## Human Elo ratings: averages and standard deviations.

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Ajedrecista
Posts: 1397
Joined: Wed Jul 13, 2011 7:04 pm
Location: Madrid, Spain.
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### Human Elo ratings: averages and standard deviations.

Hello:

I do not know where to put this thread in a computer chess forum, so if moderation is needed, it will be welcomed. I calculated the average and the standard deviation of FIDE rating list ratings (downloads here) with a small programme in Fortran 95. Here is the code:

Code: Select all

``````program normal
implicit none
integer&#58;&#58;i
integer,parameter&#58;&#58;n=141286
real&#40;KIND=3&#41;&#58;&#58;Elo&#40;1&#58;150000&#41;,sum, average, s, sum2, t0, t1, time
t0=cpu_clock@()
open&#40;unit=111,file='outT.txt',status='unknown',action='read')
do i=1,n
read&#40;111,*) Elo&#40;i&#41;
end do
sum=0d0
do i=1,n
sum=sum+Elo&#40;i&#41;
end do
average=sum/&#40;n+0d0&#41;
sum2=0d0
do i=1,n
sum2=sum2+&#40;Elo&#40;i&#41;-average&#41;*&#40;Elo&#40;i&#41;-average&#41;
end do
s = sqrt&#40;sum2/&#40;n-1d0&#41;)
t1=cpu_clock@()
time=&#40;t1-t0&#41;/3d9  ! 3 GHz.
open&#40;unit=110,file='Results.txt',status='unknown',action='write')
write&#40;110,'&#40;A,I6,A&#41;') 'Number of rated players&#58; ', n,'.'
write&#40;110,*)
write&#40;110,'&#40;A&#41;') 'µ&#58; average; s&#58; standard deviation.'
write&#40;110,*)
write&#40;110,'&#40;A,F7.2,A,F6.2&#41;') 'µ ~ ', 1d-2*nint&#40;1d2*average,KIND=3&#41;, '; s ~ ', 1d-2*nint&#40;1d2*s,KIND=3&#41;
write&#40;110,*)
write&#40;110,'&#40;A,I3,A&#41;',advance='no') 'Finished. Approximated elapsed time&#58; ', nint&#40;1d3*time,KIND=3&#41;, ' ms.'
close&#40;110&#41;
end program``````
I had to change manually the number of players each time (I hope no typos). The TXT utility txtTruncate by Norm Pollock was fundamental, so thank you very much. This programme did its calculations between 0.1 and 0.14 seconds more less (each time), so I consumed more time in downloading the lists and preparing (truncating) them than in the calculations; the consumed time in writing this source code was low because it is somewhat trivial. Inactive players are included because I did not know how to filter them...

I have always found interesting this ChessBase article although I have not read it carefully. I know that rating inflation exists, but comparing averages of rating lists between January 2009 and May 2012, these averages are decreasing! I suppose that it is due to the increasing number of players (most of them novice) that should decrease the average rating; standard deviations also grow, maybe due to those novice players with lower rating. I have obtained the following results (rounded up to 0.01 Elo):

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``````January 2009&#58;

Number of rated players&#58;  99232.

µ&#58; average; s&#58; standard deviation.

µ ~ 2044.50; s ~ 197.59

Finished. Approximated elapsed time&#58;  99 ms.``````

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``````April 2009&#58;

Number of rated players&#58;  99997.

µ&#58; average; s&#58; standard deviation.

µ ~ 2038.43; s ~ 200.33

Finished. Approximated elapsed time&#58;  98 ms.``````

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``````July 2009&#58;

Number of rated players&#58; 105242.

µ&#58; average; s&#58; standard deviation.

µ ~ 2031.04; s ~ 204.44

Finished. Approximated elapsed time&#58; 104 ms.``````

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``````September 2009&#58;

Number of rated players&#58; 107392.

µ&#58; average; s&#58; standard deviation.

µ ~ 2023.92; s ~ 207.77

Finished. Approximated elapsed time&#58; 111 ms.``````

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``````November 2009&#58;

Number of rated players&#58;  99522.

