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:

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!

thanks for the cool information 🙂

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Could you talk about the odds of each player taking the number two spot in the world after this Grand Prix event on the next rest day? I like the information you already have, by the way.

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Very cool indeed. It’s an overwhelming amount of information already! But since you specifically invite requests for more stats, how about a graph showing the likelihood that the qualifying GP score will fall in different intervals? This would illustrate the uncertainty of the 327 value as a target. And maybe also a table og graph showing the changes in each players’ chances over time?

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Hmm, well the graph is both a great idea and also super easy. I edited it in to the original post. Thanks for the idea!

The changes in various players’ chances over time is tougher, because it requires me to save snapshots of the odds over time… and I haven’t been doing that so much. I have the odds now, and did save the pre-Tbilisi odds for comparison’s sake, but did not save the odds after rounds 1, 2, or 3 were completed. There’s also the consideration that I only just this past week built my simulation model, so I have no idea what the odds would have been (by this methodology) before or during the first two events of the Grand Prix. Without being able to show how individuals’ odds ebbed and flowed through the entire Grand Prix cycle, I fear such a chart would lose some of its impact.

I can still at least run it with limited snapshot points though. Pre-Tbilisi, Rest day 1, Rest day 2, Post-Tbilsi, Pre-Khanty-Mansiysk, Rest day 1, Rest day 2, and Final. It won’t be perfect, but I’ll certainly track it, and share the results at the end of May when this whole Grand Prix is over with. Plus there’s always the NEXT Grand Prix cycle (presumably 2016-2017), which I can track fully from beginning to end, now that I have the method 🙂

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