Cream Rises in Cuba & Romania

"There should be a rule against getting a 2700 rating without beating 2700+ players."

All we ask of masters is that they consistently beat experts; all we ask of 2700 players is that they consistently beat 2600 players.

"All we ask of masters is that they consistently beat experts; all we ask of 2700 players is that they consistently beat 2600 players."

Ah, yes. All we ask of the world’s 2800-rated players, is that they consistently beat the 2700-players.

He he... Currently there are two 2800-players, and Magnus Carslen is the only one fulfilling this expectation. Moreover, he is doing so with a vengeance, leaving the competition in the dust. :) :)

"There should be a rule against getting a 2825 rating without beating 2825+ players."

Word has it that Carlsen has repeatedly beaten the world’s only 2850 player – behind closed doors. :) :)

Unless you beat someone higher rated, the game should not count towards your rating. ;)

Which would mean that losses don't count...

"We may need (or want) different statistics about how player X performs against different types of opposition (>2700, 2600-2700, 2500-2600, ...)?"

You won't have to wait long. I've dubbed this "Performance Profiles", and it'll be available for the 2700+ players on chess.liverating.org shortly.

I agree - unless you beat someone higher rated it shouldn't count toward your rating. This should especially be so if you actually lose to someone higher or lower rated.

Karpov over 2800??

These one time spike or #1 ratings doesn't fascinate me any more, however accurate the rating system might be. simply because of the possibility of fixing games or possible foul plays. Did not Kasparov have highest ratings in or around 2000 and how come Kramnik chancelessly beat him? Must Kramnik be in the neighborhood of 2900 then? However, if you actively and consistently show the highest rating that could mean something.

Performance profiles? Wow, that's great, I'm looking forward to it. I'm really curious to see what they will show. They might blow up a few stereotypes we have about certain players... or confirm them!

"However, if you actively and consistently show the highest rating that could mean something."

Carlsen is actively and consistently showing the highest rating -- and, yes, that definitely means something. :) :)

"Did not Kasparov have highest ratings in or around 2000 and how come Kramnik chancelessly beat him? Must Kramnik be in the neighborhood of 2900 then?"

It seems there is a bigger problem with how you _interpret_ the ratings than with the rating system itself.

Chess ratings quite accurately describes your PAST results against EVERYONE you have played. That's why you can't make strong conclusions about the internal strength relationship between two specific players based on their ratings only; their ratings have NOT been obtained by exclusively playing each other.

"There should be a rule against getting a 2700 rating without beating 2700+ players."

Laj, without beating _one_ 2700+ player? Or maybe two - or a handful - over which period?

I think that what you intend here, is that a 2700+ player should PERFORM at 2700+ against 2700+ players. If you play 8 games against all 2700+ players with average rating of 2750, then no matter how you score your points (e.g. 4 wins and 4 losses, or 8 draws), a score percentage of 50 demonstrates the same level as that of your opponents, doesn't it?

Hypothetically, if Nakamura scored +2 -4 =2 against a 2730 average and Wang Yue scored +0 -0 =8 against the same opponents, who deserves a 2730 rating do you think? Who performs better against the 2730 average?

For most a 50% score is better than a -2 score.

"Did not Kasparov have highest ratings in or around 2000 and how come Kramnik chancelessly beat him? Must Kramnik be in the neighborhood of 2900 then? However, if you actively and consistently show the highest rating that could mean something."

It can also be added that I think it's fair to say that Kasparov "actively and consistently show(ed) the highest rating". :o)

I dare to predict: if "stereotypes about certain players" are blown up, some people will question frogbert's approach or reality rather than their own prejudices ... .

BTW, there is another point to Laj's initial question (not applying to Wang Yue): De facto, you first have to get a 2700+ rating and keep it for a while before you get top invitations and a chance to play such opposition on a regular basis. For players like Vitiugov, Wang Hao (the other Chinese) and Malakhov, the issue may be how many games they _played_ against fellow 2700ers, rather than how many games they won against them!?

Next you will be saying that someone can not become the world champ without beating the world champ i.e. if topa had beaten vishy in tiebreaks then it would not count??
Give it a rest...it should not matter how you get your points/rating as long as you get it:-)

Irv | June 24, 2010 8:06 AM
"I think Leko may have won a grand total of 3 games (with 578,963 draws) against 2700+ players during his career."

I did a quick visual count of Leko vs. 2700+ players and came up with about 39 (mostly with White). That was not counting blitz, rapid or blindfold, only "regular" time controls/conditions. I was surprised a little bit because I didn't think he was that good. Some of his wins were vs. 2700 "tourists", but there were also many quality wins as well. Interesting.

Yeah, Carlsen is doing good at the moment. We'll see.

Rating calculations I also think are just fine but the system I don't know. By system I mean I believe the same rating calculations would work better with Tennis style knockouts system instead of with a swiss system. You don't win, you don't advance, you don't get rating improvements. When you have such knock outs, I think you can really boast about your #1 ranking. Is it practical to implement knockouts, don't know.

Well, Leko was a top10 player for many years; he qualified for and tied a WCh match against Kramnik - so it should be obvious that he is (or at least was) "quite good".

To reach that level, he had to win some games. To stay there, a solid style (i.e. many draws) may help, but he also had to win at least once in a while - because it's near to impossible to avoid losing altogether.

"By system I mean I believe the same rating calculations would work better with Tennis style knockouts system instead of with a swiss system. You don't win, you don't advance, you don't get rating improvements."

Huh?

First, the ATP tennis ranking is a really bad ranking system compared to the FIDE rating system. Really, really bad.

You can also easily become #1 in the tennis system without playing any of the old number 1-5 ranks if you play a big tournament where neither of them participate or are knocked out before they face you.

In general: ranking systems with randomly appointed ranking points don't exactly give extra bragging rights for becoming #1 - or guarantees about any meaningful ordering of the players in terms of _strength_. They do however often have a very strong _activity_ component - meaning that in case you go on vacation, skip some events or become ill for shorter or longer periods, you'll typically drop (a lot) in the rankings as your past results (for which you obtained "random points") slide out of the relevant ranking window (last 12 months, last 2 seasons, or whatever, depending on the sport).

Indeed. Carlsen (or whoever is #1) should be required to play Rybka exclusively until he falls to the #2 spot. ;-)

"Carlsenesque" also has a good sound in my opinion.

@we cannot discount the possibility of Carlsen surpassing Garri Kasparov’s record 2850

http://gambit.blogs.nytimes.com/2009/01/14/are-todays-top-players-better-than-20-years-ago-not-necessarily/

@Ovidiu: Thanks for the link to an interesting article!

The following quote from that New York Times article caught my eye:

"Glickman said in the United States, instead of rating inflation, “there is more of a tendency for deflation.”"

Well, that certainly explains why there are currently no Americans in the world chess elite. ;) Unless, of course, you’re content with Kamsky and Nakamura.

Carlsen also mentions that he is the best tournament player in the world right now and that it's no longer him who has something to prove but his opponents.

Quite true, I suppose...

@Kasparov's record high rating is still fairly recent

We can try to compare.
Judging from the inflation rate given in that NYT-article (FIDE averages) the 2829 ELO now of Carlsen would have been 2783 in July 2000, while that of Kasparov was 2849.

Carlsen will probably face Kramnik, the (arguably) second-best tournament player at the moment, in the semifinals of the candidates event - albeit with a slightly different format.

@chesshire cat: Maybe Kasparov put a curse on Radjabov, after the 15-year old kid beat him in Linares 2003 and received the prize for "most beautiful game" - Garry was not amused to say the least
http://www.chessgames.com/perl/chessgame?gid=1260681
http://www.chessbase.com/newsdetail.asp?newsid=851
Of course I am kidding ... .

@If by "mature" you mean that they "had learned everything they could ever know about the game", then yes, but why should that be the case?

it mere age, it is a sport, a fight, not philosophy, it is not that Carlsen at 20 is more mature, knows more chess-wise at 20 than Gelfand at 42
People as Gelfand, Anand or Ivanchuk kept their level, remained at the top and merely got higher ratings since 2000 due to inflation (imo, of course)

It may not be philosophy, but it's generally held that you can improve your chess by studying the game. Gelfand never stopped studying, so in ten years he might perfectly well have improved enough to warrant an increase in rating.

If your opinion is that his level of chess is the same, then I certainly can't prove you wrong, but your initial argument wasn't sound (imo, of course).

I'm with dreamer on this one. It is absurd to think players like Anand, Gelfand and Ivanchuk, some of the most industrious and creative players around, have learnt nothing in the past ten years. And it is even more presumptious to state that 'Carlsen at 20 is more mature, knows more chess-wise at 20 than Gelfand at 42'. Remember Korchnoi stating a while back that Carlsen still had to know several thousands of different positions and...Carlsen agreeing with him.

@it's generally held that you can improve your chess by studying the game

If that were true they would only improve as years go by. Not necessarily at the same rate of improvment of course but in any case the older they got the stronger they would they play since knowledge accumulates.

But that's hardly the case what one can see happening. The chess players have their peak in late 20s or early 30s after which their performnace begins decrease. An even the age of the peak strenght is has continually decreasing (see bellow why) nowdays the peak is somewhere around 25 years old.

What you (so candidly) say is true only at the beginning, true for a while (6-8 years) after you have started playing chess seriously. It is true only during the period when you have to learn the principles, the general laws of playing the middle game and the endgame.

After that what makes the difference is :
1)how hard you can work off-board and (if you do work hard) how successful you are in memorizing exact lines and preparic specific positions (not general understanding deriving conclusions OTB out of your general understanding)
2) and how hard (stamina) you can fight on-board when the preparation ends.
Both are are function age obviously.

