grand Prix points earned on average (EV) and odds of winning the event outright, along with each players “Score Today”, or how many Grand Prix points they would earn based on the current standings, so that you can see at a glance who is favored to improve their situation in the last three rounds and who is more likely to regress:

Player K-M EV Score Today Odds of Clear 1st (Pre-Event Odds)
 Hikaru Nakamura (USA) 125 140 22% 14%
 Fabiano Caruana (ITA) 120 140 17% 17%
 Leinier Dominguez (CUB) 123 140 15% 2%
 Sergey Karjakin (RUS) 87 80 3% 5%
 Dmitry Jakovenko (RUS) 86 80 2.8% 3%
 Boris Gelfand (ISR) 83 80 1.8% 3%
 Peter Svidler (RUS) 67 55 0% 2%
 Alexander Grischuk (RUS) 62 55 0.29% 11%
 Anish Giri (NED) 47 40 0.00% 7%
 Baadur Jobava (GEO) 26 25 0.00% 1%
 Evgeny Tomashevsky (RUS) 31 25 0% 3%
 Maxime Vachier-Lagrave (FRA) 13 10 0% 3%

Notice that all three co-leaders are expected to earn, on average, fewer Grand Prix points than they currently stand to pick up. This is because maintaining a lead is fundamentally difficult. You don’t just have to outperform one player behind you (which you might be a favorite to do), you must avoid being passed in the standings by ANY of the players behind you. Seldom would anyone be favored to outperform the entire field – perhaps excepting Magnus Carlsen who is not a part of this event.

After the rest day, round 9 will be played on Sunday. Caruana will have the black pieces against Karjakin as he tries to hold on to his place atop the Grand Prix standings. Our other leader in the current projections, Nakamura, will have white against Grischuk.

That game, Nakamura – Grischuk, presents an interesting scenario (first brought to my attention by Martin Bennedick, @bennedik on Twitter) where it’s possible that Grischuk’s overall odds of qualifying for the Candidates Tournament could possibly be highest if he LOSES this game. To understand why, we must remember that the Grand Prix will determine only two of the eventual eight players in that field. Two other Candidates will be the players with the highest average rating across all 12 rating lists from 2015 who did NOT already qualify in another manner.

Right now that average ratings list shows potential qualifiers as 1. Caruana; 2. Topalov; 3. Nakamura; 4. Grischuk; 5. Kramnik. This means that as it stands right now, if Caruana and Nakamura both qualify via the Grand Prix, Grischuk moves up to second on the list and becomes a projected Candidate (which he currently is not). If Caruana and, say, Tomashevsky finish top two in the Grand Prix, then Topalov and Nakamura would get in by ratings and Grischuk would be left out.

So how much could Grischuk help Nakamura’s chances by losing that game? We estimate Nakamura at 76% to finish in the top two as it stands, but if we assume a Nakamura win over Grischuk while keeping everything else random, those odds climb to 93%! On the other hand, if Grischuk were to shoot himself in the foot and beat Nakamura, Naka’s chances would plummet to roughly 45%.

So why isn’t it a no-brainer that Grischuk is better off with a loss? What’s the downside, that led us to use hedging terminology like “it’s possible” and “could be”? First there is of course a morality aspect. We want to be completely clear that we are absolutely not advocating an intentional loss. Throwing a game is never acceptable, especially in an event of this magnitude, regardless of whether the math indicates you might benefit from a loss. However there’s also a mathematical downside. With the loss, Grischuk’s rating would drop, and he would have only a small lead over not just Kramnik but also Aronian in our projected average ratings. There’s a lot of chess left to be played in 2015, and a strong chance that Grischuk could be overtaken. The principle we discussed earlier where it’s particularly difficult to maintain a lead against multiple challengers applies here as well. With a loss in this game, Grischuk would temporarily be our projected #2, but would be an underdog to hold that spot. On the other hand, with a win, he would gain rating points and his projection in the average rating standings would be much stronger. He would have a commanding lead over those behind him, and while he would be #3 behind Nakamura it would be by a small margin. 45% of the time Naka would qualify via the Grand Prix anyway, and he’d be #2 in rating by a large margin, and the other 55% of the time he’d certainly have ample opportunity as the year progresses to surpass Nakamura in the projected rating standings.

Overall, I don’t have a good algorithm to predict odds of various rating shifts through the rest of the year, so I can’t put precise predictions on how likely players are to finish top two in the ratings race. However the 10 point rating swing of a win versus a loss, carried through 7 future rating lists, will have a lot of impact. All told, I can’t prove it, but I think Grischuk is more likely to eventually find himself in the 2016 Candidates Tournament if he beats Nakamura on Sunday than if he loses on Sunday. I do suspect, though, that a draw might be worse than either, so perhaps it would be in his best interest to play aggressively and see what happens! It’s not entirely clear though. I’d love to hear other thoughts on this scenario in the comments.

