# World Cup qualifiers: how to calculate?

Last weekend we published a preliminary list of European Championship participants who qualified for the next World Cup. We noted that Vladimir Potkin, Peter Svidler and Rauf Mamedov had already qualified (info that was duly copied by other media), without mentioning Dmitry Jakovenko.

The next FIDE World Cup is scheduled for 26 August - 21 September 2011, again in Khanty-Mansiysk, Russia. FIDE will publish the official list of participants by the end of May, when all zonal and continental events will be completed. In our final report on the European Championship we already noted that at the closing ceremony there was much confusion among the top finishing participants about the way the organizers dealt with the tie-breaks for the World Cup qualification spots. (Unlike in previous years the European Championship didn’t have play-off rapid matches for this.) Especially the calculation of the first tie-break rule (Performance Rating) was controversial, to say the least.

According to the tie-breaks used in Aix les Bains, the first 23 players were Potkin, Wojtaszek, Polgar, Moiseenko, Vallejo, Ragger, Feller, Svidler, Mamedov, Vitiugov, Zhigalko, Jakovenko, Korobov, Inarkiev, Postny, Azarov, Khairullin, Kobalia, Guliyev, Zherebukh, Riazantsev, Iordachescu and Lupulescu.

However, we knew that Potkin, Svidler and Mamedov had already qualified, and so the numbers 24-26 were also in: McShane, Fridman and Motylev. One of the players who just missed the qualification because of the strange tie-break calculation is Danish grandmaster Peter Heine Nielsen. He told us that he is going to file an official protest:

The other players negatively affected were Parligras, Esen and Saric, as was pointed out on Tuesday by Vladica Andrejic in the following elaborate and critical essay, which we (and Chessdom) were allowed to cross-post (we tidied up the English a bit).

A few days ago the Individual European Championship finished in Aix Les Bains (22.3-2.4.2011). It is a very important tournament for European chess players. People have come to win one of the 23 spots for the World Cup 2011. However, the first tie-break rule which decided these spots is tragicomic. Putting aside the fact that a few days after the tournament there is no official announcement on who has qualified for the World Cup.

In previous years at the European Championship we had play-off matches for the World Cup places. This time the matches were cancelled and additional criteria would generate the invitations to the World Cup. However, some smart guy figured out that the first tie-break rule had to be something what is called a performance rating.

FIDE calculates rating performance in a very ridiculous way, but this time it was much worse. Specifically, the first tie-break at the European Championship was a kind of average rating performance, which is calculated by removing games that were played against the weakest and the strongest opponent by rating. Yes, it removes these ratings from the account for an average rating, but it removes their results, too. Players who defeated the strongest opponents were therefore drastically punished!

For example, look at grandmaster Parligras. He entered with 7.5 points in the section of places that qualified for the World Cup. He has the second best Buchholz in the tournament (only 5th placed Vallejo Pons has a better Buchholz), actually all possible reasonable criteria indicate that he must be the best in the group which shares 16th to 44th place, but he eventually finished on the 29th place and was not qualified for the World Cup! Why? This is why he was punished, because he defeated European champion Nepomniachtchi (the opponent with the highest Elo). Unbelievable! How long will people who have no basic logical understanding decide on major issues of chess? Therefore, I appeal to the FIDE President, that one of his six personal World Cup invitations will be delivered to Parligras!

If we want to use some kind of rating performance we can do much better. The following table is similar to the official table of players who have at least 7.5 points, but we add some columns. The column "official" gives the official FIDE performance without results against the worst and the best opponent by rating. The column "average" gives the modified average rating of the opponent (without the worst and best Elo). Players with the same number of points have the same percentage, so this is proportional to the normal performance that would be much fairer. The column "FIDE" gives a performance without any exclusions, but it harmed players who played against a player with enormous low ratings. The column "Andrejic" gives the 'Andrejic rating performance', which is the fairest, and gives a realistic picture of strength of play. At the end of the article you can read the details and explanations about the 'Andrejic rating performance'. Columns marked with # are related to the column to the left of it, and represents the placement if the relevant column taken as the first tie break.