Futhermore, in the last 10-20 years since computer analysis and databases, the importance of the power of memory has only increased. This power is far higher for 15-25 years olds than for 40-years and that's why we have got a lot "geniuses" and prodigies in the last decade, a lot of "baby-GMS".
Carlsen himself will start being "old" (and start playing weaker) in 5 years from now.

A bit careless and unfocused.
Gelfand played as if the tournament was over for him after the draw with Carlsen. He pressed to win in that game but he could not make it.
After that he drew Ponomariov (in a complex position whe he could have played) and, I suppose, he would have accepted a quick draw yesterday if Radjabov would have wanted.

@If Magnus is Federer of chess, who will be Nadal?

Way too early say, at this moment he has barely finished learning how to read and write. But he is spending a lot of time in front of the comp and he is already playing chess acceptable in random postion; and quite strong in memorized positions and sequences, his favourite now ( he knows it by heart and plays it instantly) is the Marshall-attack whose variations and thematic manouvers and sacrifices (an too early f2-f4 trying to stop black's f5-f4 is simply met by Nxf4! /Re6-Rae8 set-up already played/). Of course he is childish with this bellicose preferences but he will become an expert in the sterotyipical manouvers of Berlin and, in 5-8 years (when Magnus will start his downhill involution) he will just beat him and become the new top guy, for a short while.

@I keep referring to the recent Crestbook interviews with Gelfand and Khalifman... but they're totally relevant to this debate.

They are relevant, especially that of Khalifmann..if only they would be read too, we would save time debating here.

Another thing to read is Kasparov's "Modern Chess" book :

http://www.jeremysilman.com/book_reviews_js/Kasparov_Modern_Chess_Vol_One.html

at the end of the book there is a collection of "interviews" (replies to a set of questions from Kasparov )-you can read the replies of Portish, Averbach, Nikitin, Taimanov, Sveshnikov, and others who have lived through to see how things have changed in the competitional chess the last 30 years.

@and the question was why.

it's a mystery, but if you read Gelfand's intreview (translated by Mishanp) you will find that he doesn't believe himself that he really got better he believes that the correct explantion is an about 5points/year ELO inflation

The Gelfand interviews are excellent - thanks mishanp!

But... while it's true that he doesn't think he is better ("I’d avoid giving a definitive answer to the question"), he talks a lot about how he is always working on improving various aspects of his game. Now, unless I'm overlooking a key quote, there is no direct assertion that this work doesn't bear any fruit. And certainly no assertion that it would have been impossible for it to do so.

And yeah, he does say that there is a 5pt/year inflation, but that's in answer to a different question. You're extrapolating more than a little to go from that quote to "correct explanation [for why his rating has improved since 1993]".

A strict interpretation of the 5pt/year, means that Gelfand has maintained his strength from the year 2000, while other players, like Kramnik, Leko and Shirov have deteriorated (in the case of Leko: horribly). Despite his best efforts, Gelfand still is not close to the level Leko had 10 years ago.

All of this could very well be true, but the convincing arguments still aren't there... In fact, we're moving further and further away from what can be objectively measured. A mystery? Indeed.

There is no "problem." It's just that if Reshevsky could play his best chess in his forties, why is it almost inconceivable that an Anand might do the same. ... I don't even mention Korchnoi; he's too much of an anomaly.

It's inconceivable for the simple reason that if Anand is at his peak now, this could lead to the idea that there is no rating inflation at the top level, and that chess might not have degenerated into an unbearably poor state after all.

As a religious person was kind enough to explain to me once - this is impossible. Since the cataclysm, all life forms are degenerating (which is why you cannot today build an ark of the same size as you could back then), and all human thought is becoming weaker and shallower by the second. QED.

@..if Anand is at his peak now, this could lead to the idea that chess might not have degenerated into an unbearably poor state after all

It has flourished extraordinarily in fact, just like the economy and currency of Zimbabwe.
For instance in 2009 Movsesian's ELO was 2751, that's way above what Boris Spassky ever got (2690 in 1971).

Nicely spotted :) I also failed not to misunderstand the original author's statement.

Ovidiu,
I'm not sure what is the point you are trying to make but anyway forget Movesian, how do you compare Spassky and Nakamura? Who in your opinion is greater?

Your prognostication that Carlsen will be toppled by an unknown upcoming player in 5-8 years would be a reasonable conjecture if Carlsen was a "normal" world champion. Note that he is not yet world champion, but that will happen given the normal course of events. However, Carlsen is not a "normal" world-class player. He is one of those once-in-a-generation players like Lasker, Capablanca, Fischer, and Kasparov who simply eclipse their contemporaries and dominated them for many years. Once Carlsen becomes world champion, I fully expect he will continue to dominate his fells GMs for many, many years.

Karpov was also a once-in-a-generation type of player. Kasparov never eclipsed Karpov even though he was something like 12 years younger than the great Karpov. Kasparov was better than Karpov in Karpov's career twilight only.

Just because a Zimbabwean has one thousand times as much cash as he did a decade ago doesn't mean he's better off. Just because Anand might be higher rated now than he was ten or fifteen years ago doesn't mean he's been playing better chess lately.

It's interesting to read about "statistical facts" according to some (very) strong GMs. :o)

Gelfand:

"in any case inflation continues at about 5 points a year."

Khalifman:

"I have considered and still consider that the optimal age in contemporary chess is around 25."

What is the latter supposed to mean? What is "contemporary chess"?

I mean: which players are Khalifman talking about? Those that are at the top now, or those who will be at the top 10 years from now? Is it a purely theoretical consideration - "players from the 'new generation' should play their best chess at 25" - or is it an effort of describing the actual situation of when players have their best results (as reflected in their ratings)?

What we DO know for a fact, is that historically, in the past 20 years, players have NOT had their best results at 25. And the beauty of this problem, is that we can prove this using historical ratings and COMPLETELY IGNORE "rating inflation" as a source of error, based on rather simple statistical observations - that for some reason the majority of those making bold statements about inflation and statistics haven't bothered (or been able) to do.

The statistical observation I'm talking about, is the following:

First assume that the strength in a (mostly) randomly selected group of players from the rating pool stays the same, on average, from one year to the next. Hence, their results should basically be the same and so their ratings. Of course, on the individual level some will be improving and others declining in strength - due to factors like age, (lack of) activity/studying and so on - while probably the majority of the players only experience normal variations in their results that aren't indicative of any real change of level in their play.

Next, assume the existence of some postulated general inflation of 5 points per year (Sonas, Gelfand, etc.). What should be the consequence of the average rating of our selection of players if the rate of inflation was 5 points per year? I think that the only natural consequence of this hypothesis being true, would be that the average rating of our sample would also go up by 5 points, from one year to the next - even if we assumed that the average strength of the group had remained the same and hence that their results on average had been the same.

Choosing our "sample" as "all players in a given rating list that also could be found in the rating list one year later" I have found that between july 1990 and july 2009 there basically is almost NO SUCH GENERAL NOMINAL INFLATION in the system as a whole; e.g. considering july to july rating lists in this 19 year period, the accumulated year-to-year change is ONE POINT - much less than 0,1 points per year on average. (It can be shown that the RATE of "inflation" has varied, though, with "positive inflation" in some years and "negative inflation" (i.e. "deflation") in others.)

Of course, even if the system as a whole appears very stable in terms of inflation, it's been proposed that inflation works differently in different parts of the system - with most people suggesting that the inflation is "higher at the top".

I've looked at the case for 3 different definitions of "the top" - everyone rated above 2500, everyone above 2600 and everyone above 2700 - and I've done this in detail (so far) for every rating list between july 1990 and july 2006. [Extending it to covering the latest 4 years is easy, and I'll do that this summer.]

Again, assuming that the strength of "everyone above 2500" and so on ON AVERAGE remains the same, we should expect similar results and hence similar ratings from one year to the next. Given a nominal "inflational boost" of 5 points per year, the group's average rating should also increase by 5 points if the hypothesis holds true.

So, what do we find when we consider the data? The data here is drawn from 45 different rating lists and includes (for each group) 41 different year to year comparisons.

The average yearly rating changes for these groups are as follows over these 41 comparisons:

[Note: 2700+ players is a subset of 2600+ players which again is a subset of 2500+ players in the following.]

2500+ 1990-2006: -1,58 points
2600+ 1990-2006: -3,02 points
2700+ 1990-2006: -2,51 points

Considering the trend only since 2000 yields the following (22 yearly comparisons):

2500+ 2000-2006: -1,56 points
2600+ 2000-2006: -2,87 points
2700+ 2000-2006: -3,65 points

Returning to the age of the players that demonstrably have had the best results (as reflected in their ratings, inflated or not), there is a certain trend of the very elite players being slightly younger than the average GM. However, their ages have been far from 25 this far.

Average ages of top players since 1990:

2500+ 1990-2006: ca 33-34 years (33,6)
2600+ 1990-2006: ca 32-33 years (32,3)
2700+ 1990-2006: ca 29-30 years (29,7)

Restricting it to lists since january 2000 (possibly giving an idea about trends):

2500+ 2000-2006: ca 33-34 years (33,9)
2600+ 2000-2006: ca 32-33 years (32,4)
2700+ 2000-2006: ca 29-30 years (29,9)

[The ages given with decimals might need to be adjusted a little, since I lazily counted someone born in e.g. 1972 as 28 years old in all lists of 2000, and so on, but that's not too relevant for the overall picture.]

I would say that the data suggests that the "old" 30+ year olds appear to be holding up well against the younger players (no matter what Khalifman considers to be the optimal age for a chess player), and if there really is a 5 points nominal inflation per year, the only conclusion that can be drawn, is that on average - including young and old - ALL chess players are becoming weaker literally by the minute.

