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. 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.

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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.

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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.