Using careful analysis of the previous table, we can conclude that many players are drastically affected. For example, the bronze medal was "stolen" from Moiseenko, as a penalty, because he beat a strong player, McShane! Many players have been postively affected because they lost against the strongest opponents. According to my calculations, Parligras, Esen, Nielsen, and Saric are damaged for World Cup place, and that places get Riazantsev, Lupulescu, Fridman and McShane. At the end, you can read a slightly modified part of my chess ratings study, concerning the performance rating, which will explain why it is better to use the 'Andrejic performance rating' rather than the FIDE performance rating.

It is a common occurrence at many tournaments that certain opponents have ratings so small that beating them actually decreases one's performance; hence, for the sake of norm performance the rating of the worst rated player is boosted so that the game can potentially be improved. Now, there is a recent grandmaster tournament example of IM Miša Pap's performance at Paleochora Open 2010. In the first three rounds he won all the games he played (against lower-rated opponents), and in the following six rounds he made 3.5 points against opposition with an average rating of 2576. The result he obtained in the last six rounds is equivalent to the FIDE performance of 2633, but with his three initial wins that performance (with the additional rating increase of the weakest player) fell onto 2600 sharp (without the additional rating increase it would be 2536). Luckily enough, last year the requirement for the grandmaster norm was set down from 2601 onto 2600, and thus Pap managed to get it.

I would suggest defining the performance as the rating for which the acquired result is also the expected result at the same time. It is actually the rating of a player that would remain the same after subsequent rating calculations after the tournament in question. It can easily be calculated iteratively, and the good thing is that iterative calculation does not depend on the (small) development coefficient that is included in the calculation. For these calculations I would not use rounded values from the table, but the real values for expectation function, and most certainly without any rating limits like those of 400 rating points that are artificially imposed by FIDE today.

Whatever the case may be, winning the game certainly can not do any harm (as it actually did in the previous paradoxical example) and some other things are also improved. For example, let's assume that a player gains 1.5 points in two games playing against opposition with an average rating of 2400. FIDE's calculation of such a performance would be 2591 (or 2593 according to the tables); that would also be the value of my calculation, but only if both players have 2400 each. However, rating is not linear so if the players have 2300 and 2500 instead, the performance is 2605, and if the players have 2200 and 2600 the performance is 2648!

An even better illustration of the present illogical FIDE calculation can be derived from the similar situation, i.e. in case of a score of 1.5 points from two games against a certain rating average. To calculate the performance, we will create a new situation where a stronger opponent has a rating that is higher than the calculated performance while the weaker opponent has such a rating that the rating average is the same as in the first situation (a good example would be the abovementioned average of 2400 against the opponents with 2200 and 2600). If 1.5 points are gained by means of a draw against the stronger opponent and a win against the weaker opponent, if we disregard a triumph over the weaker opponent, then logically the performance can not be smaller than the rating of the stronger opponent, but according to FIDE calculations it actually is (i.e. 2591 compared to 2600)! According to my calculation, Pap's performance at the mentioned tournament is 2648.

There has recently been a discussion at the Chessbase website about the rating performance and it was proposed to calculate the performance with an additional virtual draw against oneself. Nevertheless, this concept breaches the fundamental rating performance principle according to which rating performance does not depend on the rating of the player whose rating we are calculating. The aim is not to get more realistic numbers (closer to players' ratings), but to define that both in case of all wins or all losses rating performance should not be calculated. As for Navara's fantastic result 8.5/9 at the Czech championship (FIDE performance 2963), in my opinion the appropriate performance should be 2982. It simply means that if Navara had entered the tournament with this rating (2982) and played it the way he did, he would not either gain or lose any rating points.

Meanwhile, Vladica Andrejic has published a new article Above or below the line in which he points out that Serbian GM Ivan Ivanisevic should have qualified for the World Cup as well. The reason? Because Dmitry Jakovenko already qualified before the European Championship.

