The two active world champions, current one Anand and former one Kramnik, have interesting FIDE Rating Progress Charts in the past decade.

Anand: http://ratings.fide.com/id.phtml?ev...

Kramnik: http://ratings.fide.com/id.phtml?ev...

They seem to have had widely fluctuating performances compared to other top masters such as Carlsen (http://ratings.fide.com/id.phtml?ev...), Aronian (http://ratings.fide.com/id.phtml?ev...), Radjabov (http://ratings.fide.com/id.phtml?ev...), Karjakin (http://ratings.fide.com/id.phtml?ev...), Nakamura (http://ratings.fide.com/id.phtml?ev...), and Grischik (http://ratings.fide.com/id.phtml?ev...).

On the other hand, the other top ten masters have even bigger fluctuations: Topalov (http://ratings.fide.com/id.phtml?ev...), Morozevich (http://ratings.fide.com/id.phtml?ev...), Ivanchuk (http://ratings.fide.com/id.phtml?ev...).

A widely fluctuating rating performance may be bad, or good. For Topalov, Morozevich, and Ivanchuk, it might represent the tendency to choke. During crucial times when a Candidates slot or a World Championship shot is at stake, their performances tend to fall. For Anand and Kramnik, their performances tend to rise. Anand and Kramnik might have the ability to focus and raise the level of their game at times when they need to.

Selective acceptance of opinions? My criterion of selection is unique knowledge. NOBODY knows Kasparov as well as Kasparov - so his opinion on himself carries more weight than anyone else's. If you believe that he is deceiving us, you should provide a motive. Do you really believe that you know his career history better than he does?

Kasparov's opinion on other players carries much less weight, because he only sees the results - not the internal processes.

<'And lest also not forget the central point here: I am looking for the prime period of at least 5-7 years, not just one year. It's possible that he was in great form in 99 but it certainly doesn't mean that he was in his prime.'>

If you want to look at 5-7 year peaks then that is your issue. Given that the period covers TWO entire World Championship cycles - you have to justify why such a long peak is required to validate one match. GK was in tremendous form over most of 1999 & 2000. Say around 80 weeks. The match took 4 weeks. Since the duration of his 'prime' was 20 TIMES longer than the match required to sample his strength - the duration would seem to be statistically significant sample for judging the match.

When did you see me say I require 5-7 years prime for a single match? Come on, lets not start muddying the waters once again. I believe the prime period of a player of such caliber should be at east 5-7 years, not less - a 25+ year career should have at least 5 prime years.

<NOBODY knows Kasparov as well as Kasparov>

But as I said, you can't accept his opinion only when it's convenient for you. If you believe that he was right about being his best in 99 then you also have to accept that he was in terrible form during the 2000 match and simply "went mad" according to his words. Now both of these opinions are about himself so even your selective acceptance of opinion doesn't work here. Moreover, from his words one can easily conclude that the match in 2000 was just a fluke for afterall if one of the players is "going crazy" during the match (for whatever personal reasons) it means that he is performing at a much lower than usual level and in this sense it was certainly a fluke.

lambda, but they did <not> perform equally well all the time during their active careers - <defining> karpov's "prime" to be for instance 1977 to 1996 doesn't solve any problem, really. and talking about a "really long peak" is close to meaningless, since his performances were up and down by quite a lot in that time span.

consider players like gelfand and ivanchuk too: long careers with no single identifiable peak in performances & results.

<If you plot a load of ratings on a graph, you can see all the small random variations, and then you can also see - for some players a sharp peak, for some players a long plateau of excellence, and for some a gradual ascent then descent>

as i said, several of those very "sharp peaks" are examples of phenomena that i would probably ascribe to "randomness" as much as anything else.

and while your idea of considering rating graphs like you've suggested isn't one i find totally wrong, the obvious problem is the relative nature of ratings: what might look like "decline" can equally well be explained by the addition/upgrowth of more strong, active players than before; someone can drop out of the world top 50, then world top 100 and later maybe out of top 150 without actually having become much (or any) worse as a chess player - just unable to keep up with recent developments and young blood.

of course, there's a subtle issue there regarding whether "prime" and "peak" should be thought of in absolute terms or in relative terms. at any rate, i still think the idea of single primes and peaks does more to muddy the waters than to improve understanding.