Either way I certainly find it to be a very interesting situation to analyze, if you happen to have an interest in game theory as I do.

Khanty-Mansiysk Round 7 Update

Today’s big winner was Nakamura. Not only did he literally win a game, his first of the tournament after starting with six straight draws, but he also gained ground thanks to a loss by Tomashevsky, his biggest rival in the standings. Nakamura is now a strong favorite to finish second overall behind likely winner Caruana in the Grand Prix standings:

Player Live Rating Baku Tashkent Tbilisi Khanty-Mansiysk CURRENT TOTAL ODDS (PRE K-M) ODDS (CURRENT)
 Fabiano Caruana (ITA) 2812.0 155 75 170 400 71% 97.7%
 Hikaru Nakamura (USA) 2799.5 82 125 85 292 49% 58.0%
 Sergey Karjakin (RUS) 2762.4 82 75 125 282 8% 18.8%
 Evgeny Tomashevsky (RUS) 2740.5 82 170 20 272 52% 18.9%
 Boris Gelfand (ISR) 2745.9 155 15 65 235 7% 3.7%
 Dmitry Jakovenko (RUS) 2747.2 30 140 65 235 9% 2.8%
 Shakhriyar Mamedyarov (AZE) 2735.0 35 125 75 235 0% 0%
 Teimour Radjabov (AZE) 2738.0 50 50 110 210 0% 0%
 Leinier Dominguez (CUB) 2750.0 10 75 125 210 0% 0%
 Dmitry Andreikin (RUS) 2717.9 20 170 10 200 0% 0%
 Peter Svidler (RUS) 2744.7 82 20 85 187 0.1% 0.1%
 Alexander Grischuk (RUS) 2776.3 82 40 40 162 3% 0.04%
 Baadur Jobava (GEO) 2699.8 75 40 40 155 0.2% 0.01%
 Anish Giri (NED) 2768.5 40 75 40 155 1% 0.01%
 Maxime Vachier-Lagrave (FRA) 2723.3 75 40 10 125 1% 0.0%
 Rustam Kasimdzhanov (UZB) 2703.8 35 15 75 125 0% 0.0%

As we can see, if the event ended today Caruana would win the Grand Prix in dominant fashion, on the strength of a first place finish here at Khanty-Mansiysk. Nakamura would be second, 10 points ahead of Karjakin and 20 points ahead of Tomashevsky.

The bad news for Nakamura and Caruana is that the event is not over yet. There are four more rounds left to play! Although Nakamura’s odds improved drastically from the 31% mark where they sat after round 6, there is still better than a 40% chance of someone else surpassing him for the #2 spot. Most likely this “someone else” would be Karjakin or Tomashevsky, but other long shots remain mathematically in contention as well. Gelfand, for instance, is predicted by our model to climb into the top two of the Grand Prix standings roughly once every 27 tries, and Jakovenko has a 1/36 shot (the same odds as rolling snake eyes on a pair of six sided dice!) And while we’re speaking of relatively unlikely scenarios, notice also that our presumed victor, Caruana, actually has a 2.3% chance of not only failing to win the Grand Prix, but in fact falling outside of the top two in the standings!

In other words: the picture got a lot clearer today, and it’s easy to project Caruana and Nakamura to finish 1 and 2 in the standings and earn their Candidates Tournament berths. Nevertheless, nothing is set in stone yet, and the final four rounds still have the potential to bring major surprises. It’s not over yet!

Here’s our current projections for the results of just this leg, ignoring the broader standings of the multi-event Grand Prix, complete with each player’s average Grand Prix points earned and odds of winning the leg outright:

Player K-M EV Odds of Clear 1st (Pre-Event Odds)
 Fabiano Caruana (ITA) 147 47% 17%
 Leinier Dominguez (CUB) 115 8% 2%
 Sergey Karjakin (RUS) 109 8% 5%
 Hikaru Nakamura (USA) 98 4% 14%
 Peter Svidler (RUS) 90 2% 2%
 Dmitry Jakovenko (RUS) 60 0.3% 3%
 Boris Gelfand (ISR) 65 0.2% 3%
 Alexander Grischuk (RUS) 50 0.05% 11%
 Anish Giri (NED) 51 0.03% 7%
 Baadur Jobava (GEO) 38 0.01% 1%
 Evgeny Tomashevsky (RUS) 34 0% 3%
 Maxime Vachier-Lagrave (FRA) 13 0% 3%

One Khanty-Mansiysk Scenario

I saw a claim floating around Twitter that for Nakamura to qualify for the Candidates Tournament (finish in the top two of the final Grand Prix standings), he *HAD* to outscore Tomashevsky by at least 1.5 points over the final 5 rounds, which would be an extremely difficult task. I doubted this could be true if if our numbers were right (estimating Naka at 30% to qualify) so I ran a few simulations until I managed to find an exception. The following is a set of results in all remaining games that allows Nakamura to finish second in the final Grand Prix standings despite “only” outscoring Tomashvesky by 1 point (3/5 to 2/5). As a bonus, this scenario even involves Naka losing a game, and still getting in!:

