World Cup Recap: Day 15 (Conclusion of quarterfinals)

We finally get a rest day, so let’s start with a deep breath. After 15 days of frantic chess action, a starting field of 128 players from around the world has finally been whittled down to the Final Four. In tie break action the last two players eliminated before the break were Wei Yi and Shakhriyar Mamdyarov. The former, a superprodigy at just 16 years old, had been owning the headlines with his remarkable deep run, but finally it came to an end at the hands of Peter Svidler. The latter, from the host country of Azerbaijan, was also a pleasant story to follow as he carried the flag for local fans, but his run too came to an end with his loss to Sergay Karjakin.

By finalizing who their opponents would be, these two matches also of course had small impacts on Anish Giri and Pavel Eljanov (the players that had already punched their own tickets to the semifinal round the day before). Here are the new odds of reaching the finals for all six players, and how those odds changed based on the tie break results:

Seed Player Rating New Odds of Reaching Finals Change
11  Sergey Karjakin (RUS) 2764.6 55.1% 24.2%
16  Peter Svidler (RUS) 2733.6 29.7% 15.1%
4  Anish Giri (NED) 2795.7 70.3% 0.4%
26  Pavel Eljanov (UKR) 2751.4 44.9% -3.2%
24  Wei Yi (CHN) 2737.0 0.0% -15.5%
19  Shakhriyar Mamedyarov (AZE) 2745.0 0.0% -21.0%

With just four players left, there are only two matches for us to discuss. These are arguably the two most important matches of the entire tournament, however, as the winners of these semifinals will each earn a place in next year’s Candidates Tournament, arguably a bigger prize than can be won in the finals where “only” the title of World Cup Champion is at stake. So let’s take a close look at those two matches:

Anish Giri vs. Peter Svidler

Giri is the top remaining seed, and highest rated player left in the field. Our model of course sees him, therefore, as a strong favorite in this match (70% to win), and the most likely eventual tournament winner (44%). He is also the player with the least to lose, as that strong rating of his will almost certainly earn him a spot in the Candidates Tournament even if he doesn’t advance here. How did his path to this point look?

Giri has perhaps been a little bit underwhelming in the classical games, settling for more draws than his rating would indicate and dropping 2.4 rating points in the process. However this solid approach has worked well, as he has not lost a classical game either. Three times he has won one of two classical games, drawn the other, and advanced without tie breaks. The other two times he drew both classical games, then proceeded to win the first set of tie breaks 2-0. Despite having been made fun of by none less than Magnus Carlsen for his drawish tendencies, they have provided him a remarkably comfortable path to the semifinals with very little danger of elimination at any point so far in the process.

Svidler, on the other hand, comes into this round as an underdog (30% to win the match, and just 12% to win the whole tournament). He got here after a tense back and forth tie break with Wei Yi. Svidler has in fact been more solid even than Giri, with just two wins and eight draws (but no losses) in the classical games so far. Of course one of the wins was against Veselin Topalov, and Svidler entered the event rated much lower, so this performance has been enough to impress the Elo system and add 6.6 points to Svidler’s rating.

Svidler also has not lost a rapid game, but hasn’t been as convincing as Giri in tie break matches. He won his first two tie break matches in the first pair of games with one win and one draw, but got severely tested by Wei Yi drawing both G/25 games and the first G/10 game, before he finally broke through to win and advance in the fourth rapid game.

We have two players who have faced relatively little adversity, and have drawn many of their classical games. Svidler has the experience edge, having won the 2011 World Cup when his opponent was just 17 years old. However Giri is now all grown up and the strong favorite by rating. We estimate that Giri is a 70% favorite to win, and will begin to find out the reality of the match tomorrow.

Sergey Karjakin vs. Pavel Eljanov

This match is much closer by rating. Karjakin has the edge, but our model (which does not look any further than current live ratings in its prognostications) says he is a 55% favorite (with a 25% chance to win the event). Not too far from a coin flip. Karjakin was seeded #11, and is the second highest seed to reach this stage. He survived adversity in round two, losing his first game to Onischuk, but bounced back to force tie breaks, which he won. Overall Karjakin has four wins, but also the one loss, in his classical games, for a net rating gain of 2.6 points, showing less drawish of a nature than our two players on the other side of the bracket, however it has still left him in tie breaks three times so far.

Against Onischuk, he drew both G/25 rapid contests, before winning 2-0 in the G/10 portion. Against Andreikin he won the first G/25 game and held with black to end the tie break match there. Against Mamedyarov he again drew both G/25 games, but then both G/10 games. So his classical loss to Onischuk is his only defeat so far in the tournament, but he has been tested a fair bit.

Eljanov, meanwhile, is the underdog story. Seeded 26th, and entering the tournament rated just 2717, he opened up on an absolute tear winning his first six classical games! While he settled down to draw twice with Jakovenko, he was back to his winning ways against Nakamura taking home the classical match with a win in the first game, and a comfortable draw in the second. This insane +7 score in classical games has meant Eljanov’s rating has risen an astounding 34.4 points, bringing him up to #14 in the live ratings, a gain of 18 spots on the rating chart! It has also meant he has only played one tie break match, giving us less of an idea of what to expect from him in that phase. Against Jakovenko he drew the first three rapid games, before winning the fourth.

