Carlsen is less than 20 points away from immortality.

so your saying someone like emory tate would beat magnus

@elubas: Look, I think we're 95% in agreement. I'm not talking about style, I'm talking about relative strengths. There are a lot of reasons why we might believe that such distortions are common. I mean, look at the tournament table for any club tournament, and compare it to a GM tournament table. It probably jumps out that GMs draw a lot, whereas club games are almost always decisive. You don't think that the positive correlation between draw rate and strength is going to impact rating? Of course it will (it may have a fairly substantial effect in the 1900-2200 range, where there seems to be a big uptick in the ratio of draws to decisive games).

I'd also point to guys like Morozevich, Aronian (in his earlier years), and Shirov, who'd gain tons of rating points whenever they entered a tournament with mainly 2500-2650 guys, but then lose them when they played Linares. Also, it seems very plausible that if Kramnik or Anand played 2500-2650 range tournaments, they might lose points due to their relatively high rate of draws. They're super solid, so I doubt they'd ever lose, but they just don't play a style that wins often enough to gain points.

Okay, that's just a handful of cases (which are speculative anyway), but to compound my sins with some anecdotal evidence, I find that I perform exceedingly well against inferior opponents. I'm rated about 1750 OTB, but I practically never lose to opponents rated 1550 -- I certainly don't draw half or lose 25% of my games with them. I win 95% of them.

But I often have trouble with opponents rated 1650-1750, and I do okay (about 50%) against opponents rated 1750-1850. I never win against opponents rated 1900 or higher. 

These results are independent of style or geography (I've played in MN, Chicago, and NYC). So from my own personal experience, I think the curve is nonlinear.

Note: I'm not saying that a 1750 opponent is easier than a 1650 opponent for me. It is almost always the case that higher rated opponents are more difficult. What I'm saying is that a 1750 opponent is not proportionally more difficult than a 1650 opponent for me, on average. This means that there's some sort of nonlinearity that ELO isn't capturing... 

Wijk is Wijk...can't really skip it, now can one?  Too prestigious.

No. How could you possibly infer that from what I wrote? That's definitely not what I'm saying.

We oughta get Josh Waitzkin to challenge, and beat him to teach him a lesson.

2900 will be the celebrity point.

3000 is the immortality point.

And Magnus will be immortal.

Hard to see him getting there without a little help from inflation.

There's a difference between what "many said" and what I said.  They were wrong and don't understand the system.  Then or now.  So, it's not really kosher to imply that people of the opposite opinion are just a part of some ignorant public mass that flip-flops on their opinions ;).

@Post#69: How do draw rates impact rating as you claim in the first paragraph? If anything a higher draw rate simply makes your rating more steady; it doesn't change the general trend of your rating.

Your personal case is interesting. Still I would say the fact that you don't do well against higher opponents is balanced out by your consistency against weaker players. Sure, why that is may be a slight mystery, but I would assess your general knowledge and skill to be as good as any other 1750, just in subtly different ways perhaps.

These kinds of things just don't convince me too much. Just think of how many times ratings predict exactly what happens -- beware cognitive bias. Even this world championship was beautifully predicted by the ratings -- the performance ratings of Anand and Carlsen were nearly identical to their actual ratings. Another easy example -- Carlsen is higher rated than his rivals; guess what, he does better at tournaments than them. Oh wait sometimes he gets second place... bad rating system, bad!

Oh btw, that reminds me. Remember all of those people saying Anand's "match experience" totally complicates things? And yet the rating predictions worked totally fine there. I think we are imagining more problems with the rating system than there really are. Maybe we don't like the idea of us being defined by a number, I dunno. Why don't we just admire how well ratings can do rather than look for every exception we can find?

Any "match experience" advantage Anand had was more than outweighed by the fact that his game has been in freefall for a while now...and this freefall is only partly reflected in his current ratings...the same way (but in the reverse direction), for example, that a 16 year old CM playing in the US chess league is always chosen as a team's 4th board, because their playing strength is actually higher than their rating has "caught up" to yet.  You can play the meta-game if you understand it, and exploit the ratings system to your benefit.  A player does not have to go the extremes of sandbagging to eke something out of the system, either.

Anand's rating should continue to drop over time (overall trend, there is will upticks and downticks).  Where the floor will be we don't know yet.  Anand is just a player on the downslope of his career.

@Elubas: Being an economist who spends his time constructing mathematical models, I'm pretty comfortable defining people in terms of numbers.  

I think you may be misunderstanding my point. I'm not saying that my rating is "wrong." I'm basically a fan of ratings, and I think that overall, they tend to do a good job (though more accurate profiles could be constructed than just one numerical value, if we used finer-grained analytical tools). In my case, to the extent that an overall number applies, yeah, 1750 is probably about right (actually, I'd guess I'm a little underrated). My point is that the overall number can be analytically coarse-grained, not that the rating was "wrong."

