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Accuracy, Ratings, and GOATs

Accuracy, Ratings, and GOATs

hissha
| 165 | Chess Players

There have been many attempts to estimate ratings of chess players, both past and present, by looking at their game scores and comparing the moves with a top engine's choices, including one notable study here on Chess.com in 2017. 

These attempts have been generally correct in showing the steady advance of chess skill over time, but they have mostly been rather unconvincing at actually comparing individual players; one study even ranked Jose Capablanca as the objectively best player of all time! He may have been the best of all time relative to his peers or had the most talent (though that is not my conclusion), but to suggest that he actually played as well as GM Garry Kasparov or GM Vladimir Kramnik at peak (this study was done before GM Magnus Carlsen arrived on the scene), even after the opening, is just not plausible; chess knowledge has advanced tremendously since 1920.

Capablanca
Capablanca: The greatest ever? Not really.

The main reason for the difficulty in comparing players is that those who prioritize not losing and excel in endgames (Capablanca, GM Tigran Petrosian, GM Anatoly Karpov, perhaps Carlsen) get more draws than those who prioritize winning and excel in attacking (Alexander Alekhine, GM Mikhail Tal, Kasparov, GM Veselin Topalov), and draws show much higher accuracy (or lower error rates) than decisive games in general.

In fact, strong players generally show a higher Chess.com accuracy on average for draws than they do for wins! This creates a huge bias for the cautious/endgame players if you derive ratings from accuracy scores or error rates. My solution to this major problem is simple—just exclude draws from the data! This appears to put wild and cautious players on an equal footing.

The second issue is the opponents' strength. It is easier to get a high accuracy (low error rate) against a weaker opponent than against a stronger one; the stronger opponent will pose problems that are not easy for a weaker player to solve. Players who generally play much weaker opponents will look better on accuracy than similar players who normally play equal or stronger opponents.


Accuracy vs. Quality

In general, a win or loss is only partly due to your own good or bad play; it may also be due to your opponent's poor or good play. Since wins typically get about six Accuracy points more than losses with equal players, by adding 1.5 to the Accuracy score of the loser and subtracting 1.5 from the winner, I am moving them about halfway to the middle, which amounts to sharing the credit for the result between good play of the winner and poor play of the loser, a reasonable, neutral assumption. Doing this dramatically improves the accuracy of rating estimates based on Accuracy scores for individuals.

In general, a win or loss is only partly due to your own good or bad play; it may also be due to your opponent's poor or good play.

I will use the word "Quality" to mean the Chess.com Accuracy scores for a player, excluding draws, and with the wins and losses adjusted as explained above. In this sidebar, I show how these quality numbers correlate quite well with Chess.com ratings across a wide range, both for classes of players and for individual top players, and that the relationship is close enough to linear for the purposes of this article.

Methodology

For this historical study of games played at standard time limits, I limited the data to classical world championship matches and tournaments (including women's championships), as well as games played in Candidates matches leading up to the World Championship, or double/multiple round-robin (RR) Candidates and Interzonal RR events when they were run, as well as other matches between world champs and top contenders even if not title-related. By "World Championship," I mean events that were generally accepted as valid for deciding who was the best player, regardless of who ran it or whether it was technically called a "World Championship."

Steinitz
Wilhelm Steinitz: Officially, the first world champion, but not for our purposes.

I started with Louis de la Bourdonnais vs. Alexander MacDonnell in 1834, which was generally deemed to be the first match (actually six matches) between the world's best. I also included some top-level RR tournaments in which most of the players were among the world's best at the time in order to have enough games to compare all the world champs and their challengers, and only considered games for a given player during what I determined to be his or her peak years (a minimum of three years and two qualifying matches when possible). By limiting the events considered in this manner, I greatly reduced the "strength of opponent" problem, with the above 1.5 win/loss adjustment further minimizing this issue. I required at least 20 non-drawn games (19 for the first two women champions) for inclusion on the list; most have between 30 and 60 such games.

Estimating Elo

To translate the quality numbers to an estimated FIDE rating, one complication was that FIDE ratings have not been constant, meaning that a given rating does not necessarily translate to the same quality of play at different times. It is pretty clear that ratings inflated from the start in 1970 until about 2006, when the floor dropped below 1600, and then soon started to deflate; FIDE is now considering a proposal to reverse the recent deflation, at least below the 2000 level. My estimate is that the recent deflation has roughly canceled out the earlier inflation at the grandmaster level, so 2500+ ratings from the 1970s and today's ratings are fairly comparable, while such ratings in and around the 1990s were inflated by 30 to 50 points.

