What gender gap in chess?

by Wei Ji Ma
10/15/2020 – If you want to compare chess achievements between men and women, writes Professor Wei Ji Ma of NYU, given their vastly unequal numbers, it is a very bad idea to focus on the top male and female players. If you do you will need to account for the participation gap using an analysis similar to the one he presents. Prof. Ma supplies the tools needed to refute the theory of female inferiority.

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Long before fake news was a thing, there were articles about the supposed inferiority of women to men in chess. In most other domains of life, such ideas would be considered reactionary and repulsive; yet, when writing about chess, they are somehow not only acceptable but even mainstream. A few days ago, we saw the latest installment in this unsavory series: an article on the Indian website Mint, titled “Why do women lose in chess?” and reprinted here on ChessBase. Like so many of its predecessors, this article asserts a gender gap in chess achievement, and then speculates about possible contributing factors, such as male gatekeepers, lack of role models, and biological differences. It quotes GM Humpy Koneru as saying that men are just better players, “You have to accept it.”

In good tradition, the article is incredibly sloppy in arguing that there is an achievement gap between women and men to begin with. The author notes that the top two female players, Hou Yifan and Koneru Humpy, are ranked only 86th and 283rd in the world, that no woman has been world champion, and that the gap between the best female and best male player is 205 Elo points. These arguments are all variations on a common theme: whatever metric of top players you use, women are clearly worse than men. There is a huge flaw in this argument: to fairly compare an underrepresented to an overrepresented group, you should never use the top individuals. That is a form of statistical malpractice that wouldn’t stand in an introductory college course.

The Mint article starts out promising. It points that only 16% of the players registered with the All India Chess Federation are female, and states, correctly, “Fewer participants at the entry level results in fewer chances for the top slots.” It then promptly abandons this key argument while giving extensive coverage to folk psychology about “killer instinct” and “emotional sensitivity”.

A thought experiment

Why is this a key argument? It’s really quite simple. Let’s say I have two groups, A and B. Group A has 10 people, group B has 2. Each of the 12 people gets randomly assigned a number between 1 and 100 (with replacement). Then I use the highest number in Group A as the score for Group A and the highest number in Group B as the score for Group B. On average, Group A will score 91.4 and Group B 67.2. The only difference between Groups A and B is the number of people. The larger group has more shots at a high score, so will on average get a higher score. The fair way to compare these unequally sized groups is by comparing their means (averages), not their top values. Of course, in this example, that would be 50 for both groups – no difference!

Indian women play as well as men on average

At this point, you might think that this is just a theoretical argument – surely, when looking at chess ratings, it cannot be that simple? So let’s have a closer look at chess ratings. I downloaded the October 6, 2020 FIDE Standard rating list, selected all players of the Indian federation, and removed all junior players (born 2000 or later), since their ratings are often not reliable. I was left with 19,064 players, of whom 17,899 (93.9%) were male and 1,165 (6.1%) were female. The best male player was a certain Viswanathan Anand at 2753, and the best female player was Humpy Koneru at 2586 – a gap of 167 points. GM Koneru, ranked 15th among all Indian players, is the only female in the top 20. On the surface, these facts superficially seem to point to a gender gap in achievement.

They don’t. With our thought experiment in mind, let’s look at the full rating distributions of male and female Indian players. They look like this (binned from 1000 to 2800 in bins of 50):

The huge discrepancy between the blue and orange lines reflects the participation gap. To compare the distributions more easily, we change the vertical axis from number of players to proportion of players (within each gender):

The line for female players is more jagged because there are fewer of them, but other than that, these two distributions don’t look radically different from each other. Indeed, the average ratings of men (1434) and women (1466) are comparable. And averages are the fairer metric for comparing men and women.

Is 167 points an unexpectedly large gap?

But this does not answer our questions. Is, for example, a gap of 167 points between the male and female top players unexpectedly large? To answer this question, we are now going to look at all ratings as a single pool, dropping the gender identifiers altogether. We then randomly draw 17,899 ratings from this pool. These form the “overrepresented” group, and the remaining 1,165 ratings form the “underrepresented” group. These numbers are exactly the numbers of male and female players in our data, but we have instead created completely arbitrary groups with these numbers of individuals. We record the top rating in both groups. We repeat this process 100,000 times. (For the aficionados: we are following the logic of permutation tests.)