We’ve discussed before that we are highly skeptical of the idea of “form”, believing instead that most results that are better or worse than expectations are simply the expression of random variance. However if “good form” is in fact a thing, Eljanov has it right now. The model does give him some credit, in that it uses his massively improved live rating to estimate his chances, rather than judging him on his much lower rating from before the tournament began, but his 45% chance to reach the finals (and 18% chance to win the whole thing) are still based on his current live rating of 2751. He certainly looks to be playing at beyond that level so far, and if that continues then Karjakin may be in far more trouble than the model gives him credit for.

It is worth mentioning that Eljanov isn’t exactly coming out of nowhere. Rather, he’s coming back. Five years ago he was rated 2761 and ranked sixth in the world, so he’s been here before, just not recently.

Tomorrow games will begin again after this brief respite, and we will see if anyone jumps out to a 1-0 lead with a decisive victory in the first classical game. Until then, let’s consider one other question: what merit do our predictions actually have? Many readers may be wondering how accurate our predictions actually are. Well, we’ve provided odds for 124 matches so far in this event that we now know the results of. Let’s divide those up into groups, by the odds we gave the favorite, and see how we’ve done:

Odds Range Matches Favorite Win%
90-100% 21 95%
80-89% 22 91%
70-79% 31 71%
60-69% 23 65%
50-59% 27 59%

Overall our model seems to have done a pretty good job, considering nothing but live ratings. Players in the 80-89% range have won a little more often than expected, and players in the 70-79% range a little less, but one or two matches going differently would true up those numbers, and these sample sizes are small.

Of course it’s always possible to cherry pick cutoff points to imply differently. Statistics don’t lie, but they can be manipulated and selectively presented in ways that will cause people to draw bad conclusions. If you wanted to make the case that our model has underrated strong favorites, you could set a cutoff point at exactly 80.4%. Players given an 80.4% chance, or better, of winning did in fact win 39 matches in this event, with just one loss. That’s a 97.5% edge, when we’d expect a mere 90% edge or so. There should have been four upsets in that range and there was only one!

However five players rated as between a 79.4% and 80.4% favorite, just below the cutoff point, and three of those five lost. Cherry picking data can be fun, but doesn’t help if you want the truth. Overall, if our odds on the 124 matches so far have been accurate, we should have expected an average of 92 favorites to win with 32 underdogs advancing. In actuality, players we’ve deemed to be favorites have won 93 matches and lost 31. Seems like our predictions have been pretty valid to us.


World Cup Recap: Day 14 (Quarterfinals, second classical game)

And then there were six.

Hikaru Nakamura could manage no more than a draw today, when he needed a win to stay alive. Consequently the #2 seed heads home, and Pavel Eljanov heads into the semifinals. Meanwhile Anish Giri overcame his drawish reputation and scored his own victory, the only decisive game of the day, sending Maxime Vachier-Lagrave packing. Giri is now the only top-ten seed left in the competition, and has taken over as the favorite to win it all.

Two other matches were drawn, as they were yesterday, and will be settled tomorrow with tie breaks. That means Peter Svidler and Wei Yi will battle for the right to face Giri, while Shakhriyar Mamedyarov and Sergay Karjakin will face off to see who must contend with Eljanov. The two players who got the results they needed today to avoid tie breaks are of course the biggest winners of the day, while the two eliminated players saw the biggest drops in their odds of reaching the finals:

Seed Player Rating New Odds of Reaching Finals Change
4  Anish Giri (NED) 2795.7 69.9% 27.1%
26  Pavel Eljanov (UKR) 2751.4 48.1% 13.6%
19  Shakhriyar Mamedyarov (AZE) 2745.0 21.0% 4.5%
16  Peter Svidler (RUS) 2733.6 14.6% 0.1%
11  Sergey Karjakin (RUS) 2764.6 30.9% 0.0%
24  Wei Yi (CHN) 2737.0 15.5% -3.9%
2  Hikaru Nakamura (USA) 2806.0 0.0% -18.1%
21  Maxime Vachier-Lagrave (FRA) 2764.4 0.0% -23.3%

Note that Giri is one of two players who entered today playing somewhat by proxy for others who had already been eliminate. He is nearly guaranteed a spot in the Candidates Tournament regardless of his remaining results, thanks to his strong rating over the course of the year, but this win brings us up to nearly a 70% chance now that he will earn his berth via the World Cup, opening a ratings vacancy for either Kramnik or Grischuk. If Giri does end up in the finals, then every classical game played by those two later this year (particularly at the European Club Cup) will be of the utmost importance as they are separated by the slimmest of margins in the rating calculations. The other proxy player was Nakamura, who could have carried Jakovenko into the Candidates Tournament by reaching the finals here. Unfortunately for Dmitry and his fans, the Russian’s chances fell to zero with Hikaru’s elimination.

The grueling schedule continues tomorrow with the 15th straight day of action, as two crucial tie break matches are played. Afterward an actual scheduled rest day finally shows up in the tournament calendar, so those players who advanced today actually get to enjoy two days off to recuperate, and to prepare for the next round.