Kasparov
Kasparov: Peaked during a period of rating inflation, but don't let him hear of it. Photo: Maria Emelianova/Chess.com.

So the ratings I quote are intended to be fairly accurate recently and in the 1970s, not so much in between. I determined that a Quality score of 90 equated quite closely to a 2600 FIDE rating and that the "slope" of the line that best fits the data (in the 2200+ range at least) is about 80, meaning that every quality point above or below 90 equates to 80 elo points. So the formula is:

estimated FIDE rating = quality * 80 - 4600

A player with the minimum FIDE rating of 1000 would have a quality of 70, while perfect Accuracy would get 3400, roughly the level of the reference engine. This seems reasonable enough.

The first conclusion of my study is that the level of play of the top players has improved by about 2.5 Elo points per year from 1900 to now. The rate of improvement was faster in the 1800s, but has been reasonably steady since 1900. It has probably accelerated recently due to the internet and engines, but there isn't enough data to measure this, so I'm treating the gain as a constant per year.

What's In A GOAT?

I propose three ways to define the "GOAT" or "Greatest Of All Time." First, we can simply compare the quality of play (this excludes the opening moves that are in the Chess.com book, but this leaves a big advantage for the more modern players). This will, of course, usually show the more recent top player to be stronger.

The second method is to credit the older players with the 2.5 Elo per year between their peak years and Carlsen's, which basically defines the top player of 1900 and Carlsen as "equal," interpolating/extrapolating for the others.

Carlsen
Carlsen: The standard of comparison. Photo: Maria Emelianova/Chess.com.

The third method reduces the credit to two points per year to allow for the fact that there are many more serious players now than in 1900, so being the best in 1900 might be only comparable to being number ten or twenty now. This method estimates how they would rate now if they were around age 30 today and had the same benefits of engines and the internet as today's stars; you might call this a measure of chess talent.

These three methods lead to very different results.

Method 1

Using the first method, the following are the players who were the Greatest Of All Time during their peak period. All but two of the players were world champions (or deemed world number one prior to Wilhelm Steinitz), but several world champions didn't make the list—because even if they were the best at their prime, they failed to surpass one or more predecessors.

Greatest players of all time, as of their peak years. FIDE ratings are average during those years. Est. Elo by the Q x 80 - 4600 formula.

Player Peak Years Quality Est. Elo FIDE Rating
Louis de la Bourdonnais 1834 80.74 1859 -
Howard Staunton 1843-1851 82.2 1976 -
Paul Morphy 1857-1859 87.64 2411 -
Wilhelm Steinitz 1872-1886 88.22 2458 -
Harry Pillsbury 1897-1898 89.43 2554 -
Emanuel Lasker 1907-1914 89.95 2596 -
Jose Capablanca 1921-1931 90.24 2619 -
Alexander Alekhine 1927-1934 90.6 2648 -
Reuben Fine 1932-1949 90.64 2651 -
Mikhail Botvinnik 1948-1955 90.74 2659 -
Vasily Smyslov 1953-1957 91.09 2687 -
Mikhail Tal 1958-1960 91.39 2711 -
Bobby Fischer 1970-1972 92.52 2802 2762
Garry Kasparov 1993-2001 92.76 2821 2809
Magnus Carlsen 2013-2021 93.23 2858 2863

Some notes: The first three played before the use of chess clocks, and both de la Bourdonnais and Paul Morphy reportedly played much faster than their opponents, probably basically playing what we would call rapid instead of standard. Because of this, their Quality and estimated Elo are probably too low; perhaps they would be 100 Elo or so higher if they played under Steinitz-era time limits and took their time.

We don't really know if Bourdonnais was the GOAT in 1834 since his great French predecessors Francois Philidor and Alexandre Deschapelles played mostly handicap games (and Philidor even played with different rules, under which no player could have two queens). There aren't enough surviving game scores of even games against worthy opponents to judge them. The Edo chess website rates Bourdonnais and Deschapelles as virtually tied in 1821, the one year where they both played a decent number of games. I am assuming that the standard of play had risen by 1834, the year when Bourdonnais played the first matches that we might now call "World Championships." So he was probably the GOAT in 1834, with a true level in standard chess in 1900 to 2000 FIDE range by today's standards.

The British Howard Staunton was clearly stronger, close to 2000, and our second GOAT. Adolph Anderssen didn't clearly pass Staunton until after Morphy dominated, so he was never GOAT.

