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, who was?
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 Boris Spassky.
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...