Andrejic gives the following table:

And so, according to Andrejic's calculations (which seems accurate to us), the list of qualified players by rating is the following: Carlsen, Aronian, Topalov, Kramnik, Mamedyarov, Grischuk, Ivanchuk, Radjabov, Nakamura, Eljanov, Shirov, Svidler, Gashimov, Wang Hao, Leko, Wang Yue, Jakovenko, Kamsky, Bacrot, and Navara. This means that Jakovenko already qualified and opens up a place for Ivanisevic.

**GM Peter Heine Nielsen**told us he's planning to file an**official protest**and meanwhile Dr Vladica Andrejic wrote an**elaborate and critical essay**about the tie-break system used in Aix les Bains.The next FIDE World Cup is scheduled for 26 August - 21 September 2011, again in Khanty-Mansiysk, Russia. FIDE will publish the official list of participants by the end of May, when all zonal and continental events will be completed. In our final report on the European Championship we already noted that at the closing ceremony there was much confusion among the top finishing participants about the way the organizers dealt with the tie-breaks for the World Cup qualification spots. (Unlike in previous years the European Championship didn’t have play-off rapid matches for this.) Especially the calculation of the first tie-break rule (Performance Rating) was controversial, to say the least.

According to the tie-breaks used in Aix les Bains, the first 23 players were Potkin, Wojtaszek, Polgar, Moiseenko, Vallejo, Ragger, Feller, Svidler, Mamedov, Vitiugov, Zhigalko, Jakovenko, Korobov, Inarkiev, Postny, Azarov, Khairullin, Kobalia, Guliyev, Zherebukh, Riazantsev, Iordachescu and Lupulescu.

However, we knew that Potkin, Svidler and Mamedov had already qualified, and so the numbers 24-26 were also in: McShane, Fridman and Motylev. One of the players who just missed the qualification because of the strange tie-break calculation is Danish grandmaster Peter Heine Nielsen. He told us that he is going to file an official protest:

"If players would like to join me, they are welcome. I do however lack contact info on the relevant parties. Nevertheless my protest is on the final standings, so this would include their results as well as the bronze medal too."

The other players negatively affected were Parligras, Esen and Saric, as was pointed out on Tuesday by Vladica Andrejic in the following elaborate and critical essay, which we (and Chessdom) were allowed to cross-post (we tidied up the English a bit).

## European Championship Scandal

**How long will people who have no basic logical understanding decide on major issues of chess? The latest example concerns the calculation of the first tie-break rule at the European Championship.***By Vladica Andrejic*A few days ago the Individual European Championship finished in Aix Les Bains (22.3-2.4.2011). It is a very important tournament for European chess players. People have come to win one of the 23 spots for the World Cup 2011. However, the first tie-break rule which decided these spots is tragicomic. Putting aside the fact that a few days after the tournament there is no official announcement on who has qualified for the World Cup.

In previous years at the European Championship we had play-off matches for the World Cup places. This time the matches were cancelled and additional criteria would generate the invitations to the World Cup. However, some smart guy figured out that the first tie-break rule had to be something what is called a performance rating.

FIDE calculates rating performance in a very ridiculous way, but this time it was much worse. Specifically, the first tie-break at the European Championship was a kind of average rating performance, which is calculated by removing games that were played against the weakest and the strongest opponent by rating. Yes, it removes these ratings from the account for an average rating, but it removes their results, too. Players who defeated the strongest opponents were therefore drastically punished!

For example, look at grandmaster Parligras. He entered with 7.5 points in the section of places that qualified for the World Cup. He has the second best Buchholz in the tournament (only 5th placed Vallejo Pons has a better Buchholz), actually all possible reasonable criteria indicate that he must be the best in the group which shares 16th to 44th place, but he eventually finished on the 29th place and was not qualified for the World Cup! Why? This is why he was punished, because he defeated European champion Nepomniachtchi (the opponent with the highest Elo). Unbelievable! How long will people who have no basic logical understanding decide on major issues of chess? Therefore, I appeal to the FIDE President, that one of his six personal World Cup invitations will be delivered to Parligras!