Staunton
Staunton: The best to that point, but compared to what was to come...

Morphy was by far the largest leap over his predecessors and contemporaries of anyone in chess history. His estimated Elo jumped over 400 points from Staunton as well as over his strongest opponents, into modern international master range (2400+), and in view of the above comments about his rate of play, he might have reached the GM range (2500+) if he had continued to play into the era of chess clocks with long time limits. This makes it quite clear that Staunton had good reason to dodge Morphy. In fact, he would have been crushed even with pawn and move handicap, an estimated 175 Elo handicap, as Morphy eventually offered to anyone in the world, quite justifiably from my numbers. Even today, Morphy would be the GOAT if your criterion is lead over the next best player in the world.

Morphy
Morphy: 400 points ahead of his time.

Steinitz did surpass Morphy per the raw figures at his peak, which came about twenty years later than Morphy's peak, even though they were born the same year! Had they actually played a match in the 1860s, the only decade in which they were both active, Morphy would easily have won, but Steinitz continued to improve. In view of the speed of play issue, my belief is that Morphy would have even beaten Steinitz in his prime, assuming that Morphy had kept up his level of play and that he took Steinitz seriously and used equal time, but we don't have enough info about time taken in matches to be confident of this. Players who played against both judged Morphy to be the stronger; in fact, two of them took knight odds from Morphy but played Steinitz on even terms!

Harry Pillsbury was the first player on the list to fall clearly in grandmaster territory, and is also one of only two who was never world champion (or even challenger). His status as GOAT in his prime years 1897-1898 is questionable only because Emanuel Lasker was already about the same level then, even though his own peak was still a decade away, but Lasker's "Quality" in his final match with Steinitz was a tiny bit below Pillsbury's peak, so I awarded GOAT to Pillsbury.

Pillsbury: Never world champion, but one of the greatest. Photo: Cleveland Public Library/Wikimedia, public domain.

With an estimated peak Elo near 2600, Lasker was a very clear GOAT over an eight-year peak period. His gain over his world champion predecessor (Steinitz) was the largest in chess history during the years of a formal world championship. Capablanca passed Lasker by a modest amount during his peak and was the first to pass 2600 by my formula; Alekhine, in turn, surpassed Capablanca by a similar amount, so both were GOAT during peak years.

GM Reuben Fine was the next GOAT and the second who was never a world champion or challenger. Since his margin over Alekhine was just three Elo, which is statistically meaningless, his GOAT status could be questioned. He shared first place ahead of Alekhine with GM Paul Keres in the great AVRO tournament of 1938, which was supposed to select Alekhine's challenger, but World War II interfered. GM Max Euwe, who was briefly world champion during Alekhine's reign, did not reach the Quality levels of Capablanca, Alekhine, or Fine, which is no big surprise, as few ever rated him as world number one.

Euwe
Euwe: Champion, but never the GOAT. Photo: Harry Pot/Dutch National Archives, CC.

The next GOAT, GM Mikhail Botvinnik, was world champ for many years intermittently, although his margin of superiority over Alekhine and Fine at their peaks was tiny, a statistical tie. His successor (both as GOAT and world champion), GM Vasily Smyslov surpassed him by a surprisingly large margin; Smyslov was perhaps stronger than he is generally given credit for.

The next GOAT, and the first to pass a 2700 estimated Elo, was the great Tal from 1958-1960. Unfortunately, his health was poor, and so his results after that period were too inconsistent to extend this peak. The next two World Champs, Petrosian and GM Boris Spassky, had accuracy figures close to Smyslov, but neither reached the remarkable level of peak Tal, so they were never GOAT. Note that all of these Soviet champs from Botvinnik through Spassky peaked before the official FIDE rating system but had unofficial estimated Elos in the 1960s quite close to my estimated Elos for them.

Tal
Tal: His crazy moves made him crazy good. Photo: Bert Verhoeff/Dutch National Archives, CC.

Now we come to the amazing GM Bobby Fischer, who leapfrogged all opponents and predecessors to surpass 2800 by my method during his 1970-72 peak. His actual FIDE rating averaged 2762 during those years, with a peak of 2785, but if one were to calculate his performance rating for the three years, I believe it would also exceed 2800, quite consistent with my estimate. His 90-point estimated Elo jump over all previous world champs was the largest except for Emanuel Lasker. It is interesting that my Elo estimate for him exceeds all later players except Carlsen and Kasparov, and curiously the only players now rated above 2800 are Carlsen and Kasparov (last rating 2812 in 2005).