World Cup Recap: Day 13 (Quarterfinals, first classical game)

Today saw three draws, two big losers, and one big winner. First, let’s discuss Pavel Eljanov. The 32 year old Ukrainian is the lowest seeded player left in the competition, and entered the event rated just 2717. Not exactly patzer material, but not a rating you expect to see in serious contention at a tournament like this either. Then he breezed through the first three rounds winning every single classical game, and earning a rest every third day like clockwork. The third opponent whom he dispatched so unceremoniously was Grischuk, who entered the event ranked among the top ten players in the world, but could put up no resistance against Eljanov. In the fourth round it looked like perhaps Pavel had hit a stumbling block against Jakovenko, when he merely drew his first two games, but a comfortable 1.5/2 win in the first round of tie break games move Eljanov along to the quarterfinals. And that brought us to today, when he returned to his winning ways with an upset win over Hikaru Nakamura!

The thing is, at this point it’s hard to even call the win an upset. Eljanov is now rated 2750 in the live ratings, making him the 15th best player in the world and now just 57 points the inferior of Nakamura, the top remaining seed and current #2 player in the world. Add in the advantage of having the white pieces, and in retrospect today’s matchup was pretty close to equal according to Elo, not the shocking upset it seemed to be. With today’s win, Eljanov is now the favorite to win his half of the bracket, advance to the World Cup finals, and earn a spot in next year’s Candidates Tournament. Certainly Eljanov is today’s big winner.

The obvious big loser, of course, is Eljanov’s victim: Nakamura. Now the American faces a must-win game tomorrow, where our model gives him a 41% chance of winning to force tie breaks, but a 59% chance of being eliminated for good. Overall, by virtue of his gaudy rating, our model still rates Nakamura as having a decent 18% chance of reaching the finals, but that looks far more disappointing when we remember he was sitting at 50% to reach the finals yesterday. However we said in the intro that there were two big losers today. The thing about Nakamura is that while he would undoubtedly be disappointed to lose here, it only costs him a chance to win the World Cup. He doesn’t need to reach the finals for the sake of his World Championship aspirations, as he already clinched a berth in the Candidates Tournament with his second place finish in the Grand Prix earlier this year. There is another player who perhaps has more investment in Nakamura’s results than Nakamura himself: Dmitry Jakovenko.

Jakovenko finished third at the aforementioned Grand Prix, which sufficed merely to make him the first alternate for the Candidates. However the World Cup takes precedence as a qualifying method, so if one of the players ahead of him (Nakamura) were to reach the World Cup final, then Jakovenko would become a Candidate via the Grand Prix standings. Of course before he was eliminated, Jakovenko also had another path to the Candidates Tournament: simply reach the World Cup finals himself. Two days ago, before his tie break round with Eljanov began, we rated Jakovenko’s chances of reaching the Candidates Tournament at almost 58%, a 6.4% chance for himself, and a 51.4% chance for Nakamura on his behalf. Now, two days later, and entirely at the hands of Eljanov, those hopes have been cut down to a mere 18%. It hasn’t been a great two days for Dmitry.

The other three games today were drawn, which ultimately benefits black slightly, but has relatively little impact on the predicted results in comparison to the one decisive result. Overall here are how everyone’s odds of reaching the finals changed today, along with their updated chances:

Seed Player Rating Odds of Reaching Finals Change
26  Pavel Eljanov (UKR) 2750.1 34.5% 21.8%
11  Sergey Karjakin (RUS) 2765.0 30.9% 7.8%
4  Anish Giri (NED) 2791.4 42.7% 2.3%
19  Shakhriyar Mamedyarov (AZE) 2744.6 16.5% 2.1%
24  Wei Yi (CHN) 2737.1 19.5% 1.7%
16  Peter Svidler (RUS) 2733.5 14.5% -1.7%
21  Maxime Vachier-Lagrave (FRA) 2768.7 23.3% -2.2%
2  Hikaru Nakamura (USA) 2807.3 18.1% -31.8%

Note that Karjakin is the second biggest beneficiary of Eljanov’s success today, as he’s favored to reach the semifinals, where his opponent is now more likely to be Eljanov and less likely to be Nakamura. Our model still rates Eljanov as the easier opponent (though you certainly wouldn’t know it from his play so far in this tournament), and so sees the result as helpful to Karjakin’s chances as well. If we do end up seeing a matchup of Karjakin versus Eljanov (which should occur about 45% of the time), then we’ll find out if the model was right to consider it a blessing for Karjakin, or whether it proves instead to be a curse.

Tomorrow brings us another potential elimination day, where in three matches any decisive result sends someone home, and in the fourth match anything but a comeback win will end the tournament of yesterday’s favorite to win it all. However it all shakes out, there should be no shortage of drama!

World Cup Recap: Round 4

Four tie break matches were played today, and when the dust had settled we were left with just eight players remaining in the field at the 2015 World Cup. Two more top ten seeds saw their tournament hopes disappear, in Ding Liren and Dmitry Jakovenko, with the latter’s hopes of a berth in next year’s Candidates Tournament now entirely in the hands of Hikaru Nakamura. Also leaving us today were Radoslaw Wojtaszek and Dmitry Andreikin.

The eight remaining players are each just two more matches away from a berth in the finals, which would be enough to earn a place in the Candidates Tournament next year. As we get closer to the prize, a surprising result grows more likely. Only half of the remaining field was seeded within the top 16, so four players have overachieved their seed’s “chalk” results by two rounds already. Local favorite Shakhriyar Mamedyarov (seeded #19) and 16 year old superprodigy Wei Yi (#24) are among the underdog contenders still alive, along with Maxime Vachier-Lagrave (#21) and Pavel Eljanov (#26). When the tournament began, these players had a combined 10.5% chance of reaching the finals (that’s just adding their totals together, ignoring that those probabilities of course weren’t independent). Now their chances add up to 70.4%!