If we want to use some kind of rating performance we can do much better. The following table is similar to the official table of players who have at least 7.5 points, but we add some columns. The column "official" gives the official FIDE performance without results against the worst and the best opponent by rating. The column "average" gives the modified average rating of the opponent (without the worst and best Elo). Players with the same number of points have the same percentage, so this is proportional to the normal performance that would be much fairer. The column "FIDE" gives a performance without any exclusions, but it harmed players who played against a player with enormous low ratings. The column "Andrejic" gives the 'Andrejic rating performance', which is the fairest, and gives a realistic picture of strength of play. At the end of the article you can read the details and explanations about the 'Andrejic rating performance'. Columns marked with # are related to the column to the left of it, and represents the placement if the relevant column taken as the first tie break.

# | name | fed | elo | points | official | # | average | # | FIDE | # | Andrejic | # |

1 | Potkin,V | RUS | 2653 | 8.5 | 2849 | 1 | 2629 | 1 | 2822 | 1 | 2838 | 1 |

2 | Wojtaszek,R | POL | 2711 | 8.5 | 2826 | 2 | 2606 | 2 | 2812 | 2 | 2826 | 2 |

3 | Polgar,J | HUN | 2686 | 8.5 | 2799 | 3 | 2579 | 4 | 2781 | 4 | 2792 | 4 |

4 | Moiseenko,A | UKR | 2673 | 8.5 | 2755 | 4 | 2589 | 3 | 2790 | 3 | 2800 | 3 |

5 | Vallejo Pons,F | ESP | 2707 | 8.0 | 2819 | 5 | 2599 | 7 | 2764 | 6 | 2769 | 7 |

6 | Ragger,M | AUT | 2614 | 8.0 | 2783 | 6 | 2617 | 5 | 2768 | 5 | 2786 | 5 |

7 | Feller,S | FRA | 2657 | 8.0 | 2766 | 7 | 2600 | 6 | 2763 | 7 | 2774 | 6 |

8 | Svidler,P | RUS | 2730 | 8.0 | 2751 | 8 | 2585 | 9 | 2757 | 8 | 2764 | 8 |

9 | Mamedov,R | AZE | 2667 | 8.0 | 2751 | 9 | 2585 | 8 | 2754 | 9 | 2759 | 9 |

10 | Vitiugov,N | RUS | 2720 | 8.0 | 2741 | 10 | 2575 | 10 | 2744 | 10 | 2750 | 11 |

11 | Zhigalko,S | BLR | 2680 | 8.0 | 2732 | 11 | 2566 | 13 | 2731 | 13 | 2736 | 12 |

12 | Jakovenko,D | RUS | 2718 | 8.0 | 2719 | 12 | 2553 | 14 | 2704 | 14 | 2724 | 14 |

13 | Korobov,A | UKR | 2647 | 8.0 | 2697 | 13 | 2572 | 11 | 2740 | 11 | 2750 | 10 |

14 | Inarkiev,E | RUS | 2674 | 8.0 | 2695 | 14 | 2570 | 12 | 2735 | 12 | 2736 | 13 |

15 | Postny,E | ISR | 2585 | 8.0 | 2633 | 15 | 2508 | 15 | 2676 | 15 | 2703 | 15 |

16 | Azarov,S | BLR | 2615 | 7.5 | 2776 | 16 | 2610 | 18 | 2723 | 17 | 2744 | 18 |

17 | Khairullin,I | RUS | 2634 | 7.5 | 2771 | 17 | 2605 | 19 | 2720 | 18 | 2735 | 19 |

18 | Kobalia,M | RUS | 2672 | 7.5 | 2754 | 18 | 2588 | 22 | 2716 | 19 | 2721 | 22 |

19 | Guliyev,N | AZE | 2522 | 7.5 | 2739 | 19 | 2573 | 27 | 2652 | 39 | 2711 | 26 |

20 | Zherebukh,Y | UKR | 2560 | 7.5 | 2739 | 20 | 2614 | 17 | 2712 | 21 | 2751 | 17 |

21 | Riazantsev,A | RUS | 2679 | 7.5 | 2728 | 21 | 2562 | 29 | 2687 | 27 | 2693 | 29 |

22 | Iordachescu,V | MDA | 2626 | 7.5 | 2725 | 22 | 2600 | 20 | 2716 | 20 | 2732 | 20 |

