Khanty-Mansiysk Preview (FIDE Grand Prix, FINAL LEG)

The pairings have been drawn for the fourth and final event in the 2014-2015 FIDE Grand Prix. Games begin in just over 6 hours! Here is our look at the event, to whet your appetite.

First and foremost, this event is critical because it will determine the final Grand Prix standings, which in turn will determine two of the eight candidates for the 2016 World Chess Championship match against defending champion Magnus Carlsen. The top two players in the Grand Prix standings will join six others in a Candidates Tournament in early 2016, with the winner of that event slated to take on Magnus later in the year. Without the relevance to the World Championship, it’s unlikely this event would be of quite so much global interest as it is – although it’s also certainly a wonderful showcase of 12 fantastic chess players in its own right.

Worth mentioning is that third (and possibly even fourth) place in the final Grand Prix standings could also matter. The official rules for the Candidates Tournament say that the first qualifier is the loser of the 2014 match (Viswanathan Anand), and the second and third qualifiers are the top two finishers in the 2015 World Cup, which will be held later this year. The top two Grand Prix finishers *not already qualified* earn spots four and five. It’s relatively unlikely that one player will finish top-two in both events, but it’s not impossible that someone like Fabiano Caruana might do so, and in that case the third place Grand Prix finisher would earn a spot as well. Furthermore, if any player who qualifies for the Candidates Tournament is unable to participate, or chooses to withdraw, then the first alternate candidate is the third place finisher from the Grand Prix.

How do the standings work? Each of 16 players competes in three of four tournaments. They earn Grand Prix points based on their finish in each event, ranging from 170 points for a clear first place (not tied with anyone) down to 10 points for a sole last place finish. Each player totals their points from the three events, and the player with the most total points wins the Grand Prix! Of course most audience members aren’t concerned with just the winner, we’re also watching closely to see who finishes second.

So what will happen? We can’t know of course, that’s the fun of watching. However we have designed a model to predict the results. Using each player’s current live rating from 2700chess.com we can estimate odds of a white win, a black win, or a draw for every game that will be played. We then simulate the event 20,000 times, tally up each player’s finish (and the resulting final Grand Prix standings) after each simulation, and tabulate the results for your reading pleasure!

So enough with the prelude, who are our combatants?

The Favorites

  • Evgeny Tomashevsky – 2749 – currently ranked #15 in the world. Tomashevsky leads the Grand Prix standings with 252 points, driven by an absolutely stellar performance in the third leg held in Tbilisi in February. He entered that event as an underdog, rated just 2716, and given just a 2% chance of finishing in the top two of the final standings by our model. However he crushed that field, winning five games and drawing the rest, winning clear first by a huge margin of a point and a half, and earning 170 GP points (and 29 rating points) for his efforts. The performance was so remarkable and unexpected that it prompted us to take a deeper look at whether we should have seen it coming. Now our model gives him a much more impressive 51.8% chance of holding his lead and earning one of the coveted candidates berths. His job is not yet complete though. Even with his rating improved to 2749 our model still views Tomashevsky as more likely to finish in the middle of the pack than on top, projecting him to earn an average of 65 GP points from this final leg and giving him only a 3% chance of winning this event outright like he did the last one. He’s bucked such odds in the past, but two highly rated challengers are nipping at his heels, ready to soar past him if he should stumble this time around. One extra challenge in holding his spot: he has to play six games as black and only five as white.
  • Fabiano Caruana – 2803 – currently ranked #3 in the world. Caruana is second in the current standings (ignoring players who already completed their three events and are completely eliminated from contention for the top two spots) with 230 Grand Prix points. He got there by tying for first place in leg one, and adding a middle of the pack result in leg two. As the highest rated player in the field, and with the extra advantage of six games as white, our simulations give him a 17% chance of winning this event outright, while projecting him to earn an average of 106 GP points from the leg. To win, he would need to outscore Tomashevsky by 22 points, and we expect him to do so more often than not (with a 41 point lead in his average projected result). Of course to win the whole thing he also needs to avoid being passed by anyone else, but then again to reach the Candidates Tournament he doesn’t need to win, just finish in the top two. All told, this works out to a 71.1% chance of finishing in the top two of the final standings.
  • Hikaru Nakamura – 2799 – currently ranked #4 in the world. Nakamura is third in the (relevant portion of the) current standings with 207 points. He trails Tomashevsky by a much larger margin (45), and also benefits in our projections from a high rating (although unlike Caruana, he has the tougher draw with six black games). We expect him to score an average of 99 points in this event, with a 14% chance of winning it all, and as with Caruana he of course also could qualify for the Candidates Tournament from second place even without catching Toma. Our numbers show him as the smallest of underdogs to finish in the top two, at a 49.1% chance. Might as well flip a coin!