Two more players are one round deeper than they were “supposed” to get. #16 seed Peter Svidler and Sergey Karjakin (#11). And at the top are two players whose seed say they “should” not only be here, but advance: #2 seed Hikaru Nakamura and #4 Anish Giri. Even the players who are now favored have of course seen their odds rise greatly as they’ve survived (so far) this grueling event. Here are each remaining player’s odds of reaching the finals on a round by round basis:

Seed Player Initial After Rd 1 After Rd 2 After Rd 3 Current
2  Hikaru Nakamura (USA) 27.0% 27.3% 27.0% 32.5% 49.9%
4  Anish Giri (NED) 18.7% 18.8% 17.1% 21.6% 40.5%
21  Maxime Vachier-Lagrave (FRA) 4.9% 5.6% 6.3% 8.9% 25.5%
11  Sergey Karjakin (RUS) 7.2% 7.2% 6.8% 13.4% 23.0%
24  Wei Yi (CHN) 1.7% 2.3% 3.6% 4.2% 17.8%
16  Peter Svidler (RUS) 1.8% 1.8% 2.1% 3.0% 16.2%
19  Shakhriyar Mamedyarov (AZE) 2.7% 2.9% 4.0% 4.9% 14.4%
26  Pavel Eljanov (UKR) 1.2% 2.0% 2.3% 6.9% 12.7%

We can see that winning the first three rounds had relatively little impact on players’ chances. Even surviving round three left a lot of work to be done, and lower rated players remained unlikely to pull it off. However we see, with both favorites and underdogs, that players who had barely gained any ground at all through the first rounds all skyrocketed when they survived the fourth round as well. The winner of the match between Svidler and Wei will have chances in the range of 34%, way higher than either player currently boasts. If Nakamura were guaranteed a win over Eljanov he would be a 69% favorite, rather than a coin flip, for the final. In other words, it’s crunch time. As hard as it was to get to this point – ask Topalov or Caruana about that – the challenges are only beginning. These next matches are the most important yet!

Here is a look at the bracket, and how each of the players odds of reaching first the semifinals, and then the finals, map out. Hopefully this presentation makes it clearer where the numbers above come from by showing the exact path each player must traverse, and who they are most likely to face in the upcoming rounds should they survive this one.


Given that our two most common topics in this blog are the world championship cycle and young prodigies, it is taking tremendous willpower to remain fair to the other seven players in the field and not just scream about how amazing Wei Yi’s results are so far. However really, when it comes down to it, what more is there to say? He’s just 16 years old, and he is more likely to compete in the Candidates Tournament than you are to roll a seven on two dice. It’s crazy that he’s doing so well in this incredibly difficult tournament, but at the same time this tournament is tough enough that it’s really no less impressive what the other seven players have accomplished to be here.

So instead let’s just close with a look at who were the biggest winners and losers in today’s action specifically:

Seed Player Rating Change in Odds Today New Odds of Reaching Finals
4  Anish Giri (NED) 2792.1 16.6% 40.5%
24  Wei Yi (CHN) 2737.2 10.7% 17.8%
11  Sergey Karjakin (RUS) 2765.4 9.0% 23.0%
26  Pavel Eljanov (UKR) 2743.8 5.9% 12.7%
16  Peter Svidler (RUS) 2733.4 2.1% 16.2%
21  Maxime Vachier-Lagrave (FRA) 2768.0 -0.7% 25.5%
2  Hikaru Nakamura (USA) 2813.6 -1.5% 49.9%
19  Shakhriyar Mamedyarov (AZE) 2744.2 -1.8% 14.4%
27  Dmitry Andreikin (RUS) 2729.0 -5.2% 0.0%
10  Dmitry Jakovenko (RUS) 2742.2 -6.4% 0.0%
20  Radoslaw Wojtaszek (POL) 2741.9 -6.6% 0.0%
8  Ding Liren (CHN) 2780.6 -22.1% 0.0%

It’s not particularly confusing, the four players who won tie breaks today are the top four gainers, while the players they eliminated saw the biggest drop in their chances. No real surprises here, but we’ve presented these numbers every day so far and feel we would be remiss if we didn’t do so today. Something else that should be pretty safe to say is that anyone who earns a victory in one of tomorrow’s four games will find themselves at the top of tomorrow’s chart, and anyone who loses a game tomorrow will take a major hit to their odds and drop to the bottom of this chart for the day.

Let the quarterfinals begin!

World Cup Recap: Day 11 (Round 4, second classical game)

On the first day of round four we saw four draws and four decisive games. With half the field pushed to the brink of elimination, it was reasonable to expect to see four players knocked out of the tournament today. And that is exactly what happened, but it wasn’t quite all four of the ones you might have thought.

Three of yesterday’s victors, Nakamura, Svidler, and local favorite Mamedyarov, did convert today, drawing their games to clinch berths in the quarterfinal round. This of course means that two of the top three seeds, Topalov and Caruana, failed to mount comebacks and are now gone from the tournament! Also eliminated, although less shockingly, was Michael Adams. What about the fourth player who won yesterday, though? Ding Liren fought hard against Wei Yi, but his 16 year old ultimately managed to find a way to win today and even the score. The two Chinese players will now have to settle the matter tomorrow with rapid (and perhaps blitz) tie breaks.