µ&#58; average; s&#58; standard deviation.

µ ~ 2016.46; s ~ 209.09

Finished. Approximated elapsed time&#58;  97 ms.``````

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``````January 2010&#58;

Number of rated players&#58; 109556.

µ&#58; average; s&#58; standard deviation.

µ ~ 2014.49; s ~ 211.47

Finished. Approximated elapsed time&#58; 107 ms.``````

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``````March 2010&#58;

Number of rated players&#58; 113629.

µ&#58; average; s&#58; standard deviation.

µ ~ 2011.87; s ~ 213.11

Finished. Approximated elapsed time&#58; 112 ms.``````

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``````May 2010&#58;

Number of rated players&#58; 116524.

µ&#58; average; s&#58; standard deviation.

µ ~ 2007.00; s ~ 214.82

Finished. Approximated elapsed time&#58; 114 ms.``````

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``````July 2010&#58;

Number of rated players&#58; 119042.

µ&#58; average; s&#58; standard deviation.

µ ~ 2001.75; s ~ 217.48

Finished. Approximated elapsed time&#58; 117 ms.``````

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``````September 2010&#58;

Number of rated players&#58; 121878.

µ&#58; average; s&#58; standard deviation.

µ ~ 1995.43; s ~ 220.68

Finished. Approximated elapsed time&#58; 120 ms.``````

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``````November 2010&#58;

Number of rated players&#58; 123519.

µ&#58; average; s&#58; standard deviation.

µ ~ 1991.60; s ~ 222.55

Finished. Approximated elapsed time&#58; 121 ms.``````

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``````January 2011&#58;

Number of rated players&#58; 122615.

µ&#58; average; s&#58; standard deviation.

µ ~ 1986.24; s ~ 225.15

Finished. Approximated elapsed time&#58; 119 ms.``````

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``````March 2011&#58;

Number of rated players&#58; 126695.

µ&#58; average; s&#58; standard deviation.

µ ~ 1982.77; s ~ 227.06

Finished. Approximated elapsed time&#58; 125 ms.``````

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``````May 2011&#58;

Number of rated players&#58; 129843.

µ&#58; average; s&#58; standard deviation.

µ ~ 1977.59; s ~ 229.26

Finished. Approximated elapsed time&#58; 127 ms.``````

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``````July 2011&#58;

Number of rated players&#58; 132263.

µ&#58; average; s&#58; standard deviation.

µ ~ 1972.49; s ~ 231.96

Finished. Approximated elapsed time&#58; 131 ms.``````

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``````September 2011&#58;

Number of rated players&#58; 135353.

µ&#58; average; s&#58; standard deviation.

µ ~ 1966.51; s ~ 234.73

Finished. Approximated elapsed time&#58; 136 ms.``````

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``````November 2011&#58;

Number of rated players&#58; 137694.

µ&#58; average; s&#58; standard deviation.

µ ~ 1961.87; s ~ 237.12

Finished. Approximated elapsed time&#58; 139 ms.``````

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``````January 2012&#58;

Number of rated players&#58; 139007.

µ&#58; average; s&#58; standard deviation.

µ ~ 1956.57; s ~ 239.41

Finished. Approximated elapsed time&#58; 137 ms.``````

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``````March 2012&#58;

Number of rated players&#58; 141286.

µ&#58; average; s&#58; standard deviation.

µ ~ 1952.70; s ~ 241.44

Finished. Approximated elapsed time&#58; 139 ms.``````

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``````May 2012&#58;

Number of rated players&#58; 145026.

µ&#58; average; s&#58; standard deviation.

µ ~ 1947.04; s ~ 243.21

Finished. Approximated elapsed time&#58; 138 ms.``````
I have measured a decrease of more than 97 (!) Elo in the average rating... in around two and a half years only! Also standard deviation has grown almost 46 Elo, while the number of rated players (active and inactive, all of them together) raised over 46%. I guess that this trend will continue in the next FIDE rating list of July 2012.

