Greatest Chess Player of All Time – Part II
By Jeff Sonas
This is the second installment in a four-part series where I am using various
statistical techniques, applied to my brand-new Chessmetrics
data, to explore the following question:
Was Garry Kasparov the most dominant chess player of all time? If not,
In Part I
we saw that Emanuel Lasker spent the most months at the top of the rating list,
with Garry Kasparov second. And in terms of a single peak time, Wilhelm Steinitz
had the largest gap ever between a #1 player and the rest of the world, in
1876, with Bobby Fischer having the second-largest gap ever, in 1971. Both
of those calculations could be made without attempting to "calibrate"
historical rating lists against each other. However, if you try to assign comparable
numbers across the eras, so that a 2800-rating a century ago means roughly
the same as a 2800-rating today, it opens new opportunities for analysis. For
one thing, you can see who was the highest-rated player of all time. Now, in
Part II, we will use these calibrated ratings to explore peak ratings and peak
performance ratings. I will leave it to my Chessmetrics site to explain how
that actual calibration is done; for now you'll have to trust me that the ratings
are roughly comparable across the eras, and they are matched up with the current
magnitude of the FIDE ratings.
Bobby Fischer's rapid rise to the chess throne in the early 1970's is well-known.
Along the way he demolished several top-ten opponents in match play. He defeated
#9 Mark Taimanov with an almost unprecedented 6-0 score, and followed that
up with an identical 6-0 defeat of #3 Bent Larsen. He then defeated #6 Tigran
Petrosian, 6.5-2.5, to qualify for the championship match against world champion
For an eight-month period, from the end of the Larsen match until a few months
before the Spassky match, Fischer had a higher Chessmetrics rating than anyone
else in history. The ratings are calculated each month, and include any completed
games from ongoing events. Thus there was a new rating list as of October 1st,
1971, between the first and second games of the Fischer-Petrosian match. As
of that rating list, Fischer had won nineteen straight games, and was awarded
the highest Chessmetrics rating of all time (2895). Obviously, any comparison
between eras is uncertain and depends heavily on how you adjust the rating
lists against each other. But based upon my method, the second-best peak rating
of all time was held by Garry Kasparov with a 2886 rating on the March 1993
Chessmetrics list, right after his +7 score in Linares 1993 (one of the two
strongest tournaments of all time).
As I mentioned previously, one of my latest inventions is a new way to calculate
a player's performance rating in a single event. Current approaches do not
account for the length of an event, and they are often "undefined"
when trying to evaluate a 100% score. This has been problematic because it
was impossible to calculate a performance rating for Bobby Fischer in some
of his historic perfect-score performances. Now, however, based on my new improved
formula, I can say that his match performance against Larsen was indeed the
strongest match performance of all time, with a 2887 performance rating. The
exact meaning of that 2887 is that if we knew nothing else but the results
of that one match, our best guess at Fischer's rating would be 2887. Emanuel
Lasker actually holds both the second-best and third-best match performances
of all time, for his +8 scores in the 1896 return match against Steinitz (2882
performance) and in the 1907 match against Frank Marshall (2876 performance).
Here are the top seven match performances of all-time:
After Fischer resigned his world championship, Anatoly Karpov took over the
chess crown. It is difficult to seriously suggest that Anatoly Karpov was a
more dominant player than Garry Kasparov, simply because their peak years overlapped
so closely and Kasparov outperformed Karpov directly most of the time. However,
there were a few areas in which Kasparov never did surpass Karpov. One of them
was the ability to sustain the highest level of performance into middle age.
Obviously, Kasparov's abrupt retirement makes any further comparisons difficult,
but if you align their historical rating charts so as to compare Kasparov and
Karpov at the same ages, you can see that the 41-year-old Karpov (from 1992)
had already caught up to the 41-year-old Kasparov (from 2004) by the end of
Linares a year ago:
Although most players reach their peak in their early thirties and begin
to decline significantly by the time they reach their early forties, Karpov
was just as dominant (in terms of rating) at age 45 as he had been at age 25.
In fact, Karpov's greatest tournament accomplishment was achieved in 1994 at
Linares, a few months before his 43rd birthday. Moreover, it was the strongest
performance by any player, in any tournament, in the history of chess, according
to my calculations. In a tournament including nine of the top eleven players
in the world, Karpov had a +9 score (11/13, or 85%). For the tournament, his
Chessmetrics performance rating was 2899, meaning that if we knew no other
results for Karpov than this one event, we would have estimated that his rating
should be 2899. It was even a higher performance rating than Fischer achieved
in his match against Bent Larsen. Although Fischer did score 100%, that was
across six games, compared to thirteen for Karpov, and thus on balance not
quite as impressive as Karpov's performance:
I would like to clarify one thing about the Chessmetrics performance ratings,
because I have already seen some people (accustomed to traditional performance
ratings) confused by a notion that initially does seem paradoxical. It is quite
possible to have a peak Chessmetrics rating that is higher than any of your
individual Chessmetrics performance ratings. You may have noticed that Bobby
Fischer reached that peak rating of 2895, despite never having any event performance
ratings higher than 2890. The reason? No one single event was enough evidence,
all by itself, to suggest that Fischer’s strength was so high. But when
viewed as a whole, the group of performances provided sufficient evidence to
push Fischer’s rating to that all-time high. Just as someone who plays
rarely is "punished" by my rating formula, someone who plays a shorter
event is "punished" in the same way by the performance rating formula.
The formula is less convinced by smaller numbers of games, but several short
events added up together (like when a monthly rating is calculated) can lead
to a whole that is greater, in a sense, than the sum of its parts.
I know this concept will take some getting used to, but when you think about
it, isn’t a performance rating supposed to estimate someone’s playing
strength based on just the one event? It makes sense to be more conservative
when there are only a few games involved, and to be more generous once the
number of games gets higher. Anyway, sorry for the digression. You can read
lots more about the formulas on my Chessmetrics
site if you really care. The performance rating formula is actually quite
simple. All you need to know is your number of games played, your percentage
score, and the average rating of your opponents. It doesn't even have to use
Chessmetrics ratings; you could use FIDE ratings instead. It's just that the
Chessmetrics ratings are not subject to the same sort of inflation that the
FIDE ratings face, and so it is easier to compare performances across the years
if you use older Chessmetrics ratings rather than older FIDE ratings. But for
performances right now it really doesn't matter too much which ratings you
use since they both reach the same magnitude.
In Part I we saw that Emanuel Lasker spent the longest amount of time at the
top of the rating list in chess history, as well as the longest amount of time
as world champion (unless it was Steinitz). We saw that Wilhelm Steinitz and
Bobby Fischer had the largest rating gaps compared to the rest of the world.
And now we have seen that Bobby Fischer had the highest rating of all time,
and that the two greatest single-event performance ratings of all time were
achieved by Anatoly Karpov (best tournament performance) and Bobby Fischer
(best match performance). Where, then, is the justification for claiming that
Garry Kasparov might be the most dominant player of all time?
Oops, I'm out of space again. But trust me, there is plenty of justification.
Stay tuned, and in a few more days we will look closely at some of Garry Kasparov's
career accomplishments, in Part
III, the next installment of this series.
Again, feel free to browse around my Chessmetrics website, and also please
feel free to send me email about any of this. Most of the research for these
articles has simply come from clicking around on the site, so if you just can't
wait a few more days for Part III, maybe you can find some answers there...