The Other Contenders

  • Dmitry Jakovenko – 2746 – #17. Tied for (relevant) fourth place in the current standings with 170 GP points, Jakovenko is still in the running if he can swing a good result here. While he has only a 3% chance of winning the event outright, and is only expected to average 68 points from this leg, if he does manage to finish first or second and two of the top three stumble, he’s definitely still alive. We project him to climb into the top two of the final standings and win a berth in the Candidates Tournament 8.6% of the time.
  • Boris Gelfand – 2744 – #18. Tied with Jakovenko for fourth is Gelfand with 170 points of his own. The same principles apply, and their ratings are almost dead even, however his odds are hurt by having the black pieces six times, while Jakovenko only has them five times. He has the same 3% chance of winning the whole event, but projects to average only 62 points. We have him finishing in the top two 7.0% of the time.
  • Sergey Karjakin – 2753 – #12. Next, at #6 in the standings, is Karjakin with 157 points. A slightly higher rating and a good draw (six games as white) actually make his projections marginally better than Gelfand’s, even though he trails currently. We have him averaging 72 points from this event, winning outright 5% of the time, and cracking the overall top two 7.5% of the time.
  • Alexander Grischuk – 2785 – #6. At #7 in the (relevant) standings is Grischuk with just 122 points. That’s an awfully steep hill to climb, but he is the third highest rated player in the field, with six games as white, so his projections are quite good. We expect him to earn an average of 93 GP points, and win this event outright 11% of the time, but even that clear first place result isn’t enough to guarantee he’ll reach the top two position he needs in the overall standings. We expect him to earn a Candidates berth just 3.1% of the time.

The Super Longshots

  • Anish Giri – 2776 – #10. One of three players tied for (relevant) 8th place with 115 points, Giri at least projects well thanks to his top-ten world rating. A 7% chance of winning the event, and an expected average of 82 points, are nice but he needs a lot of help even if he does win it all. To overcome the massive standings deficit and finish in the top two he needs tremendous luck, as we see it happening only 1.1% of the time.
  • Maxime Vachiere-Lagrave – 2743 – #19. The second player with 115 points, MVL is in even worse shape as due to his lower rating he only projects to score 65 points with a 3% chance to win the leg. His odds of reaching the Candidates Tournament are a meager 0.6%.
  • Baadur Jobava – 2699 – #47. The third player with 115 points is Jobava, who is also the lowest rated player in the field. We give him only a 1% chance of winning the event, and project that he’ll earn an average of only 42 points, although he’s very likely to do it in an exceedingly entertaining fashion given his reputation for playing “exciting” chess! Unfortunately for fans of his style, there is only a 0.2% chance he’ll earn the opportunity to showcase that style in the Candidates Tournament.
  • Peter Svidler – 2736 – #23. In 11th place with just 102 points is Svidler. We all see how this works by now: with a mediocre rating (at least in this field… millions of players around the world would love to be able to call 2736 “mediocre”) he projects to add just 58 points, win the event only 2% of the time, and reach the top two just 0.1% of the time. Or, as optimists everywhere would note: “So you’re saying there’s a chance!” Yes there is a chance. It is approximately 1 in 1,000.
  • Leinier Dominguez – 2737 – #22. Finally we have our last place contestant. Dominguez has just 85 points right now, and unfortunately that’s almost certainly not enough. Even if he came in first, he’d have just 255 points, meaning his best case scenario is a second place finish to Tomashevsky (who will add a minimum of 10 to his current 252). Second place is good enough in the Grand Prix, but it would also require Caruana to finish in the bottom two of the field, and Nakamura to finish in the bottom five, and none of the other contenders to pass him either. This is not technically impossible, and a previous simulation gave him a 0.003% shot of everything coming together, but our new simulation today that we ran after the official pairings were released did not see him reach the top two a single time in 20,000 times. His odds are essentially, but not technically, zero.

The Eliminated

  • Shakhriyar Mamedyarov
  • Teimour Radjabov
  • Dmitry Andreikin
  • Rustam Kasimdzhanov

These four players have already completed their Grand Prix run, playing the first three events and sitting this one out. Mamedyarov managed the highest score of the group, amassing 235 points, which is enough for him to technically be #2 in the standings at this moment, but that’s a spot it’s impossible for him to hold. It is 100% guaranteed that none of these four will reach the Candidates Tournament by finishing in the top two of the Grand Prix standings. When we referred to players’ “relative” standings above, it was ignoring these four eliminated players, which is why we said Caruana was in second place right now, when technically Caruana is currently third behind the eliminated Mamedyarov.

Other Notes

  • The eagle eyed (or obsessive) among you may have added up the stated odds of each player winning this event outright, and seen that of course they add up to just over 70%. Our simulation predicts a 28% chance that first place in this leg will be a tie between two or more players.
  • Here are projected results for all 12 players in this leg:
    Player K-M AVERAGE SCORE Odds of Clear 1st
    SHARED FIRST 28%
     Fabiano Caruana (ITA) 106 17%
     Hikaru Nakamura (USA) 99 14%
     Alexander Grischuk (RUS) 93 11%
     Anish Giri (NED) 82 7%
     Sergey Karjakin (RUS) 72 5%
     Dmitry Jakovenko (RUS) 68 3%
     Evgeny Tomashevsky (RUS) 65 3%
     Maxime Vachier-Lagrave (FRA) 65 3%
     Boris Gelfand (ISR) 62 3%
     Peter Svidler (RUS) 58 2%
     Leinier Dominguez (CUB) 58 2%
     Baadur Jobava (GEO) 42 1%
  • Here is how each player’s chances at reaching the Candidates Tournament have ebbed and flowed since we began tracking them before the third leg began:
    Player ODDS (PRE-TBILISI) ODDS (POST-TBILISI) ODDS (PRE-KHANTY-MANSIYSK)
     Fabiano Caruana (ITA) 58% 70% 71%
     Evgeny Tomashevsky (RUS) 2% 49% 52%
     Hikaru Nakamura (USA) 39% 52% 49%
     Dmitry Jakovenko (RUS) 1% 2% 9%
     Sergey Karjakin (RUS) 5% 7% 8%
     Boris Gelfand (ISR) 6% 8% 7%
     Alexander Grischuk (RUS) 40% 3% 3%
     Anish Giri (NED) 14% 7% 1%
     Maxime Vachier-Lagrave (FRA) 15% 0.2% 0.6%
     Baadur Jobava (GEO) 0.5% 1% 0.2%
     Peter Svidler (RUS) 5% 0.1% 0.1%
     Leinier Dominguez (CUB) 0.3% 0.002% 0%
     Shakhriyar Mamedyarov (AZE) 6% 0% 0%
     Teimour Radjabov (AZE) 0.02% 0% 0%
     Dmitry Andreikin (RUS) 10% 0% 0%
     Rustam Kasimdzhanov (UZB) 0% 0% 0%
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Is Tomashevsky Proving Us Wrong?