Any insight, comment... will be welcomed.

Regards from Spain.

Ajedrecista.

Uri Blass
Posts: 8557
Joined: Wed Mar 08, 2006 11:37 pm
Location: Tel-Aviv Israel

### Re: Human Elo ratings: averages and standard deviations.

Fide reduced the minimal rating list so the trend of reducing the average rating is obvious.

many years ago the minimal rating was 2200
Later fide reduced the minimal rating to 2000 and in the last years fide reduced the minimal rating to 1800 and later to 1600 and later to 1400 and later to 1200

Sven
Posts: 3822
Joined: Thu May 15, 2008 7:57 pm
Location: Berlin, Germany
Full name: Sven Schüle
Contact:

### Re: Human Elo ratings: averages and standard deviations.

To find out more about "inflation" or "deflation" you could calculate the average ratings of only those players who are present in all lists (i.e. all those you already selected). You could also exclude all "new" players with less than N games but this does not filter out all players who appeared on the list after the FIDE reduced the minimal rating since some lower rated players will have exceeded N games at some point in time.

Sven

Ajedrecista
Posts: 1397
Joined: Wed Jul 13, 2011 7:04 pm
Location: Madrid, Spain.
Contact:

### Re: Human Elo ratings: averages and standard deviations.

Hello again:
Uri Blass wrote:Fide reduced the minimal rating list so the trend of reducing the average rating is obvious.

many years ago the minimal rating was 2200
Later fide reduced the minimal rating to 2000 and in the last years fide reduced the minimal rating to 1800 and later to 1600 and later to 1400 and later to 1200
@Uri: I thought that the minimum rating was always 1400, so I was a little surprised when I saw a bunch of 1200 and 1300 ratings. So, in the first times, the minimum rating was 2200! Incredible. Thanks for the answer: you are right, the trend is obvious due to the minimum rating.
Sven Schüle wrote:To find out more about "inflation" or "deflation" you could calculate the average ratings of only those players who are present in all lists (i.e. all those you already selected). You could also exclude all "new" players with less than N games but this does not filter out all players who appeared on the list after the FIDE reduced the minimal rating since some lower rated players will have exceeded N games at some point in time.

Sven
@Sven: Thanks for your suggestions, but I am not so smart to do such complicated things for me! The most I have done is recalculate averages and standard deviations of people over an arbitrary minimum rating (idea taken from Uri), which I took 2300 Elo (included). I still maintain active and inactive players together because I do not know how to filter the inactive players in the Notepad. So, what I have just done is a bad job, but a little better than the former: the same players are not present in all my samples (well, top GMs yes, for sure...) but at least I obtained more stable results (I hope no typos):

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``````January 2009&#58;

Number of rated players with at least 2300 Elo&#58; 8228.

µ&#58; average; s&#58; standard deviation.

µ ~ 2387.86; s ~ 80.13

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````April 2009&#58;

Number of rated players with at least 2300 Elo&#58; 8080.

µ&#58; average; s&#58; standard deviation.

µ ~ 2388.08; s ~ 80.69

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````July 2009&#58;

Number of rated players with at least 2300 Elo&#58; 8306.

µ&#58; average; s&#58; standard deviation.

µ ~ 2388.16; s ~ 80.69

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````September 2009&#58;

Number of rated players with at least 2300 Elo&#58; 8249.

µ&#58; average; s&#58; standard deviation.

µ ~ 2388.75; s ~ 81.08

Finished. Approximated elapsed time&#58; 20 ms.``````

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``````November 2009&#58;

Number of rated players with at least 2300 Elo&#58; 7210.

µ&#58; average; s&#58; standard deviation.

