Gender and Chess : : It's a Numbers Game

Sex Differences in Intellectual Performance
January 31, 2007

Apparently two professors (Christopher F. Chabris and Mark E. Glickman), have done a research study and concluded that:

"Only 1% of the world's chess grandmasters are women. This under-representation is unlikely to be caused by discrimination, because chess ratings objectively reflect competitive results. Using data on the ratings of more than 250,000 tournament players over 13 years, we investigated several potential explanations for the male domination of elite chess. We found that (a) the ratings of men are higher on average than those of women, but no more variable; (b) matched boys and girls improve and drop out at equal rates, but boys begin chess competition in greater numbers and at higher performance levels than girls; and (c) in locales where at least 50% of the new young players are girls, their initial ratings are not lower than those of boys. We conclude that the greater number of men at the highest levels in chess can be explained by the greater number of boys who enter chess at the lowest levels."

According to chessbase.com:

"Here are some highlights from the summary provided by Chabris and Glickman:

"There could be some innate difference in ability between men and women overall with respect to the skill required to play chess well. This difference in average or in variability need not be large; at the upper tail of the distribution where chess players operate for say spatial ability, a small difference would result in a large difference in representation. They call this the ability distribution hypothesis.
Discrimination could result in a difference in participation through different standards. However, they not that this is not a problem for this particular study because Chess rankings are objective measures. You can't discriminate against someone when their gender cannot be calculated into their performance.

"There could be a differential drop-out rate between boys and girls. Equal numbers of boys and girls with equal abilities could begin chess training, but fewer girls could see it through to becoming chess grandmasters. They call this the differential dropout hypothesis.
Fewer women could self-select to participate in chess. If fewer talented women choose to participate in chess in the first place, by attrition alone there will be fewer in the resulting grandmaster pool. They call this participation rate hypothesis.

"After examining the data Chabris and Glickman come to the following conclusions:

	Men and women differed in chess ability in all age groups even after differences like frequency of play (read: level of training) or age were taken into account. The disparity between men and women in ability exists at the beginning and persists across all age groups.
	No greater variance is to be found in men than women Ð if anything in most age groups women had a higher variance then men.
	Women and men do not drop out more or less frequently when ability and age are factored out. For example, if you are not very good at chess you are more likely to stop playing tournaments, but girls and boys that are equally good are equally likely to stop playing. This strikes a blow at the differential dropout hypothesis.
	If you look at the participation rate of women and relate that to performance, you find that in cases where the participation rate of women and men is equal the disparity in ability vanishes."

Since the beginning of Goddesschess, we've published articles that have addressed the ongoing debate. Over the years, the question has been phrased in various ways:

The debate about whether men are innately better chess players than women continues, but the mathematical study discussed in the Chabris and Glickman article indicates that it is purely a numbers game; Chabris and Glickman have concluded that the lack of "top" female players is due more to cultural factors that deter girls, and particularly, teenagers and women, from pursuing chess as a career. It is not, ultimately, because females do not play chess as well as men.

This makes a great deal of sense to me as a woman. It may be due to cultural imprinting - or it may be due to other as yet unidentified factors - but many studies have shown that women are generally more pragmatic than men when it comes to making life-changing decisions, such as whether or not to marry (and if they do marry, who they marry), whether or not to go to college, whether or not to relocate, whether or not to pursue a certain career path. The one area of major life-changing events in a woman's life where pragmatism does not seem to outweigh other factors (religious/moral and emotional factors, among others) is whether or not to have a child.

This is not to say that male chess players fail to realize that one cannot feed oneself if one is not making much money playing chess, no matter how appealing winning that next tournament that is just over the mountain may be - and it is well known that the vast majority of players (of both sexes) are not going to make much money pursuing chess-playing as a career. It's just that, to date, women are more apt to conclude that there are certain mountains they have scant chance of climbing all the way to the summit, and so they either scuttle the attempt half-way up the mountain, or they don't even bother to suit-up and attempt the climb because they know what the end result will be - scuttling and going back down. It makes more sense, from their point of view, to pour their energies into other areas of endeavor.