Fischer
Fischer: Almost 100 points higher than the previous GOAT. Photo: Dutch National Archives, CC.

Fischer's successor Karpov surpassed all previous champs but not Fischer himself, so he doesn't make the GOAT list. Kasparov did pass Bobby by about 20 Elo, and so he does qualify as GOAT (his peak FIDE rating was 66 above Fischer, but much of that was due to rating inflation in the 80s and 90s and also to Fischer's rating not having enough chance to catch up to his performance due to his sudden withdrawal from competitive play). While Kasparov did have a higher and much longer peak than Fischer, it came a quarter of a century later, during which time a 62 true Elo gain would have been about expected.

Karpov
Karpov: Tough to get your due with Fischer and Kasparov on either side. Photo: Marcel Antonisse/Dutch National Archives, CC.

None of the champs after Kasparov surpassed him either by estimated peak Elo or by actual peak FIDE rating until Carlsen became champ. Surprisingly to me, none of them even passed Fischer in estimated peak Elo. But given that none of them is above Fischer's 2785 peak FIDE rating today now that inflation has been reversed, perhaps it's true. Kasparov's estimated peak of 2821 seems pretty consistent with his FIDE peak of 2851, given that this was near the height of rating inflation.

Carlsen surpassed Kasparov by 37 estimated Elo by my method, and in fact, his peak FIDE rating was 31 points higher than Kasparov's. His estimated peak Elo and his actual average FIDE rating during those years differ by a mere five points.

Carlsen is clearly the GOAT in terms of actual quality of play, but of course, that is partly due to the many tools he has available that his predecessors lacked. His successor GM Ding Liren doesn't yet have enough qualifying games for inclusion, but so far, his "Quality" is not up to the level of his rating or of other recent world champs.

Next is a list of non-GOAT champs:

Player Peak Years Quality Est. Elo FIDE Rating
Max Euwe 1935-1938 88.87 2500 -
Tigran Petrosian 1963-1969 90.94 2675 2650
Boris Spassky 1965-1970 91.01 2681 2671
Anatoly Karpov 1974-1984 91.82 2746 2706
Vladimir Kramnik 2000-2007 92.31 2785 2776
Veselin Topalov 2005-2009 92.16 2773 2787
Viswanathan Anand 2007-2014 92.25 2780 2791

Note that the last three champs on this list all had very similar Quality scores and hence estimated Elo, as well as average FIDE ratings. They also all had peak FIDE ratings within a few points of 2820, which probably equates to about 2780 in today's ratings. Almost all of the estimated ratings for the world champs and other GOATS seem very reasonable, except perhaps for Euwe, which seems too low for a player who was probably among the top five in 1935-1938. Having most of his games against one opponent, Alekhine, who played super-sharp openings which lead to large error rates for both sides, is the likely reason.

Now comes a list of challengers and other great players:

Player Peak Years Quality Est. Elo FIDE Rating
Alexander McDonnell 1834 78.8 1704 -
Morphy's 4 top opponents 1857-1859 82.76 2021 -
Adolph Anderssen 1861-1866 85.17 2214 -
Louis Paulsen 1861-1862 85.4 2232 -
Johannes Zukertort 1872-1886 85.78 2262 -
Mikhail Chigorin 1889-1893 84.3 2144 -
Siegbert Tarrasch 1893-1908 87.52 2402 -
Geza Maroczy 1905-1907 87.03 2362 -
Akiba Rubinstein 1908-1912 88.18 2454 -
Efim Bogolyubov 1928-1934 87.68 2414 -
David Bronstein 1950-1954 89.78 2582 -
Sam Reshevsky 1953-1961 90.69 2655 -
Paul Keres 1956-1965 90.79 2663 -
Viktor Korchnoi 1974-1981 90.72 2658 2689
Vasyl Ivanchuk 1990-1992 90.67 2654 2718
Ian Nepomniatchi 2020-2022 92.32 2786 2788
2020-21 Candidates 2020-2021 92.21 2777 2770

Amazingly, Morphy's top four opponents averaged barely over 2000 and nearly 400 below Morphy, an obscenely large gap! He could easily have given them all pawn-and-move odds (as was often done then) and won, perhaps even knight odds. Paulsen and Anderssen each reached at least national master (2200) level and would each have been GOAT in the 1860s if Morphy never played.