12 days ago, we published our “pre-Tbilisi” estimations of each player’s odds of finishing top-two in the final standings of the FIDE Grand Prix, and earning a berth in the 2016 Candidates Tournament. In that initial posting, we listed Evgeny Tomashevsky as having a meager 2% chance of climbing into that top-two tier. Today, nine undefeated rounds (and five wins) later, we just updated our odds to list Tomashevsky as having a 49% chance of reaching that same tier. In light of such a drastic shift, it makes sense to pause for a moment and ask ourselves: was the original prediction wrong?

The classic statistician’s defense would be to point out that we never claimed Tomashevsky had NO chance of reaching the Candidates Tournament (nor has he done so yet), we just considered it highly unlikely. 2% still means, though, that one time out of fifty the event WILL occur. If you make a lot of predictions, then you will see “longshots” like this come through from time to time. So one possibility is that our prediction was perfectly right, given what we knew at the time, about Tomashevsky’s odds, and what we’re seeing from him in reality was his absolute best case scenario – a highly unlikely event coming to pass.

However it would be lazy of us to simply assume that was the case. It’s also possible that we made a mistake in building our model, and incorrectly underestimated his chances originally. Maybe what he’s done so far was more likely than we originally thought. So before we write this off to simple “positive variance” for Tomashevsky, let’s dig into the model a little deeper and probe for potential errors.

The most obvious consideration is the accuracy of the ELO system. Our entire model is built on the basis of using players’ ELO ratings to predict the results of each game. Tomashevsky’s odds before the tournament began were based on his rating of 2716, third lowest in the Tbilisi field. Many studies have shown that the ELO system as a whole is quite effective at predicting results in the broad sense, and we don’t feel inclined to consider any possibility that using ELO as our basis is methodologically unsound in general, but that doesn’t necessarily mean ELO is accurate for every player at all times. In fact it’s a given that at any time there must always be some players who are overrated and some others that are underrated. An ELO-based model will, of course, miscalculate the odds involving players whose rating is not accurate to that player’s “true playing strength”. Perhaps Tomashevsky was underrated before the event began, and his expected results were artificially deflated in our model, as a result?

Here is a graph of Tomashevsky’s rating, by age, over the course of his life. The blue line shows every official published rating he has ever had, while the orange spike at the end shows his live ratings after each round at Tbilisi:

Toma

What we can see here is that a little over five years ago, at the age of 22.35 years old, Tomashevsky had a published rating of 2708 – his first rating above the 2700 barrier. His 47 published ratings since then, up to and including his February 2015 rating of 2716 that we mentioned earlier, have ranged from as low as 2695 to as high as 2740, but averaged 2714. We can drill in on just those last 5 1/2 years of his ratings history, and have Excel plot a trend line. This allows us to see whether he has been showing any signs of improvement (or decline) over the time span:

TomaTrend

Our trend line is almost perfectly flat, at our average rating of 2714 (very slightly trending downward, actually.) In other words, we have over five years of professional chess results from Tomashevsky showing that while he has of course fluctuated above and below his average at times, he has on the whole maintained a very steady rating in the range of approximately 2715. This is quite a strong argument in favor of our model’s usage of 2716 as his baseline rating in the original predictions. Additionally, at almost 28 years old it seems unlikely that there was any particular reason to suspect that now might be a likely time for Tomashevsky to suddenly make a major improvement in his game, and begin playing at a higher level.

We have plans to eventually do a detailed study of “ratings plateaus” – long periods in a chess player’s career where he or she maintains a relatively consistent rating – in the future. Many players have notably had a prolonged plateau, and then suddenly seen their rating spike. Maxime Vachiere-Lagrave is one such example. We have plans to examine factors such as age and the length of the plateau, and evaluate whether there might be any way to predict when a player might be likely to make a “breakthrough” soon. Since that analysis lies in the future, not the present, we can’t prove our position mathematically at this time, but we suspect that any plateau model we might develop will probably NOT identify a 28 year old, whose plateau has lasted five or more years, as a “likely breakthrough candidate”.

If all our data suggests that 2716 was a very good baseline for Tomashevsky’s rating, in our initial simulations, then it suggests that our original idea might be right. The pre-Tbilisi odds were correct representations of the odds at that time, and what has happened so far truly has just been an extraordinary event. We can call it “positive variance” if we want to be clinical, or “good luck”, or “good fortune”, if we want to couch it in more mystical terms, or perhaps we could even say Evgeny has been “clutch” if we want to borrow a term from our favorite sportscasters. Regardless of the terminology, this raises a new intriguing consideration:

Might our CURRENT predictions be wrong?