Guess what? The difference between the top ratings in the Overrepresented and Underrepresented groups is a whopping 153 points on average (with a standard deviation of 93). Again, remember that these groups are completely identical to each other except in their number of individuals. The mere fact that the underrepresented group constitutes only 6.1% of the population causes a large difference in top ratings. In this light, the real gap of 167 points could easily be due to chance instead of due to a real difference between women and men, just like the gap in our thought experiment. It is that simple.

Other widely used metrics don’t show evidence for a gender gap either. For example, based on participation alone, one would expect only 1.2 female players in the top 20 overall. So Humpy Koneru being the only female in the Indian top 20 is completely in line with statistical expectations based on the participation gap.

Conclusion

We conclude that at least among non-junior FIDE-rated Indian players, there is no evidence that the “achievement gap” is anything but a participation gap. That is not to deny the first-person perspective of top female players, who might feel that they have reached a personal ceiling in their performance. But statistically, there is nothing to suggest that top female players are underperforming given the overall ratio of female to male players. In fact, taking into account the systemic injustices and biases that they had to overcome to get where they are, they are likely overperforming.

Take-aways:

  1. If you want to compare chess achievements between men and women, given their vastly unequal numbers, it is a very bad idea to focus on the top male and female players.

  2. If you insist to focus on the top players, you will have to account for the participation gap using an analysis similar to the one presented here. Just a casual remark won’t do it!

  3. Even if, hypothetically, you were to find a gender difference based on average ratings (rather than top ratings), you cannot jump to the conclusion that that difference is due to innate or biological factors. The first place to look would be systemic disadvantages and stereotype threat experienced by female players.

The statistical arguments presented in this article are elementary enough for an introductory statistics class in university. In case you want to repeat the analysis for different countries, you can check my Matlab code for the details. If you prefer to read a published paper, look no further than this excellent paper by Merim Bilalić, Kieran Smallbone, Peter McLeod, and Fernand Gobet (2009). (The free PDF can be found through Google Scholar.) Its title is the first question everyone should be asking: Why are (the best) women so good at chess? And everyone’s second question should be: How can we reduce the insane participation gap?

About the author

Wei Ji (also Whee Ky) Ma is a Dutch FM rated 2324 and a Professor of Neuroscience and Psychology at New York University. He previously explained for Chessbase how a “genius culture” in chess might contribute to excluding women.


Wei Ji (also Whee Ky) Ma is a Dutch FM rated 2324 and a Professor of Neuroscience and Psychology at New York University. He previously explained for Chessbase how a “genius culture” in chess might contribute to excluding women.

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Kekskonsument Kekskonsument 2/14/2021 09:58
Excellently worked out. No more wondering about that gap! :-)
Vibov Vibov 2/2/2021 11:53
"Why isn't it fair to look at the best players? Say you have a nation of 10 states. Each state has the same population and the same amount of people playing chess. Now the chance that the best player in the country will come from any particular state is much smaller than that it will come from one of the other 9 states, but certainly, each state will have 10% of the top 100 players, on average?"

Fine, let's use your example as a starting point.
So, let's say that your state, call it state A, got 10 players into the top 100 - as you'd expect. And the rest of the country got 90 players.
So far so good.

Now, I'd expect the 10 players from state A to have a similar average rating to the 10 players from state B - and the 10 players from state C - and 10 players from any other state.
Which means, your 10 players should have a similar average rating to the remaining 90 players from the rest of the country combined.
In fact, you'd expect them to be equal - some randomness notwithstanding - because why not; there's nothing inherently special about state A.

But what happens if we compare the average rating of top 10 guys from state A - against the average rating of top 10 guys picked from the rest of the country?
Your 10 guys are all you have, you can't improve on your selection.
But I do: I get to pick the best 10 out of my 90.
The entire 90 had the same average as your pack. BUT, since we're only comparing the 10 best ones now - I'm getting rid of the weaker 80. Meaning my average rating jumps up!
You have one state champion, and I have nine, plus the best runner-up from one of my nine states.
Suddenly, the rating gap.

And there's still nothing special about state A. You'd obviously end up in the same spot whichever state you'd pick at the beginning.

