Some analyses of the FIDE top20 rating list

# Introduction

Expanding on the experience I am forming analysing the gladiabiots ratings (articles:2017-06:elo-inights here), I noticed that the world of chess, that stimulated the work of Arpad Elo, is missing some analysis on the top ratings. Or maybe those analysis are available but I didn't find them.

Therefore I would like to extend some analysis I did for gladiabots on the FIDE ratings.

# Sources and resources

There are many sources online, at least at the moment (yes, internet forgets).
There are different collections of the FIDE ratings, starting before 1970 (the first official fide rating), for example:

For the initial work, as quality builds on time, I will use the ratings of 2700 chess that are easy to use and there is plenty of data.

# Remarks

• Actually to have better comparisons players should be active in the periods considered. An inactive player may hold a rating that is actually higher than his current form. Anyway at first I am going to consider the ratings as good representative of the relative strength of a player (ratings are always relative to the playerbase contemporary to the rating!), even if the player doesn't play much. That of course could be wrong in some cases; although it is likely that the rating of a player doesn't change much in a year or so (unless the player is raising quickly).
• I am not going to consider every 2700chess list, rather once in a year (more or less spaced 12 months from the previous one, if possible) presuming that aside from rising players, the others are quite stable.
• By all means this is just one possible perspective on the FIDE ratings list, if you have a better one, go compiling it and then share! I am interested.
• Another important point about ratings is the kfactor (that determines how many points are exchanged in a match in case of a not expected result). It is very likely that the kfactor used in the past by FIDE was different than now, as one can see very "round" scores, always multiple of 5. This may also have helped the formation of larger gaps between scores. To be fair one should compare ratings only when the kfactor used is the same. If the kfactor is very small, for example, accumulating a 20 point gap may be harder compared to a 100 point gap with a larger kfactor. So far, 2018-09-23, I was not able to find the kfactor values pre 2010. Anyway the kfactor difference may matter to compare gaps between different decades, not between players playing at the same time.
• Note that if one player is dominating compared to his contemporaries, his rating is going to explode. This does not mean that he is better than all the future players. An interesting comparison between players of different eras is the CAPS system. That compares each move of renowned chess players against stronger-than-human chess engines to see how many times the move chosen by the player matches the one chosen by the chess engine. Given that the chess engine employed could compute for a specific amount of time. https://www.chess.com/article/view/who-was-the-best-world-chess-champion-in-history . Carlsen, Kasparov and Fisher are very close. Although one can say that Alpha/Beta chess engines play differently from humans and therefore are not that much comparable.

# Analyses

## Rating distance between ranks.

As I wrote in my other page about the elo insights from the statistics of gladiabots, the Elo's formula is based on rating differences. Rating differences are used to compute the expected result. Therefore the larger the rating gap between players, the larger the gap in average performance between the two players, with the player having the higher score being better.

Let's pick the elo formula component for the expected result

(1)
\begin{align} \frac{1}{ 1 + 10^{ \frac{ sA - sB } {400} } } \end{align}

having the player B at 1000 points and the player A at 600, so 400 points of difference, implies that the player B is expected to win 90% of the time. The formula is based on differences. The expected winning percentage remains the same even if B has 1 000 001 000 points and A has 1 000 000 600 points, even though 400 points when one score is 600 seems a lot, while 400 points when one score is 1 000 000 600 seems nothing.

Not only this. Measuring distances between ratings of different ranks (for example: no5 vs no20) gives also an idea how the strength in the field is distributed.

To avoid considering only the very top players, that may play not much, after a while I am considering the ranks immediately under the no1, as there should be always someone playing in the, say, top5, and therefore the ratings are more "live".

Notice also that if a player has a high rating but he doesn't play, there is little to do, he is not going to lose points.