Our odds of Tomashevsky reaching the Candidates Tournament depend heavily on what we think he will do in the final leg of the Grand Prix at Khanty-Mansiysk. Right now, we are predicting his results in that event using his current live rating of 2744.9, courtesy of 2700chess.com. This is the highest rating he has ever had in his life (or will be, once it is officially published by FIDE), and it comes courtesy of his remarkable results so far at Tbilisi. However, if we have established that 2715 (or so) is a good baseline for him, based on a large sample size of previous results, then isn’t he perhaps overrated now? If we’re deeming his results at Tbilisi to be above his reasonable expectation, and rejecting the theory that he has truly broken through his plateau and achieved objective 2750+ strength, then we also have to consider that by using his current live rating in our model we may be overestimating his chances at Khanty-Mansiysk. Maybe we should be expecting more regression to the mean, and lowering our expectations for him at that event, which would leave his odds of finishing in the final Grand Prix top-two at lower than our currently projected 49%.

However we have one final idea to consider. Let us return, now, to a word I used earlier: “clutch”. Borrowed from the world of sports, we often talk about athletes who have an uncanny ability to perform their best when on the biggest stage. The basketball player who takes over a playoff game in the fourth quarter, for instance. Can chess players be “clutch”, and if so, is Tomashevsky?

If we look carefully at his six-year ratings graph, we will notice three major upward spikes. On the November 2011 ratings list, he gained 30 rating points, jumping from 2710 to 2740 (his highest published rating so far in his career). That rating then slowly sank downward to a nadir of 2703, before spiking back up to 2720 in October 2013. Then his rating sank steadily once more, until it sat at 2701, and then in the November 2014 rating list it spiked again, to 2714.

What events did Tomashevsky have such great success at, to cause these three spikes? The first spike included his rating gain from the 2011 World Cup. Although he was eliminated in the third round that year, he managed a performance rating for the event of 2800. The second spike is entirely the result of the 2013 World Cup, when despite being seeded 32nd, he managed to reach the semifinals, coming just one round from earning a spot in the 2014 Candidates Tournament, and posting a performance rating of 2813. And the final spike came from his results at Baku last fall, the first leg of the current Grand Prix that all these odds we keep mentioning refer to, where his performance rating was 2792. And of course we will see a fourth spike show up on the March 2015 rating list, when his absurdly great results at Tbilisi are factored in. His performance rating through round nine is an out-of-this-world 2969!

So in other words, Tomashevsky has spent the last five plus years demonstrating consistently that he is roughly a 2700-level player when the World Championship is not in play, but in the four events he has played during that span that serve as qualifiers for Candidates Tournaments (and potentially as steps towards the World Championship) his combined performance rating has been well above 2800.

Perhaps the answer is that Tomashevsky is simply an incredibly clutch chess player, who saves all his best efforts for events that might get him closer to an eventual World Championship. If that is the case, then thanks to his performance in Tbilisi, the 2016 Candidates Tournament is now well in his sights – and woe be unto his unfortunate opponents at Khanty-Mansiysk who must play the juggernaut that is Toma With Purpose, rather than the 2700ish Tomashevsky we see the rest of the time. If this idea has genuine merit, then perhaps we need to consider that we might still be underestimating his chances.

Ultimately we have no intention of changing our model at this time, but if “Clutch Tomashevsky” is a real thing then we may well have erred when we gave him only a 2% chance before Tbilisi began. Certainly if we had instructed the model to treat him as a 2800+ player, which so far he has consistently proven to be in World Championship qualifying events, then the model would have given him much higher odds.

Tblisi Grand Prix – Second Rest Day Update

While our top story from the first rest day (the rise of Tomashevsky) has continued unabated, there is now a second key story line at play in this event: the fall of Grischuk. While Tomashevsky scored 2.5/4 and maintained his full point lead over the field, Grischuk dropped two games, scored only 1/4, and fell firmly out of contention. In this post we will be examining the deeper ramifications (both obvious and subtle) of these two players’ results, as everything else depends on them.

First the obvious: Tomashevsky’s position has improved greatly. While his lead hasn’t actually grown, it should be obvious that a full point lead over just one player, with only three games left, is a far stronger advantage than a full point lead over three different players, with seven games left. Evgeny didn’t particularly need to extend his lead, merely hold serve as others fell off the pace. In this case it was Grischuk and Giri who dropped further behind, while noone else closed the gap. How much better is Tomashevsky looking at this point, than before? In the last four rounds his odds of winning the event outright have improved from 31% to a whopping 79%! His expected score (in Grand Prix Points) is now 164 – keeping in mind that you score 170 for a clear first, and just 140 for second. Even the one time in five that he doesn’t win outright, he will almost always share first, usually with only one other player, and still bring home 155 points. His odds in the overall Grand Prix standings, meanwhile, are now up to a 42% chance of finishing top two (and qualifying for the Candidates Tournament). This is a humongous gain over his round four position, when despite his great start he had just a 17% chance, or especially over his pre-tournament odds when we evaluated him as having only a 2% chance of being a Candidate for the World Championship next year.