Strangely, based on the development of the average ratings cited above, the YOUNGER players rated 2600+ and 2700+ must be declining FASTER than the OLDER 2500+ players.

An alternative explanation is that although players today reach high levels faster and earlier than before, it is largely a myth that experience and accumulated knowledge is becoming increasingly irrelevant as a major factor at the very top - similar to how "considerable rating inflation" also appears to be largely a myth; the phenomenon widely described as "rating inflation" rather seems to be - for the most part - an instance of "inflation" (read: increase) in the number of very, very strong players.

I challenge anyone to find basic flaws in the above reasoning; the numbers themselves are all easily reproducable and verifiable, of course - but in order to do large scale verifications one obviously has to do some kind of programming (like I usually do regarding these things) to allow individual rating development comparisons in the numbers of tens of thousands.

Btw - I believe in numbers, facts and scientifical methods much more than "opinions" of authorities like chess stars of by-gone years when it comes to analysis of rating development.

Also, note that I don't advocate rating comparisons (or performance comparisons) that spans much more than 5 years; as the difference in "the time of the rating" approaches 10 years, the ratings become increasingly INCOMPARABLE, even when assuming NO NOMINAL rating inflation - simply because ratings is a RELATIVE measure, saying something about how one compares to the rest of the CURRENT pool of players. I repeat: even given NO rating inflation, one shouldn't at all compare ratings more than roughly 10 years apart - such comparisons are, per definition, not meaningful, due to the major changes to the pool we've experienced during the last 25 years.

If more people would really understand the implications of the latter, it would do wonders to improve the level of the typical rating discussion. Also, if it would sink in that there is NO DIRECT MAPPING between absolute "chess skills"/"quality of chess"/"chess level" and the chess ratings of FIDE (or any other widely used rating system), there would be a chance that rating discussions could get anywhere. Any schemes of "rating adjustment" or "adjusting for inflation" will invariably tend to cloud this matter, since it seems to reinforce rather than contradict the notion that ratings somehow can be compared between eras (or over 10s of years) - as measures of ABSOLUTE skills.

Chess ratings is a competitive measure describing results and outcomes in the game of chess as it is being played now (or at the time of the rating). When lots of external factors change - like the time allotted for a game (shorter time controls), the number of professional chess players (and events) increases a lot, adjournments are abondoned, opening preparation goes through disruptive/revolutional changes due to chess engines and databases and instantly available game scores on the internet, and so on - then the game of chess changes too. It wouldn't be much different if one would've introduced a new piece or allowed the bishop to jump over one piece diagonally, given that it didn't move more than 2 (or 3) squares.

Alas, chess ratings simply describe who currently has (and recently has had) the best results, given how chess is being played and competed at NOW. If one fails to realize the major changes to top level chess in the last 30 years, one will also fails to understand some of the inherent limitations of any rating system that is locked to COMPETITIVE RESULTS in some type of sport. It doesn't measure absolute skills (in whatever the competition is really about these days), it measures one's results.

Among your contemporaries, in the current pool of players, results is a decent approximation of absolute skills at the current game - but it's limited to the demonstrable skills during competition, with the ever-changing nature and characteristics of the environment in which the competition takes place. It's quite useless as a tool for comparing (different) skill sets being demonstrated 20 or 30 years apart.

It's hard to predict the future ... let's have a look at the top 10 juniors from five and eight years ago:

July 2002 - Ponomariov, Grischuk, Bacrot, Vallejo Pons, Radjabov, Dominguez, Bu Xiangzhi, Bruzon, Aronian, Naiditsch

July 2005 - Radjabov, Volokitin, Navara, Timofeev, Nakamura, Mamedyarov, Karjakin, Harikrishna, Efimenko, Cheparinov

What happened to those players? Many reached the world top (this includes relative late bloomers as Aronian and Nakamura), some didn't quite make it (Vallejo, Naiditsch, Cheparinov). What happened to Volokitin? I checked, basically he didn't make further (Elo) progress since 2005.

Now May 2010 - Carlsen, Karjakin, Vachier-Lagrave, Nepomniachtchi, Le Quang Liem, Caruana, So, Andreikin, Giri, Nguyen Ngoc Truong Son

For sure, the CTRL-V component has increased. What will be their upper limit, allowing for the possibility of late blooming? It seems hard to close the (emerging and increasing) gap with Carlsen, but is it altogether impossible? And obviously I cannot discuss the potential of a currently unknown 10-13 year old player.

@Just because

Umm, yeah, that much is clear. But that wasn't the point in the particular branch of the argument he was responding to, which is why the statement looks weird.

Anyone know if they have these discussions in sports, btw? Do they argue that there is inflation in, say, the 100 metres dash - where improved training and doping techniques allow even mediocre runners to achieve successes they never would otherwise. That from was the most natural runner and would've squashed Ursain Bolt given equal conditions?

(Just curious, although I'll probably be surprised if they don't have these discussions.)

@It could be as simple as...

Vita nostra brevis est, brevi finietur.
Venit mors velociter, rapit nos atrociter
Nemini parcetur.
Post jucundum juventutem, post molestam senectutem
Nos habebit humus.

You could argue that Karpov was a better player than Kasparov. He was rated #1 or #2 for 30 years and Kasparov only obtained an overall winning record vs. Karpov after Karpov began to decline in the '90s. Kasparov was only +2 vs. Karpov in World Championship games; +1 after '86 and +2 only after '90 when Karpov's results were beginning to show signs of inconsistency and overall decline (although Karpov played his best tournament at Linares '94, 11/13, 1st place over Kasparov who finished 8.5/13).

@Carlsen has to be admired for making Chess a Sport.Playing chess like tennis!

H.E. Kirsan saw it coming long ago that's why he introduced doping tests.
But aren't Svidler or Gelfand too fat for being good at it ?

"I think - but I have no evidence - that the average player peaks at around 30."

Do we really care about the average player?

I would think that those we care about regarding the very elite GMs are almost exclusively the "exceptions". The top 20-30 in the world are all exceptional almost per definition, and when it comes to players capable of reaching top 5 - which nearly automatically makes them World Championship candidates - they are all pretty darn atypical compared to the "average player".

How many World Champions had their best results _before_ they were 30? How many _after_?

Both Gelfand and Ivanchuk are exceptional and "exceptions" already in a number of ways, and so are obviously Kramnik and Anand too.

The concepts of "peak" and "prime years" are also rather fuzzy. Performances will always vary, and rating and results will always be relative to one's competition at the time. Hence, there doesn't need to be a strong correlation between a player's most successful year(s) and the period when s/he objectively was performing best and most consistently.

Carlsen has to be admired for making Chess a Sport.Playing chess like tennis!
**********************
I see nothing admirable in that. What the future will see is the score of the game, and Carlsen's wins will be puzzling in many cases.

Ahhh... That is clarifying. Thanks:)

"Second, note that when he does year to year comparisons, he is comparing the rating of an individual player to that same player in another year, not comparing a pool of players. (Then he averages together all the rating changes of individuals.)"

Well - adding together the changes and averaging them, but yes. That's equivalent of calculating the sum of the ratings for the group in the two lists of interest and dividing on the number of players, though. The important thing is that we're talking about the same fixed set of individuals in both lists.

"You silently assume that 2500+ players at one time are comparable to 2500+ players at a different time"

bondegnasker, I don't think I do any such thing. I fix a group of players and considers the exact same players one year later. If there's a general level of nominal inflation, it would impact the average of these players. The 2500+ (or 2600+ or 2700+) group is simply the "top players" at any given moment - the players for which it is claimed that the "rating inflation" is most heavily at work.

"Suppose my rating goes over 2500 (don't worry, it won't). 10 years later, it drops below 2500. So how much did it change per year on average?"

I calcuate individual changes for every year for every (distinct) player in a selection. I only calculate ONE year-to-next-year change for each of the 41 selections. Each 2500+ (or 2600+ or 2700+) selection is different from the previous and the next (and every other), and each single selection is only compared to the SAME selection of players one year later - and the average is over a number of such one-year changes, not an average over a single rating change over a 10 or 20 year span for single players averaged to change per year.

The "above 2500" selection doesn't yield much different results regarding rating changes than "pick 500 random players from the pool", so the 2500 cut-off is hardly causing the nearly net 0 increase in ratings. The only assumption the method hings on, is that the strength of the selection of players on average stays the same - i.e. that there is the same amount of improvement and decline in this closed group of players.

Of course, if the reality is that the group of players rated above 2500 at a given time (including everyone above 2600 and above 2700) as a whole (or on average) always is becoming weaker by the minute, then a net lack of rating change can be argued to indicate "rating inflation". It's not hard for me to break down the year-to-next-year changes either, showing for instance

* Average gain of players rated (in year 1):
2500-2549
2550-2599
2600-2649
2650-2699
2700-2749
2750-2800

* Average loss of players rated (in year 1):
2500-2549
2550-2599
2600-2649
2650-2699
2700-2749
2750-2800

* Number of players in a given range that loses, respectively gains rating

* The same as above, but limited to gains/losses of 20+ or 40+ points, for instance

* Average age of players who gain, respectively loses rating

* The same as above, but only for those who gain/lose more than 10/20/40 points, for instance

Btw - in july 1990 there were about 200 2500+ players, with an average rating of 2553,4 and an average age of 33,4 years. In july 2005, 15 years later, there were about 600 2500+ players, with an average rating of 2561,4 and an average age of 33,7 years. In other words, 3 times as many players, but essentially the same age of the group as a whole.