another example: shirov

was his "prime" around 92-94 (at 20-22) when he was fresh into the world elite, was it around 1999-2000 (at 27) when he qualified to play kasparov (note: he was higher on the world rank in the early 90s), or was it around 2007/2008 (at 35-36) when he again was top 10 in the world for basically a full year in a <clearly more crowded> elite field of players compared to the situation back in 92-94?

to me it feels much more logical to say that shirov had 3 (4?) distinct periods where he performed better than in the rest of his 20 year long career than saying that his "prime" was from 1992 to 2010, assuming that he won't be able to climb back to the top 10 again.

regarding kasparov, i'm totally convinced he was a better player at 36 in 1999 than he was at 21 in 1984 - the world top 10 in july 1984 was mostly a group of "old men" compared to kasparov, but these "old men's" <names> are seemingly supposed to convince us that kasparov was out of this world already back then, <while today the similar presence> of 30 and 40 year olds in the current top 10 is supposed to be "proof" that all these "old" players "peaked" and were in their "prime" a decade or more ago; hence, anand as world champion and world number 2 (with kramnik as a top contender) is further "proof" that carlsen & his contemporaries are relatively "weak". which is absolutely brilliantly consistent reasoning :o)

here's the july 1984 top 10 with players' ages listed:

1. kasparov 21
2. karpov 33
3. timman 32
4. portisch 47
5. kortchnoi 53
6. vaganian 32
7. polugaevsky 49
8. ljubojevic 33
9. huebner 35
9. smyslov 63

when a 47, a 49, a 53 and a 63 year old could still be among the top 10 it's natural to consider it a sign that one was approaching a generation change at the top, with kasparov beating his contemporaries to it by nearly a decade. 15 years later only kasparov and karpov (two of the youngest above) were left in the top 10; the rest had by then been replaced by players born between 1969 (anand and ivanchuk) and 1977 (morozevich).

however, note that there were 5 (five!) other players within 50 points of kasparov back in january 1996, with kramnik tied with kasparov at 2775 (so 95-96 can hardly be considered a peak period for kasparov in terms of relative dominance), while from july 1999 until april 2001 there wasn't a single player within 50 points of kasparov. the only other long period where the same holds was on the rating lists between january 1992 and january 1994. (the same was true for a much shorter period in 1990 and <never> between 1983 and 1989.)

the <questions that are harder to answer> though are these: did kasparov suddenly improve a lot during a few years (at 36-38) for then to decline/fall back again (at 39-42)? or did he first improve and then the others catched up with him again (as they seemingly did back in 1996)? or is the 1999-2000 "peak" (in terms of relative dominance) as of <little significance> as the 1990-peak and the 92-94 peak - when it comes to assessing <absolute strength and skills>?

note also that karpov and kasparov were head and shoulders above the rest from january 1983 until july 1989, most of the time 35 points or less apart. january 1990 was the first time the difference was more than 40 points between the two in those 7 years - and then it suddenly jumped to as much as 70 points (6 months earlier it was only 20 points ...)

strictly in terms of relative dominance it appears that kasparov's "prime" was from 1990 to 2001 - except that he didn't at all look that dominant around 1995-96. based on the dominance of the duo karpov and kasparov during most of the 80s (say, from mid-1982 and the rest of the decade), it's tempting to consider the 80s a rather <weak decade> for top chess, with lots of "older men" holding on to top 10 positions for most of the decade. hence, it makes a lot of sense to assume that kasparov played his best chess, objectively speaking, in the the two <distinct> periods 1989-1994 and 1999-2003. the loss of the title to kramnik in 2000 represents no refutation at all, imho.

yeah, let's debate this: should something need to last for 5-7 years in order to be called someone's "prime", should we be happy with 2-3 years, or maybe require 10 or 15? or should we just abandon the entire futile concept as i'm suggesting?

certain kibitzers "requiring" that "a prime" should last 5-7 years in order to be considered someone's "prime" is simply further evidence that the concept in itself is pretty void and is only useful as a rhetorical tool which is tailor-made to support this or that argument - although mostly to "excuse" someone's weaker performance and/or to devalue somebody else's great performances.