(Photo left: Judit Polgar and first born child, Oliver) Add to this - the fact that yet in the 21st century women continue overwhelmingly to be the primary caregivers for children - and more layers of complication are introduced into the equation. Will the expense of participating in an event where you may place somewhere in the middle (i.e., out of the money) outweigh the monetary expense of arranging and paying for child-care and the emotional expense of being away from your babies for two weeks? Will the prospect of being on the road 40 and more weeks a year doing the grind of the tournament circuit (whether in the United States, in Europe, or in other countries that, unfortunately, do not offer as many "big money" tournament opportunities) and perhaps making net $10,000 or $20,000 (which in the United States puts you just above the officially defined "poverty" level for a family of four but I defy anyone to live on alone), pay you back for being away from your children for that long? We have not had enough discussion about the true costs of being a professional chess player when one has a family. What was it that award-winning songwriter Harry Chapin wrote about in his hit song "Cats in the Cradle"...

It's no accident that historically the three strongest female chess players in the world - the Polgar sisters - have severely cut back their OTB events and tournaments since they have had children. As far as I am aware, Sofia no longer plays in events. Since before the birth of her second child, Judit has cut back her schedule to events where there's most likely a nice sum of money offered by way of an appearance fee (something not much discussed on the internet) and usually not much required by way of serious chess-playing. This is not to say that she hasn't earned the right, at this point in her life, to participate in such events. If Judit can make money this way, more power to her. Judit and her sisters are chess-playing icons and they deserve every single penny they make.

At Susan Polgar's blog, she is quite frank in stating that she has to plan her calendar two and more years in advance because - among other commitments - as a single parent trying to make a living, arranging child-care for her two boys is an ongoing concern, and she has by-passed more than one event because dates weren't decided upon far enough in advance to allow her to make the necessary arrangements and adjustments in her busy schedule in order to play in those events - such as the 2007 U.S. Chess Championship. Aside from having to deal with those issues, it doesn't begin to address the issue of what she says is the needed preparation for such an event. Her life now is not one where she can throw a couple pairs of jeans and a few sweatshirts into a carry-on bag and jet across the country, living on protein bars and Mountain Dew, to appear at a $10,000 total prize event in the hope of sharing first with three other players. Susan Polgar has moved on from the never-ending round of traveling from tournament to tournament in the quest of making a living. These days she is intensely involved in promoting the cause of getting more girls and women to play chess in the United States through promoting a series of tournaments and blog-websites for young female and male players, and is currently campaigning for a seat on the Executive Board of the United States Chess Federation. People who criticize her for not playing in enough "serious" events are out of touch with the reality of Susan Polgar's present life as a single mother trying to make a living, as thousands of other women are doing every single day the world over, or they are out of their minds.

And so, the most famous female chess players of our age have moved on. And yet - and yet - one of the primary motivations for my reporting on women's performances in chess events that no one except the participants may have ever heard is just that - the women and their performances. They keep on playing. I've been following women's chess since 1999 - a newby when it comes to chess journalism and I certainly don't consider myself a chess journalist. I simply report the results. The women chess players just amaze me and continue to do so. No matter what tournament I may report on, chances are most of the female players are finishing somewhere in the middle to lower rankings. It is not uncommon for a female player to be ranked dead last. Very few finish in the top 10 of any given event. And yet they continue to come out in event after event, and play, and play, and play... They just keep on playing.

(Photo right: Hastings, 2007) I've never played in an official OTB event in my life and probably will never do so. I do not comprehend the level of chess that they play - or the countless hours they must have put in studying, memorizing and playing hundreds of games, perhaps thousands of games. I do not understand opening theory, middle-game theory, or end-game theory, and I have no desire to study my butt off to begin to start to do so! I have memorized nothing, I play only for my amusement and yet I get so %$%&**^$# when I lose a game! I am not - and never will be - a ready for prime-time player.