23 | Lupulescu,C | ROU | 2626 | 7.5 | 2722 | 23 | 2556 | 31 | 2677 | 31 | 2692 | 31 |

24 | McShane,L | ENG | 2683 | 7.5 | 2718 | 24 | 2552 | 32 | 2684 | 30 | 2687 | 33 |

25 | Fridman,D | GER | 2661 | 7.5 | 2717 | 25 | 2551 | 33 | 2684 | 29 | 2690 | 32 |

26 | Motylev,A | RUS | 2677 | 7.5 | 2716 | 26 | 2591 | 21 | 2710 | 22 | 2713 | 25 |

27 | Ivanisevic,I | SRB | 2617 | 7.5 | 2712 | 27 | 2587 | 23 | 2704 | 24 | 2727 | 21 |

28 | Jobava,B | GEO | 2707 | 7.5 | 2711 | 28 | 2545 | 37 | 2656 | 38 | 2678 | 38 |

29 | Parligras,M | ROU | 2598 | 7.5 | 2709 | 29 | 2629 | 16 | 2735 | 16 | 2758 | 16 |

30 | Romanov,E | RUS | 2624 | 7.5 | 2709 | 30 | 2543 | 38 | 2668 | 37 | 2682 | 36 |

31 | Esen,B | TUR | 2528 | 7.5 | 2707 | 31 | 2582 | 24 | 2669 | 35 | 2718 | 23 |

32 | Nielsen,PH | DEN | 2670 | 7.5 | 2703 | 32 | 2578 | 25 | 2707 | 23 | 2713 | 24 |

33 | Cheparinov,I | BUL | 2664 | 7.5 | 2698 | 33 | 2573 | 26 | 2693 | 25 | 2697 | 28 |

34 | Gustafsson,J | GER | 2647 | 7.5 | 2687 | 34 | 2562 | 30 | 2687 | 28 | 2693 | 30 |

35 | Kulaots,K | EST | 2601 | 7.5 | 2669 | 35 | 2503 | 41 | 2633 | 41 | 2648 | 40 |

36 | Smirin,I | ISR | 2658 | 7.5 | 2668 | 36 | 2543 | 39 | 2675 | 32 | 2684 | 35 |

37 | Saric,I | CRO | 2626 | 7.5 | 2651 | 37 | 2571 | 28 | 2692 | 26 | 2708 | 27 |

38 | Pashikian,A | ARM | 2642 | 7.5 | 2649 | 38 | 2524 | 40 | 2640 | 40 | 2645 | 41 |

39 | Edouard,R | FRA | 2600 | 7.5 | 2634 | 39 | 2468 | 44 | 2602 | 43 | 2621 | 43 |

40 | Bologan,V | MDA | 2671 | 7.5 | 2629 | 40 | 2549 | 34 | 2673 | 33 | 2676 | 39 |

41 | Beliavsky,A | SLO | 2619 | 7.5 | 2627 | 41 | 2547 | 36 | 2668 | 36 | 2685 | 34 |

42 | Rublevsky,S | RUS | 2678 | 7.5 | 2627 | 42 | 2547 | 35 | 2672 | 34 | 2678 | 37 |

43 | Volkov,S | RUS | 2621 | 7.5 | 2625 | 43 | 2500 | 42 | 2630 | 42 | 2643 | 42 |

44 | Sjugirov,S | RUS | 2643 | 7.5 | 2594 | 44 | 2469 | 43 | 2584 | 44 | 2599 | 44 |

Using careful analysis of the previous table, we can conclude that many players are drastically affected. For example, the bronze medal was "stolen" from Moiseenko, as a penalty, because he beat a strong player, McShane! Many players have been postively affected because they lost against the strongest opponents. According to my calculations, Parligras, Esen, Nielsen, and Saric are damaged for World Cup place, and that places get Riazantsev, Lupulescu, Fridman and McShane. At the end, you can read a slightly modified part of my chess ratings study, concerning the performance rating, which will explain why it is better to use the 'Andrejic performance rating' rather than the FIDE performance rating.