Note that the pool went from ca. 9000 players in july 1990 to ca. 630000 in july 2005 - or a seven-fold increase. In other words, the relative number of 2500+ players in july 2005 was less than half of that in july 1990.

"You silently assume that 2500+ players at one time are comparable to 2500+ players at a different time"

If what you meant to say, is that I check _different_ 2500+ groups of players in all the different year-to-next-year comparisons, then that's obviously true.

I do fix a group of players and considers the exact same players one year later. Then I look at a similar (but different) group of players in the next list and look at how their ratings change over one year.

Of course, if your assumption (or concern) is that it's the same (old) group of players that have their ratings "inflated" (while the "new" players don't), then I can also make comparisons with 2 year rating changes, or 5 year rating changes (and I already did that 3-4 years ago btw - but only for more recent lists, from 2001 and later).

The pitfall of considering changes over as much as 5 years (for a closed group of players), is that the chance increases that there are higher number of players that have actually experienced a change in playing strength, resulting in better (or worse) results. Hence, the assumption that the group's strength on average doesn't change is possibly no longer that valid - unless one starts adding further requirements for the sample on things like age composition which again would be based on new (and possibly wrong) assumptions (like, which mix of younger and older players should on average constitute a "stable" pool, and so on).

But if you think I would get notably different results by doing 2, 3 or 5-year change calculations instead (or in addition), I'll happily do that as well. :o)

Impressive. You've come up with a pretty convincing way to measure Type I (individual) inflation. Now if somebody wants to claim rating inflation exists, he has either to say where he differs from your findings, or resort to Type II (#100 spot) or fuzzy Type III (relative to playing strength) inflation.

It's amazing that the numbers should be stable with all the widening of the pool, and lowering of the threshold that took place. I suspect that the effort the average 2500+ player puts in to keep his rating, is a self-regulating factor that decreases with inflation, increases with deflation, and effectively overrides the purely mathemicatical tendencies.

In itself minor rating inflation is not a problem. Not at all. It doesn't change anything important for practical issues, for FIDE's titles or their use of rating as a qualifier for events.

The "problem" is when people think that existence of rating inflation can prove that players 10, 20 or 30 years ago were better chess players than today's world elite because their ratings were higher after one has "adjusted for inflation".

For example, several people will argue that there has been a 50 point inflation (or 40 or 60 or similar) since 2000. Ok, let's compare the July 2000 top 10 with the January 2010 top 10 list, "adjusting for inflation", assuming 50 points to be correct:

Kasparov2000 2849
Kramnik2000 2770
Anand2000 2762
Morozevich2000 2756
Adams2000 2755
Shirov2000 2746
Leko2000 2743
Ivanchuk2000 2719
Topalov2000 2707
Krasenkow2000 2702

Carlsen 2760 (2810)
Topalov 2755 (2805)
Anand 2740 (2790)
Kramnik 2738 (2788)
Aronian 2731 (2781)
Gelfand 2711 (2761)
Gashimov 2709 (2759)
Ivanchuk 2699 (2749)
Wang Yue 2699 (2749)
Svidler 2694 (2744)

Some observations:

* in July 2000 there were 5 players rated 2750+
* in January 2010 there are only 2 rated 2750+ (despite the more and faster learning and developing young players, due to modern tools - or so we're told)
* in July 2000 there were 11 players rated 2700+
* in January 2010 there are only 7 rated 2700+
* all of Morozevich, Adams, Shirov and Leko were higher rated in 2000 than the World Champion Anand in 2010
* for those who think ratings accurately maps strength: Morozevich, Adams, Shirov and Leko were in July 2000 all stronger than the current trio of Anand, Kramnik and Aronian.
* Moro and Adams were as strong in 2000 as Carlsen and Topalov are today
* Krasenkow were higher rated in 2000 than the trio Ivanchuk, Wang Yue and Svidler in 2010.

In fact, Krasenkow2000 (2702) was also 10 to 50 points higher rated than the January 2010 versions of

Mamedyarov 2691
Leko 2689
Ponomariov 2687
Grischuk 2686
Radjabov 2683
Morozevich 2682
Jakovenko 2680
Shirov 2673
Karjakin 2670
Dominguez 2662
Nakamura 2658

just to mention some. And if we consider the adjusted rating losses of our January 2000 top 10 friends, it looks like this (with ages for reference):

Kramnik 2770 -> 2738 = -32 points (25 -> 35)
Anand 2762 -> 2740 = -22 points (30 -> 40)
Morozevich 2756 -> 2682 = -74 points (23 -> 33)
Adams 2755 -> 2644 = -111 points (29 -> 39)
Shirov 2746 -> 2673 = -73 points (28 -> 38)
Leko 2743 -> 2689 = -54 points (21 -> 31)
Ivanchuk 2719 -> 2699 = -20 points (31 -> 41)
Topalov 2707 -> 2755 = +48 points (25 -> 35)
Krasenkow 2702 -> 2606 = -96 points (37 -> 47)

Everyone except Topalov has dropped a lot of rating points, even the relative youngsters Moro and Leko.

If the above says something meaningful about the absolute skills of the top level players, then we probably must conclude that world elite chess isn't developing at all but is rather declining at a fast pace, and that the new "talent" is mostly rubbish, unable to play chess after they turn 30 (ref. Leko and Moro).

If the "breadth" in top level chess continue to grow at the current rate, thereby increasing the rating of #100, we'll soon have only one player above the "year 2000-level" of 2750 with this kind of "rating adjustment", and a few years later maybe only 2 or 3 above the "year 2000-level" of 2700 - back when 11 players were 2700+.

I think this looks a bit odd - that more professional players and better tools (and many more semi-professional players) only make the best players weaker and weaker, and will probably continue to do so, if we extrapolate the current estimates of 4-5 points of "rating inflation" per year.

---

But of course, this is only a problem for those who believe in a strong mapping from ratings to chess skills. I've already argued that such a strong mapping does not and can not exist - over time, that is. Only in pools not too different and quite close in time, among contemporary players, co-existing and competing against each other, does it make sense to equate results (= ratings) with skills. :o)

@Choosing our "sample" as "all players in a given rating list that also could be found in the rating list one year later" I have found that between july 1990 and july 2009 ... the accumulated year-to-year change is ONE POINT - much less than 0,1 points per year on average.

That's neat. Now you should look again and your data and tell us what is the avearge age of the players of your sample.

If, for instance, it is 31 yr in 1990 then 19 years later when it is 50 yr one should expect (if there is no inflation) that their average ELO as group it is significantly less.

If it isn't, as you found, then only inflation would explain such anomaly. You hardly see people at 50 as strong as at 31 (or even stronger so as to compensate statistically for those who have become weaker in the meantimes).

Hi frogbert, why don't you consider putting up all your arguments on rating at one place; may be your website. They are worth it, and probably deserve more than just being piled under heaps of dirt in the comments section here.

Let me second piyush's suggestion. You should definitely publish your findings at your live ratings site. If you write it up neatly, you'd easily get some coverage from Chessbase (unless their allegiance to Sonas deters them) and the other major news sites.

You've essentially debunked simple inflation in this thread, and although there may be subtle and rather insignificant drifts in the system, this wouldn't matter in any practical context as the comparative power of the system degrades over time as the pool changes.

If the only purpose of this discussion is to prove wrong the people who compare historical ratings with modern ones over vast swaths of time, that's still a worthy cause! I'm probably as sick of this as you are.

@You've essentially debunked simple inflation in this thread

He may have succeeded proving it. It depends of the average age of his sample. If it happens that the average age is ~31 yr and the group's mean rating doesn't show an overall decrease 19 years later when group's age avearge is 50 yr then it follows that there is inflation.

"That's neat. Now you should look again and your data and tell us what is the avearge age of the players of your sample.

If, for instance, it is 31 yr in 1990 then 19 years later when it is 50 yr one should expect (if there is no inflation) that their average ELO as group it is significantly less."

I'm not sure if you've understood what I did here: For every of those years, there was a NEW selection of "all players in a given rating list that also could be found in the rating list one year later".

The average rating of these "all players" samples was more than 200 points lower in July 2008 compared to in July 1990, but NOT because people had grown older, but because the distribution of young and old, amateurs and professionals, was completely different in 2008 compared to in 1990. I consider it likely (although I didn't check - but it's easy to do so) that the average age will be lower in the 2008 sample.

Anyway, I'm primarily interested in studying the presence and rate of inflation, not the effects of people growing old, and I don't expect a fixed group of players of an initially BALANCED age distribution to have (on average) the same skill level when everyone has grown 10 years older, obviously. If I chose a group where everyone was 25 years old and considered these players' ratings 10 years later, I wouldn't be too surprised to find a very similar rating level, but a random (but fixed) group of 30 year olds would probably result in a notably lower rating level indicating a decline in strength 10 years later.

"You've essentially debunked simple inflation in this thread"

Actually, I'm more interested in understanding these phenomenons than "debunking" other theories, but I certainly agree that there are myths related to "rating inflation" that lack foundation in serious analysis.

However, I don't consider the subject "solved" in any way, because it's perfectly possible to choose samples with certain characteristics that quite consistently will yield increases in average ratings from one year to the next, for example.

For instance, if we pick players that are younger than 25 years and who have played 50 or more games over the 12 months from the "current" list to the list we compare to in the next year, we get average year-to-next-year rating increases of ca. 35 points per player - considering the same 45 lists as before (July 1990 to July 2006). Of course, in this case we aren't talking about inflation but rather the average improvement of young players that take chess seriously and play a lot of FIDE rated games every year.

But in general, how should we best try to differentiate between "improvement" and possible "inflation/deflation" just by analysing the rating changes?

