Carlsen, Caruana & Yifan: a ratings analysis

Leko

That's pretty close to what the real thing would say, kay(k)night, but you have to add, "...just sayin"

I'm getting paid to sit here and do nothing.

... and I'm an unemployed theoretical physicist. I need to keep my game on.

Anyway, I made a graph of the data you provided me, along with today's top male and female players for comparison. I didn't do any inflation correction, since Kramnik's rating would have risen off the chart. Here it is:

To me, this is disappointing. I always thought that Judit Polgar was head and shoulders above the other female players, but it turns out that she's about the same as Hou Yifan. Then again, we can't really accurately quantify the effect of ratings inflation, so we have to make our comparison with players around her age.

What is remarkable is that just like Yifan, Polgar also started with a high rating early on, but then fell behind the male age curves as she matured into adulthood, staying a consistent ~100 points below Kramnik. Another interesting thing is that we don't see the same asymptotic behavior with Kramnik and the others as we see with Carlsen and Yi; perhaps they didn't represent the very top of their age group, with the likes of Kasparov and Karpov still active around then.

Where did you get this data? It would be nice if we could go even further and get the numbers for Kasparov.

Almost. On page 3, I made a graph with an offset of 50 points for every eight years. That was based on an article in which the average rating of the top N players was calculated and found to increase at that speed during the investigated time period. It sounds like a lot, but even so, it wasn't enough to alter the results decisively with players who were around the same age. Naturally, inflation isn't a linear thing anyway, but it was a way of approximating the size of the effect.

If we use that same offset, Polgar gets about a 100-point bonus compared to today's young players. That would be enough to distinguish her from Yifan, but not enough to reach Carlsen. What's interesting is that with the same treatment, Kramnik is then elevated close to 2900 during his prime, making him about the same as Carlsen; the record of the games between these two is actually fairly even, even though Kramnik's current rating is clearly lower.

So, all we can do is speculate that Polgar was/is better than Yifan if there's a noticeable amount of inflation going on; if not, then they're just about equal players. Then again, the comparison between Carlsen and Kramnik indicates that some inflation must have taken place.

http://www.olimpbase.org/Elo/

It goes back to 1967.  You can get a zip file of all the data also.  With a little clever scripting you could probably automate this.

http://www.olimpbase.org/Elo/data/elo1967-2001.zip

Thanks! That looks like a lot of data, but clever scripting is in my job description; I'll look at it in more depth when I have the time. At first glance it looks like there isn't any data for Kasparov before 1979, when he was already 16 years old, so we can't get those crucial early years to clearly see whether there's any kind of asymptotic behavior. But his chart seems interesting enough: it looks like a fluctuating upwards curve similar to Nakamura's, and it even has some kind of inflation correction that seems to be equal in size to the one I've used (100 points over 16 years - I wonder where they got this from).

Apparently, Kasparov was a late bloomer when compared to Carlsen. It makes me wonder just how much better Carlsen is compared to all the others.

Back then I don't think players got elo ratings as young as they do now.  It was more of an exception.  Even with Polgar's age peers, most of them didn't get rated until they were 15/16 when Polgar and Leko were getting rated in their pre-teens.

Carlsen, Nakamura, Karjakin all had ratings by the time they were 11.  It seems were in a different era when it comes to youth chess.

At some point, you as a scientist will have to ditch your theory of inflation. 

In the mean time, Hou Yifan is indeed special, and the logical successor to Judit Polgar's crown. So yes, Polgar is special. That just shows how great Hou Yifan is.

Again though, you are using a very small dataset and trying to draw broad conclusions based on stereotypes. That isn't very good science.

+1.

I think dominance would be more accurate factor than just inflation. Also its not about best play but mental strength to maintain consistency and hunger to win and then win some more.

Anand has probably been the most consistent player in terms of rankings. Both Kasparov and Carlsen defeated him convincingly. While he is also convincingly equal to or better than other players in the playing field.Between Carlsen and Kasparov, it is hard to hand the baton to one. To me it will be Carlsen, because of his solid positional game, almost never letting an advantage go away, and very good defensive skills. But I have never seen Kasparov play live, so I could very well be biased. And he held the position of World No 1 amazingly well too.

Yifan too is far better than her contemporaries. And just like polgar, she can play at equal footing with anyone.

And from the rest, to me,  Fischer, Tal, Botvinnik and Morphy are all right up there, each for unique reasons.

Also Kasparov said Carlsen is like Karpov on steroids, who was equal to him in terms of mutual play. I guess Karpov on steroids must be better than your normal variety Karpov, so...

Kasparov and many other Soviet era GMs were held back from international competition and FIDE ratings until they were deemed ready. That's why Tal and others burst so suddenly onto the scene.

Yes, being "ready" definitely included being politically acceptable. Boris Gulko's biography is an excellent example of how the system didn't operate in the best interests of the players.

Discussing inflation: Probably it's not existing. For club players exist data of failure checks from 1500 till 2100. Elo has no inflation on this level. The higher ratings of the top players is easily explained by the grown number of rated strong players and knowledge effects. Accepting here this is under serious discussion the knowledge effects in content and methods are to see.

Well, let's get this matter on the table. It's not really "my theory", since it was brought up by X_PLAYER_J_X on page 2 with a high degree of sarcasm; also, it is used in that ratings archive from where SilentKnighte5 found the ratings I needed. I'm assuming that they use the same principle there as in that article which I cited way back, i.e. the offset of the average rating of the N top players. Also, I'm not adamant about whether this inflation exists and in what proportion; so far, I've been displaying data both with and without inflation correction.

The case for the existence of inflation is simple: a couple of decades ago, FIDE liberated the ratings registration process to include ratings below 2000. This means that a surge of players with low ratings entered the pool, "feeding" the ratings of the higher-rated players. This effect cumulates all the way to the top, but whether the effect is noticeable is not easy to determine.

The problem is that ratings from different eras are not comparable either way, because the pool of players is different. Therefore, this inflation correction would be viable only short-term, if at all. The only thing that can be analyzed with enough viability is ratings differences in the same time period, or what I'm doing here, the shape of the progress curves of individual players. Please note that these two things are completely unaffected by inflation.

My conclusions are not broad. I must have stated them before (page 6), but I can reiterate with more detail if you wish:

• Carlsen, Yi, and maybe Caruana are/were much better players than anyone else at a young age, and Yi's progress in particular looks promising (asymptotic curve);
• Hou Yifan has been facing a field of players better than her ever since she was about 13 (fluctuating curve);
• it's not impossible for Yifan to improve to the level of Carlsen & co., but that seems unlikely since nothing indicates that she's any better than Judit Polgar (comparison to curve shapes and heights of Carlsen, Kasparov, and Polgar)

That's all that I can say with enough confidence; you'll note that the last part is not definitive. As for the "stereotypes" that you mention, I don't understand what you're saying; are you talking about gender? Many people in this thread seem to make this a gender issue, but the only time I brought up gender myself was to point out that Polgar and Yifan had high ratings at a young age, which was probably due to the (established) fact that girls mature faster than boys. I do single out these two players, but that's because, as far as I know, they're the two best female players of all time, or at least the era that we can investigate; it should by no means be construed as an attempt to represent the entire female gender and its abilities. Like I said before: if you know of another female player who shows promise, please let me know and I will run this analysis on her.