The low, sub-2200 rating of Mikhail Chigorin surprises me here, as does also the low rating (barely IM) of GM Efim Bogoljubow. In the case of Chigorin, the reason is surely his predilection for gambits, which led to large error rates for both sides. In the case of Bogo, the problem is the same as for Euwe, that they only had one repeated match opponent (Alekhine) who favored razor-sharp openings. I really should require two distinct match opponents to be on my lists!

Chigorin
Chigorin: Challenged Steinitz twice for the world championship, but not the most accurate player it turns out. Photo: Cleveland Public Library/Wikimedia, CC.

GM Samuel Reshevsky deserves special mention as he even surpassed his great rival Fine, who made the GOAT list, but because he did so after Botvinnik's peak, he missed out on the list by a mere four Elo points. Similarly, Keres would have been GOAT, except he failed to pass Smyslov. GM Viktor Korchnoi's peak was in the same range as Keres and Reshevsky but only later, after Fischer's peak.

Recent two-time challenger GM Ian Nepomiachtchi comes out within two Elo of his average FIDE rating during those years, ahead of all the world champs except for the "big three" of Fischer, Kasparov, and Carlsen, with Kramnik just one Elo behind in fifth place overall, followed closely by GM Viswanathan Anand. I would have liked to include GM Fabiano Caruana in the list, but his title match had no decisive results (in standard games), and so he lacks enough games for this list. He might well be number two of all time, based on peak FIDE rating and the deflation since Kasparov's peak, but I cannot confirm that.

Caruana and Nepomniachtchi: The winners of the last three Candidates Tournaments; not quite GOATs. Photo: Maria Emelianova/Chess.com.

Note that Pillsbury, Fine, and Reshevsky all appear on the Chess Metrics website as world number one for at least a few months, confirming my "Quality" findings.

Now we come to the women's world champions, their challengers, and of course, GM Judit Polgar, who chose to compete only in mixed tournaments.

Greatest women players of all time, as of their peak years. FIDE ratings are average during those years. Only FIDE ratings after 1986 are shown for women, as parity with men's ratings was only established at the end of 1986.

Player Peak Years Quality Est. Elo FIDE Rating
Vera Menchik 1929 84.44 2155 -
Elisaveta Bykova 1958-1960 85.68 2254 -
Alla Kushnir 1965-1972 87.45 2396 -
Nona Gaprindashvili 1969-1975 89.11 2529 -
Maia Chiburdanidze 1978-1988 89.81 2585 2550
Susan Polgar 1990-1996 90.2 2616 2542
Judit Polgar 1998-2005 90.86 2669 2712

Menchik's Quality figure is based on a double RR event against the top men in 1929, so it is a bit unfair to her since she was pitted against stronger opposition; I'll award her an honorary "NM" or "WIM" title (2200) due to this.

Noteworthy is the huge jump by GM Nona Gaprindashvili over her predecessors (WGM Alla Kushnir being a contemporary rival), larger than any jump among the top men since Morphy. My data confirms that she did indeed play at a level worthy of the grandmaster title, whether by today's standards or the standards of her time (when she got the title, actually, GM only required a 2450 rating).

Gaprindashvili
Gaprindashvili: A leap in standards comparable to Morphy. Photo: Fernando Pereira/Dutch National Archives, CC.

GM Susan Polgar showed a level of play significantly above her FIDE rating, which did not benefit from the 100-point bonus given in 1987 to all other women except her and GM Pia Cramling. Curiously, Susan's sister Judit came out 43 Elo below her FIDE rating during her peak years, though this is still good enough to make her the women's GOAT. Her preference for very sharp openings may explain some of this gap, plus the fact that her peak was near the FIDE inflation peak.

World Champs and Challengers

Player Peak Years Quality Est. Elo FIDE Rating
Xie Jun 1991-1999 89.02 2522 2511
Hou Yifan 2011-2016 90.64 2651 2646
2019 Women's Candidates 2019 89.13 2530 2528
Ju Wenjun 2018-2023 89.57 2566 2572

Noteworthy is that all four of the above-estimated Elo ratings are within a few points of the actual FIDE ratings. It certainly looks like there is no reason to think that women's FIDE ratings are either too high or too low in general, which they could be since they mostly play each other at the top. It is also noteworthy that GM Hou Yifan would easily have been GOAT, but she didn't quite reach the level of Judit Polgar. She would be a big favorite to regain the world title if she chose to compete for it.

It is rather remarkable that the current women's world champion, GM Ju Wenjun, is only 37 Elo stronger by my measure than Gaprindashvili at her peak half a century ago, and that Gaprindashvili at her peak would fall right in the middle of the 2019 Women's Candidates! She was really remarkable for the time, and is still winning Senior Women's titles! In fact, her peak compares with today's top women about the same as Fischer's peak (at the same time!) does with today's top men, i.e. a bit below the current champ but on a par with the Candidates.