And so, I love those women who play in tournaments, wherever the are, whoever they are. I don't know any of them, chances are I will never meet any of them face to face. But I have such enormous respect and admiration for them. They have such GUTS. More guts than me, that's for damn sure! And I'm a pretty gutsy broad. But not gutsy enough to play "serious" chess. Wow. I salute them.

Participation Explains Gender Differences in the Proportion of Chess Grandmasters

Category: Gender

Posted on: January 30, 2007 12:06 PM, by Jake Young

We have had an ongoing discussion on this blog about whether the disparity between women and men in the sciences is the result of a innate difference in cognitive ability or the result of some social phenomena such as selective participation or discrimination. Unfortunately, one of the complexities of this debate is that there is really no good objective standard for how good a scientist is. You can look at publication rates and journal impact, but comparing these numbers across fields is difficult. We lack objective measures.

It would be interesting to look at an analogous system to science -- something that requires lots of spatial and mathematical skill -- but has objective measures. This system should also have a male:female disparity. Looking at this system we might be able to better understand why there are fewer women and apply this knowledge to science as an occupation.

With this in mind, Chabris and Glickman, publishing in the latest issue of the journal Psychological Science, have done a huge retrospective study using data from the 13 years of matches and players in the US Chess Federation.

The US Chess Federation has a ranking system whereby players are followed throughout their playing lives. This allows us to monitor how well boys versus girls are doing at their earliest years, how many of them stay involved or leave, and how many of them become grandmasters. Furthermore, the disparity issue is larger than in science -- making this data set very interesting. Of the 894 Chess grandmasters in 2004, only 8 of them are women.

Introduction

Before I talk about their data, Chabris and Glickman summarize very nicely the explanations that could be presented for the disparity between men and women in chess performance:

First, there could be some innate difference in ability between men and women overall with respect to the skill required to play chess well. This difference in average or in variability need not be large; at the upper tail of the distribution where chess players operate for say spatial ability, a small difference would result in a large difference in representation. They call this the ability distribution hypothesis.

Second, discrimination could result in a difference in participation through different standards. However, they not that this is not a problem for this particular study because Chess rankings are objective measures. You can't discriminate against someone when their gender cannot be calculated into their performance.

Third, there could be a differential drop-out rate between boys and girls. Equal numbers of boys and girls with equal abilities could begin chess training, but fewer girls could see it through to becoming chess grandmasters. They call this the differential dropout hypothesis.

Finally, fewer women could self-select to participate in chess. If fewer talented women choose to participate in chess in the first place, by attrition alone there will be fewer in the resulting grandmaster pool. They call this participation rate hypothesis:

Anyone who visits an open chess tournament will be struck less by the lack of women at the top of the results table than by their near absence at all levels. Only 9.7% of all USCF-rated games in 2004 were played by women. It is possible that the lack of women at the top is an artifact of their lower overall participation rate (Charness & Gerchak, 1996): Even if men and women have the same underlying ability distribution, a larger number of top-rated players will be men if the overall number of men competing is greater (the participation-rate hypothesis). That is, if fewer women than men even begin to participate in organized competition, dropout rates (and cognitive endowments) could be equal, but women would still be relatively absent at the top.

Data

The study examined all chess players that were active from 1992 to 2004 -- looking at age, sex, zip code, and rankings. More information about the USCF ratings system can be found here. They describe the ratings score as follows:

A player's USCF rating is an estimate of his or her current playing strength on a scale that ranges generally from 100 to 3000; higher ratings are associated with better playing ability...Average tournament players are usually rated between 1400 and 1600, chess masters are rated above 2200, and world-class players tend to be rated above 2500. USCF ratings are essentially estimates of merit parameters from Bradley and Terry's (1952) model for paired comparisons, calculated using an approximately Bayesian filtering algorithm to update ratings over time (Glickman, 1999).

After examining the data the researchers made four statements summarized below:

They found that men and women differed in chess ability in all age groups even after differences like frequency of play (read: level of training) or age were taken into account. The disparity between men and women in ability exists at the beginning and persists across all age groups. At least ostensibly this would lend credence to the ability distribution hypothesis in the sense that it suggests the mean ability between men and women are innately different. The last piece of data looks at whether that is true.