Look back on the thread - I accepted both these statements. I only objected to your 'paraphrasing' that GK stated that VK had to 'prove his victory was not a fluke'.

... yet you seem keen to reject the numbers of the WCC 2000 match (+2 =13 to Kramnik) & of their lifetime (classical) head to heads (+5 -4 =40). http://en.wikipedia.org/wiki/List_o...

no, no. you've got it all wrong, drik!

<everyone> knows it's a <fact> that a prime needs to be of 5-7 years to count as a prime, and hence it's a <fact> that kasparov was way past his prime when he lost to kramnik in 2000 and indeed when the two played the big bulk of their head-to-head games. it follows that it's a <fact> that kasparov in his prime would've defeated kramnik easily, due to the <fact> that he's the greatest player in the history of chess.

see, drik - no subjective opinions, only <facts> ;o)

I believe that the Kasparov quote implied that he felt that his ABSOLUTE level of performance was at a peak in 99. To me this seems a more logical measure than 'dominance' over contemporaries. But on the whole I agree with what you say.

<By your requirement of 5-7 year primes for a single match >

yes, i think that's what he meant, too. but my personal view still is that it's basically impossible to tell by any objective measure currently available to us, and - as i've said a couple of times - i don't see much point in trying to pinpoint a <single> period (regardless of which length) where a player was at his/her best;

for instance, in kasparov's case, assuming that we could objectively say it's between a) 1989-1994 or b) 1999-2003 and further assume that one of the two could be decided to be a tiny little "better" than the other: in which way is that useful <if> the difference is so small that it's insignificant for any practical purpose? [and in particular: it's utterly useless if the "practical" purpose is guessing/predicting the outcome of an entirely hypothetical match that didn't take place. :o)]

<this seems a more logical measure than 'dominance' over contemporaries>

well, one of my arguments is indeed that "dominance over contemporaries" can't be trusted as a measure of "absolute strength/skills" (even if i'm not 100% sure what we would be trying to measure then).

as i put in my last "serious" post:

<"relative dominance" has so many pitfalls that the best it can do is to convince us that most players have multiple, distinct periods in which they obtain their best <results>. unfortunately relative measures (like ratings) <fail to explain why>. (were they playing better chess or were the competition simply weaker in a limited period?)>

my main beef here is still with the concept of the <singular> prime and/or peak: the postulation of its existence and significance is just that, a postulation. there are lots of evidence contradicting those notions to be universally true, and even if it were "generally true" that players have a <single> peak period (not interrupted by temporary downs), it would be exactly when facing the <exceptions to that rule> that people would try to argue using the "generally true rule"; however, the point's exactly that there doesn't exist any such universally true & valid rule, and hence that things that might be more or less true for a big majority (of people/players) are <not> true for everyone. there's no law of nature that dictates that a chess player can't have two equally strong periods 10 years apart, with (at least) one major down in performance inbetween.

On top of this, the new 1990s generation was by itself almost anomalously strong. Anand, Gelfand, Ivanchuk, Kramnik, Topalov, Kamsky (still young and hungry), Shirov, Svidler, Morozevich, Leko.

The world championship cycles since 1995 have been dominated by these guys. It's a wonder chess fans aren't tired of seeing these same faces over and over again, especially when it comes to the world championship cycle, when all masters have to give their best.

The 2010s will see an inevitable decline of this exceptional generation. Enter Carlsen, Aronian, Grischuk, Nakamura, Radjabov, Karjakin.

No argument here. Comparing 'primes' over decades is particularly nebulous, since the results being compared are against very different pools of players.

<The number of unconditionally devoted chessman , as Vitaly Valeryevich was , is small and getting smaller. He was also independent , proud , he didnt like any kind of pressure and behind-the-scenes stuff. Most likely for that reason he wasnt getting to play much international tournaments , because in those times you had to `oil the machine` here and there , a smile , a small present on the right place ... He really was above that , so he was not playing much abroad.

In that sense he belonged to `The Lost Generation`.I believe that , if he could go abroad as Korchnoi , he would become top player , the level of , Lessay, Timman , he would be constantly in top 10. Although its very hard to me to imagine Vitaly abroad , he was so much ours , so connected to the Russian culture and heritage.