### Rating distance no1 vs no2

year no1 rating no2 rating distance no1 player no2 player notes
1967.06 2670 2670 0 Spassky Fischer
1968.04 2710 2690 20 Fischer Botvinnik
1969.01 2720 2690 30 Fischer Spassky
1970.01 2720 2670 50 Fischer Korchnoi
1971.01 2740 2690 50 Fischer Spassky
1972.07 2785 2660 125 Fischer Spassky
1973.07 2780 2660 120 Fischer Karpov
1974.05 2700 2670 30 Karpov Korchnoi Fischer first at 2780 but not playing, so skipped this time
1975.01 2705 2665 40 Karpov Korchnoi Fischer again skipped at 2780
1976.01 2695 2670 25 Karpov Korchnoi
1977.01 2690 2645 45 Karpov Korchnoi
1978.01 2725 2665 60 Karpov Korchnoi
1979.01 2705 2695 10 Karpov Korchnoi
1980.01 2725 2705 20 Karpov Tal
1981.01 2690 2650 40 Karpov Portisch
1982.01 2720 2655 55 Karpov Timman
1983.01 2710 2690 20 Karpov Kasparov
1984.01 2710 2700 10 Kasparov Karpov
1985.01 2715 2705 10 Kasparov Karpov
1986.01 2720 2700 20 Kasparov Karpov
1987.01 2735 2710 25 Kasparov Karpov
1988.01 2750 2715 35 Kasparov Karpov
1989.01 2775 2750 25 Kasparov Karpov
1990.01 2800 2730 70 Kasparov Karpov
1991.01 2800 2725 75 Kasparov Karpov
1992.01 2780 2725 55 Kasparov Karpov
1993.01 2805 2725 80 Kasparov Karpov
1994.01 2740 2715 25 Karpov Shirov Kasparov had problems with FIDE
1995.01 2805 2765 40 Kasparov Karpov
1996.01 2775 2775 0 Kramnik Kasparov
1997.01 2795 2765 30 Kasparov Anand
1998.01 2825 2790 35 Kasparov Kramnik
1999.01 2812 2781 31 Kasparov Anand first year that the ratings do not seem rounded to a multiple of 5
2000.01 2851 2769 82 Kasparov Anand
2001.01 2849 2790 59 Kasparov Anand
2002.01 2838 2809 29 Kasparov Kramnik
2003.01 2847 2809 38 Kasparov Kramnik
2004.01 2831 2777 54 Kasparov Kramnik
2005.01 2804 2786 18 Kasparov Anand
2006.01 2812 2801 11 Kasparov Topalov
2007.01 2783 2779 4 Topalov Anand
2008.01 2799 2799 0 Kramnik Anand
2009.01 2796 2791 5 Topalov Anand
2010.01 2810 2805 5 Carlsen Topalov
2011.01 2814 2810 4 Carlsen Anand
2012.01 2835 2805 30 Carlsen Aronian
2013.01 2861 2810 51 Carlsen Kramnik
2014.01 2872 2812 70 Carlsen Aronian
2015.01 2862 2820 42 Carlsen Caruana
2016.01 2844 2801 43 Carlsen Kramnik
2017.01 2840 2827 13 Carlsen Caruana
2018.01 2834 2811 23 Carlsen Caruana
2018.09 2839 2827 12 Carlsen Caruana

#### Top 5 distances no1 vs no2, showing the domination of a player over the rest of his contemporaries.

year no1 rating no2 rating distance no1 player no2 player notes
1972.07 2785 2660 125 Fischer Spassky
1973.07 2780 2660 120 Fischer Karpov
2000.01 2851 2769 82 Kasparov Anand
1993.01 2805 2725 80 Kasparov Karpov
1991.01 2800 2725 75 Kasparov Karpov