Method 2

Now comes a very interesting list, a comparison of players' peaks relative to their times. In effect, it assumes that the peak player each year would have improved by an average of 2.5 Elo per year until 2017, the midpoint of Carlsen's peak period.

Greatest players of all time in 2017, crediting all previous players with 2.5 Elo per year from the midpoint of their peak period. This compares the players relative to their peak time period, not absolutely.

Rank Player Time-Adjusted Elo
1 Bobby Fischer 2917
2 Garry Kasparov 2871
3 Alexander Alekhine 2864
4 Emanuel Lasker 2862
5 Magnus Carlsen 2858
6 Mikhail Tal 2856
7 Harry Pillsbury 2853
8 Jose Capablanca 2847
9 Vassily Smyslov 2842
10 Reuben Fine 2842
11 Anatoly Karpov 2841
12 Mikhail Botvinnik 2823
13 Vladimir Kramnik 2819
14 Paul Morphy 2809
15 Boris Spassky 2805
16 Samuel Reshevsky 2805
17 Paul Keres 2804
18 Tigran Petrosian 2803
19 Wilhelm Steinitz 2803
20 Veselin Topalov 2798
21 Vishy Anand 2796

Some comments: No matter how you slice it, Fischer stands alone as the greatest relative to his time period, with Kasparov as a distant second. Although Kasparov didn't top either the time-adjusted or the absolute list, he is the only player to make the top two on both!

Alekhine was racking up huge scores against top opposition in his prime, as also did Lasker, so it seems reasonable that these players should be above Carlsen on this basis. Morphy suffers from the fact that progress was much more than 2.5 per year before 1900, plus the fact that he usually played faster than all the others; he might have rivaled Fischer for the top spot if we could properly correct for these factors.

Alekhine
Alekhine: Better than Magnus? By some ways of looking at it. Photo: Library of Congress, public domain.

This list can be compared with ChessMetrics.com, which also ranks players relative to their time (stopping at 2005, though) but by performance, not by play. We both have the same two players at the top (in reverse order), and most of the names are the same on both top 20 (excluding Carlsen and Topalov due to the 2005 cutoff). He excludes Fine, Keres, Spassky, and Morphy, with the first three within the next dozen spots. I exclude GM Geza Maroczy, Korchnoi, Siegbert Tarrasch, and GM Vasyl Ivanchuk, but Korchnoi came close while Maroczy and Ivanchuk didn't play title matches, so I need more data on them. Anyway, it's a nice confirmation of the methodology.

Method 3

Next is another list reducing the adjustment to two Elo per year, which I estimate should make the list a fairly accurate estimate of how these players would, in fact, rate in 2017 if born around 1987.

Greatest players of all time in 2017 (midpoint of Carlsen's peak), crediting all previous players with 2 Elo per year from the midpoint of their peak period. This estimates how they would rate in 2017 if born around 1987.

Rank Player Est. Elo If Age 30 Now
1 Bobby Fischer 2894
2 Garry Kasparov 2861
3 Magnus Carlsen 2858
4 Mikhail Tal 2827
5 Anatoly Karpov 2822
6 Alexander Alekhine 2821
7 Vladimir Kramnik 2812
8 Vassily Smyslov 2811
9 Emanuel Lasker 2809
10 Reuben Fine 2804
11 Jose Capablanca 2801
12 Vishy Anand 2793
13 Veselin Topalov 2793
14 Harry Pillsbury 2793
15 Mikhail Botvinnik 2790
16 Boris Spassky 2780
17 Tigran Petrosian 2777
18 Paul Keres 2776
19 Samuel Reshevsky 2775
20 Wilhelm Steinitz 2734
21 Paul Morphy 2729

Again Fischer stands alone at the top, with Kasparov edging out Carlsen for second. No one else is close, but all the other players on the list post-Steinitz have estimated ratings in or above the range of Nakamura, Caruana, Ding, Nepomniachtchi, and GM Alireza Firouzja, numbers two through six on the August 2023 FIDE list.

In other words, all of the players from fourth to 19th on this list had the aptitude for chess to be candidates today if they were around age 30 now and grew up with the same tools as Carlsen and his rivals. I'm sure Morphy also belongs on this list due to the above-mentioned factors. Any of the players above 2800 on the list would likely be Carlsen's closest rival today under these conditions.