They found no greater variance in men than women. It had been suggested that since science selects for individuals at the upper tail of the distribution, a higher variance in men than women might explain their greater representation. However, the researchers found that -- with respect to chess -- if anything in most age groups women had a higher variance then men. Upper tail effects do not explain the differences in the numbers of grandmasters.

They found that women and men do not drop out more or less frequently when ability and age are factored out. For example, if you are not very good at chess you are more likely to stop playing tournaments, but girls and boys that are equally good are equally likely to stop playing. This strikes a blow at the differential dropout hypothesis.

Finally, here is the interesting part. If you look at the participation rate of women and relate that to performance, you find that in cases where the participation rate of women and men is equal the disparity in ability vanishes. Basically, this means that in zip codes where there are equal numbers of men and women players there is no great disparity between male and female ability -- and certainly not a disparity in ability large enough to explain the difference in the numbers of grandmasters. In their words:

Finally, we addressed the participation-rate hypothesis. If in the general population the number of boys who play chess is substantially larger than the number of girls, the best ones ultimately becoming USCF members and playing competitively, then it follows statistically that the average boys' ratings will be higher than the average girls' ratings (among competitive players) even if the distribution of abilities in the general population is the same (Charness & Gerchak, 1996; Glickman & Chabris, 1996). In fact, far fewer girls than boys enter competitive chess, which suggests that the general population of chess-playing girls is much smaller than that of boys. External factors like the relative lack of female role models among the world's top players and the prospect of playing a game dominated by boys may be discouraging to girls (or their parents), either directly reducing their likelihood of learning how to play in the first place or indirectly reducing their initial performance in competitive play via test anxiety or stereotype threat (Steele, 1997). Thus, it is possible that, on average, girls have the chess-relevant cognitive abilities, but the larger number of boys playing chess leads to significantly higher male ratings in the USCF population.

. . . .

Boys generally had higher ratings than girls, particularly in the male-dominated ZIP codes. However, in the four ZIP codes with at least 50% girls (areas in Oakland, CA; Bakersfield, CA; Lexington, KY; and Pierre, SD), boys did not have higher ratings. In Oakland, with the greatest proportion (68%) of girls in the sample, the average rating of girls was higher than that of boys, though not significantly so. Combining all ZIP-code areas where the proportion of girls was at least 50%, the sex difference was only 35.2 points in favor of males, which was not significant (p = .59). The same result was obtained in an age-adjusted analysis, which yielded a sex difference of 40.8 points (p = .53).

The fairly constant mean male advantage until the 50% female participation rate was reached suggests a threshold effect: Factors limiting girls' performance levels may depend on their being in the minority, but not on the relative size of the male majority (in other words, 50% girls may constitute a "critical mass").

Making sense of this data

I am going to make an analogy to make this data make more sense. Why does it seem like the US has substantially fewer good soccer players than the rest of the world? We clearly have good athletes. We play other sports well. We train athletes just as well. Why do other countries do so much better?

The answer is that when you are a good athlete in the US, you do not play soccer. You end up playing something else like football or basketball. The difference in performance is related to a difference in participation.

This data strongly argues that the difference in performance of women in chess is also a problem of participation. The problem is not that women can't play chess well. The problem is that enough women who play chess well are not choosing to play chess. There may be several reasons socially why they choose not to do so or are discouraged from doing so -- I will let you speculate about that at your leisure. However, this data strongly supports the participation rate hypothesis.

We could apply this data to our experience in science. There were -- I think -- 4 women in my graduating class at Stanford who majored in Computer Science along side 100 or so men. The problem is not that there are no women who could be Computer Science majors. (The women I met at Stanford were certainly gifted enough.) The problem was that for whatever reason they either didn't want to or weren't encouraged to participate in that major.

The finding that there is a critical mass of participation is also interesting. I think it will certainly inform the debate to know that at least with respect to this system, if you can get the participation up to 50% you can solve the performance problem.

Will we ever reach a "critical mass" of chess femmes? I sure hope so. I hope I live long enough to see it within my lifetime.