Note: I'm not commenting on the subject itself. I don't see author's point to be as conclusive as he seems to think, but that's another story. I only commented on this particular aspect of statistics
Avendesora84 Avendesora84 12/28/2020 03:35
It's amazing how even after an entire article detailing how much influence participation rates impact the probability of a top-rated player appearing in a given group... there are still block-headed commenters completely ignoring it.
Avraks Avraks 11/14/2020 11:48
Why isn't it fair to look at the best players? Say you have a nation of 10 states. Each state has the same population and the same amount of people playing chess. Now the chance that the best player in the country will come from any particular state is much smaller than that it will come from one of the other 9 states, but certainly, each state will have 10% of the top 100 players, on average? If not, where do all the top players come from?

Now, if 10% of the people in our nation were women, and they all lived in the same state without any men, would it be unreasonable to expect that they had 10% of the top 100 chess players?

If the average rating of the genders is the same, but there are far more male champions, then that seems to indicate that female players are from the right tail of the female chess talent bell curve?

Maybe I'm missing something, or maybe the stereotype this article went furthest in killing is: Asians are good at math.
Thejollydodger Thejollydodger 11/3/2020 11:12
This is a simple example of ignoring genetics.

Men have the XY dichotomy which means that they do not have the inherent genetic error correction that women have with their XX configuration.

This is why men are 90% more likely to have genetic variants and defects then women have.

Intelligence is a genetic variant thus you will find in intellectual pursuits 10% of men will out perform the best women just as 10% of men will under perform against the worst woman.

Woman rule the averages and as such women on average will be smarter then the average man but men will dominate the extremes.

To play with the averages in a very poor and pathetic attempt to ignore this known and highly documented fact is either intellectually disingenuous or very ignorant.

This is a very poor academic stand but to be expected in our postmodern world.
KlumsyK KlumsyK 11/3/2020 01:19
Yeah most of the NBA is black also because of "participation bias". Keep licking that progressive boot - theres a prize in the center of it
IraGraves IraGraves 10/31/2020 12:37
It is uncomforting that the author does not hide his strong bias towards "political correctness", yet claims to present a scientific argument. No wonder that, as others have already pointed out, the statistical argument presented is invalid.

I reproduced the distribution presented by the author in Excel with the current FIDE rating list. The excel file can be downloaded here: https://ufile.io/3wm8jirb

Using the excel file, you can choose any other filter conditions or just take the whole world and all players. The ELO gap in the data is then simply undeniable. For example, the curve for Germany simply shows a clean bell-curve-like distribution with the female curve being around 200 elo below the male curve (140 for non-juniors). The curves for other federations vary, but allow similar conclusions.

One can only conclude that the author cherrypicked "Indian non-juniors" and then tried to rationalize this by saying junior ELO would be unreliable and that he had been working with Indian data in another project and therefore picked this country. If he had been interested in the truth, seeking that he went to great lengths to code his statistics tool, it is very hard to believe he didn't also try other filter critera and just neglected the rest of the FIDE rating list he downloaded. However, also for Indian non-juniors the author simply fails to present any argument why woman are underrepresented at the top. It is just sad that a professor would argue in such an obviously biased way neglecting any counter-evidence.
Britex Britex 10/29/2020 05:23
Rather bizzare that a professor of psychology is either unaware of greater male variability ; or unwilling to mention it, when this is clearly what is at hands ; and that he would suggest that ''you cannot jump to the conclusion that that difference is due to innate or biological factors. The first place to look would be systemic disadvantages and stereotype threat experienced by female players'' when this is precisely jumping to conclusions, except in the other direction.

''If you want to compare chess achievements between men and women, given their vastly unequal numbers, it is a very bad idea to focus on the top male and female players'' What is this supposed to mean? It could very well be that a gap between two groups is mostly found at the top level rather than as an average gap constant at all levels, and in that case you'd obviously want to focus on the top echelons.