I think one of the most interesting things I've found, is the strong relationship between activity (number of games played) and rating development (whether caused by improvement/decline or some systemic flaw, like "inflation"). Age is obviously also a very interesting factor with big impact.

I still need to spend more time to digest the data I have. Luckily it's now rather easy for me to test a new hypothesis using the tool(s) I've developed to make very detailed "queries" about the rating lists from 1990 until today. [Older lists lack very useful data like number of games played/rated in a new list...]

"I am, however, concerned that you may have forgotten about the statistical phenomenon called "Regression towards the mean"."

Don't be concerned - I never claimed that the "negative increases" I quoted were signs that the top players are experiencing "deflation" or anything as such. I'm actually rather convinced that the tendency we see by comparing the averages of these selections to the same players next year, is linked to (many) players being "temporarily overrated" when they end up at the far "right end" of the distribution. (Btw, he closest "next" number isn't that one year into the future, but that of the next list - so the "rebound-effect" might have been even stronger in other scenarios - I don't know (until I check ;o).)

Note however that when I considered ALL players from the year 1 list identifiable in the year 2 list, I essentially got zero changes (the accumulated year-to-next-year changes was 1,0 for the July lists 1990 to 2009).

A possible improvement in order to hopefully remove some of the "rebound-effect", would be to only consider players that have satisfied the criteria of 2500+/2600+/2700+ in 2 or more prior lists - or similar. It's not very hard for me to calculate something like that either.

"Hi frogbert, why don't you consider putting up all your arguments on rating at one place; may be your website."

I'm (hopefully) going to publish better prepared and more well-written and clearer articles about these matters - when I find the time to.

I intend to discuss some of my methods with people that have more mathematical and statistical knowledge than I do first, in order to avoid potential fallacies and to make some reasoning more rigorous and "bullet-proof".

Regarding where to publish, it will probably be a combination of making calculations and large amounts of data available on my site, while offering a write-up of the most important points to e.g. Chessbase; When I wanted to comment on things in the past, it wasn't very hard to get it published. Chessdom will also gladly publish anything interesting I might have on the subject, and probably Peter of ChessVibes too.

It's a bigger issue making the time I feel I need to do these things "properly" than actually getting things published. :o) Meanwhile it's useful to throw ideas and results around in order to get feedback, suggestions, criticism and generally an idea about to which extent the approach is considered meaningful and which parts that need to be (most) carefully presented, in order to avoid misunderstandings.

@For every of those years, there was a NEW selection

OK, that's different, you assume that your "ELO-slice around 2500" selection is reprezentative for the whole.
I find'it unconvincing because the distribution as a whole is bell-shaped and (without inflation) I would expect to be a negative difference (not zero as you found) between average of your "ELO slice" a year later : less people from this ELO group will win points and move upwards (toward the top of the pyramid where there is littles space-less people) and more will lose and move downwards, where there is plenty of space.

But your idea is interesting nonetheless. If you could take a "vertical" slice ( a group which will have a people from all ELO-leveles, and equally from which level) and you do the same than I suppose that the difference, if any, would be exactly the inflation (or the deflation).

"you assume that your "ELO-slice around 2500" selection is reprezentative for the whole. "

Eh... no? It seems like you haven't quite understood, still.

"I find'it unconvincing because the distribution as a whole is bell-shaped"

It certainly isn't, for several reasons.

"I would expect to be a negative difference (not zero as you found) between average of your "ELO slice" a year later : less people from this ELO group will win points and move upwards (toward the top of the pyramid where there is littles space-less people) and more will lose and move downwards, where there is plenty of space"

I'm not 100% sure if I understand exactly what you mean, but let me one more time remind you what the numbers were for the "high-rated" selections:

2500+ 1990-2006: -1,58 points
2600+ 1990-2006: -3,02 points
2700+ 1990-2006: -2,51 points

Considering the trend only since 2000 yields the following (22 year-to-next-year comparisons):

2500+ 2000-2006: -1,56 points
2600+ 2000-2006: -2,87 points
2700+ 2000-2006: -3,65 points

Isn't that exactly what you said you would expect, if there was no inflation? The average of the highest rated players (2700+, 2600+, etc.) went down, and the average rating loss was bigger the more extremely rated the players were (not more than between 1,5 and 3,5 points on average, but still).

As I wrote before, for the samples spanning ALL players present in both compared lists, the average change was much less than +0,1 points per player on average - pretty close to 0, in fact. For the single comparisons, in the entire period July 1990 to July 2009, the two "extreme" average changes from one year to the next, was in fact from July 1990 to July 1991, when 9231 players gained on average 1,3 points, and from July 1992 to July 1993, when 11330 players lost on average 0,5 points.

The July 2008 to July 2009 comparison included as much as 92387 individual players, btw - with an average rating of (only) 2059,2 in July 2008. The 9231 players compared between July 1990 and July 1991 were rated on average 2281 in 1990 - and 2282,3 one year later.

Frogbert:

I think my point is that "regression towards the mean" is expected if you resample a group which is distinctly divergent relative to the mean.

I have no idea what the mean FIDE rating is, but in my opinion, you also have to look at a random sample which is an equivalent number of sigmas distant from the mean (in the negative direction). If that sample tends to move towards the mean with a similar annual rate of change ~+3.00, then you have an indication that there is little or no rating inflation. Otherwise, the apparent point loss of the higher rated groups could be explained as
+ 5 (due to points rating inflation) - 8 (due to regression towards mean) = -3

Just to make it abundantly clear: The following,

2500+ 1990-2006: -1,58 points
2600+ 1990-2006: -3,02 points
2700+ 1990-2006: -2,51 points

and

2500+ 2000-2006: -1,56 points
2600+ 2000-2006: -2,87 points
2700+ 2000-2006: -3,65 points

listed average change per player PER YEAR-TO-NEXT-YEAR comparison - an average over 41 such comparisons in the first case, and over 22 such comparisons in the second. I.e. in EACH of the 41/22 comparisons, the change was between -1,5 and -3,65 points (on average) over 12 months.

The individual year-to-next-year changes varied as much as from +3,8 to -6,7 for the 2500+ samples and even more for the much smaller 2600+ and 2700+ samples. Naturally the variations tend to become smaller as the sample size increases...

@Isn't that exactly what you said you would expect, if there was no inflation? The average of the highest rated players (2700+, 2600+, etc.) went down, and the average rating loss was bigger the more extremely rated the players were (not more than between 1,5 and 3,5 points on average, but still).

Yes, and you could have guessed that even without doing any calculations but based only on the obvious fact that "the higher the ELO the smaller the number of people with such ELO"..this is telling you the shape of the distribution nothing about whether there is inflation

@As I wrote before, for the samples spanning ALL players present in both compared lists, the average change was much less than +0,1 points per player on average - pretty close to 0, in fact.

such a sample in order to be relevant for what you want to prove must have an equal number of players from each ELO interval and span ALL intervals.
You need to divide the ELO intervals (2700-2600 , 2600-2500, 2500-2400..) and then get an equal number in each, and in all of them. Then do the averages over a year. The result should be the inflation.

If don't do so, if you "at random" ( based on the mere fact that "they appear on the next list so I can compute the average") then it stands to reason that there will be more of lower ratings and less of higher ratings ( not equal number from each intervala)..and therefore the result MUST be zero exactly as you got. and that so regardless whether there is or not inflation.
The reson is that now your slice

hopefully now you see my point, and your mistake, but the idea is good now that you have the data

get one of your samples with people which you can find in the next year list, make sure that there are an equal number in each interval ( more people in each and the finer the divisions (say 10 in 2600-2650, 10 in 2550-2600, etc.) the better ..and do the calcuations.
I won't be surprised if you find the same result as Sonas, about 5p/year.

"you also have to look at a random sample which is an equivalent number of sigmas distant from the mean (in the negative direction). If that sample tends to move towards the mean with a similar annual rate of change ~+3.00, then you have an indication that there is little or no rating inflation. "

I suppose you did notice that I also did this exercise for each and every identifiable player between two lists?

Regarding the mean of the FIDE pool: it has changed a lot and downwards, due to the new lower limits for FIDE ratings. Also, there's a clear assymmetry in the distribution for the time being, with a rather stable "right tale" where the players in general have a high level of activity and have been in the pool for a long time, while the "left tale" consists of (mostly) many newly added players that play very, very little. I'm a bit unsure what the logical impact of this would be for your suggestion.

One of the important relationships I've observed, is that there's a very clear correlation between activity and rating gain, regardless of where in the pool a player is. But there are much fewer players with high activity among the lower-rated players for instance than among the IMs and GMs. To some extent this is the difference between "amateur" and "professional", of course, but it's probably also a result of several other mechanisms, where it's unclear what is cause and what is effect.

Does successful players want to play more, or does players that play more become more successful? Does lack of good results (and rating gain) make people play less, or is lack of good results (and rating loss) due to playing too little?

In fact, I've got another interesting statistic over "all players identifiable from one list to another" with the added restriction that the players must have registered activity (rating change or having played at least one game) between the two lists of interest. Given that restriction, requiring activity, I got an average "inflation" of 1,7 points per year - or 33 points accumulated from July 1990 to July 2009. The portion of the entire pool for which I registered activity in these 19 cases ranged from (only) 28-29% in 2002-2004 all the way to 59-62% in 1997-1999. Based on the available data, on average 43% of the entire population played 1 or more games during the "sample year" - the remaining 57% did seemingly not play any rated games [but due to some missing data I suspect that the reality might be closer to a 50-50 situation].

Btw, do you have any suggestion about ways to estimate how strong the "regresssion towards the mean" might be? Any suggestions are welcome - and thanks for pointing out this potential issue. :o)

You were wrong to average them ALL from on list to the next and draw conclusions about inflation from such a result. You don't have equal numbers in each of the ELO interval but likely you have more of lower ratings and less of higher ratings.
Just construct out of them a sample with equalsnumbers in every interval (10 in say 100ELO intervals) and then do the change in averages.