### Rating distance no1 vs no5

year no1 rating no5 rating distance no1 player no5 player notes
1967.06 2670 2650 20 Spassky Tal
1968.04 2710 2650 60 Fischer Larsen
1969.01 2720 2650 70 Fischer Petrosian
1970.01 2720 2650 70 Fischer Larsen
1971.01 2740 2640 100 Fischer Petrosian
1972.07 2785 2640 145 Fischer Portisch
1973.07 2780 2650 130 Fischer Portisch
1974.05 2700 2645 55 Karpov Portisch Fischer first at 2780 but not playing, so skipped this time
1975.01 2705 2645 60 Karpov Polugaevsky Fischer again skipped at 2780
1976.01 2695 2630 65 Karpov Spassky
1977.01 2690 2625 65 Karpov Portisch
1978.01 2725 2630 95 Karpov Spassky
1979.01 2705 2625 80 Karpov Timman
1980.01 2725 2635 90 Karpov Polugaevsky
1981.01 2690 2635 55 Karpov Spassky
1982.01 2720 2630 90 Karpov Portisch
1983.01 2710 2625 85 Karpov Huebner
1984.01 2710 2630 80 Kasparov Andersson
1985.01 2715 2635 80 Kasparov Portisch
1986.01 2720 2645 75 Kasparov Yusupov
1987.01 2735 2625 110 Kasparov Korchnoi
1988.01 2750 2640 110 Kasparov Korchnoi
1989.01 2775 2640 135 Kasparov Speelman
1990.01 2800 2645 155 Kasparov Gurevich Mikhail
1991.01 2800 2650 150 Kasparov Bareev
1992.01 2780 2670 110 Kasparov Anand
1993.01 2805 2690 115 Kasparov Gelfand
1994.01 2740 2710 30 Karpov Kramnik Kasparov had problems with FIDE
1995.01 2805 2715 90 Kasparov Kramnik
1996.01 2775 2735 40 Kramnik Kamsky
1997.01 2795 2740 55 Kasparov Ivanchuk
1998.01 2825 2740 85 Kasparov Ivanchuk
1999.01 2812 2723 89 Kasparov Morozevich first year that the ratings do not seem rounded to a multiple of 5
2000.01 2851 2748 103 Kasparov Morozevich
2001.01 2849 2745 104 Kasparov Leko
2002.01 2838 2742 96 Kasparov Morozevich
2003.01 2847 2736 111 Kasparov Leko
2004.01 2831 2736 95 Kasparov Shirov
2005.01 2804 2749 55 Kasparov Leko
2006.01 2812 2752 60 Kasparov Aronian
2007.01 2783 2750 33 Topalov Ivanchuk
2008.01 2799 2763 33 Kramnik Svidler
2009.01 2796 2771 25 Topalov Morozevich
2010.01 2810 2781 29 Carlsen Aronian
2011.01 2814 2776 38 Carlsen Karjakin
2012.01 2835 2773 62 Carlsen Radjabov
2013.01 2861 2781 80 Carlsen Caruana
2014.01 2872 2785 87 Carlsen Topalov
2015.01 2862 2797 65 Carlsen Anand
2016.01 2844 2787 57 Carlsen Caruana
2017.01 2840 2796 44 Carlsen Vachier-Lagrave
2018.01 2834 2793 41 Carlsen Vachier-Lagrave
2018.09 2839 2780 59 Carlsen Vachier-Lagrave

#### Top 5 distances no1 vs no5, showing the domination of a player over the rest of his contemporaries.

year no1 rating no2 rating distance no1 player no5 player notes
1990.01 2800 2645 155 Kasparov Gurevich Mikhail
1991.01 2800 2650 150 Kasparov Bareev
1972.07 2785 2640 145 Fischer Portisch
1989.01 2775 2640 135 Kasparov Speelman
1973.07 2780 2650 130 Fischer Portisch

### Rating distance no5 vs no20

It is incredible to see that the world no1 (for FIDE) is able to distance himself from the no5 more, in some cases, than the no5 is able to distance himself from the no20. The group of players between no5 and no20 was always quite packed together in terms of ratings (and therefore relative strength).