Also, there's a dullard down here in the comments linking to research on IQ, and saying that ''... Eysenck and Jensen's IQ studies back in the 70s, but has lately added a veneer of pseudo-scientific sophistication'', when this is exactly the kind of comment one makes to give himself a veneer of credibility and intelligence, when one is completely devoid of it.
isgodahypocrite isgodahypocrite 10/29/2020 04:55
Lol no, you are just in denial because people like him and you got called out with actual facts. You are undermining the efforts that other people put into chess just to make yourselves feel better. Other people achieve high ELO ratings by putting a lot of time and efforts into it, be it a man or woman that doesn't matter. But people like you will always find a way to drag them down to your level because you could never achieve that? ya, fuck you. Like I said before, it doesn't matter what your gender or race or country you are from. In the end, what matters is how much you put into it. Get that through your thick skull and stop pretending you don't have basic human level comprehension ability.
rosa_luxemburg rosa_luxemburg 10/29/2020 02:59
the level of saltiness in this comment section is amazing 😂 who knew there were so many dudes with fragile egos?
Robvalkeneers Robvalkeneers 10/28/2020 09:08
We could put this hypothesis to thé test by eliminating the participation Gap. I take it there are countries where chess is obligatory in schools for both boys and girls. However, this might still not resolve thé issue: last time i checked, i believe until puberty boys and girls did equally well (or girls outperformed boys). After puberty, thé gender gap became more apparent (for whatever reason). This might also be explained by a more extreme distribution of chess talent in males...i believe this is also thé case with IQ/math tests, there are much more males with an extreme low score than women, but also males are over represented in thé group with extreme high scores....on average men and women have thé samen average scores, but males are more extreme...At least that might be thé case
interested_reader7717 interested_reader7717 10/28/2020 07:15
Downloading the full dataset used by the author and running the author's code provided without choosing only non-junior players from India (i.e. running the author's code on the full dataset) yields the following averages:

mu_M =

1677.62758064466

mu_F =

1509.05114157645

That is to say, a discrepancy of ~170 rating points on average. Quite similar to the discrepancy in rating points between the best male player and the best female player (~190 points). A quick check of the standard deviation and higher order moments suggest the distributions are very similar in other regards (std_M = 345, std_F = 339).

It would be interesting to hear the author's comments on this. Thanks for providing data + code, always preferred to black box papers.
dimia dimia 10/28/2020 05:16
What kind of article is this? by a college professor and Chess player?

"A thought experiment
Why is this a key argument? It’s really quite simple. Let’s say I have two groups, A and B. Group A has 10 people, group B has 2. Each of the 12 people gets randomly assigned a number between 1 and 100 (with replacement)."

randomly assigned?!?!?!
ELO is randomly assigned?!?!?
since when is ELO randomly assigned?
The top Chess players above 2700 have dedicated COUNTLESS hours or hard work and practice to achieve that level

How about the NBA, why is nobody questioning the race gap between black and white players?
You say that the black players are biologically better than the white players?
Isn't that racist?

I dare the author to post an article about the race gap in the NBA, saying the exact same things about numbers and statistics as he did in this article
M19938 M19938 10/28/2020 03:51
Psuedoscience, start to finish. What are the ages of the Indian women vs. Indian men they're playing? What region of India, a poorer one or a richer one? Is India a 1:1 microcosm of the global experience, excluding economic factors? Excluding all other factors? Over what period of history? How promoted is chess in India for women vs. men in school or as an extracurricular activity? Now that chess from 0-<some relative, elementary FIDE rating, likely 2000> is largely studying, openings and "solved" positions, are women gaining representation because they're more academically inclined than men, (as is arguably statistically proven globally)?