µ ~ 2387.70; s ~ 80.64

Finished. Approximated elapsed time&#58;  9 ms.``````

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``````January 2010&#58;

Number of rated players with at least 2300 Elo&#58; 8038.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.13; s ~ 81.82

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````March 2010&#58;

Number of rated players with at least 2300 Elo&#58; 8273.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.34; s ~ 81.44

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````May 2010&#58;

Number of rated players with at least 2300 Elo&#58; 8325.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.04; s ~ 81.65

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````July 2010&#58;

Number of rated players with at least 2300 Elo&#58; 8334.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.27; s ~ 81.71

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````September 2010&#58;

Number of rated players with at least 2300 Elo&#58; 8316.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.65; s ~ 81.84

Finished. Approximated elapsed time&#58; 15 ms.``````

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``````November 2010&#58;

Number of rated players with at least 2300 Elo&#58; 8326.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.61; s ~ 82.10

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````January 2011&#58;

Number of rated players with at least 2300 Elo&#58; 8132.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.79; s ~ 82.23

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````March 2011&#58;

Number of rated players with at least 2300 Elo&#58; 8308.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.48; s ~ 82.22

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````May 2011&#58;

Number of rated players with at least 2300 Elo&#58; 8363.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.28; s ~ 82.28

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````July 2011&#58;

Number of rated players with at least 2300 Elo&#58; 8361.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.28; s ~ 82.42

Finished. Approximated elapsed time&#58; 12 ms.``````

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``````September 2011&#58;

Number of rated players with at least 2300 Elo&#58; 8335.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.46; s ~ 82.66

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````November 2011&#58;

Number of rated players with at least 2300 Elo&#58; 8331.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.69; s ~ 82.72

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````January 2012&#58;

Number of rated players with at least 2300 Elo&#58; 8253.

µ&#58; average; s&#58; standard deviation.

µ ~ 2390.06; s ~ 82.87

Finished. Approximated elapsed time&#58; 11 ms.``````

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``````March 2012&#58;

Number of rated players with at least 2300 Elo&#58; 8272.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.90; s ~ 82.82

Finished. Approximated elapsed time&#58; 10 ms.``````

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``````May 2012&#58;

Number of rated players with at least 2300 Elo&#58; 8298.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.84; s ~ 82.76

Finished. Approximated elapsed time&#58; 10 ms.``````
The used programme was the same as before; the preparation of the input data was more difficult than before because I had to sort ratings for select the ones over 2299, but txtSort utility did not handle well such big data, so previously I had to split it with txtSplit... so it was more time consuming. But it is finished!

I noticed that November 2009 list may be incomplete (it was much smaller than other lists) but I used it like the rest of the lists.

The average rating of people over 2299 Elo has increased around 2 Elo since January 2009 until now; the standard deviation has grown more than 2.5 points; I consider rather stable the number of players with 2300 Elo or more (except in November 2009, as I said).

I encourage some people to do more exhaustive studies... mine is only a meaningless one.

Regards from Spain.

Ajedrecista.

Ajedrecista
Posts: 1397
Joined: Wed Jul 13, 2011 7:04 pm
Location: Madrid, Spain.
Contact:

### Re: Results of July 2012 lists.

Hello again:

Just for curiosity, I have done the same calculations for July 2012 list:

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``````July 2012&#58;

Number of rated players&#58; 147724.

µ&#58; average; s&#58; standard deviation.

µ ~ 1941.75; s ~ 245.94

Finished. Approximated elapsed time&#58; 143 ms.``````

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``````July 2012&#58;

Number of rated players with at least 2300 Elo&#58; 8293.

µ&#58; average; s&#58; standard deviation.

µ ~ 2389.98; s ~ 82.81

Finished. Approximated elapsed time&#58; 10 ms.``````
I also found rapid and blitz lists. Here are the results from rapid list:

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``````July 2012&#58;

Number of rated players in rapid TC&#58; 4300.

µ&#58; average; s&#58; standard deviation.

µ ~ 2003.84; s ~ 265.86

Finished. Approximated elapsed time&#58; 7 ms.``````

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``````July 2012&#58;

Number of rated players in rapid TC with at least 2300 Elo&#58; 593.