Here are average expected points scored at Tbilisi, and odds of winning first place outright, for all players. You may notice that it isn’t much of a race at this point.

Player Score (Out of 8) Tbilisi EV Odds of Clear 1st
 Evgeny Tomashevsky (RUS) 6 164 79%
SHARED FIRST 15%
 Dmitry Jakovenko (RUS) 5 124 5%
 Rustam Kasimdzhanov (UZB) 4.5 89 1%
 Teimour Radjabov (AZE) 4.5 87 1%
 Anish Giri (NED) 4 77 0%
 Shakhriyar Mamedyarov (AZE) 4 72 0%
 Baadur Jobava (GEO) 4 65 0%
 Leinier Dominguez (CUB) 4 57 0%
 Alexander Grischuk (RUS) 3.5 59 0%
 Maxime Vachier-Lagrave (FRA) 3 32 0%
 Peter Svidler (RUS) 3 26 0%
 Dmitry Andreikin (RUS) 2.5 20 0%

While it has little bearing on the overall Grand Prix standings, or even on the results at Tbilisi, we would like to highlight how impressively Jobava has bounced back from an atrocious start. After managing just one draw and three losses in the first four rounds, he has won three and drawn one in his last four rounds, returning to an even 50% score for the event, and bringing his live rating back above 2700.

Grischuk, on the other hand, has fared most poorly over the past four days. As the highest rated player in the field, he was expected to score well more often than not, so after round four we saw him as the most likely contender to potentially chase and catch Tomashevsky. Instead he tumbled. Where before we expected him to score an average of 113 Grand Prix Points, now we see him picking up only 59, which would not keep him alive in the overall Grand Prix standings. By virtue of his rating, he remains one of the favorites in the final event at Khanty-Mansiysk, but at this point his overall odds of reaching the Candidates Tournament via the Grand Prix are just 12%, whereas four games ago we had him at 41%. If he is going to get there, it will have to start over the final three rounds of Tbilisi. He has no realistic hope of winning this event, but if he can win a game or two and rise in the standings, it would gain him critical extra Grand Prix points that would keep him at least somewhat in contention overall, and keep his results relevant at Khanty-Mansiysk.

Here is where all 16 players in the Grand Prix stand, for average final score expectations, as well as odds of actually reaching the Candidates Tournament:

Player Baku Tashkent Tbilisi EV Khanty-Mansiysk EV TOTAL EV Top-Two Odds
 Fabiano Caruana (ITA) 155 75 100.9 330.9 68%
 Evgeny Tomashevsky (RUS) 82 164.4 60.7 307.1 42%
 Hikaru Nakamura (USA) 82 125 97.6 304.6 49%
 Alexander Grischuk (RUS) 82 59.0 97.3 238.3 12%
 Boris Gelfand (ISR) 155 15 64.1 234.1 8%
 Shakhriyar Mamedyarov (AZE) 35 125 72.0 232.0 1%
 Sergey Karjakin (RUS) 82 75 70.6 227.6 7%
 Dmitry Jakovenko (RUS) 30 123.7 62.0 215.7 5%
 Anish Giri (NED) 40 76.7 93.8 210.5 5%
 Dmitry Andreikin (RUS) 20 170 19.9 209.9 0%
 Teimour Radjabov (AZE) 50 50 86.8 186.8 0.05%
 Baadur Jobava (GEO) 75 64.7 41.2 180.9 1%
 Maxime Vachier-Lagrave (FRA) 75 31.7 74.0 180.7 1%
 Peter Svidler (RUS) 82 25.7 54.0 161.6 0.4%
 Rustam Kasimdzhanov (UZB) 35 15 88.8 138.8 0%
 Leinier Dominguez (CUB) 10 56.8 53.8 120.5 0.03%

You may notice, from the numbers above, two other major beneficiaries of Grishcuk’s collapse: Hikaru Nakamura and Fabiano Caruana. While sitting on the sidelines, these two have seen their chances improve significantly over the past four rounds, improving eight percentage points each over where they stood at the first rest day. Why? As the leaders in the overall Grand Prix standings prior to this event, they were in the best position to benefit from the rise of a relatively weak favorite at Tbilisi. While we don’t wish to take anything away from how impressive Tomashevsky has been at this event, he is still rated 50-60 ELO lower than the top rated players in the Grand Prix, and so our model projects him as less likely to repeat his success at Khanty-Mansiysk than, say, Grischuk or Giri would have been. So having more of Tbilisi’s Grand Prix points likely to be awarded to lower rated players puts Caruana and Nakamura in much better positions to maintain their leads through the final leg of the Grand Prix.