That means the fourth elimination came in a match where the first game was drawn. Specifically Maxime Vachier-Lagrave, playing the black side today, defeated Wesley So to earn a place among the final eight players. This was the only decisive game among players who drew yesterday, with the other three pairings on their way to tie breaks.

So four players were eliminated and four move on to the next round, while eight must play rapid games tomorrow. How did today’s results impact the picture if we look further ahead? Here is everyone’s new odds of reaching the finals, along with how many percentage points those odds increased or decreased:

Player Rating New Odds of Reaching Finals Finals Change
 Maxime Vachier-Lagrave (FRA) 2768.0 26.2% 17.2%
 Wei Yi (CHN) 2737.2 7.1% 6.2%
 Peter Svidler (RUS) 2733.4 14.1% 5.8%
 Shakhriyar Mamedyarov (AZE) 2744.2 16.1% 4.3%
 Hikaru Nakamura (USA) 2813.6 51.4% 3.8%
 Anish Giri (NED) 2792.1 23.8% 3.3%
 Dmitry Andreikin (RUS) 2729.0 5.2% 1.1%
 Dmitry Jakovenko (RUS) 2742.2 6.4% 0.8%
 Radoslaw Wojtaszek (POL) 2741.9 6.6% 0.5%
 Pavel Eljanov (UKR) 2743.8 6.8% -0.3%
 Sergey Karjakin (RUS) 2765.4 14.0% -0.6%
 Michael Adams (ENG) 2736.6 0.0% -1.0%
 Fabiano Caruana (USA) 2791.7 0.0% -8.0%
 Ding Liren (CHN) 2780.6 22.1% -9.3%
 Veselin Topalov (BUL) 2802.5 0.0% -10.9%
 Wesley So (USA) 2761.7 0.0% -12.8%

Four of the five biggest drops were of course from those players who were eliminated, but it’s perhaps interesting that Ding Liren, despite still being a favorite to advance tomorrow, took a bigger hit than two players who are now completely done. It makes some sense, perhaps. After his win yesterday, Ding was a huge favorite to move past Wei Yi, and now suddenly there is some immediate risk. Letting Wei off the hook with today’s loss does put a major dent in his goals, as he lost almost a third of his significant equity in reaching the finals. Yesterday he was the favorite to reach the finals from his half of the bracket, and today that favorite is instead Vachier-Lagrave (today’s biggest gainer by far).

It would be fair to argue that going from an 8% chance of reaching the finals down to a 0% chance (Caruana) is “worse” than dropping from 31.4% to 22.1% but still being in pretty good shape in the tournament. On the other hand, in terms of absolute percentage points Ding’s drop is better, and that’s how we choose to sort the table above. Part of this is that the table is looking only at the one-day change. If we go back to the beginning of the round, then we see that in the last two days Caruana’s odds dropped 26.1 percentage points, while Ding’s chances have actually improved by 5.7 percentage points. It’s just that most of Caruana’s fall came yesterday, and Ding’s net gain is due to a large leap yesterday, which today’s loss largely negated.

The four matches that went to tie breaks, and our estimation of the odds at this point, and how those odds changed with today’s result, are as follows (including what opponent awaits the victor in the quarterfinals):

Favorite Rating Quarterfinal Odds Change Today Underdog Rating Quarterfinal Opponent Rating
4.  Anish Giri (NED) 2792.1 64.7% 3.4% 20.  Radoslaw Wojtaszek (POL) 2741.9 21.  Maxime Vachier-Lagrave (FRA) 2768.0
8.  Ding Liren (CHN) 2780.6 63.1% -31.1% 24.  Wei Yi (CHN) 2737.2 16.  Peter Svidler (RUS) 2733.4
11.  Sergey Karjakin (RUS) 2765.4 60.9% -5.8% 27.  Dmitry Andreikin (RUS) 2729.0 19.  Shakhriyar Mamedyarov (AZE) 2744.2
26.  Pavel Eljanov (UKR) 2743.8 50.6% -5.1% 10.  Dmitry Jakovenko (RUS) 2742.2 2.  Hikaru Nakamura (USA) 2813.6

World Cup Recap: Day 10 (Round 4, first game)

Today provided the most drastic swings in the expected final results of the tournament that we’ve seen so far, despite nobody actually being eliminated, as half of the eight games produced decisive results. Two of the top three seeds, Veselin Topalov and Fabiano Caruana, lost their games today and now must win tomorrow to stay alive. Having entered the day among the favorites to reach the finals, these two losses were huge blows that dramatically shifted our projections. On the other hand, two other games involving top-eight seeds were won by the favorites, and these victors (Hikaru Nakamura and Ding Liren) saw huge gains in their own chances to reach the finals as a result. They are now the front runners on their respective sides of the bracket, and there is now roughly a 15% chance that they will face each other in the finals!