I'd love to believe women have the natural talent to be as represented as men (globally) in chess, too. Chess needs more players and more diverse demographics, but this article is absolute bunk, start to finish. He's grabbing attention by appealing to a controversial topic. Only desperate scientists do that. Thrown out the window.
isgodahypocrite isgodahypocrite 10/28/2020 03:33
While there is no basis for gender influencing gameplay, the argument you present is completely invalid. In order for women to participate more, they have to like the game first and there is nothing you or I can do about that. If they don't like the game, that's their choice. You try to make this a statistical argument but the base of your argument is rendered invalid by this simple fact. Gameplay has nothing to do with gender but that does not automatically imply that if more women played the results would automatically get better. The reason is, people tend to do things they will enjoy. It's basic human instinct. If there are suddenly 10 million more women playing chess, you cannot simply assume they are going to be better than Judit Polgar. That is not how it works. You have to put efforts in it. How you do depends on how much you are willing to put into it, not on gender or race or geography or anything like that. It's as simple as that. I do not know if you did this intentionally, but your whole argument is invalid at this point. Men are not biologically better does NOT imply more women participation = better results. And I did not even go into the validity of the tests you are using here. Usually, your test would probably hold true. But this is not a case where you can assume every event is equi-probable. I have no idea how you did not even state that in your article. Given that you are into stats, I am fairly certain you have an idea about probability and yet you chose to ignore that completely. It's not that gender makes men better. Most likely men put more effort into chess than women and that's what makes them better, not gender. How do you not even consider something as basic as this?
Lemocl Lemocl 10/28/2020 02:54
Brilliant article, the belief that men are somehow biologically better than women reeks with sexism and pseudoscience.
javfer42 javfer42 10/18/2020 08:09
As pointed out by @rls53 , the conclusions do not seem to generalize to other countries: https://medium.com/@josecamachocollados/the-gender-gap-in-top-level-chess-15591d8990ba
IntensityInsanity IntensityInsanity 10/17/2020 08:29
My point: the men-women gap is just the tip of the iceberg. There are strange things going on. Are certain ethnic groups better at a certain thing? Or are there simple socio-economic reasons? There's much to learn and discuss. Let's not label everyone a racist. Let's remove ourselves (our gender, race, ethnicity, etc) from the argument and think objectively.
IntensityInsanity IntensityInsanity 10/17/2020 08:28
Folks, there are many strange groupings in chess. We keep concentrating on men and women. Yes, it is strange why men have better results. There are several theories, all of them, if presented well, could appear to be valid. The one in this article is a good presentation of one of those. I have heard other arguments, about women biologically (child birth, not having the 'killer' instinct, etc) being inferior to game of chess - again, I have heard this presented well and it can also be convincing. Let's not automatically label someone a racists of chauvinist. For instance, as a kid I took TaeKwonDo. All instructors used to teach us that this is a great sport for women - since it is an attack-based style with kicking being predominant. I was thought therefore, that TaeKwonDo is specifically good for women, because they have more hip power than men. This never appared 'unfair' to me as male: if women had stronger hips, so be it, good for them. This did not offend me in any way.

Now, let's go deeper. We have males and females in chess and all these theories. But what about other strange unexplained statistics? Let's take Armenia, for example. Currently, its population is about 3 million (according to Wikipedia). 3 million? And yet they have produced 1.5 world champions (Petrosian and Kasparov who is half Armenian). They have pretty much ALWAYS had a top 10 guy (Vaganian, Lputian, Aronian). How do you explain this? Such a tiny country and yet such representation in the chess world? So, understanding THIS is similar to understanding the men-women gap in chess.

How about Jews? Aren't like half the world champions in chess Jewish? And like at least a quarter of the top 100? Yet Jews are a tiny percentage of the world. How do you explain this?
paulo1176 paulo1176 10/17/2020 06:58
Exactly, @James Satrapa, it's the same arguments! It's really sad to see so many people here so affected and mobilized by a simple article defying prejudices. If we told Steinitz, Lasker or Tarrasch that and Indian would be chess champion in 2000's or told Botvinnik that a norwegian would be chess champion in 2010's, they would probably smile. The story told by @frederic it's so amusing because it provokes the same surprise, defying what could be taken for granted.

There are two questions that escape from deterministic arguments:
1) If there are a genetic, intrinsic difference, why there are a perception that the gap between males and females is decreasing? At the top, 100 years ago there are only Vera Menchik, 50 years ago, Gaprindashvili, and after that we have a myriad of strong female players 2) Why the gap is so different by country? Take not only India, but also Georgia, for example.

Many years ago, I read a french chess magazine that interviewed chess trainers and they said they observed no difference in performance or participation at early ages, but a great exit of girls at adolescence age. I'd really love if @Frederic could share his theory with us. Congratulations to @Frederic and Chessbase team for one more great article.
KingMatti KingMatti 10/17/2020 05:41
"Incidentally you guys might be interested in a not directly related quiz question: how would 19-year-old Katie Ledecky fare in a swimming contest against Johnny Weissmuller, the greatest swimmer of the first half of the 20th Century? Etc."

With all due respect, this is idiotic! The comparison. It`s called anachronism. Is it really because female swimmers are as good as male swimmers? No, of course not. Why would you compare current top female to past top male anyway? If not for the desperate religious equality motive...