"You don't have equal numbers in each of the ELO interval"

If 10000 players in one rating interval lose 3 points on average, and 50 players in another EQUALLY SIZED rating interval (spanning say 100 points) gain 3 points on average, do you consider that the system is "stable" or experiencing massive deflation?

-3 * 10000 = -30000
3 * 50 = 150

Just wondering ...

RuralRob: Good one! :-)

Frogbert:
1. I didn't notice that you had done a similar analysis of the players below the mean (e.g. players rated <1600 <1700 <1800). Did you do that?
2. I have absolutely no idea how you would have to compensate for "regression towards the mean". Perhaps there are some useful links from the wikipedia link that I posted earlier.

> the players below the mean (e.g. players rated
> <1600 <1700 <1800)

I don't understand why you think the regression should influence the stableness of the rating change on the left edge (much), but things get messy when you look at the right edge. For starters, in 1990 the lower threshold of the men's list was 2200, and 2000 for women. There were no players rated below that.
By the way: Do you talk about the mean of the rated players, or the hypothetical mean of playing strength of all players?

"the stableness of the rating change on the left edge (much), but things get messy when you look at the right edge."

Bartleby, just to be sure: is your "left" the "other left", or the "standard" left?! I.e. did "left edge" refer to the lower or higher end of the rating distribution graph here? I got a bit confused when you started to talk about the lowered thresholds and the "right edge" at the same time - since change in the lower threshold impacts the "left edge" in my mental image of the distribution... :o)

Bartleby:

As I said before, I am no statistician, and I haven't been digging deep into the numbers.

Earlier someone said that FIDE rating of players was distribted along a bell-curve, thus indicating a normal distribution.

I am still convinced that the statistical phenomenon known as "regression towards the mean" (http://en.wikipedia.org/wiki/Regression_toward_the_mean) could - at least partly - explain the average annual changes that Frogbert has calculated (for players rated >2500, >2600 and >2700).

I therefore questioned whether this phenomenon had been compensated for when he was drawing his conclusions.

One way that immediately occured to me as a plausible strategy for eliminating the effect, would be to try to measure the relative tendency for regression towards the mean at THE OTHER tail of the bell-curve.

After rethinking this idea, it appears that the idea is probably flawed, due to the fact that the majority of active players make efforts every year to improve his or her chess.

@So rating inflation represents greater opening knowledge + better computer preparation.

sounds plausible but cpmouter-chess become common only in the mid 90s while the rating inflation started suddenly with the Jan. 1986 list, before that (1971-1986) there was no inflation, see :

http://members.shaw.ca/redwards1/

I guess that something else must have happened in the late 1985, maybe a FIDE decision which affected the ratings

Zats a bingo ! :)

I assume you are old enough to have played the 1800s of 25 years ago, Irv. What would you estimate their ratings to be in today's terms?
This can't be attributed to your decrepitude? (just kidding)

"I assume you are old enough to have played the 1800s of 25 years ago, Irv."

Guilty as charged, I'm afraid :-)

"What would you estimate their ratings to be in today's terms?"

My guess would be a good 50-100 points less (1700-1750).

"This can't be attributed to your decrepitude? (just kidding)"

Yes, it could very well be my "decrepitude" :-), by I think that weaker players today have a much greater awareness in the opening and tactics department that makes them harder to beat. I often encounter players that show a very poor understanding of the game, but play the opening like a master and have a very good idea of the thems behind the openings they play. The days of dispatching a weaker player in 25 moves with a little combination on h7 or f7 are gone.

"Sad to see these nations suckered in by false promises. Too bad all of the promised monies will magically vanish after the vote!"

In all fairness, it is not like Karpov is running a great, transparent campaign. Nobody knows what he brings to the table, except for some vague promises of some mysterious russian backers.

This might be a classical case of "a bird in the hand is worth two in the bush".

> did "left edge" refer to the lower or higher end
> of the rating distribution graph here?

Sorry for mixing up directions. The "left edge" related directly to my mental picture of the bell curve, which had the bigger numbers to the left, and probably no base in reality.

Leko has won many games vs 2700+ including more than one wins against each of the very top (Anand and company), except Kasparov.

Only recently, since about the end of last year, did his overall performance drop. Even so, just last month he won a game vs a 2700+.

Thomas:
Only recently he had bad results and thus dropped to #25 (2720) on the live rating list, based on Bazna and two games played on 7th and 10th of June (Chinese league?).

The 2 games were in rounds 4 & 5 of the chinese league, on June 7th and 8th. Wang Yue lost against Zhao Jun, and drew against the 17 yr old Ding Liren, who surprisingly won the chinese championship last year. As both are 2500+ players, this result took a lot of points.

As to regression towards the mean, I really wonder in what way this would apply in this case. If Magnus Carlsen had a kid with Judith Polgar, then maybe that child would tend not to reach quite the same heights as his parents, and I would get your point.

But what do you think regression towards the mean really means in chess Elo terms? I think players have a tendency to regress towards their own mean, for sure (for example, going 8/10 versus an expectation based on your rating of 6/10 would make it likely for you not to do as well in your next tournament). But I fail completely to see how this would apply to inflation in the general pool.

What mean do you think everybody is regressing towards? Isn't everybody regressing towards his own mean, which would be his actual present (and changing) strength, whatever that is?

If you are talking purely in terms of chess strength, taking a bunch of highly motivated, hard studying pack of 2500+ GMs and giving them a year of work on their chess, they'll as a bunch certainly be getting stronger by increasing their chess knowledge (though that won't be reflected in the ratings as they are playing against each other, with their adversaries improving as well). What I don't see them doing is regressing towards a hypothetical mean.

Of course, I might not be getting your meaning at all, no pun intended, in which case I would be happy for you to correct my misimpression.

Correction:

Wang Yue's record against Gelfand is +1-1=3

" But I fail completely to see how this would apply to inflation in the general pool."

In a closed system, I doubt it makes sense to talk of inflation. So you have to look at the "injection point", aka the rating procedures for previously unrated players.

It used to be (I've no idea how it works anymore, and couldn't find any readily available info at the fide site) that you had to achieve a certain rating performance over a certain number of games to qualify for a FIDE rating. So, if your "real" level was lower than the entry level set by FIDE, you could try over and over until you eventually "overachieved" and got listed at an inflated level. And then you'd be likely to regress towards your mean, feeding fresh points into the circuit.

Conversely, there will of course be players who underachieve when they get their first rating, and as they progress towards *their* mean, they will soak up points from the rest of the system, which will in some contrived sense amount to a "deflatory" effect.

I'm totally incompetent about these matters, though, so I'm in no position to suggest what this all means. I don't even understand why it's important: If you cannot look at the *games* and decide who was the stronger of Fischer and Kasparov, what are you going to learn from projecting their ratings?

"One way that immediately occured to me as a plausible strategy for eliminating the effect, would be to try to measure the relative tendency for regression towards the mean at THE OTHER tail of the bell-curve."

Simen, one important thing to take into consideration is that the "bell curve" has been somewhat "broken" for most of this decade due to repeated lowerings of the threshold for FIDE ratings (2000 -> 1800 -> 1600 -> 1400). And the "mark" from when the limit was lowered from 2200 to 2000 is also still quite "visible". Hence, the actual distributions of the players have been rather far from perfectly symmetrical around the mean. For a couple of illustrations, see the some plots here:

http://chess.liverating.org/elo/dist.html

[These include ALL players, also inactive ones. The y-axis shows number of players in the 20-point rating intervals - 2000 means 2000 to 2019, and so on.]

Of course, when the cut-off was 2200 or 2000 for longer periods, the "bell-curve" had its lower tail cut off at 2200, respectively 2000, making the "lower tail" basically non-existent, and the cut-off point a bit crowded...

"Otherwise, the apparent point loss of the higher rated groups could be explained as
+ 5 (due to points rating inflation) - 8 (due to regression towards mean) = -3 "

One question: Is there any other way to estimate "regression towards the mean" in a given population than by empirical methods? If we measure that the regression towards the mean in this case is -3 points, on which grounds can you claim that it's something else - like -8 or -43? Both "inflation" and "regression towards the mean" are in my head meant to be descriptions of something we actually can observe and describe, not vague things that we're free to postulate. If the rating average of a group of players go down, then it doesn't at the same time go up, to put it bluntly.

Next question: What is your definition of rating inflation? If there's "5 point inflation" - does or does not that describe that the average rating of a closed group of players go up with 5 points? [That is, a closed group of players that it is natural to assume is stable on average. The only way a negative rating development can still theoretically be described as "inflation", would be if there were pressing reasons to expect it to be even more negative (which I suspect was your point) - but that expectation must be anchored to something substantial and concrete, IMHO.]

In a way, the reason why the 2500+ players don't experience rating increase on average isn't that interesting; as long as this group of players don't get "inflated ratings" on average, we know that those players who do increase their ratings do that because they have better results than those who don't. And not because everyone's ratings are artificially fuelled by "new-born" rating points, equally spread out on everyone.

Note that I don't care much about "absolute strength". As explained in a previous post, there simply is no good way to compare "absolute strength" or "chess skills" over 10s of years, and higher or lower ratings on average (or at the upper end of the rating scale) is certainly no appropriate tool to do such comparisons.

As I've already written, both here and elsewhere, I don't rule out an amount of systemic inflation - but I want a meaningful way of defining and describing it. Anchoring it to the rating of the player ranked #100 is no such thing, in my opinion.