year no5 rating no20 rating distance no5 player no20 player notes
1967.06 2650 2580 70 Tal Hort
1968.04 2650 2590 60 Larsen Gligoric
1969.01 2650 2590 60 Petrosian Taimanov
1970.01 2650 2570 80 Larsen Najdorf
1971.01 2640 2580 60 Petrosian Gipslis
1972.07 2640 2575 65 Portisch Vasiukov
1973.07 2650 2585 65 Portisch Taimanov
1974.05 2640 2595 50 Portisch Byrne
1975.01 2645 2580 65 Polugaevsky Taimanov
1976.01 2630 2575 55 Spassky Ribli
1977.01 2625 2580 45 Portisch Byrne
1978.01 2630 2575 55 Spassky Sosonko
1979.01 2625 2590 35 Timman Ljubojevic
1980.01 2635 2590 45 Polugaevsky Gulko
1981.01 2635 2585 50 Spassky Ribli
1982.01 2630 2590 40 Portisch Ribli
1983.01 2625 2580 45 Huebner Torre
1984.01 2630 2580 50 Andersson Romanishin
1985.01 2635 2570 65 Portisch Miles
1986.01 2645 2575 70 Yusupov Velimirovic
1987.01 2625 2585 40 Korchnoi Nunn
1988.01 2640 2595 45 Korchnoi Seirawan
1989.01 2640 2610 30 Speelman Seirawan
1990.01 2645 2610 35 Gurevich Speelman
1991.01 2650 2620 30 Bareev Huebner
1992.01 2670 2620 50 Anand Adams
1993.01 2690 2630 60 Gelfand Adams
1994.01 2710 2630 80 Kramnik Tiviakov
1995.01 2715 2645 70 Kramnik Nikolic
1996.01 2735 2650 85 Kamsky Hracek
1997.01 2740 2650 90 Ivanchuk Khalifman
1998.01 2740 2660 80 Ivanchuk Krasenkow
1999.01 2723 2670 53 Morozevich Timman first year that the ratings do not seem rounded to a multiple of 5
2000.01 2748 2672 76 Morozevich Svidler
2001.01 2745 2679 66 Leko Karpov
2002.01 2742 2683 59 Morozevich Dreev
2003.01 2736 2688 48 Leko Karpov
2004.01 2736 2682 54 Shirov Dreev
2005.01 2749 2685 64 Leko Volokitin
2006.01 2752 2698 54 Aronian Bareev
2007.01 2750 2700 50 Ivanchuk Akopian
2008.01 2763 2711 52 Svidler Alekseev
2009.01 2771 2723 48 Morozevich Svidler
2010.01 2781 2723 58 Aronian Shirov
2011.01 2776 2726 50 Karjakin Wojtaszek
2012.01 2773 2732 41 Radjabov Kamsky
2013.01 2781 2734 47 Caruana Jakovenko
2014.01 2785 2734 51 Topalov Wang Hao
2015.01 2797 2734 63 Anand Radjabov
2016.01 2787 2744 43 Caruana Adams
2017.01 2796 2742 54 Vachier-Lagrave Grischuk
2018.01 2793 2745 48 Vachier-Lagrave Harikrishna
2018.09 2780 2742 38 Vachier-Lagrave Wei Yi

## Concentration of points

Another phenomena I observed working on the gladiabots dataset is that in general the rich gets richer. The strong players slowly go farming points from other players - also retaining points from players that quit playing - and therefore the points slowly accumulate at the top. This can be seen with the amount of points collected in the first positions (in this case top20).

### weight top5 and top 20 total points

In a equal rating table, the top5 would have exactly 25% of the ratings points of the top20. One can see that in some moments the top5 was able to add a 0.61% more than its fair share.

What is interesting to notice is that round about the dissolution of the soviet union and then for almost all the years after, the top20 started to accumulating points. As points are created by new players and then move slowly upwards as stronger players collect them. Likely new countries joined FIDE and/or produced more and more rated player that helped injecting points in the system.

year top5 points top20 points top5 % weight top5 points diff 1 year top20 points diff 1 year notes
1967.06 13300 52390 25.38 0 0
1968.04 13370 52530 25.45 70 140
1969.01 13400 52480 25.53 30 -50
1970.01 13370 52480 25.47 -30 0
1971.01 13390 52520 25.49 20 40
1972.07 13375 52490 25.48 -15 -30
1973.07 13405 52545 25.51 30 55
1974.05 13445 52640 25.54 40 95
1975.01 13440 52585 25.55 -5 -55
1976.01 13265 52275 25.37 -175 -310
1977.01 13240 52260 25.33 -20 -15
1978.01 13280 52275 25.4 40 15
1979.01 13305 52335 25.42 25 60
1980.01 13415 52430 25.58 110 95
1981.01 13260 52355 25.32 -155 -75
1982.01 13290 52345 25.38 30 -10
1983.01 13300 52290 25.43 10 -55
1984.01 13310 52425 25.38 10 135
1985.01 13345 52330 25.5 35 -95
1986.01 13355 52390 25.49 10 60
1987.01 13360 52365 25.51 5 -25
1988.01 13425 52670 25.48 65 305
1989.01 13455 52690 25.53 30 20
1990.01 13520 52845 25.58 65 155
1991.01 13570 53105 25.55 50 260
1992.01 13580 53145 25.55 10 40
1993.01 13640 53415 25.53 60 270
1994.01 13590 53490 25.4 -50 75
1995.01 13715 53750 25.51 125 260
1996.01 13790 53885 25.59 75 135
1997.01 13800 53920 25.59 10 35
1998.01 13865 54110 25.62 65 190
1999.01 13793 54212 25.44 -72 102
2000.01 13877 54266 25.57 84 54
2001.01 13902 54427 25.54 25 161
2002.01 13888 54447 25.5 -14 20
2003.01 13888 54473 25.49 0 26
2004.01 13857 54557 25.39 -31 84
2005.01 13850 54474 25.42 -7 -83
2006.01 13922 54671 25.46 72 197
2007.01 13832 54702 25.28 -90 31
2008.01 13906 54916 25.32 74 214
2009.01 13913 55016 25.28 7 100
2010.01 13974 55073 25.37 61 57
2011.01 13989 55165 25.35 15 92
2012.01 14013 55273 25.35 24 108
2013.01 14047 55370 25.36 34 97
2014.01 14045 55363 25.36 -2 -7
2015.01 14089 55441 25.41 44 78
2016.01 14022 55473 25.27 -67 -32
2017.01 14082 55548 25.35 60 75
2018.01 14039 55477 25.3 -43 -71
2018.09 14070 55520 25.34 31 43