Here is how much ground everyone gained or lost in their quest for a berth in the finals (and correspondingly a berth in the 2016 Candidates Tournament):

Seed Player Rating New Odds of Reaching Finals Change
2  Hikaru Nakamura (USA) 2814.6 47.6% 15.1%
8  Ding Liren (CHN) 2786.3 31.4% 15.0%
19  Shakhriyar Mamedyarov (AZE) 2743.2 11.8% 7.0%
16  Peter Svidler (RUS) 2732.2 8.3% 5.2%
5  Wesley So (USA) 2767.1 12.8% 2.1%
20  Radoslaw Wojtaszek (POL) 2741.2 6.1% 1.4%
11  Sergey Karjakin (RUS) 2766.0 14.7% 1.3%
26  Pavel Eljanov (UKR) 2743.4 7.1% 0.2%
21  Maxime Vachier-Lagrave (FRA) 2762.6 9.1% 0.1%
27  Dmitry Andreikin (RUS) 2728.4 4.1% 0.0%
4  Anish Giri (NED) 2792.8 20.5% -1.1%
10  Dmitry Jakovenko (RUS) 2742.6 5.7% -1.2%
24  Wei Yi (CHN) 2731.5 0.9% -3.3%
15  Michael Adams (ENG) 2739.6 1.0% -4.2%
3  Fabiano Caruana (USA) 2792.7 8.0% -18.1%
1  Veselin Topalov (BUL) 2803.7 10.9% -19.5%

So how about tomorrow? For the sake of interesting scenarios it benefits fans that all four decisive wins came with the white pieces today, as that means everyone in a must-win situation tomorrow gets to fight for their survival with the advantage of the first move. Let’s look at the eight matchups individually.

Topalov’s side of the bracket:

Topalov vs. Svidler

Peter Svidler upset the number one seed with white in the first game, and is now a 69% favorite to advance to the quarterfinals. It’s not over yet, though. Topalov is still rated 72 points higher, plus has the advantage of the white pieces tomorrow, and our model gives him a 44% chance of achieving the equalizing win he needs to stay alive. If he wins, he’s considered a little better than a 70% favorite to win the tie breaks as well. So it’s not over yet, but Svidler certainly added a lot of intrigue to the top of the bracket with his win today! The winner of this match will face the winner of Ding Liren vs. Wei Yi in the next round. The loss was bad news for Topalov’s hopes of reaching the finals, with his odds now down under 11%, from a gaudy 30% before the game. Fortunately for Veselin any World Championship aspirations he may have did not suffer as a result, since if he doesn’t reach the finals here he will still qualify for the Candidates Tournament on rating. On the other hand Kramnik and Grischuk saw their World Championship hopes shaken by today’s result, as they are relying on a finals appearance by either Topalov or Giri in order to put one of them into the Candidates Tournament on rating.

Ding vs. Wei

This clash between two Chinese stars opened with tactical fireworks in a game that could easily have gone either way, but was ultimately won by the older and more experienced player. Favored by 55 rating points and leading 1-0, Ding is now considered a 94% favorite to advance by our model. On the other hand, Wei Yi has shown remarkable resilience, and a great ability to create sharp and unclear positions in order to give himself winning chances, and tomorrow he gets to try to do so with the white pieces, which our model sees as a 17% chance for a win given the ratings. If Wei does manage to force tie breaks, a 55 point ratings favorite is expected to advance 66% of the time in the rapid/blitz format of this tournament.

These two countrymen have some history, as one would expect, having now played nine classical games against each other. With today’s win, Ding is now +2, with three wins and one loss (they’ve drawn five times). On the other hand, those results go back to a draw in 2012 when Wei was just 13 years old and rated 2371. In the last two calendar years (so going back to January 2014) they have played six times, with three draws, two wins (now) for Ding, and one win for Wei (at the Chinese championships earlier this year, an event which Wei won).

This quadrant of the bracket (Topalov, Svidler, Ding, and Wei) will produce one semifinalist, and right now Ding is the most likely, at 57%, with Svidler just under 23%, Topalov just under 18%, and Wei at just over 2%.

Giri vs. Wojtaszek

A drawn game here didn’t change the status quo too much, but slightly benefited black (as first-game draws do in this format). Wojtaszek now has a 39% chance of pulling off overcoming his 52 point rating deficit to pull the upset. Since our model rates the white pieces as worth 40 rating points, we still see Giri as slightly more likely to win tomorrow should the game be decisive, predicting a 20% chance of a Giri win, a 17% chance of a Wojtaszek win, and a 63% chance of a draw. This is not player specific though, and given Giri’s reputation I imagine some observers might argue that the odds of a draw are higher than that. If it does go to tie breaks, Giri’s rating edge is enough to generate a 65% chance of victory in that phase, according to our model. The winner of this matchup will then face either Wesley So or Maxime Vachier-Lagrave.

So vs. Vachier-Lagrave

Another of today’s draws, again we saw just a small shift in the odds, again in favor of the player who gets the white pieces tomorrow, which in this case is So. These two players are separated by a mere five rating points, and So entered the day as the smallest of favorites, at 52% to advance. With his draw today, he gained slightly and is now a 57% favorite to move on. Thanks to having the white pieces, our model gives So a 28% chance of winning to end things immediately, and just a 16% chance of being knocked out with a loss. The rest of the time the match would go to tie breaks where So’s five extra rating points earn him a 51% chance of advancing – basically a coin flip.

In this quadrant of the bracket, where noone yet has an scoreboard edge, the odds of earning the one available semifinal spot are simply an exercise in “sort by ratings”, with Giri the favorite at 37%, So at 27%, MVL at 20%, and Wojtaszek at 16%. If he gets that far, Giri would be a small favorite over Ding in the semis, but Ding would be favored over the other three, and so Ding is the most likely finalist in this half, but at only 31%. Things are pretty wide open, with seven of the eight players still having at least a 6% chance (sorry Wei Yi).