I'm not sure if you noticed, but I also had a different approach to measuring the rating development for the "entire" population where my selection was limited to those that I _knew_ had played at least one rated game over the period I sampled. Between 1990 and 2009 the percentage of the population that actually played rated games in the following year varied between ca. 30% and ca. 60% - for example 48% of a population of ca. 9500 in July 1991 and ca. 41% of a population of ca. 93000 in July 2008 - on average ca. 43%.

One interesting feature observed here, was that the average rating of those having played games in the July 1990 sample was ca. 25 points higher than the average of the entire population - i.e. a tendency of more activity among the higher rated players overall. However, in 2008 the average rating of those with activity was ca. 15 points LOWER than the average of the entire population. Moreover, this change in tendency seemed to have taken place rather smoothly over the entire 19 year period, saying something about the activity of the "newly" added amateur players.

Anyway, focusing "only" on those with activity, I got these numbers that are a bit different:

1990-2009: +1,7 points per player per year
1999-2009: +2,1 points per player per year

2004-2005: +3,4
2005-2006: +1,3
2006-2007: +1,8
2007-2008: +2,1
2008-2009: +1,8 points per player per year

Hence, also 2004-2009: +2,1 per year. The 4 years with highest yearly increase for the active players were 90-91 (+3), 91-92 (+2,7), 00-01 (+3,3) and 04-05 (+3,4). And note: it was a positive change in all the 19 sampled years - but as little as +0,2 for 92-93. [And again, this was based on actual, observed activity - not FIDE's pretty strange "activity" flag.]

If this method gives a more "true" picture of the rating increase since 1990, then we've had around 33 (+/- 3) points inflation since 1990 and around 21 (+/- 2) inflation the last decade.

Trying to map this observation to the fuzzy "strength per rating point" inflation speculations, I personally think that +2 points per year during the last decade "feels" much more right - and unlike the estimates of 4-5 points that clearly don't take the increased player base into account (at all), my estimate is based on the ACTUAL rating change of players with rated games, from ca. 4000 in my 90-91 sample to ca. 38000 in my 2008-2009 sample.

A final note: reducing the sample to those with activity make little difference for the top players, since almost all of them are still active and play games every year. Hence, the top players lose rating on average, no matter which of these two alternative methods is used.

"I am still convinced that the statistical phenomenon known as "regression towards the mean" (http://en.wikipedia.org/wiki/Regression_toward_the_mean) could - at least partly - explain the average annual changes that Frogbert has calculated (for players rated >2500, >2600 and >2700).

I therefore questioned whether this phenomenon had been compensated for when he was drawing his conclusions. "

Which conclusions? I've simply shown that the top players as a group don't earn rating points.

And if (some of) the top players lose rating points, why should that be "compensated" for? I'm simply interested in the rating development for various closed, presumedly stable (on average) groups of players in the pool.

A possible conclusion is that the group of 2500+ players shouldn't be expected to be "stable" for various thinkable reasons (age distribution, the number of "temporary visitors", etc.) - but I've drawn no strong conclusions about this either.

And I've certainly not drawn any conclusions about the overall inflation levels based on the observable rating development for the top rated players (as a group). :o)

The only problem with that observation Irv is that you can't say something is better than nothing. In this case, "nothing" isn't better than nothing, it's still just NOTHING!

The definition of STUPID is repeating the same thing over and over and expecting a different result. Geez, especially chess players should understand that. If you're happy with how FIDE is, keep the course. If you want better, you have to change. Simple.

"The only problem with that observation Irv is that you can't say something is better than nothing. In this case, "nothing" isn't better than nothing, it's still just NOTHING!"

In all fairness, Kirsan has brought his own money into chess. There is ample evidence of that. Even Mig has confirmed it writing (in the past, of course!. Check Chessbase's old columns by Mig).

Now, I DO NOT think Kirsan is good for chess. The guy is certainly guilty of everything he is accused of. No question about it. However, Kirsan is not the reason for FIDE's troubles. If anything it's the opposite: FIDE's troubles are the reason Kirsan is in power.

"The definition of STUPID is repeating the same thing over and over and expecting a different result. "

It's usually referred to as the definition of "CRAZY", not "stupid, but that's a minor point. That said, I don't know how it applies here. People who support Kirsan DO NOT expect different results.

"Geez, especially chess players should understand that. If you're happy with how FIDE is, keep the course. If you want better, you have to change. Simple."

It's not so simple: I want better, like you. The difference is that I, unlike you, realize that change can happen for BETTER or for WORSE (I hope you agree with this - but you're free to choose your own way of analyzing it). In the case of selecting a FIDE President, I don't know if Karpov represents a change for better or worse. Or if he represents a change at all. And that was my point: his lack of a clear campaign platform, his association with corrupt former Kirsan supporter Kasparov and a bunch of shady russian characters has to worry any neutral observer.

And this is coming from me, a guy who thinks Kirsan is a low life and who also thinks that Karpov is one of the two the most talented chess players ever.

Apologies for hijacking this thread but I see that the debate has started on this thread so...

This appeared on Chessbase (quoting from official FIDE notice):

Concerning the FIDE elections, the Russian Chess Federation (RCF) informed FIDE on 28 June 2010 that the Supervisory Board of the RCF, during its meeting of 28 June, confirmed the letter of its Chairman Mr Arkady Dvorkovich to FIDE on 21 April, nominating Kirsan Ilyumzhinov as Russia's candidate for the office of FIDE President 2010-2014. Furthermore, the RCF informed FIDE that the letter sent by Mr. Alexander Bakh on 23 June is not valid on nominating a candidacy from the Russian Chess Federation. Attached are all the relevant documents as sent by the RCF.

Seems disingenuous IMO. I think that if it can be proved in court that the RCF supports Karpov and not Kirstan his nomination is void and therefore there is only one candidate for the elections, namely Karpov, since the condition for the nomination of Kirstan (namely the nomination by his home federation) is not fulfilled...therefore no election necessary if Karpov proves in court that Kirstan has not fulfilled the condition for his nomination...

A further twist: Chessbase lists Karpov's supporting documents and it is clear that his nominating federation as "Russia"...so how can this debate be resolved without a court order deciding who the Russian federation votged for...the FIDE site seems to suggest that Karpov's nominating federation is not Russia....interesting also is that the FIDE website says : "Please view the statement letters of the Russian Chess Federation to support the candidacy of Kirsan Ilyumzhinov for the office of FIDE President 2010-2014." There is nothing corresponding stated for Karpov....

Also Fide website says Karpov nominating federations are "Mr. Anatoly Karpov nominated by France, Germany and Switzerland," Clearly therefore they have already arrived at the decision on the validity of karpov's nomination before their actual meeting to ratify the candidates later in July. It seems to me there is enough grounds to challenge the inevitable decision of FIDE to back Kirstan on this issue by claiming bias and that FIDE has already pre judged the issue without deliberating on it... another sad saga by FIDE, Kirstan and their supporters....would love to be on the legal team of Karpov for this one...;))

"In all fairness, Kirsan has brought his own money into chess. There is ample evidence of that. Even Mig has confirmed it writing (in the past, of course!. Check Chessbase's old columns by Mig)."

ROTFLMAO! Kirsan is abusing the Kalmykian treasury and taxing the citizens into poverty while living in his "Chess City". Nice.

"Now, I DO NOT think Kirsan is good for chess. The guy is certainly guilty of everything he is accused of. No question about it."

Well, we agree on that!

"However, Kirsan is not the reason for FIDE's troubles. If anything it's the opposite: FIDE's troubles are the reason Kirsan is in power."

Riiiiiiiiiiiight.... C'mon Irv, you're smarter than that! Chess was doing pretty good, even under Campomanes until Kirsan.

"It's not so simple: I want better, like you. The difference is that I, unlike you, realize that change can happen for BETTER or for WORSE (I hope you agree with this - but you're free to choose your own way of analyzing it)."

Uh, define please exactly what would be WORSE than FIDE under Kirsan? Are the players happy? Are sponsers (what few haven't been driven away) happy? Are organizers happy? Are fans happy, again what few haven't been driven away, to say nothing all of the ones that have been failed to be attracted...

"In the case of selecting a FIDE President, I don't know if Karpov represents a change for better or worse. Or if he represents a change at all. And that was my point: his lack of a clear campaign platform, his association with corrupt former Kirsan supporter Kasparov and a bunch of shady russian characters has to worry any neutral observer. And this is coming from me, a guy who thinks Kirsan is a low life and who also thinks that Karpov is one of the two the most talented chess players ever. "

Come into the light Irv, come into the light. Even if Karpov doesn't deliver, you have to get the proverbial ball rolling. It's time!

@Chess was doing pretty good, even under Campomanes until Kirsan.

FIDE went bankrupt because of Campomanes, that why Kirsan managed to buy it and become FIDE pres.
Campomanes was the guy who sold FIDE to Kirsan.

"FIDE's finances were in turmoil and in 1995 it became clear that FIDE was bankrupt and that Campomanes had lost the support of the Federations (Campomanes re-election in 1994 in Moscow was accompanied by accusations of threats against delegates and candidates). He didn't give up however and he found a young Russian multi-millionaire, Kirsan Ilyumzhinov who ran his own former Soviet Republic (Kalmykia), to bail the organisation out and he got the support for him to be elected. I believe that FIDE should have been allowed to go bankrupt and the officials should have faced the consequences of their profligacy. Also that was the time for a long needed root and branch reform of the organisation. Campomanes became an honorary life President with a large stipend from Ilyumzhinov."

Mark Crowther, The Week in Chess
http://www.chess.co.uk/twic/chessnews/obituaries/florencio-campomanes-1927-2010

There are no clues in Karpov's platform to the effect that he intends to reform FIDE, to address its problems, to transform it in a viable organization.

