Carlsen, Caruana & Yifan: a ratings analysis

In another thread, we were discussing Hou Yifan's rise to fame and the possibility of her rising to the very top of the FIDE ratings pool and eventually winning the world championship. So I thought to myself: why not investigate the likelihood of that happening? I went to the FIDE ratings website and downloaded the ratings progress data for Magnus Carlsen, Fabiano Caruana, and Hou Yifan. I then plotted their age on the x-axis, and on the y-axis, their rating in January of the year where they were that age. This is what I obtained:

It's interesting to see how the age progress curves of Magnus Carlsen and Fabiano Caruana, the top two male players, are nearly identical, whereas the curve of Hou Yifan, the top female player, is clearly different. Yifan starts out very strongly, but after about 13 years of age, her progress slows down considerably when compared to her male counterparts.

What conclusions can we draw from this? One possible explanation is that girls are known to mature faster than boys, giving Yifan an edge at a younger age. And one possible outcome is that Yifan most likely will never reach the level of Carlsen or Caruana.

Further conclusions and discussion are welcome.

It would be interesting to have some more women plotted against man to see whether women surpassing men at younger ages is a common occurence. 

I guess it's not - I searched for players born 2005-2015 and the no.1 girl right now would come 14th among boys.

I'm working on processing more data as we speak. The players have to be young (born in the 90's) so that there is enough data on the FIDE webpage to cover their ratings rise from childhood - so unfortunately, we can't use the data for Kasparov or Polgar. With some more data, it looks like Giri and So have rating profiles similar to Carlsen and Caruana, but Nakamura is a kind of late bloomer - Yifan is fairly much even with Nakamura when he was her current age, but she now needs to keep up her current rate of ascent for another seven years to keep up with him.

I'll look into more female data and I might post another graph soon.

Your country has made a significant leap in women rights in past 44 years.

"What conclusions can we draw from this"

Invalid data.  Put two socks in red dye liquid and one in blue.  What is the point?  Let's see purple.  Let's see how young players can compete with each other in the same pool without the separation.

Then you can go hog wild with your graphs.  Until then, you are just plotting skewed data points.

I would like to just add this picture from the other thread:

It was a very interesting and subtle way of going back to what I believe should be obvious as to why some "people" perform better than others in things like board games. It is all about the individual, not about the sex. Of course, I believe people aren't born sexists. It is a conditioning result of their environment which leads to social prejudices. I believe we can all choose to negate our own ignorance and prejudices by trying to do so:)

What separation are you talking about? The top players of each sex play in the same tournaments.

Add Wei Yi.

That was sad.

No they don't.  This thread is getting ridiculous and absurd.  Now you have other people showing brain scans of bipolar and depressed people to validate differences between gender?  Serious?  I hate to win logical debates when people use weak evidence as if it were the strongest.

If you want to show differences, then show me a rating which represents ONLY both genders.  None of this separation.  There is a separation, just look.  Open your eyes.  Gibraltar had Nakamura and Hou Yifan.  This wasn't 1 tournament with mixed players.  Did Nakamura even play Hou Yifan? Nope.

She didn't lose to Svidler Howell or Rapport (or anyone else for that matter).  She beat Rapport. 

Let's graph that and see where she lies.

Well, as promised, here's more data. This time, there's five from the top ten of each sex, with males depicted in solid lines and females in dashed:

We can immediately see that Yifan's early rise to fame is not a female characteristic, but rather a fluke. We can see a striking uniformity in the profiles of the top male players, with the exception of Nakamura; the top women are likewise comparable to each other, with the exception of Yifan. One new thing that we can notice is what happens to women players at around 2500-2550 rating points (and not to male players): for Yifan and Humpy, it's where their rise slowed down considerably, and for the others, it seems to be some kind of limit. If Yifan's rating profile becomes further similar to Humpy's, it will manifest in an inability to increase her rating much further - it will be interesting to see what happens to Yifan in the future.

It's subtle so I think I should explain it to you. The graph of the brains is a way of showing personality types. By no means the only way, of course. By adjusting one's thinking from the sexes to the individual personalities I believe you will get closer to the truth of the matter concerning high performance in competitive fields:)

Sorry, I missed your post. Looks like Wei Yi is poised to become the next world champion:

10 data points is still nowhere close to statistically significant.

Here's another graph in your quest to compare brain and gender with unreliable data.  Let me know what your final "results" are.  I need to go listen to the weather forcaster because they will tell me the weather for tomorrow.

Well actually, that's about 12-15 data points per player, multiplied by ten players (11 with Yi included). So, over a hundred data points. And it's meant to provide an educated basis for discussion, not a scientific breakthrough.

True enough, and yet my point still holds up at any number less than 4-5 digits ;)...if you were posting these graphs and not following with conjecture, it would not be a problem.  

Anyone who is educated enough will know this smells....try to guess why.