Nakamura’s side of the bracket:

Nakamura vs. Adams

Given that Nakamura is a 75 point ratings favorite and also holds a 1-0 lead, this is not a good spot for Adams. Our model gives him less than a 5% chance of reaching the quarterfinals at this point, down from 27.5% before today’s game. Even with the white pieces, we only expect a player surrendering that many rating points to win 16% of the time, and should he manage to do so he would have less than a 30% chance of winning the tie breaks – and that doesn’t even account for the fact that his specific opponent is the strongest in the field in rapid and blitz chess, and is almost certainly underrated by the model in tie break scenarios. It would be a complete shocker, at this point, if Nakamura somehow failed to reach the quarterfinals. Nakamura (or if a shocker occurs, perhaps Adams) will face the winner of Eljanov/Jakovenko in the next round.

Jakovenko vs. Eljanov

Jakovenko was the favorite by seed, but ratings said these two were exactly equal. Today’s result said the same, as the game was drawn. While Eljanov saw the end of his streak of perfection (he had won his first six World Cup games, before finally being held to a draw for the first time today) he still gains from the rule that draws with black are good, and is now a small 56% favorite to advance thanks to the benefit of the white pieces in tomorrow’s game. We see him winning 27% of the time, and losing 16% of the time. Otherwise it will go to tie breaks where the odds will return to 50/50.

In this quadrant, Nakamura is a commanding ratings favorite over the other three, and the only player with a win to his credit so far this round. As such he is a strong 69% favorite to reach the semifinals, with Eljanov at 16%, Jakovenko 13%, and Adams just 2%.

Caruana vs. Mamedyarov

Today’s other major upset was the last remaining player from the host country knocking off the #3 seed. Mamedyarov surrenders 50 rating points, but his 1-0 lead makes him a 75% favorite to advance. Like the other players who lost a game today, though, Caruana gets the white pieces tomorrow in his battle for survival. His effective 90 point rating advantage (including the value of the white pieces) gives him a 39% chance to win and force tie breaks, where he would be expected to win about 65% of the time. If he manages to do so, he would face either Karjakin or Andreikin in the quarterfinals. However his 1-0 deficit is a major hurdle that, as with Topalov, means his chances of reaching the final took a huge hit today. He now has just an 8% chance of reaching the final, down from 26%. Of course like Topalov this isn’t a huge problem for him, as he will be in the Candidates Tournament either way having already won the Grand Prix. It’s more of a problem for Jakovenko, who needs one of Caruana, Nakamura, or himself to win in order to reach the Candidates Tournament. Success for any of the other five players in the bracket (Mamedyarov in this case) hurts Jakovenko’s World Championship hopes.

Karjakin vs. Andreikin

Another draw, another small gain for the black player, which here was Karjakin, also the favorite by rating. Between his 38 point rating edge and the white pieces tomorrow, Karjakin is now up to a 67% chance of moving on to the next round. In particular he has a 36% chance to advance immediately with a win tomorrow, and just a 14% chance of being eliminated with a loss tomorrow. If we see another draw instead, Karjakin would rate as a 61% favorite in the tie breaks.

In this quadrant, Mamedyarov’s status as the only player with a win under his belt benefits him, of course, but his relatively low rating works against him and he’s actually only the second most semifinalist in the group. Karjakin is 36%, Mamedyarov 34.5%, Caruana 16%, and Andreikin 13.5%. With no clear favorite in this group, when the opposing group does have a clear leader (who’s also the highest rated player in the field), that leader is of course the most likely finalist. Nakamura is very close to becoming the first player tabbed as a true favorite (over the entire rest of his bracket combined) to reach the finals, at almost 48%. Only two other players, Karjakin and Mamedyarov, have better than a 10% chance of earning that spot.

World Cup Recap: Round 3

The third round of the World Cup again saw relatively few upsets; this tournament so far has been an impressive showing by the top players. We did lose two of our top eight seeds, with Grischuk being eliminated yesterday in the classical games and Kramnik knocked out today in tie breaks. However the top five seeds remain intact, and deeper down the seeding lists we see that everyone seeded lower than 27th has now been eliminated. There are no longer any huge Cinderella stories to follow as we enter the fourth round, all 16 remaining players are strong contenders, with the lowest rated player in the field (Svidler) still boasting a strong 2726 rating, making him the 28th highest rated player in the world by current live ratings.

So we aren’t going to see a crazy run from a 2600 or below player. Lu Shanglei was our last hope for a sub-2700 player to continue on, but he lost to Topalov in the first pair of tie breaks today. Instead we’re going to see eight very competitive matches in round four, since the best and worst remaining players (by rating) are separated by just 85 rating points. Upsets would be minor at this point, meaning no remaining player is safe.