"ROTFLMAO! Kirsan is abusing the Kalmykian treasury and taxing the citizens into poverty while living in his 'Chess City'. Nice."

I didn't say it was nice. I said that he DID bring money (dirty or otherwise) into FIDE, something you denied in your post.

"Riiiiiiiiiiiight.... C'mon Irv, you're smarter than that! Chess was doing pretty good, even under Campomanes until Kirsan."

Not true. See Ovidiu's post. You seem to be very misinformed about FIDE , its reality and history.

"Uh, define please exactly what would be WORSE than FIDE under Kirsan?"

FIDE under Kasparov and without any money (dirty or otherwise) coming in.

"Are the players happy?"

I have no idea - and neither do you, I'm sure.

"Are sponsers (what few haven't been driven away) happy?"

There are no sponsors that were "driven away". FIDE never had any serious sponsorship at any time - before or during Kirsan. Once again, you seem to be arguing based on whatever comes to your mind, not on facts.

"Are organizers happy? Are fans happy, again what few haven't been driven away, to say nothing all of the ones that have been failed to be attracted..."

We can imagine whatever we want - but I'd rather deal with facts, to be honest.

"Come into the light Irv, come into the light. Even if Karpov doesn't deliver, you have to get the proverbial ball rolling. It's time!"

I'd rather not get "the ball rolling" - whatever that means within the context of this conversation - unless I'm reasonably certain it is a step in the right direction. Finally, so that some of your confusion goes away: I'm NOT pro Kirsan. I wouldn't mind seeing the guy get the axe. I'm only interested in FIDE getting a replacement that will make things better. I'm not sure that Karpov/Kasparov is that replacement.

Is this the first time when there are three players rated 2800 or more at the same time?
********
It may well be, but give it a few years and inflation will give us thirty more 2800 players. Super GM tournaments just ain't that super anymore.

I guess we have to define supertournaments based on the number of top10/top30 players participating, regardless of rating and (what some people call) rating inflation ... .

Time Machine: "Rating inflation may be more due to a larger pool of players and more games being played. Even if its a zero sum game, more points to be distributed, should favor those with better chance of scoring those points i.e the top bunch."

I think this is a valid observation. To expand a little, ...

Chessbase has posted the peak rating for some players (courtesy Mr. Przemek Jahr) as follows:

# Player Nat. Rtng FIDE list
1 Kasparov, Gary RUS 2851 1999 / 07
2 Carlsen, Magnus NOR 2826 2010 / 07
3 Topalov, Veselin BUL 2813 2006 / 07
4 Kramnik, Vladimir RUS 2811 2002 / 01
5 Anand, Viswanathan IND 2803 2006 / 04
6 Morozevich, Alexander RUS 2788 2008 / 07
7 Ivanchuk, Vassily UKR 2787 2007 / 10
8 Aronian, Levon ARM 2786 2009 / 11
9 Fischer, Robert USA 2785 1972 / 04
10 Karpov, Anatoly RUS 2780 1994 / 07

My observation is that, given that the above hypothesis is valid, #9, a rating achieved almost 40 years ago (!), and 27 years before Kasparov's peak, shows a significant superiority to not only his contemporaries, but probably to the modern elite as well.

And I would observe that it also supports that rating is not necessarily a reflection of ability, especially through different player pools.

OK, these are observations, and not meant to relight the debates on who was 'best ever,' but only to comment upon inflation and the meaning of ratings.

CO

"My observation is that, given that the above hypothesis is valid, #9, a rating achieved almost 40 years ago (!), and 27 years before Kasparov's peak, shows a significant superiority to not only his contemporaries, but probably to the modern elite as well. "

My observation is that you've made dozens of observations more profound than this one. How a rating from nearly 40 years ago can show "superiority to the modern elite", regardless of the relationship between the actual numbers, is way beyond me - unless you're talking about relative domination. But in that case we need more than Fischer's rating; we also need to know that his rating was in a different stratosphere than those of his contemporaries. However, that observation can be made competely without any regard to "rating inflation" and as such isn't very relevant for the current topic of debate.

My second observation is that CO is a big Fischer fan. :o)

Well, quib, I think that the reality is that Mig's next blog might be about practically anything, but ultimately the conversation will be reduced to rating discussions, Kirsan vs. Karpov, or, god forbid, something about Topalov/Danailov. It's kind of like that maxim about the longer an Internet thread becomes, the greater the possibility of comparisons to Hitler will arise.

Someone should take that Hitler "Bunker" video that keeps popping up on YouTube and subtitle it so he's raving about the Kirsan/Karpov debate.

:-)

Yep, relative domination is a good point - we would need another list about biggest rating gaps between #1 and #2? Much was already written (elsewhere) about the current 23 point gap between Carlsen and Topalov - I think it is not [not yet?] that special in a historical context.

"Sensu CO", Karpov at his career peak would also be superior to the modern elite? Towards the bottom of the Chessbase article, there is a full list of all-time Elo highs: 67 players, all that ever crossed or touched 2700. #s 11-26 are all currently active world-top players, only then follow Bareev and Judit Polgar.
Unlike Fischer, Karpov continued playing and gradually went down on the rating lists. And we don't know how Fischer and Karpov would have fared in a match, would Fischer have been as dominant as the whopping 5 point difference in peak ratings suggests? ,:)

Well, let's all support Germany tomorrow against Argentina! ,:)
But actually Mig's posts might remain sporadic until the end of the Karpov campaign?

@"What happens inside the elo system: Is there inflation, and if so what drives it?"

Murphy's Law, if something can go wrong it will

@"the results may be significant for certain things, like for example adjusting the rating requirements for the international titles."

The only way to solve this is to create objective standards for the title.
For instance each wannabe GM should win a match against Fritz, with the software set to play at, say, 2600. ELO.
An "official" software is to be chosen by FIDE (say Fritz10) and a fixed ply depth/move will be agreed-so it won't depend on hardware.
Such a strenght-standard will not fluctuate with ELO inflation, to the contrary will help us to correct the ratings for inflation.

> Such a strenght-standard will not fluctuate with ELO inflation, to the contrary will help us to correct the ratings for inflation.

The problem with such a fixed standard is that the strenghts and weaknesses of the official program will be studied to the extreme ("How to beat the 2600-rated Fritz for dummies", with players adjusting their style accordingly. So what starts out as a strong challenge will become easier over time.

> Bur not easier and easier over time, it will stabilize after few months.

Since it's a "neutered" version of the program, there will be hardwired flaws, and as the non-neutered version becomes stronger and stronger it will be possible to uncover more and more of these flaws (for example by having the fixed version version play the currently best version). So it won't be completely stable, but perhaps more stable than today.

Probably won't do anything to change the idea that today's grandmasters play "computer-like", though.

@in a couple of decades there will be so many IMs and GMs that the titles really will be meaningless for elite chess.

yes, the solution is another title, besides IM and GM there must be the SGM !(super-grandmaster)...this is merely another inflationist problem, they pop up everywhere (for insatnce the mass production of PhD holders by the US universities in last 20-30 years)

"@in a couple of decades there will be so many IMs and GMs that the titles really will be meaningless for elite chess."

We passed that milestone many years ago. At this point there is no solution within FIDE. Any change would upset those who've already "earned" these titles. So dump FIDE and start over. I'd dump ratings in favor of rankings.

Nobody "retires" from the FIDE Elo system, people only go inactive. Only when you die are you removed completely.

However, players that don't play rated games (at all), can't possibly influence inflation/deflation, so they are not an interesting group (most of the time) until they start playing again, if ever.

The interesting group of players are those who play rated games, which also is the reason why I've anchored my estimates of nominal inflation to the rating development of _active_ players (of course, with "active" defined differently than the FIDE "active" flag... ;o)

"@in a couple of decades there will be so many IMs and GMs that the titles really will be meaningless for elite chess."

"We passed that milestone many years ago."

I agree with noyb and Ovidiu, but don't see the problem or the need for radical changes. Currently, a GM title means
- some sort of conditions in open tournaments, at least east of the Atlantic Ocean
- maybe a better chance to be invited, and a higher salary for writing newspaper chess columns?

Basically that's it!? For prestigious tournament invitations, selection for team events, ... Elo and ranking is already the decisive factor - plus other considerations (playing attractive chess, having a skilled manager, etc.).

"Any change would upset those who've already "earned" these titles."
Here I don't understand the scare quotes. Becoming GM or even merely IM is still an achievement - I guess most of us wouldn't succeed, or haven't even tried! One might argue if these titles should be awarded for life, but again what's the problem about GMs that couldn't confirm, or at some stage fell below Elo 2500?

Frogbert: "My observation is that you've made dozens of observations more profound than this one. How a rating from nearly 40 years ago can show "superiority to the modern elite", regardless of the relationship between the actual numbers, is way beyond me - unless you're talking about relative domination. But in that case we need more than Fischer's rating; we also need to know that his rating was in a different stratosphere than those of his contemporaries."

Well, that's what I was alluding to.

My second observation is that CO is a big Fischer fan. :o)

An excellent (though obvious, and previously admitted by me as well on this site!) observation! :)

CO

Thomas: Yep, relative domination is a good point ... Karpov at his career peak would also be superior to the modern elite? And we don't know how Fischer and Karpov would have fared in a match, would Fischer have been as dominant as the whopping 5 point difference in peak ratings suggests?

Yes, I think Karpov was about unstoppable (since Fischer didn't try!) I think Fischer was the stronger, as Karpov's peak rating came several years after Fischer's (and I lived through it).

I also think this was probably the greatest match never played.

CO (more opinions than observations today)