I mean, consider the perspective of a 1550 player facing me. Is 1750 going to give a good predictive measure of my success against him? Of course not. If I only ever played 1550 opponents, then my rating would be 2000+. Thus my rating against that group is effectively 2000+. BUT, if I only played 2000 rated opponents, then my rating would be 0. I agree that overall 1750 describes my performance, but you can't argue that it gives as good information as, say, a duple-rating would. If we just slice ratings into three parts: <A, B, C>, where A=rating vs. 1500-, B=rating vs. 1500-2000, C=rating vs. 2000+, then I'd have a profile of <2000,1750,0>. 

But the way you're talking, if my rating is 1750, then the profile should be <1750, 1750, 1750>. My point is that there are plausible reasons we can imagine why this wouldn't be the case (as indeed, it is anecdotally not in my particular case). This isn't just speculative. I'm not imagining up some unlikely individual with vastly lopsided abilities. I'm talking about myself. For example, if I were to only enter U1500 tournaments, I would have a rating of 2000+ today. That's gaming the system, plain and simple, by selecting opponents of a certain strength. I agree that this is probably not a huge general problem, and I'm inclined to think over a large population these differences tend to cancel out. But for individuals, I don't know why you'd assume these effects would be marginal. 

If we made a three-partition rating profile for super GMs, maybe we could say <A, B, C> where A=rating vs. 2500-2650, B=rating vs. 2651-2750, C=rating vs. 2750+, then I suspect we'd see some non-monotonic player profiles.

I wouldn't be surprised, e.g., if someone like Leko were <2700, 2750, 2725>, or if someone like Morozevich were <2900, 2700, 2600>. The point is that if someone's profile were thusly lopsided, they could use the fact that actual ELO ratings are a single numerical value to game that by selectively entering certain tournaments rather than others.

I suppose I "assume" these things to be marginal because as I said, chess knowledge will get you wins. Yes, I think it's strange that you might have a certain amount of knowledge but it works in vastly different ways depending on rating group, even though what makes a person better is their knowledge. We know there are exceptions; I'm perfectly willing to accept those.

I assume you are exaggerating when you say if you only play 1550 opponents, your rating would be 2000? Have you actually taken statistics of your results or were your numbers just guesses? If your results really are as you say -- you really do score 95% against 1550s (having played a sufficiently large amount of games against them too of course), and you do score as you say against 1900s and such, I'm genuinely intrigued. Those certainly aren't the kind of statistics in my games, lol.

Somehow I don't believe you would get to 2000 without improving but by virtue of only playing 1550 players :)

@Elubas:

Maybe exaggerating a bit to make my point, but I don't keep close track of my wins/losses from rated OTB games. I suppose I could start doing that. Eyeballing it, though, it can't possibly be far off. 

I'm reasonably sure I've never beaten anyone rated above 1900. If I have, it was maybe only one time. I think I'd remember if I had.

And if it's not 95% vs. 1550 competition, it's still something absurdly high and inconsistent with a 1750 rating.

Look, I agree with you that chess knowledge gets wins. But chess knowledge is not monolithic. There's endgame knowledge, opening knowledge, calculation, general principles, and subtler distinctions, so I don't know why it should be surprising that certain players might do better against players of other strengths. 

So one obvious example is endgames. If you're good at endgames, that seems like it will tend to help you against players of roughly equal strength, since you'll more likely to get into equal endgames against players of roughly equal strength more often than against mismatches (since you'll have had to keep things even through the opening and middlegame). That (plausibly) means you'll tend to overperform against peers. 

I find that I'm able to beat 1550 players fairly easily, because while they tend to be roughly equal to me in terms of calculating, they rarely have any positional sense, invariably placing pieces in some awkward place -- a knight on the rim, a bishop behind pawns of the same color. They don't pay attention to outposts and color complexes. Basically, if they were comfortable with those ideas, they wouldn't be rated 1550, and I'm pretty good at exploiting those differences efficiently, and nearly always end up winning comfortably. 

Against higher rated opposition, I am a lazy calculator and I don't study openings very rigorously, so I basically get stuck in a bad situation and lack the defensive skill to prevent it from getting worse and worse. That pretty much describes every game against a 1900+ player I've ever played. So, there are reasons to think that these things are plausible, since not all knowledge comes at once. 

Because advantages in opening knowledge are pretty useless for beginners, that knowledge isn't going to affect ratings until they get to a certain point. Likewise, between 1000-1500, it's really about being able to calculate simple 2-move and 3-move combinations. Strategy and position take a backseat. I mean, the heterogeneity is explicable.

And yeah, honestly, if I were just interested in getting a higher rating, I absolutely do believe I could top 2000 if I just restricted myself to playing 1550 opponents. Not sure how I could arrange to be in that kind of a situation, but that seems quite right to me, given my experience.

No one would argue that Elo ratings are perfect, and many alternatives have been proposed. However Elo has a certain historic impetus now.

We are talking about a simple statistical formula that works reasonably well for large sample sizes in a massive population. There will always be individual descrepancies, especially where personal experience is not one of exposure to a wider sampling of the population. To invoke the statistician's refrain: small sample size!