Also working in the leader’s favor has been the disappointing results for two other higher rated players: Giri and Vachier-Lagrave. While they never had as much hope originally as Grischuk did, making their drops less dramatic, they nevertheless have seen their odds of qualifying for the Candidates Tournament drop precipitously over the course of this event. Just like with Grischuk, these other drops from high rated players have also benefited Nakamura and Caruana… as well as helping Tomashevsky greatly, of course. Here is how each of the 16 players in the Grand Prix field has trended from before Tbilisi started, to the first rest day, to the second:

Player ODDS (PRE-TBILISI) ODDS (TBILISI REST 1) ODDS (TBILISI REST 2)
 Fabiano Caruana (ITA) 58% 59% 68%
 Hikaru Nakamura (USA) 39% 40% 49%
 Evgeny Tomashevsky (RUS) 2% 17% 42%
 Alexander Grischuk (RUS) 40% 41% 12%
 Boris Gelfand (ISR) 6% 6% 8%
 Sergey Karjakin (RUS) 5% 5% 7%
 Dmitry Jakovenko (RUS) 1% 1% 5%
 Anish Giri (NED) 14% 17% 5%
 Baadur Jobava (GEO) 0% 0% 1%
 Shakhriyar Mamedyarov (AZE) 6% 3% 1%
 Maxime Vachier-Lagrave (FRA) 15% 6% 1%
 Peter Svidler (RUS) 5% 2% 0%
 Teimour Radjabov (AZE) 0% 0% 0%
 Leinier Dominguez (CUB) 0% 0% 0%
 Dmitry Andreikin (RUS) 10% 3% 0%
 Rustam Kasimdzhanov (UZB) 0% 0% 0%

There is another, somewhat more subtle, ramification of Grischuk’s fall in the projected standings. It has become slightly less likely that the cutoff score needed to qualify for the Candidates Tournament will be extremely high. At the first rest day, when Grischuk (and his gaudy rating of 2810 at the time) was just one point off the lead, and still in legitimate contention, our model saw it as far more likely that he might post huge scores in both of the final two events, driving up the standards of qualification. Now of course Tomashevsky is still in a position to do just that, but with his lower rating he is projected as much less likely to follow up a great Tbilisi result with an equally great Khanty-Mansiysk result. Therefore, our projected cutoff has dropped 10 points. Our model now has the median points required to qualify for the Candidates as just 317, and now sees a (very remote) chance of someone qualifying with as little as 242 points, lower than our previously reported minimum. Of course there is still an extreme range of possible cutoffs, and noone should feel secure with a final score of, say, 320. In some of our simulations it still takes 392 points just to achieve second place! Here is a frequency graph of all the possible qualifying scores:

TbilisiRestTwo

One final consideration that we mentioned in our last post is the rating mark of 2800. Both Grischuk and Giri have fallen below it in the current live ratings, but they still have three rounds to rebound. Both are now underdogs to get their end-of-tournament rating (presumed to become official on the next rating list) back above the 2800 line, but neither is completely eliminated. Giri would need to score 2.5/3 in the final rounds, with the black pieces in two of those three games, and our model predicts him to do just that 14% of the time. Grischuk also needs to score 2.5/3, but has the benefit of two games with white, and so has a slightly better chance at 21%. Still, it now looks likely that the official March rating list will have only two 2800+ players on it – despite there having been five at the same time rated over 2800 in the live ratings earlier this month.

All told, the results over rounds five through eight have removed much of the drama from Tbilisi. Tomashevsky is now an overwhelming favorite to win the event, and has turned himself into a legitimate contender for one of the eventual Candidates Tournament spots. Of course he still has to navigate the last three rounds: he has roughly a 90% chance of at least sharing first place, but 10% is still 10%, and he has a job to do to close out the win. The other most tangible question is whether Grischuk can bounce back, manage at least a plus score in the last two rounds, move up the standings a bit, and enter Khanty-Mansiysk as a contender. We have about 20 hours until round 9 begins. In the meantime, hopefully this update gives you something to chew on during this rest day!

Tbilisi Grand Prix – First Rest Day Update

We probably could have titled this post “The rise of Tomashevsky”. Certainly the biggest story is Evgeny Tomashevsky’s blistering 3.5/4 start, and full point lead after four rounds (out of 11). You may already know that we are tracking the Grand Prix in detail, and running simulations to determine each player’s odds of finishing in the top two of the final standings and earning a berth in the 2016 Candidates Tournament. Well four days ago, before this event began, we were awfully pessimistic about Evgeny’s chances, giving him a mere 2% chance of doing well enough both here in Tbilisi and also in Khanty-Mansiysk to finish in the top two. Now? We have his odds up to 17%! He still has an uphill climb before he convinces our ratings-based simulation model that he’s an actual “favorite”, but he has nevertheless made tremendous progress.

In honor of the first rest day (2/19/2015), we thought we’d dig a little deeper into the results of our simulations. First of all, we’ve talked a lot about the overall Grand Prix standings, but haven’t actually said a word about the Tbilisi tournament specifically. How valuable is Tomashevsky’s full-point lead, in terms of actually winning this event? Is it worth more than the higher ratings of Grischuk and Giri, each sitting on 2.5/4? Our numbers say yes! Here are each player’s odds of winning THIS tournament, along with their average Grand Prix Points earned at Tbilisi (“EV” stands for “expected value”):

Player Score (Out of 4) Tbilisi EV Odds of Clear 1st
 Evgeny Tomashevsky (RUS) 3.5 132 31%
SHARED FIRST 28%
 Anish Giri (NED) 2.5 113 16%
 Alexander Grischuk (RUS) 2.5 113 15%
 Dmitry Jakovenko (RUS) 2.5 82 4%
 Shakhriyar Mamedyarov (AZE) 2 71 2%
 Maxime Vachier-Lagrave (FRA) 1.5 65 1%
 Rustam Kasimdzhanov (UZB) 2 61 1%
 Leinier Dominguez (CUB) 2 59 1%
 Teimour Radjabov (AZE) 2 56 1%
 Dmitry Andreikin (RUS) 1.5 55 0%
 Peter Svidler (RUS) 1.5 48 0%
 Baadur Jobava (GEO) 0.5 16 0%

Poor Jobava. His slow start has been just as bad as Tomashevsky’s has been good. At this point, pretty much his best realistic hope is just to share last place with someone. You can see, though, that if there is a clear winner it will be Tomashevsky almost half the time! His lead really is quite commanding, even with seven rounds left, but certainly nothing has been clinched yet.