## Rating performance

Throughout recent years, the rating performance of a player has been an extremely important issue as it is what brings grandmaster and international master norms as well as medals based on player's performance at the Chess Olympiad. Nevertheless, the way this performance is calculated is quite controversial and it is the total of the opponents' average rating plus the table value that depends on the player's percentage at the tournament. For many years such a way of calculation has been acceptable, but with the decrease of the rating floor it now requires certain changes. I would kindly ask for your patience in the following paragraph as I hope that the accompanying examples will help to clear up your doubts.It is a common occurrence at many tournaments that certain opponents have ratings so small that beating them actually decreases one's performance; hence, for the sake of norm performance the rating of the worst rated player is boosted so that the game can potentially be improved. Now, there is a recent grandmaster tournament example of IM Miša Pap's performance at Paleochora Open 2010. In the first three rounds he won all the games he played (against lower-rated opponents), and in the following six rounds he made 3.5 points against opposition with an average rating of 2576. The result he obtained in the last six rounds is equivalent to the FIDE performance of 2633, but with his three initial wins that performance (with the additional rating increase of the weakest player) fell onto 2600 sharp (without the additional rating increase it would be 2536). Luckily enough, last year the requirement for the grandmaster norm was set down from 2601 onto 2600, and thus Pap managed to get it.

I would suggest defining the performance as the rating for which the acquired result is also the expected result at the same time. It is actually the rating of a player that would remain the same after subsequent rating calculations after the tournament in question. It can easily be calculated iteratively, and the good thing is that iterative calculation does not depend on the (small) development coefficient that is included in the calculation. For these calculations I would not use rounded values from the table, but the real values for expectation function, and most certainly without any rating limits like those of 400 rating points that are artificially imposed by FIDE today.

Whatever the case may be, winning the game certainly can not do any harm (as it actually did in the previous paradoxical example) and some other things are also improved. For example, let's assume that a player gains 1.5 points in two games playing against opposition with an average rating of 2400. FIDE's calculation of such a performance would be 2591 (or 2593 according to the tables); that would also be the value of my calculation, but only if both players have 2400 each. However, rating is not linear so if the players have 2300 and 2500 instead, the performance is 2605, and if the players have 2200 and 2600 the performance is 2648!

An even better illustration of the present illogical FIDE calculation can be derived from the similar situation, i.e. in case of a score of 1.5 points from two games against a certain rating average. To calculate the performance, we will create a new situation where a stronger opponent has a rating that is higher than the calculated performance while the weaker opponent has such a rating that the rating average is the same as in the first situation (a good example would be the abovementioned average of 2400 against the opponents with 2200 and 2600). If 1.5 points are gained by means of a draw against the stronger opponent and a win against the weaker opponent, if we disregard a triumph over the weaker opponent, then logically the performance can not be smaller than the rating of the stronger opponent, but according to FIDE calculations it actually is (i.e. 2591 compared to 2600)! According to my calculation, Pap's performance at the mentioned tournament is 2648.

There has recently been a discussion at the Chessbase website about the rating performance and it was proposed to calculate the performance with an additional virtual draw against oneself. Nevertheless, this concept breaches the fundamental rating performance principle according to which rating performance does not depend on the rating of the player whose rating we are calculating. The aim is not to get more realistic numbers (closer to players' ratings), but to define that both in case of all wins or all losses rating performance should not be calculated. As for Navara's fantastic result 8.5/9 at the Czech championship (FIDE performance 2963), in my opinion the appropriate performance should be 2982. It simply means that if Navara had entered the tournament with this rating (2982) and played it the way he did, he would not either gain or lose any rating points.

Meanwhile, Vladica Andrejic has published a new article Above or below the line in which he points out that Serbian GM Ivan Ivanisevic should have qualified for the World Cup as well. The reason? Because Dmitry Jakovenko already qualified before the European Championship.