Explanation: development of better swimming technique, better swim suits, better swim science!
Also, the competition for female swimmers might be tougher now than for males back in the day.
With similar logic, one might say Hou Yifan is better player than Steinitz and therefore the gender gap is an illusion. Just nonsensical waste of everyone`s time. Humpy Koneru is a great player since quality of play in chess correlates strongly with objectivity of reasoning. She can admit the fact.
James Satrapa James Satrapa 10/17/2020 02:06
I come across this kind of thing when there are supposedly serious discussions about the relative intelligence of white people versus people of colour. It is always a bandwagon for white supremacists and "scientific: racism that has been going for a lot longer than Eysenck and Jensen's IQ studies back in the 70s, but has lately added a veneer of pseudo-scientific sophistication to prove that whites are the smartest, whatever that means.

Many of the comments below show there is no real difference in this form of racism (aka sexism/misogyny) where butt-hurt male supremacists rear up and proclaim that the findings of people like Wei Ji Ma can't be true, either just because (ie the evidence is obvious that men are better chess players), or because they have scientific proof he's not being scientific.
kamamura kamamura 10/16/2020 04:29
But the situation could be already so dire, and the patriarchal miasma of hatred and hostility so entrenched in the chess culture that those measures won't be sufficient, and women will still seem (on the surface of, based by vulgar statistics of results) to play worse on average. Then it's time to factor in other criteria - historical burden of oppression, centuries of psychological scars inflicted in the fight for recognition and equality, and proclaim any game reaching move 40 an automatic win for the female player. Or move 30, 20, 10, as necessary to correct the statistics to reflect the universal Truth we entered our very objective research effort with:

Women are equally good in chess as men.
kamamura kamamura 10/16/2020 04:28
Are you sure you want to involve scientists in this noble quest? Scientists are grumpy, humorless people whose conclusions have one problematic feature - they are often reproducible. The law of energy preservation is annoyingly universal, for example. Black stays black, white stays white, so to speak. On the other hand when you want to prove that black is white and vice versa, it's a task more suited for a lawyer... or an agile salesman. Once we leave the depressing world of dry statistics that keep repeating the same "wannabe" fact - that women, on average, have much worse results in chess, we can find optics that will paint us a different picture (according to the political demand).

For example, considering all the supposed toxic masculinity, bullying, sexual advances, objectification and improper humor women have to (allegedly) fight in chess clubs, we could start by counting all drawn games between men and women as victories for the female players. Because is it not a victory in itself, endure such hostile (allegedly) environment, and manage to muddle through to an inconclusive result! A heroic achievement, I say! And whenever a female draws with a female, both could receive full point as an expression of the ability of women to overcome strife and cooperate towards a common goal.
Jozef Pronek Jozef Pronek 10/16/2020 03:20
@combinatorialist

Not everything is a conspiracy. It's well known that FIDE doesn't include all players (e.g. there used to be a minimum entrance Elo, inactive players are difficult to get hold of) unlike the German chess federation, which has the records of all players. This is implicitly mentioned in the paper:

"Given that almost all German tournaments are rated, including events such as club championships, all competitive and most hobby players in Germany can be found on the rating list."

For more explicit differences between the German and FIDE databases, see this paper:
https://www.frontiersin.org/articles/10.3389/fpsyg.2014.00569/full

@rls53

There are quite a few comparisons, one would need to adjust the alpha levels because of that. Even that is probably not the best way to deal with the issue (assuming one sorts out the problem with the FIDE database mentioned in the linked paper).
fgkdjlkag fgkdjlkag 10/16/2020 03:03
If the analysis below shows that the case only applies to India, then the Indian data needs to be looked at more closely to see if there are any aberrations, and if not, then I disagree with one of the below commenter's conclusions, and submit that if median female rating in India is higher than male rating, then it suggests that it could be the case anywhere. I don't know of any special advantage that females should have over males in India.
So in other words, the direction of the data seems to be that there is no advantage of males over females and that the only special case may be at the tails.
This could fall in line with other research showing greater variability in male performance than female performance.
Frederic Frederic 10/16/2020 11:44
@rls53: Thanks for the work you did, and the effort put in. That is the kind of discussion we like to see, not just name-calling and pejorative adjectives. Scientific dialogue can be fun as well. Incidentally the initial reason Weijii Ma used data from India was because he was evaluating an article from the Indian website Mint, which had used data from India.