Here , he rusted a bit : talent without tournaments. He was even telling me that at some point he lost the interest to building serious chess career. He understood that he is not big name as Karpov , who was `given` all the possible tournaments , and without serious play you cant really raise your level. He , in a way , capitulated and decided to simply play the game for his own pleasure.>

<In 1994. our cooperation ended , because at that point chess started changing drastically. The computers emerged , and Vitaly Valeryevich was working the way he used to for decades , falling behind the enormously growing amount of data.

He analysed unbelieveably deep , but in slow , classical manner. I had the feeling that i can`t accomplish enough in preparation , deciding that its better to sacrifice a bit of depth for the `width`. So I started working with younger folks that were better in computer work.With Vitaly Valeryevich I never had any personal problems , but our ways silently parted.

He was the man of different generation, it was very hard for him to re-orient on computer preparation. He loved chess as game much more than as profession. And in those times preparation became highly professional business. I was already in top 10 , I had to play various positions no matter if I liked them or not. For example , finding clear ways of drawing the weaker endgames that emerged by force in some opening lines ...Vitaly Valeryevich wasn`t mentally prepared for such ways of work , he loved chess creatively , artistically.

I perfectly understand and support such POW , but such approach was insufficient , impractical for reaching the top. We talked few more times since then , anyway our cooperation was very useful to me.>

<It is highy symbolical that he died at the board. He played till the very end , simply because he liked the game so much...

So you're again being contradictory: if you accept that GK was in a very bad form then how can it be anything but a fluke? If a player was in an unusually bad form during the match it means that the result is a fluke.

Now remember that this is not my argument but yours - by accepting one of GK's opinion you have to accept others.

that's very interesting, drik. i never had time to produce my own contribution, but i discussed an idea with a mathematician, and this idea basically used a similar notion of "non-global" expectancies (unlike the elo-formula or sonas' linear approach), but instead of breaking it down to player-versus-player records i intended to use my own performance profiles. i.e. it turns out that players don't perform uniformly against different kinds of opposition, so my idea was to base the prediction on how a given player performed against players of different strengths.

my performance profiles are graphs that map opposition rating (x-axis) to rating performance (y-axis) (with an easy extension being breaking this down on colour too). hence for any given pair of players A and B playing a game, the prediction would be made based on A's historical performance against players rated like B, and B's historical performance against player rated like A.

do you have anything to back this opinion up with, vbd? this isn't "criticism", i'm just curious about what makes you say or believe this. why do you think kasparov was at his best between 22 and 27 (he turned 27 in 1990)? karpov and kasparov standing out like they did in the 80s is something i find just as likely to be mostly because the competition wasn't very tough in that decade.

is there anyway that you or i can document our different views on this?

similarly, why do you consider the 90s to be stronger than 00s? at least during 2006-2011 there have been an explosion in fresh talent joining the elite that even trumps the surge we saw in the 90s, with you know, the "usual suspects" joining karpov, kasparov and the "left-overs" from the 80s.

remember: if you would've made up your status in 1999, the list of accomplishments by shirov, gelfand, ivanchuk, kramnik, topalov and anand would've looked rather different than it does now, in 2011. to compare the last decade "on even terms" with the 90s, you must try to look 10 years into the future and consider what kind of merits that the aronians, carlsens, radjabovs, nakamuras, karjakins, giris, and maybe even someone currently below the radar will have added to their resume by then.

in 1999 neither anand nor kramnik had any wc titles linked to their names, topalov had never been world number one or winner of san luis 2005, and gelfand's recent world championship successes (2007, 2009, 2010) were all in the future.

The 1990s generation is still on top of the chess world when it comes to the world championship cycle. Yet this same generation of excellent players could not surpass the aging Kasparov - Karpov tandem in the 1990s. A decade with the 1990s generation plus the 2K titans is the strongest chess decade in history.

An imperfect analogy might make this statement a bit clearer. If Karpov and Kasparov were born in 1985 to 1990, one of them might be world champion today instead of Anand. The 2000s would be the strongest chess decade ever. And today's rising stars, now being contemporaries of the 2K titans, would probably be hard put to outshine those two.

If one goes through the career and games of the young Karpov and Kasparov at age 18 to 28, IMO they were generally better than today's rising stars.