The seven players eliminated today had a combined 19.3% chance of reaching the finals (almost half of that equity belonging to Kramnik – the others were all long shots to various degrees), so the remaining players saw their own odds increase by that amount in net. With only 23 players left entering today, and all but three of them seeing their odds change by at least half a percentage point (even players who didn’t play today) as every matchup has significant ramifications through the whole bracket at this point, we will show you the impact today’s results had on everyone:

Seed Player Rating New Odds of Reaching Finals Change
2  Hikaru Nakamura (USA) 2810.6 32.5% 7.7%
21  Maxime Vachier-Lagrave (FRA) 2762.2 8.9% 3.2%
1  Veselin Topalov (BUL) 2809.9 30.4% 3.2%
5  Wesley So (USA) 2767.5 10.7% 2.8%
27  Dmitry Andreikin (RUS) 2727.8 4.1% 2.6%
15  Michael Adams (ENG) 2739.6 5.2% 1.8%
11  Sergey Karjakin (RUS) 2766.6 13.4% 1.7%
16  Peter Svidler (RUS) 2726.0 3.0% 1.2%
3  Fabiano Caruana (USA) 2798.7 26.1% 0.3%
19  Shakhriyar Mamedyarov (AZE) 2737.2 4.9% 0.2%
97  Lu Shanglei (CHN) 2620.2 0.0% 0.0%
24  Wei Yi (CHN) 2735.8 4.2% -0.5%
20  Radoslaw Wojtaszek (POL) 2740.5 4.7% -0.6%
10  Dmitry Jakovenko (RUS) 2743.0 6.9% -0.7%
26  Pavel Eljanov (UKR) 2743.0 6.9% -0.7%
37  Le Quang Liem (VIE) 2702.6 0.0% -0.7%
34  Ian Nepomniachtchi (RUS) 2705.6 0.0% -0.9%
8  Ding Liren (CHN) 2782.0 16.4% -1.3%
4  Anish Giri (NED) 2793.5 21.6% -1.6%
17  Teimour Radjabov (AZE) 2730.6 0.0% -2.3%
18  Leinier Dominguez Perez (CUB) 2729.8 0.0% -2.4%
12  Evgeny Tomashevsky (RUS) 2747.8 0.0% -3.5%
6  Vladimir Kramnik (RUS) 2779.2 0.0% -9.3%

We have shown players eliminated in today’s tie break festivities with their names crossed off. They mostly were the day’s biggest losers, although in a few cases (particularly Lu) their odds of reaching the finals were so low already that today’s elimination cost them less ultimate equity in a Candidates Tournament berth than was lost by some players still in the running. It was slightly bad news for Ding and Giri, for example, that Topalov and Nakamura both advanced. And since Ding and Giri both have substantial chances of actually reaching the finals, their odds dropped further (in absolute terms of percentage points) than bigger underdogs like Lu, Le, or Nepomniachtchi.

So what are our fourth round matchups?

Favorite Rating Quarterfinal Odds Underdog Rating
1.  Veselin Topalov (BUL) 2809.9 75.4% 16.  Peter Svidler (RUS) 2726.0
2.  Hikaru Nakamura (USA) 2810.6 72.5% 15.  Michael Adams (ENG) 2739.6
3.  Fabiano Caruana (USA) 2798.7 70.3% 19.  Shakhriyar Mamedyarov (AZE) 2737.2
4.  Anish Giri (NED) 2793.5 67.9% 20.  Radoslaw Wojtaszek (POL) 2740.5
8.  Ding Liren (CHN) 2782.0 66.0% 24.  Wei Yi (CHN) 2735.8
11.  Sergey Karjakin (RUS) 2766.6 63.9% 27.  Dmitry Andreikin (RUS) 2727.8
5.  Wesley So (USA) 2767.5 52.2% 21.  Maxime Vachier-Lagrave (FRA) 2762.2
10.  Dmitry Jakovenko (RUS) 2743.0 50.0% 26.  Pavel Eljanov (UKR) 2743.0

As we said, the rating gaps have shrunk dramatically. Nobody is better than a 3:1 favorite, and our 10 vs. 26 match is actually a perfectly dead even draw. We may not have had as many upsets as those who prefer early round craziness would have wanted, but the upside is we should see some tremendous chess in the final rounds. Everyone left in the field has at least a 3% chance of advancing to the finals.

What about some of the other side stories? We’ve been following Kramnik and Grischuk’s live ratings closely, and yesterday we saw Kramnik pass Grischuk for the projected third place in the average ratings for 2015. Now Kramnik has been eliminated in rapid tie breaks (which didn’t hurt his rating) so he remains ahead in that hunt, and we now know that neither player will see further rating swings in this event. The chase isn’t over though, both will participate in the European Club Cup at the end of October, and the projected ratings are close enough that even a tiny ratings swing for either player could shift the scenario. Of course by then the World Cup will be over, and we will know whether those ratings matter. This is just the race for third place, after all, so it’s only relevant if Topalov or Giri reaches the World Cup finals. Both Kramnik and Grischuk fans should be rooting for Topalov and Giri (although Kramnik fans might find the former challenging). Right now we project a 52% chance of one of those winning their half of the bracket. If this happens it will make every game at the European Club Cup fascinating from a ratings perspective. The other 48% of the time, ratings stop mattering at all.

There’s a similar situation on the other side of the bracket. Caruana and Nakamura finished 1-2 in the Grand Prix and have already punched tickets to the Candidates Tournament. However if one of them reaches the final here and earns a berth this way instead (World Cup takes precedence) then Jakovenko would be in. Not only that, but Jakovenko himself is also still alive in the same side of the bracket, so if any of those three players reach the final (a combined 65.5% chance) then Jakovenko achieves a spot in the Candidates. It’s nice to be a 2-1 favorite for such a spot, and it helps him that Grischuk and Kramnik were both eliminated from the same half of the bracket making all three of their paths easier, but Karjakin is still a significant threat. His best bet would be to start by winning his own toss-up match against Eljanov and letting the rest sort itself out. Because winning is better than losing – we give extremely valuable advice here!