After corresponding with, personally observing and in some cases looking after a number of players: Zsuzsa, Judit, Sofi, Kartyna, Elli, Humpy, Tania, Anna, Zhu, Alexandra, Pia, Alexandra, Ekaterina, Almira, Lilit, Padmini, Peng, and many others I have a theory that there is one factor contributing to the gap between male and female performance at the highest levels that is consistently ignored. If I am feeling brave I will share it at some stage with you guys on our news page. Weijii (who is no relative of Yo-Yo, as I have ascertained) thinks it is "speculative", but many top female players agree and supply me with personal data. Give me some time...
countrygirl countrygirl 10/16/2020 10:53
Interesting article, I must brush up my stats and try to analyse it in detail!
But one point immediately occurs: the casual allegation of "systemic disadvantage" at the end is false. At least today it is. All chess clubs are happy to welcome members or competitors of any age, sex, and race, while with internet chess there are no restrictions based on sex. On the contrary, women have many more options than men: women get to choose to enter all-female competitions AND all other competitions (opens). All comps are open to them.
Katica Katica 10/16/2020 10:01
Very nice explanation, especially for those who are not familiar with statistics. However I need to add that the distribution of ratings shows a clear skewness to the right, for which mean is not an appropriate measure of location. Median would be more suitable in this case, which would also be in line with the current findings.
wethalon wethalon 10/16/2020 08:56
@rls53: thanks for redoing the analysis for other countries! Send me an email if you’d like to discuss; I have a few things to say. - wjm
combinatorialist combinatorialist 10/16/2020 08:54
The author's primary contention that the available data should be analysed properly is extremely welcome. I think ChessBase would do well to avoid a plethora of unjustified "opinion pieces" on this issue in future.

However, the author's decision to use the data from India only - an egregious example of sample selection bias - is rather detrimental to his argument (and sadly also to his academic credibility). As @rls53 points out, analysis of more extensive data would likely lead to more nuanced (and more globally scientifically valid) conclusions, while still demonstrating that a significant amount of the variation in performance is simply due to participation rate.

[Equally, it's unclear why the Proc. R. Soc. B paper considers German data only. The paper doesn't appear to present a reason (surely a primary requirement in statistical analysis). Sadly, (deliberate or unwitting) sample selection bias is a serious problem even in published peer-reviewed papers.]

To reply to @fche: Yes, when looking at the top rating gap, the discussion *does* (temporarily) assume that the rating distribution is independent of gender. It then asks the question, "Is the data consistent with this assumption?", and determines that the answer is "Yes" for India.
patzer420high patzer420high 10/16/2020 06:17
Have to agree with Frederic on this one. And the degree to which preconceived notions blind some people to basic statistics and science is amazing to behold.
royce campbell royce campbell 10/16/2020 06:02
@Frederic: Thanks, and I hope you didnt infer that I was complaining or judging. I just found it interesting! Cant blame you at all!
saturn23 saturn23 10/16/2020 04:24
In my opinion men are better in disciplines that require very hard work and full dedication (even obsession). The reason for this is that men have some biological advantages compared with women: better stamina and ability to focus for long periods of time (among other things). That's why men dominate chess, mathematics, physics and other sciences. Kasparov used to say that the ability to work hard is a talent.

Judith Polgar is frequently given as an example that women can play as well as man because she was a top 10 player at some point. But the truth is that her peak rating (2735) has been matched or exceeded by at least 50 players in the modern chess (she is number 53 according to wikipedia). We also need to acknowledge the fact that she consistently played in top tournaments (the privilege of being the strongest female player). She consistently received invitations over many higher rated players.