Round 7:

Caruana 1/2 – 1/2 Gelfand
Jakovenko 1/2 – 1/2 Grischuk
Karjakin 1/2 – 1/2 Jobava
Nakamura 1/2 – 1/2 Vachier-Lagrave
Giri 1/2 – 1/2 Tomashevsky
Dominguez 1/2 – 1/2 Svidler

Round 8:

Gelfand 1/2 – 1/2 Svidler
Tomashevsky 0 – 1 Dominguez
Vachier-Lagrave 1/2 – 1/2 Giri
Jobava 0 – 1 Nakamura
Grischuk 1/2 – 1/2 Karjakin
Caruana 1 – 0 Jakovenko

Round 9:

Jakovenko 1/2 – 1/2 Gelfand
Karjakin 0 – 1 Caruana
Nakamura 1 – 0 Grischuk
Giri 1/2 – 1/2 Jobava
Dominguez 1/2 – 1/2 Vachier-Lagrave
Svidler 0 – 1 Tomashevsky

Round 10:

Gelfand 1/2 – 1/2 Tomashevsky
Vachier-Lagrave 1 – 0 Svidler
Jobava 1/2 – 1/2 Dominguez
Grischuk 1/2 – 1/2 Giri
Caruana 1 – 0 Nakamura
Jakovenko 1/2 – 1/2 Karjakin

Round 11:

Karjakin 0 – 1 Gelfand
Nakamura 1/2 – 1/2 Jakovenko
Giri 1/2 – 1/2 Caruana
Dominguez 0 – 1 Grischuk
Svidler 1/2 – 1/2 Jobava
Tomashevsky 0 – 1 Vachier-Lagrave

Final Khanty-Mansiysk Standings:

Name Score GP Pts
Caruana 8.5 170
Nakamura 6 113
Dominguez 6 113
Gelfand 6 113
Karjakin 5.5 75
Svidler 5.5 75
Vachier-Lagrave 5 50
Grischuk 5 50
Jakovenko 5 50
Jobava 4.5 20
Giri 4.5 20
Tomashevsky 4.5 20

Resulting Final Grand Prix Standings:

Player Baku Tashkent Tbilisi Khanty-Mansiysk TOTAL
 Fabiano Caruana (ITA) 155 75 170 400
 Hikaru Nakamura (USA) 82 125 113 320
 Boris Gelfand (ISR) 155 15 113 283
 Evgeny Tomashevsky (RUS) 82 170 20 272
 Shakhriyar Mamedyarov (AZE) 35 125 75 235
 Sergey Karjakin (RUS) 82 75 75 232
 Dmitry Jakovenko (RUS) 30 140 50 220
 Teimour Radjabov (AZE) 50 50 110 210
 Dmitry Andreikin (RUS) 20 170 10 200
 Leinier Dominguez (CUB) 10 75 113 198
 Peter Svidler (RUS) 82 20 75 177
 Alexander Grischuk (RUS) 82 40 50 172
 Maxime Vachier-Lagrave (FRA) 75 40 50 165
 Baadur Jobava (GEO) 75 40 20 135
 Anish Giri (NED) 40 75 20 135
 Rustam Kasimdzhanov (UZB) 35 15 75 125

The exact scenario is of course extraordinarily unlikely (as is any one specific set of results), but it demonstrates a few key things that have to work in Nakamura’s favor in order for him to pull off second place without outscoring Tomashevsky by more than one point.

First, Caruana runs away with the event while other players at the top of the standings stumble, allowing Nakamura to catch up with (and tie for) second place. This is critical because the top three places earn (or split in the case of a tie) bonus Grand Prix points.

Second, the players at the bottom of the field bounce back in the final rounds, and catch up with Tomashevsky, so that he earns fewer points than he “normally” would with a 2/5 finish.

Please double check my math, but I’m pretty sure that this scenario is a valid case in which Nakamura could qualify (somewhat convincingly) for the Candidates Tournament with a 2nd place finish in the Grand Prix, while NOT outscoring Tomashevsky by 1.5 (or more) points over the final five rounds at Khanty-Mansiysk. If I’m wrong, let me know, so that I can identify the flaw in my model ASAP!

Update: How unlikely is this exact scenario, by the way? Extremely, but that’s true of all specific cases. Obviously, since a draw is the most likely of the three possible results in any given game, the single most likely scenario would be for every game in the final five rounds to happen. Even that, which again is the MOST LIKELY scenario, would happen less than 1 in 70 million times! With three possible results in each game (white win, draw, or black win) there are 3^30 possible permutations for how the event could finish up!