Botvinnik Smyslov
Botvinnik and Smyslov: Two of the greats, in any era. Photo: Dutch National Archives, CC.

Of course, this doesn't consider individual circumstances; for example, Reshevsky and Lasker weren't full-time chess pros and so could be even higher if they were, while Fischer did nothing but chess, so may perhaps be a bit overrated at 2894 compared to the others. But I think the basic conclusion is valid, that all the above players (except perhaps Steinitz) would be considered superstars had they grown up with the internet and engines.

What If?

Now to answer some historical questions. How about the never-played Fischer vs Karpov match of 1975? Karpov was within his peak range at 2746, while Fischer was three years out from 2802. To get more clarity, I checked Fischer's performance in his 1992 re-match with Spassky. Fischer's "Quality" was 91.50 = 2720, while Spassky's was 89.50 = 2560. So Fischer was down 82 elo from his peak, while Spassky was down 121 from his somewhat earlier peak.

Incidentally, Susan Polgar estimated for me that Fischer's level in 1993 (when they played a lot of Fischer Random Chess) was "2650 to 2700," which is not too far below my 2720 figure for 1992 (based on only 15 decisive games). So, in 1975 Fischer was about 2790 if we assume linear decay, well above Karpov's 2746. Not much doubt about this one. Had they waited until 1984, the end of Karpov's peak period, Fischer would have been about 2753, so given the uncertainty of this method, we could call the hypothetical 1984 match a toss-up.

How about an Alekhine vs. Capablanca rematch, which Alekhine managed to dodge? Assuming that it was held in 1930 (three years from the first match), that was still within the peak period for both, and Alekhine's peak was 29 Elo higher, so the advantage goes to Alekhine, though it's close enough to leave some doubt.

What if Alekhine had defended his title in 1939 or 1940 against Keres or Fine, who shared first in Avro 1938 (Keres winning on tiebreak)? Since Fine's peak included that period while Alekhine had already peaked at a slightly lower figure, Fine was a clear favorite. Keres didn't peak until the 1950s, so it's not so clear whether he would have defeated Alekhine in 1940.

Keres Fine
Keres and Fine: Without World War II, might either have become a world champion?

Emanuel Lasker was expected to play matches with Maroczy and GM Akiba Rubinstein, but neither materialized. While they were plausible challengers for Lasker prior to Capablanca, especially Rubinstein, my data shows that neither stood a chance against Lasker, who was in a class by himself until Capablanca passed him.

Lasker
Lasker: Didn't play every challenger; probably didn't need to.

Classical vs. Rapid And Blitz

Another nice feature of this Quality figure is that it allows for comparison between classical and rapid chess, or even blitz.

Let's start with Magnus Carlsen, whose Chess.com Rapid Quality in the past year (with an average time control of about 12 minutes plus three second increment, or 12+3) was 91.21, compared to 93.23 for his average at classical time controls as world champion, which would mean an estimated Elo of 2697 if someone had this result in classical time controls. So Magnus dropped 161 Elo in Quality, playing fast rapid compared to classical. His Quality in the fast rapid games exceeded the classical time control Quality of all world champions and challengers prior to 1970, except for Tal in 1958-1960.

Rapid play better than the classical of 60 years ago. Agree? Photo: Maria Emelianova/Chess.com.

For a second example, Nepomniachtchi on Chess.com Rapid in the past year showed an average quality of 89.57 (his average time control in these games being about 10+2), compared to 92.32 for Classical. So his play dropped by 220 Elo points going from classical to fast rapid, but his rapid games were, on average, shorter games than Carlsen's, which should explain part of the difference between 160 and 220. Based on the world number one and the world championship challenger in the last two cycles, I think it's fair to say that the quality of play in fast rapid, say 10+2, is about 200 Elo below classical play.

How about blitz? For top players, blitz means a mixture of 3+1 games in events like Titled Tuesday and 3+0 non-tournament games. In Nepo's case, his blitz Quality for the past year was 85.02, a drop of 4.55 from rapid, which at 80 FIDE Elo points per Quality point is a drop of 364 FIDE Elo points. For Carlsen, his blitz Quality averaged 87.96, equivalent to a 260-point Elo dropoff from rapid.