µ&#58; average; s&#58; standard deviation.

µ ~ 2430.48; s ~ 100.56

Finished. Approximated elapsed time&#58; 4 ms.``````
Here are the results from blitz list:

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``````July 2012&#58;

Number of rated players in blitz TC&#58; 3603.

µ&#58; average; s&#58; standard deviation.

µ ~ 2030.63; s ~ 262.45

Finished. Approximated elapsed time&#58; 7 ms.``````

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``````July 2012&#58;

Number of rated players in blitz TC with at least 2300 Elo&#58; 576.

µ&#58; average; s&#58; standard deviation.

µ ~ 2434.06; s ~ 97.62

Finished. Approximated elapsed time&#58; 4 ms.``````
There are much less players in both rapid and blitz lists than in the normal one, so the results are very different between them. I think that no conclusions can be reached, but anyway, I leave here the data I obtained.

Regards from Spain.

Ajedrecista.

Ajedrecista
Posts: 1397
Joined: Wed Jul 13, 2011 7:04 pm
Location: Madrid, Spain.
Contact:

### A few rating statistics about some top human players.

Hello:

I know that this is a computer chess forum, but I think that sometimes is good to pay attention on human players.

I took ratings from July 2009 (the first rating list with separations of two months between consecutive lists) and May 2013 (the latest available list). I have computed the average rating of some top active players (not Kasparov, for example) and they are rounded up to 0.1 Elo. Only players with more than 2700 Elo in average rating in those 29 rating lists are included, so you will note some missings. I hope no typos:

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``````From July 2009 to May 2013.

#      Name&#58;            Min.   Mean   Max.    sd    Games   Times without play

1  Carlsen, M.          2772  2829.5  2872   10.9    239             9
2  Aronian, L.          2768  2802.3  2825    6.5    254             8
3  Anand, V.            2772  2792.6  2817    0.9    165            12
4  Kramnik, V.          2759  2792.4  2811    6.3    208            12
5  Topalov, V.          2751  2778.5  2813    6.5    135            15
6  Radjabov, T.         2733  2766.3  2793    1.9    186            14
7  Karjakin, S.         2717  2763.5  2788    8.8    270             7
8  Ivanchuk, V.         2703  2758.8  2779   10.6    381             6
9  Grischuk, A.         2733  2756.7  2779    4.5    247            12
10  Nakamura, H.         2708  2755.5  2786    8.6    347             4
11  Mamedyarov, S.       2717  2750.4  2772    6.3    246             8
12  Svidler, P.          2722  2743.4  2769    0.8    324             8
13  Gelfand, B.          2727  2742.6  2761    2.3    288             8
14  Morozevich, A.       2694  2739.7  2770    2.1    174            14
15  Ponomariov, R.       2723  2737.2  2764    1.9    283             7
16  Leko, P.             2717  2732.4  2762    4.5    221            10
17  Jakovenko, D.        2716  2731.1  2760    5.5    297             8
Kamsky, G.           2692  2731.1  2762    2.7    325             5
19  Caruana, F.          2652  2731.0  2786   11.5    499             1
20  Wang, H.             2690  2729.3  2752    7.4    327             7
21  Domínguez, L.        2710  2721.0  2734    0.9    190            10
22  Adams, M.            2682  2717.4  2735    3.5    347             4
23  Shirov, A.           2698  2716.6  2749    2.9    339             4
24  Tomashevsky, E.      2688  2715.8  2740    5.1    226             8
25  Wang, Y.             2685  2715.0  2756    4.0    292             7
26  Malakhov, V.         2700  2711.3  2732    0.8    247             8
27  Vachier-Lagrave, M.  2680  2711.1  2731    1.5    382             3
28  Bacrot, E.           2695  2709.7  2725    2.1    413             4
29  Eljanov, P.          2678  2708.4  2761    1.4    334             5
30  Almasi, Z.           2684  2707.4  2726    4.4    159            10
Navara, D.           2679  2707.4  2731    3.9    385             7
Vitiugov, N.         2681  2707.4  2733    5.0    295             6
33  Jobava, B.           2678  2707.0  2734    4.4    230             9
34  Movsesian, S.        2688  2705.3  2723    2.0    308             8
35  Vallejo, F.          2693  2700.9  2724    1.5    319             8
36  Nepomniachtchi, I.   2626  2700.3  2735   12.9    287             8``````
I counted 36 players that satisfy my requirements (I hope I did not miss anyone). If more than one player have the same average rating, then I sorted them in alphabetic order by their surnames. The column named 'sd' is the sample standard deviation of the 29 ratings of each player (rounded up to 0.1 Elo): it gives a rough idea about the rating stability of the player, but of course I know that players with more times without rated games at classical time controls could have lower sample standard deviation, this is why I include the number of played games and the number of times that each player did not play in a two-month period. The column 'sd' should be interpreted as anecdotal and nothing more IMHO.