So if Tomashevsky does take a clear first place and earn 170 Grand Prix points, what does that mean for his overall chances of qualifying? It would give him 252 points through two events, since he earned 82 at Baku, but how many points will second place ultimately require? Well, we began tracking this in our simulations, and have determined that the average score needed for second place in the final standings is 327. So if Tomshevsky wins, he’ll still need 75 more points at Khanty-Mansiysk to reach that target. Of course there this is an oversimplification, and 327 does not magically guarantee a Candidates berth, as there is a very wide range of possibilities. Across 20,000 simulations, we saw qualifying targets as low as 255, or as high as 392! The latter value can only happen in one precise way: Grischuk must win Tbilisi outright for 170 points, then finish exactly second at Khanty-Mansiysk for 140 more, giving him 392 total, AND Caruana must win Khanty-Mansiysk outright bringing his own total to 400 points even and first place overall. Despite the fact that this is an incredibly specific series of events, our simulation shows it happening once every 200 times (0.5%). This is surprisingly often, for one exact outcome, and shows how much our model respects Caruana and Grischuk’s high ratings, in its simulations.

Here is the full range of possibilities:

Cutoff Graph

So if we know the expected average result for each player at Tbilisi, do we have it for Khanty-Mansiysk as well? Of course! Here we have every player’s actual scores for Baku and Tashkent, along with their expected scores for Tbilisi and Khanty-Mansiysk, and their average overall scores. We also included their current odds of finishing in the top two in the final standings, in order to highlight that it doesn’t necessarily track perfectly with expected scores. That is because expected scores are an average of all possible results, while top-two odds are skewed heavily towards the odds of particularly good results. Some players have a higher risk/reward factor in their remaining slate, that allows them to have higher odds of reaching the Candidates despite not having a higher expected score.

Player Baku Tashkent Tbilisi EV Khanty-Mansiysk EV TOTAL EV Top-Two Odds
 Fabiano Caruana (ITA) 155 75 99.2 329.2 59%
 Hikaru Nakamura (USA) 82 125 96.0 303.0 40%
 Alexander Grischuk (RUS) 82 112.6 104.5 299.1 41%
 Evgeny Tomashevsky (RUS) 82 131.5 56.8 270.3 17%
 Anish Giri (NED) 40 112.9 98.6 251.5 17%
 Dmitry Andreikin (RUS) 20 170 54.9 244.9 3%
 Boris Gelfand (ISR) 155 15 64.7 234.7 6%
 Shakhriyar Mamedyarov (AZE) 35 125 71.0 231.0 3%
 Sergey Karjakin (RUS) 82 75 70.0 227.0 5%
 Maxime Vachier-Lagrave (FRA) 75 65.4 77.6 218.0 6%
 Peter Svidler (RUS) 82 47.6 57.1 186.8 2%
 Dmitry Jakovenko (RUS) 30 81.6 57.6 169.2 1%
 Teimour Radjabov (AZE) 50 50 56.1 156.1 0%
 Baadur Jobava (GEO) 75 16.4 34.2 125.5 0%
 Leinier Dominguez (CUB) 10 58.6 53.8 122.3 0%
 Rustam Kasimdzhanov (UZB) 35 15 61.5 111.5 0%

And finally, we looked at one more consideration. The “2800 club”! While live ratings are something we love to follow along with, there is a certain gravitas that comes along with actual published ratings. So the question is: when the March rating list comes out, how many 2800+ players will we see? Nakamura flirted with the mark at Zurich, but fell short in the end. Caruana struggled at Zurich, but managed to stay above the 2800 plateau. Carlsen will be there of course, so that’s two. And then there are Grischuk and Giri, both of whom are playing at Tbilisi. What are their chances?

Well Grischuk is in pretty good shape. Although he loses a little bit of rating with every draw, as the highest rated player in the field, his 9.7 point cushion (current live rating of 2809.7) is enough that as long as he scores 50% the rest of the way he’ll be fine. However if he drops to a negative score, at only 3/7 or worse over the remaining rounds, his rating would fall below the magic 2800 mark. According to our simulation, his chance of scoring at minimum the needed 50% in his remaining games is 82% (as he’s a favorite in all but one of them, the lone exception being when he has the black pieces against Giri in round 8).

Giri is in a slightly tougher spot, as he has no real cushion at all, currently sitting at 2800.4 in the live ratings. Since he also loses rating points with draws most of the way, he needs at minimum a score of +1, or 4/7 the rest of the way, to keep his rating afloat above the 2800 mark. Actually, 4/7 would drop his live rating to 2799.8, but fortunately that’s good enough as FIDE would round up. Scoring +1 is a tougher task than just maintaining an even score, but Giri is favored in all 7 of his remaining games (thanks to having the white pieces, which we rate as being worth 40 rating points) against Grischuk. As such, Giri is a favorite to score at least the 4/7 he needs: we rate his chances of a published March rating of 2800+ to be 63%.