Just like some animals are naturally stronger and faster than humans, men are better equipped by nature to play chess than women.
rls53 rls53 10/16/2020 03:04
I believe the problem with this calculation is that the results hold only for India – they don’t replicate with other countries.
I downloaded the data and repeated the calculations described by Professor Ma. For India, my results agree with his. Another way to present the results is the proportion of permutation samples where the male-female difference is greater than the real data – what statisticians call a p-value. In this case, the p-value is 0.39. Statisticians usually regard a p-value of less than 0.05 as "significant", but the result for India is consistent with random permutations.
However, same test for Russia, the difference between the strongest male and female players is 230, p-value 0.0006. FIDE lists Kasparov (2812) as the highest-rate Russian player, but if we base the calculation on Nepomniachtchi (2784), the p-value is still 0.003, which is still "highly significant". For Russia, regardless of whether Kasparov or Nepomniachtchi is the male reference point, the difference cannot be explained by random permutations.
I repeated the calculation for several other countries, with p-values: China, 0.04; USA, 0.007; Germany, 0.023; France, 0.016; England, 0.12; Netherlands, 0.01. Only for England does the p-value exceed 0.05.
I also made the calculations for the tenth-highest male and female players rather than the highest - this is a more "robust" calculation that is less susceptible to outliers. However, the results are still significant (except for India) - for England, in this case, the p-value is 0.0015.
What do I learn from this? Maybe India really is doing something different, for example getting girls involved in chess at a young age. But the general hypothesis advanced by Professor Ma does not stand up to close scrutiny. If his explanation is correct, it should apply to many other countries and not just India.
SimonReinhard SimonReinhard 10/15/2020 11:52
Regarding such factors, it has been well-known in Psychology that self-perception and the idea of one's potential can significantly influence people's performance. A famous example is the math test for seniors study: Two groups of seniors, both chosen to have roughly equal basic mathematical ability and educational background, had to do a math test. One group was told that seniors usually/often have a decline in cognitive ability and that it was expected that they would not do well. The other group was told that there was no reason that they should not get a high score. What happened? The first group scored 30% worse in the test. As far as I know, these results can be reproduced. So, if such effects exist, then it does not seem impossible that the absence of a female world champion and the lack of female top players(and other factors) also have a detrimental psychological effect on many young female players. Not all, for sure, but enough to skew the distribution again, in addition to the unequal numbers of participants.

All in all, a very tricky subject, but I hope that soon another Polgar or an even stronger female player emerges. It would be exciting to see :).
SimonReinhard SimonReinhard 10/15/2020 11:52
I welcome it very much that the author has taken this approach. It has been my opinion for quite some time that before analyzing other factors one should first take a close look at the different numbers of men and women playing chess.

In my opinion it is a fallacy to only look at the best players and, based on that, to claim that a higher potential of men to be good at chess exists.

To the contrary, if one takes the approach that basically every player, male or female, has a certain chance to have a certain rating (some probabilty distribution) and that higher ratings are rarer, then the whole situation can be compared to a lottery or a drawing of lots. If the set "men" has more lots than the set "women", then obviously the chance will be higher that some of the "men" lots are from the highest categories, even if (what I deem a natural basic assumption) men and women have the same potential to excel at chess.

A useful comparison would be: Take the ratio of women playing chess, which might be around 10%. Then check what happens if you take a random sample of 10% from the male pool and see what kind of distribution you get. If then there is still some discrepancy between expected distribution and real distributon, then the discussion can start inhowfar socially adverse factors contribute to that.
Jack Nayer Jack Nayer 10/15/2020 11:26
Okay, I read the article by Bilalic et al (all men by the way). There are potential female Firouzjas, but we do not know them because they do not play chess.
In this country, there are more female students in higher education than males. There are more females taking a masters than males. We have more female PhD students than males. There are female concert pianists, female CEOs, female scientists, female bishops, you name it. I am not suggesting that everything is equal, unfortunately far from it. There are, however, very few females taking a PhD in mathematics. Why? Is it a lack of role models? What is a role model anyway? Is it the patriarchy discouraging their daughters to study maths? Is it society at large? How exactly does that work? What keeps young girls away from chess clubs? Is it discrimination or tradition? Could it be less innate interest? What explains the existence of the participation gap? As long as you do not explain this, you explained nothing.
fche fche 10/15/2020 11:23
> To answer this question, we are now going to look at all ratings as a single pool, dropping the gender identifiers altogether.

In what world is this a valid statistical transformation? It *presumes* that the ratings are independent of gender, which is precisely the proposition being analyzed. It's a circular argument.
Eric Boesch Eric Boesch 10/15/2020 11:12
This claim there is no gender gap in achievement at the highest level of chess beyond that which can be explained purely in terms of participation is simply wrong. The choice of India where the writer knows the #2 female chess player in the world comes from is pure cherry picking. If we suppose that a 6% participation rate for women is a global average, and that a priori distributions are the same, then it is easy to see that the expected number of top 100 and top 300 female chess players would be 6 and 18, not 1 and 2. If we accept the author's claim of no gender gap, the probability of just 2 of the top 300 being women, assuming 6% of all rated players are women and identical a priori distributions of rating, would be 1.6 out of 1 million. Whether there are innate differences, I don't know -- I just know that there is a gap in top level results beyond that which would be expected based solely on participation levels.