I also sorted the previous list regarding the number of games that each player played in those years:

Code: Select all

``````From July 2009 to May 2013.

#      Name&#58;            Min.   Mean   Max.    sd    Games   Times without play

1  Caruana, F.          2652  2731.0  2786   11.5    499             1
2  Bacrot, E.           2695  2709.7  2725    2.1    413             4
3  Navara, D.           2679  2707.4  2731    3.9    385             7
4  Vachier-Lagrave, M.  2680  2711.1  2731    1.5    382             3
5  Ivanchuk, V.         2703  2758.8  2779   10.6    381             6
6  Adams, M.            2682  2717.4  2735    3.5    347             4
Nakamura, H.         2708  2755.5  2786    8.6    347             4
8  Shirov, A.           2698  2716.6  2749    2.9    339             4
9  Eljanov, P.          2678  2708.4  2761    1.4    334             5
10  Wang, H.             2690  2729.3  2752    7.4    327             7
11  Kamsky, G.           2692  2731.1  2762    2.7    325             5
12  Svidler, P.          2722  2743.4  2769    0.8    324             8
13  Vallejo, F.          2693  2700.9  2724    1.5    319             8
14  Movsesian, S.        2688  2705.3  2723    2.0    308             8
15  Jakovenko, D.        2716  2731.1  2760    5.5    297             8
16  Vitiugov, N.         2681  2707.4  2733    5.0    295             6
17  Wang, Y.             2685  2715.0  2756    4.0    292             7
18  Gelfand, B.          2727  2742.6  2761    2.3    288             8
19  Nepomniachtchi, I.   2626  2700.3  2735   12.9    287             8
20  Ponomariov, R.       2723  2737.2  2764    1.9    283             7
21  Karjakin, S.         2717  2763.5  2788    8.8    270             7
22  Aronian, L.          2768  2802.3  2825    6.5    254             8
23  Grischuk, A.         2733  2756.7  2779    4.5    247            12
Malakhov, V.         2700  2711.3  2732    0.8    247             8
25  Mamedyarov, S.       2717  2750.4  2772    6.3    246             8
26  Carlsen, M.          2772  2829.5  2872   10.9    239             9
27  Jobava, B.           2678  2707.0  2734    4.4    230             9
28  Tomashevsky, E.      2688  2715.8  2740    5.1    226             8
29  Leko, P.             2717  2732.4  2762    4.5    221            10
30  Kramnik, V.          2759  2792.4  2811    6.3    208            12
31  Domínguez, L.        2710  2721.0  2734    0.9    190            10
32  Radjabov, T.         2733  2766.3  2793    1.9    186            14
33  Morozevich, A.       2694  2739.7  2770    2.1    174            14
34  Anand, V.            2772  2792.6  2817    0.9    165            12
35  Almasi, Z.           2684  2707.4  2726    4.4    159            10
36  Topalov, V.          2751  2778.5  2813    6.5    135            15``````
I sorted both lists by hand, so may contain errors although I checked them several times. Just for the record: games(Caruana)/games(Topalov) ~ 3.7 (a huge difference IMHO).

Enjoy!

Regards from Spain.

Ajedrecista.