Andrejic gives the following table:

# | name | comment | 01.07.2010 | 01.01.2011 | Average |

1 | Carlsen, Magnus | #1 | 2826 | 2814 | 2820 |

2 | Kasparov, Garry | Inactive | 2812 | 2812 | 2812 |

3 | Anand, Viswanathan | World Champion | 2800 | 2810 | 2805 |

4 | Aronian, Levon | #2 | 2783 | 2805 | 2794 |

5 | Topalov, Veselin | #3 | 2803 | 2775 | 2789 |

6 | Kramnik, Vladimir | #4 | 2790 | 2784 | 2787 |

7 | Mamedyarov, Shakhriyar | #5 | 2761 | 2772 | 2766.5 |

8 | Grischuk, Alexander | #6 | 2760 | 2773 | 2766.5 |

9 | Karjakin, Sergey | Semifinal 2009 | 2747 | 2776 | 2761.5 |

10 | Ivanchuk, Vassily | #7 | 2739 | 2764 | 2751.5 |

11 | Radjabov, Teimour | #8 | 2748 | 2744 | 2746 |

12 | Nakamura, Hikaru | #9 | 2729 | 2751 | 2740 |

13 | Eljanov, Pavel | #10 | 2755 | 2724 | 2739.5 |

14 | Ponomariov, Ruslan | Semifinal 2009 | 2734 | 2744 | 2739 |

15 | Gelfand, Boris | Semifinal 2009 | 2739 | 2733 | 2736 |

16 | Shirov, Alexei | #11 | 2749 | 2722 | 2735.5 |

17 | Svidler, Peter | #12 | 2734 | 2730 | 2732 |

18 | Gashimov, Vugar | #13 | 2719 | 2736 | 2727.5 |

19 | Wang, Hao | #14 | 2724 | 2731 | 2727.5 |

20 | Leko, Peter | #15 | 2734 | 2717 | 2725.5 |

21 | Wang, Yue | #16 | 2716 | 2734 | 2725 |

22 | Malakhov, Vladimir | Semifinal 2009 | 2732 | 2714 | 2723 |

23 | Jakovenko, Dmitry | #17 | 2726 | 2718 | 2722 |

24 | Movsesian, Sergei | European Ch 2010 | 2723 | 2721 | 2722 |

25 | Kamsky, Gata | #18 | 2713 | 2730 | 2721.5 |

26 | Bacrot, Etienne | #19 | 2720 | 2723 | 2721.5 |

27 | Nepomniachtchi, Ian | European Ch 2010 | 2706 | 2733 | 2719.5 |

28 | Navara, David | #20 | 2731 | 2708 | 2719.5 |

29 | Vachier-Lagrave, Maxime | Junior 2009 | 2723 | 2715 | 2719 |

30 | Almasi, Zoltan | European Ch 2010 | 2717 | 2719 | 2718 |

31 | Dominguez Perez, Leinier | #21 | 2716 | 2716 | 2716 |

32 | Vitiugov, Nikita | #22 | 2722 | 2709 | 2715.5 |

33 | Adams, Michael | #23 | 2706 | 2723 | 2714.5 |

34 | Caruana, Fabiano | #24 | 2697 | 2721 | 2709 |

35 | Jobava, Baadur | European Ch 2010 | 2710 | 2707 | 2708.5 |

36 | Morozevich, Alexander | #25 | 2715 | 2700 | 2707.5 |

37 | Fressinet, Laurent | #26 | 2697 | 2707 | 2702 |

38 | Tomashevsky, Evgeny | European Ch 2010 | 2708 | 2695 | 2701.5 |

And so, according to Andrejic's calculations (which seems accurate to us), the list of qualified players by rating is the following: Carlsen, Aronian, Topalov, Kramnik, Mamedyarov, Grischuk, Ivanchuk, Radjabov, Nakamura, Eljanov, Shirov, Svidler, Gashimov, Wang Hao, Leko, Wang Yue, Jakovenko, Kamsky, Bacrot, and Navara. This means that Jakovenko already qualified and opens up a place for Ivanisevic.

*Vladica Andrejic says he's "a modest chess player" (current Elo 2170, best Elo 2275 on Jan 2009). He's also a chess arbiter (national rank in Serbia) and a chess webmaster (owner and editor of Perpetual Check) and holds a Ph.D. in mathematics (thesis in Differential Geometry). Andrejic teaches at the University of Belgrade, Faculty of Mathematics in Belgrade, Serbia.*