## Observations

### Dominating players in the past used better their resources

The stats shows that the difference of strength is very small in recent years compared to the years until Kasparov dominated (and before that Karpov and then Fisher). Why? My informed guess is the following.

The players that dominated (and dominate) with large margins (80+ points from the no5) have (and had) enormous and very rare personal qualities needed for the challenge (intellectual skills, passion, commitment, and so on). Very rare otherwise they wouldn't have been alone at the top. Also they had an advantage in understanding of the game better than their peers.

I think in recent years the field leveled as it is way easier to do studies online and/or with the help of strong chess programs that provide insights to everyone and not only elite players in elite chess clubs. Therefore the ones in the past that squeezed more information from analyses of games by periodicals, chess clubs, study groups, books and other resources, to then combined those lessons learned with excellent personal qualities had a clear edge on all the others.

Reading around about players from 1900 to 1970 one can see this pattern. Lasker, Rubinstein, Capablanca, Botvinnik, Fischer and others really committed their life to chess (well Lasker up to a certain point) without resting on their laurels or just playing. They extracted more and more information from whatever possible chess source. This especially was true from Fisher, that went to read chess information in other languages, and he indeed accumulated a remarkable distance from the others when he actively played.

### Points accumulation to the top and absolute scores to take with a grain of salt rather than gold values

As explained in the section showing the total points of the top20, the ratings start to sharply increase around the fall of the Soviet Union. So around 1989-1990. From there the increase of points is (almost) unstoppable. My informed guess is the following.

Could be that around that time FIDE allowed more players to get rated. Tournaments, where ranked games were played, become more frequent and so points moved around with more velocity, drifting a bit faster towards the top players that were (and are) able to harvest them. One point more here, one point more there.

Now people obsess about a so perceived "inflation" of scores, but this because absolute scores are taken as gold value. What matters, learned the hard way on the gladiabots stats, are score differences. The Elo's formula is pretty consistent, score differences stay the same in a certain pool of players with not so fast changing skills, even if absolute values change.

What could be affected by absolute scores being higher is the number of games needed for a (new) strong player to reach a top score. But normally that doesn't take much more time as well. Since the process of getting strong new players is continuous - as new strong players appear every year - also the top scores cannot get that fast so high as they get remarkable losses from those raising players. So instead of someone needing, say, 100 games, to be in the top 20, one would need 110 games and so on. 10 games more is not a tragedy. Before the additional amount of games needed to reach the top20 by a strong player becomes unfeasible, long time will pass.

This means that 2700chess, for example, some decades ago could have been called 2650chess or 2600chess. And in some decades it will change to 2750chess. Or could also be that the velocity of points accumulating towards the top is somehow stabilizing (that is, no more ever increasing top scores). One can see this by the points accumulated by the top20 in the last 2-3 years. The top 20 starts to lose points as well after decades of ever increasing total points.

page revision: 128, last edited: 26 Mar 2020 14:52