We hope you enjoyed this interlude as a palatable replacement for actual chess on this rest day. Perhaps turn your attention to the rapid games at Zurich, to keep yourself entertained. We will post another update at the second rest day, so please let us know if there are any other stats you’d like us to take a look at!

Simulating The Grand Prix – Methodology

On our main page for the 2014-15 Grand Prix, you will notice that we list each player’s odds of finishing in the top two of the final Grand Prix standings – an important mark because those top two players earn berths in the 2016 Candidates Match, with a chance at the World Championship. If you’ve seen this, perhaps you have wondered: where did those numbers come from? How are they calculated, and how accurate are they?

So here I will discuss our methodology. First of all, the overview is relatively simple. I’ll go over that portion first, and dive deeper into the details (that may less interesting to some readers) afterward. We have built a spreadsheet that estimates the odds of a white win, a black win, or a draw, for all 132 Grand Prix games left to play (66 in Tbilisi, 66 in Khanty-Mansiysk). Further, it can use those odds to randomly calculate a result in each game, AND correctly calculate how the Grand Prix points would be awarded given those results, and who would therefore be the top two finishers.

Our simulation simply re-runs the randomizer a large number of times, recording the top two finishers each time, and spits out a result for each player: what percentage of the overall simulations had that player in the top two? Those are the odds we show you. How accurate are they? Not perfect, of course. The main source of error is that the individual game odds cannot be perfect. If you care about the details read on. Otherwise, suffice it to say that our estimates are probably the best available and if you’re interested in knowing who has the best chance of reaching the Candidates Match, you’re welcome to follow along with us! We will post regular updates throughout the upcoming Tbilisi event, and will show both the “current” odds and the “pre-Tbilisi” odds so that you can see exactly how much individual players have benefited or suffered from the results up until that point.

That’s a lot of text, so before we continue with the nitty gritty, here’s our “pre-Tbilisi” projections, in case you aren’t interested in clicking through to a different page to see them:

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%

Nevertheless, that’s our method. And once draw rate is calculated, and given that we already have an expected score from ELO (1/(1+10^(rating differential/400))), we can easily determine the needed win and loss odds to achieve the expected score. One final important note is that we DO account for colors. White scores higher than 50%, of course, so in all our calculations of rating differential (both to determine draw rate and to determine estimated score) we add 40 points to white’s ELO before calculating the differential. A “perfectly even” match, in our estimation, with full 60% draw odds, and equal winning chances for white and black, would be a game where white is rated 2720 and black is rated 2760, for instance. So that is how we estimate the odds of each game. From there, everything else is a relatively simple Monte Carlo simulation. We run it a large number of times, and get our results!The other challenge in using ELO to estimate results of specific games is that ELO only actually gives an expected score, not an expected result. Draw rate remains an unknown. We have plans to do a detailed study of draw rates in the future, but for now we’re using a simple estimation that the base draw rate for equal players is 60%, and that draws become less likely as the gap between the players’ ratings gets wider. Specifically, the draw rate is 60% – (rating difference)/1000, so ever 10 ELO reduces the draw rate by 1 percentage point. A 2800 vs. a 2700 would presumably draw 50% of the time. This is awfully unscientific, but fortunately it doesn’t make a huge impact if we’re off slightly. We tried another simulation with a baseline draw rate of 70% instead of 60%, and only one player saw their ultimate odds shift by more than one percentage point. There’s a little error in our draw assumptions, but not a huge amount. Of course in reality, draw rates probably also vary by the individual playing styles; we would figure Jobava to draw less than our formulas predict, for example.So first of all, our estimation of the win/draw/loss odds for each game are calculated based on ELO expectation, using current live ratings from 2700chess.com (one of the greatest things on the entire internet – if you’re interested enough in chess analysis to have read this far, and for some reason you don’t already have 2700chess bookmarked, go bookmark it now. We’ll wait.) Now this isn’t perfect, it works pretty well for players rated accurately, but that can never be everyone. The ELO system is pretty solid overall, but will always contain some underrated players and some overrated players at any given time. In the long run they balance out, but in the short run an underrated player will see their odds of finishing top-two in the Grand Prix badly understated by our formulas.

One other critical factor is the pairings. These are unknown until the day before play begins. Because each tournament is a 12 player Round Robin, meaning each player plays 11 games, half the field will get the black pieces 5 times, and half the field will get 6 blacks. This draw is important, given that we (correctly) factor in the white pieces as being worth an increase in expected score in a given game. When we first posted “pre-Tbilisi” odds, on Februrary 11th, we did not yet know the pairings for Tbilisi (or for Khanty-Mansiysk of course). Foolishly, we ran our simulation with static pairings (giving the same six players the favorable treatment of getting white 6/11 games). We concluded that Grischuk (to whom we had generously given six whites in BOTH upcoming events) had a 46% chance of reaching the Candidates match. When the Tbilisi pairings were released, and we re-ran our simulation with proper Tbilisi pairings, Grischuk’s odds (he will have six blacks in Tbilisi) dropped several percentage points! This shift made it clear how important the pairings are, and so we immediately re-designed our spreadsheet so that the pairings for Khanty-Mansiysk are randomly generated for each simulation. The odds now posted reflect these dynamic pairings within the simulation (and of course the actual pairings for Tbilisi, now that they are known), and we believe they are much more accurate than our previous posting.