Here are a few other notable players with at least 50 blitz and 50 rapid games in the past year, with rapid Quality, blitz Quality, and implied FIDE Elo drop-off:

Player Rapid Quality Blitz Quality Elo Change
Hikaru Nakamura 88.57 86.66 -153 Elo
Wesley So 89.11 87.13 -158 Elo
Fabiano Caruana 89.21 86.10 -249 Elo
Alireza Firouzja 87.89 86.57 -106 Elo (!!)
Nihal Sarin 89.88 86.90 -238 Elo
Vladimir Fedoseev 89.03 86.25 -222 Elo
Maxime Vachier-Lagrave 89.32 87.08 -179 Elo

Plus one much lower-rated (2085 FIDE) streamer with enough games vs. suitable opponents just to show that the drop-off isn't much different at this level:

Player Rapid Quality Blitz Quality Elo Change
Anna Cramling 83.26 80.68 -206 Elo

So the average fast Rapid to fast blitz drop-off for the ten players was 213.5 Elo, a bit more than the drop-off from classical to fast rapid. Rapid play is certainly a lot higher level than blitz, but if you want a good compromise, I can recommend 3+2 blitz, as my studies show that increment raises Quality more than a comparable addition to the base time (3+2 games are significantly higher in Quality than pure five-minute games).

It is also noteworthy that Magnus shows over a 100 Elo higher rapid Quality Elo than his nearest rival on the above list (GM Nihal Sarin), and indeed he leads the rapid list (excluding a few names who have few or no games vs. GM or IM opposition) by a wide margin.

Conclusion

Finally, to show how you can use this method to compare your own classical play at different times of your life (if you are old enough!), I looked at my own history, picking out the three periods when I was primarily focused on competitive chess and had the best results.

In 1979-1980 I easily earned the IM title with extra points in three straight events, performing well over 2500 FIDE (though my rating only reached 2440 then). My "Quality" for those years, considering all decisive games in the database against opponents rated at least 2200, was 89.53 = 2562, perhaps 50 Elo above my performance.

In 1995-1999 I returned to competitive chess after a long layoff, with a modest decline in FIDE rating (from a peak of 2445 to an average of 2414), with a "Quality" of 87.53 = 2398, very close to my performance then.

Then from 2008 to 2011, after reaching age 60, I played regularly in the U.S. and World Senior Championships, with excellent results, earning the GM title by winning the World Senior in 2008, tying for third in 2009, and tying for first in 2010. My performance in the World Seniors overall was over 2500, though my rating remained in the low 2400s during this period due to losing points in domestic open tournaments. My "Quality" during this period (mostly from the Senior events) was 89.76 = 2581, well above my actual performance.

Well, the method isn't perfect, especially with small samples, but overall for the three periods, I think it only overestimated my performance by perhaps 30 Elo or so. For me, the big surprise was that although my rating didn't differ much in these periods, my best quality of play was in my sixties! Only after age 64 did I clearly start to go downhill.

So if you want to apply this to your own past games, just remember to exclude draws, exclude opponents more than about 200 elo below you, and add 1.5 per loss to accuracy and subtract 1.5 per win. You can see when you played your best chess this way.

hissha
GM Larry Kaufman

I was born in 1947 in Washington, D.C. and still live near D.C. My first chess teacher, Harold Phillips, was the 1895 NY Champion and played against the first World Champion, Steinitz, in 1894! I won the American Open Championship in 1966 and was the nation's top rated junior then. I graduated from M.I.T. in 1968, where I worked on the first chess program (MacHack) to earn a rating in human tournaments (mid 1500s). I became a Senior Master and played in my first of four U.S. championships in 1972 (the other three were in the early 2000s). I ran a stock option trading company ("Chess Options") from 1976 to 1986, since then I've worked full time in chess in various aspects. I earned the International Master title in 1980 and was then just outside the world's top 100 according to "Chessmetrics" website. I was chairman of the USCF ratings committe for most of the 1980s, and during that time became the top ranked non-Japanese player of shogi (Japanese chess). Around 1990 I developed several chess programs in partnership with Don Dailey. I reached my highest USCF rating (2538) just before my 50th birthday. In 2008 I won the World Senior Championship and thus became a Grandmaster. I was the number two guy developing Rybka in 2007 and 2008, after which I worked on KomodoChess with the late Don Dailey thru 2013, since then with Mark Lefler. I am currently the top rated U.S. player over age 75 who still competes regularly. I have authored five chess books. I have three children, one of whom, Raymond Kaufman, is an I.M. I became part of the chess.com family when chess.com purchased a share of KomodoChess at the start of 2018. I retired from running KomodoChess in 2023 and am now a consultant for chess.com on komodochess and Torch. I am the current Maryland Chess Champion (tenth time), at age 76.