More mature local tournament players know well the experience of losing against lower rated players and taking a ratings hit - lower rated players who are young and improving so fast their rating hasn't kept up with their performance.

Elo *tries* to indicate future results based on past performance. But predictions are hard to make, especially about the future

You're making interesting points for sure. In my case I have had a rather different experience. It's funny: I consider myself a very positional player, like openings that are positional, and yet it still seems like whether I win because of tactics, positional play, endgames, even openings, are scattered all over the place. I certainly can't say like you that I generally beat lower rated players because of some particular area -- even though I try to play positionally, it seems like me winning due to a random tactical trick after an otherwise equal battle is just as common.

So I dunno -- I guess what fuels my opinion is that I've basically experienced the opposite. As I said I try to play with a specific style, yet the way I actually win might be totally different. It makes me think that while we all have different styles, it affects things a lot less than it might otherwise seem. It's like how they always tell you, do what the position calls for, not what you want to do. You may like to attack, but if the position calls for positional play, you do that. It seems like that sort of thing is what happens for me -- there are so many different ways I might win a game that there seems to be almost no order to it. And so my simplified conception of chess that chess skill is "merely" "not making mistakes" seems surprisingly accurate.

But... your experience is totally different. So that makes me confused lol. I guess it would be more useful to know the experiences of, say, hundreds of players rather than just me and you :)

@Elbuas: Fair points. Good discussion.  

Ciao.

"notice that great match players (e.g., Kramnik, Karpov, Petrosian) are not always the best tournament players, and vice versa"

I wonder if it isn't partly that players often are called great match players based on one event, while being a great tournament player usually means repeated top results.

Kramnik is called a great match player based on his match against Kasparov. That he performed below expectations in WC cycle matches against Anand, Shirov, Kamsky, Gelfand, Radjabov, Grischuk and Leko doesn't change this, but to me Kramnik's tournaments have been more impressive than his matches.

Petrosian won against the 52-year-old Botvinnik, but lost three of four matches against Korchnoi, scored a small minus in two matches against Spassky, and was beaten badly by Fischer. Still he is called a great match player, in spite of winning the Soviet Championship four times (Smyslov never won it) and the Candidates tournament in 1962.

Karpov won more tournaments than anyone else, and scored one of the most impressive results ever in Linares 1994. One of the greatest chess players ever, but I have no idea if he was greater in matches than in tournaments. Maybe he was, those matches against Kasparov were great achievements.

Topalov is one of the few players I'd say is of different strength in tournaments and matches. He is weaker in rapid/blitz than other top players, and since many matches and minimatches are so short he has lost several in rapid tiebreak. Because of this he often overpresses trying to avoid such tiebreaks, as in the title match against Anand. Maybe Larsen also could be seen as a tournament player, but it could just as well be that he always was weaker than Spassky and Fischer, and that this got more pronounced when they were the only opponent.

Good points. Obviously, matches occurring less frequently than tournaments, one needs only to win one or two very exciting/interesting ones in style to be declared a brilliant match player, whereas one needs to have a string of excellent tournament results to be called a great tournament player. The standards are different -- and rightly so.

I think Kramnik's match against Leko was not bad. True, he was expected to win handily, but given their similar styles, it was bound to be close. Being able to produce a win in the final round is reminiscent of Kasparov's feat in Seville. Also, Kramnik's win over Topalov really cemented his reputation as a great match player, I think. I think it's weird to put any of Kramnik's tournament victories ahead of his matches against Kasparov and Topalov. The latter are clearly the high water marks of his career (though there may be more yet to come).

Karpov is a bit mixed, right? Yeah, he has an outstanding tournament record, but a lot of these were mismatches, and the vast majority of them came in the 1970's and early 1980's, before he had to face Kasparov regularly, during which time his main competitor (Korchnoi) wasn't playing in the same events as him. I agree, Linares 1994 was an amazing achievement -- maybe the beset achievement in Karpov's career. 

Also, I don't think that Petrosian did badly against Fischer. Fischer bagelled everyone who came before Petrosian. Petrosian was the first player to seriously threaten Fischer, even taking a game off him, and to characterize it as a blowout is totally inaccurate. That was an intense and close contest up until the sixth game, they were holding even. I dunno whether it was bad prep or a collapse of nerves, but Petrosian just wilted away after that. But for more than half the match, he was definitely doing every bit as well as Fischer -- in some games clearly he was doing better. 

Also, I think it's just a comment on style. In a match, the primary goal is to lose as infrequently as possible. In a tournament, the goal is to win as often as possible. Solid defenders are thus regarded as having an advantage in matches, whereas double-edged attackers are regarded as having an advantage in tournaments.

@shockinn (((never say never)))

Daniel-Pi : in fact, Petrossian gave an interesting reason for his collapse against Fischer. You know that Fischer would always complain about everything when competing in tournaments or matches : scedules, boards, lights, drinks, spectators...
After the match, Petrossian said : "When Fischer wanted to play, I played. When he didn't want to play, I didn't play. When he wanted to drink coffee, I drank coffee. It might seem funny, but it isn't."