Participation Explains Gender Differences in the Proportion of Chess Grandmasters

i-40521864eabb1327496cb7ae9e2feb04-euwe.jpgWe 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.


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 diffence 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.


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.


More like this

Interesting study, but there are a few things missing. First is discussion of personality traits -- we know that eminence in any field like science or chess is log-normally distributed, so there must be more than one trait involved (and furthermore, that they interact multiplicatively). So, it's not just heritable differences in cognitive ability but in personality traits as well that matter -- the largest sex difference in personality is what the Big Five people call Agreeableness: women on average are more Agreeable than men (true across cultures). In any competitive setting, then, women will be underrepresented just considering this personality difference in empathy & aggressiveness.

Spatial ability is probably of limited importance in chess. The classic study of this tested whether top chess players could recall the configuration of a certain chess board -- they could if it was an allowable configuration, but not if the pieces were placed randomly / broke the rules of chess. The interpretation of this is that they weren't storing the images in their visuospatial sketchpad but storing the information as abstract propositions such as "Threaten (piece A, piece B)." Another clue here is that Ashkenazi Jews are vastly overrepresented among grand masters, and this group tends to excel more at verbal (and so, propositional) tasks than visuospatial tasks. So we shouldn't expect as vast of a male-female disparity in chess as in, say, mech engineering or architecture (more visual disciplines), since females tend to perform better on verbal than visual tasks.

The finding of equal variances doesn't allow the interpretation of equal variances in the population, which is the real claim -- i.e., that men are overrepresnted due greater population variance. When only considering chess geeks, you've got a biased sample, so the difference in variances might not be so surprising. Also, variances are much harder to estimate than means, so if few women are elite chess geeks, the estimate of their variance will be less reliable than if you looked at a large, random sample of women.

The analogy to soccer is partly right, but wrong in this case. In the soccer case, Americans for whatever reason opt out of the global soccer culture, but we dominate all sorts of other sports. In the chess case, it's not true that females for whatever reason opt out of chess but dominate all sorts of other brainy, geeky niches. They're underrepresented not just in chess and science, but architecture, fashion design, and so on.

They do, however, represent well in law, PR, advertising, journalism, and other disciplines where social & emotional skills are more important (in addition to high IQ). They're also well represented in less abstract, more practical areas like medicine and business. So, the proper analogy is to, say, South Asians or Ashkenazi Jews not excelling in any sports but doing very well in hi-tech industry, science, etc.

And noting that the male-female disparity in chess ability vanishes once you control for participation is non-informative: obviously, those who are beasts at chess will eat, sleep, and breathe it, participating at higher rates than those who stink at it. So, we encounter another instance of making a disparity disappear by controlling for a variable that's highly correlated with it. To steal an example I read elsewhere (but forget where), if you control for the length of the inseam in pants, men and women will be roughly equal in height -- but that's only because you controlled for a variable that highly correlates with height.

Your point, I think, is pretty good, up until your last analogy. Everything you've mentioned -- women's ostensibly higher "agreeableness" (whatever that means; it reads to me like "trained into submission"), Ashkenazic Jews' abilities with visual-spatial tasks (perhaps all that time they spend studying non-linear tasks and learning how to write in a language that goes in the opposite direction to their native one?) are all acculturated abilities. I'm seriously skeptical as to the proposition that there's something essentialist about women as a group (or Ashkenazic Jews as a group, or South Asians as a group) that just innately makes them better at certain things. The evidence just doesn't seem to be there.

Now, if you want to argue that the socialisation given to North American girls makes them less likely to be chess masters and CS majors and more likely to be journalists and lawyers, you would probably have a point. But that's really not what I'm reading in your comment, especially in light of your last analogy, since you can't acculturate someone into having a longer or shorter inseam, but you can, at a cultural level, socialise members of a group into generally being better at certain skills than others.

By Interrobang (not verified) on 30 Jan 2007 #permalink

Here's what confuses me: "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."

Unless there is some data I'm not aware of, most chess players and scientists are not geniuses (sorry, y'all). I really don't see how you can show that a small tail end difference doesn't exist, except by directly selecting for the smartest few percent in the entire population (instead of assuming science or chess or the SAT will do it for you - cause they won't).

Both innate variance and social factors could be at work. Even if we compensate for whatever is preventing girls from enrolling in chess (or science) at a rate that matches boys, we don't know if the girls in Oakland will produce female grand masters at a rate proportional to their participation, do we? It could turn out to be the case - but it could also turn out that 50-50 participation overall is still inadequate to produce a 50-50 ratio at the rarefied level of grand master.

Am I missing something important here? I don't like statistics, so I could be way off base. But I just don't see how this is evidence against the variance hypothesis, if variance only favors men at the extreme.

I don't understand how this study could not even address the #1 reason for the rating (and actual strength) disparity: women-only tournaments. This is the biggest drag on more women being top Grandmasters. I can name only one woman who does not play in women-only tournaments, and she is a 2700+ SuperGM top-10er: Judit Polgar.

No other woman has ever actually done this same experiment, so there is obviously insufficient data to draw any conclusions at all. Thus far, there is a 100% total success rate for a woman not playing in gender-segregated tournaments, using only the one sample.

The top active women players in the world, with the obvious exception of the great Judit Polgar, are in the low 2500s in rating. And they play in women-only tournaments, where most participants are under 2500. It is impossible for them to gain more strength, or more rating points, in such limited pools. Judit Polgar avoided them like a plague, playing the best, and therefore LEARNING from the best, and getting rating points from the best.

You can't be the best without playing the best, and almost all women players usually or exclusively segregate themselves from playing the best. How you can not even talk about this is a tremendous oversight in such a study. It would be like doing a study on the ingredients of ketchup and forgetting tomatoes.

By Smyslov Fan (not verified) on 30 Jan 2007 #permalink

The fact that selection "explains" everything suggests that there is no active gender discrimination within the chess playing world: women and men who advance to different stages of the chess playing career (and those who do not) are roughly similar. However, I agree with Agnostic: this tells us nothing about the underlying distribution of "chess ability", if such a thing exists.

My analogy would be with color blindness. Color blind men and women see the same colors (provided they have the same condition), but there are far more many males than females. The question is just how much of a genetic/gender biased basis chess ability has, and this is not really addressed by the paper, IMO.

I'm afraid I don't find the numbers explanation to be suffient, at least when looking at top level chess.

I am pretty positive that Judit Polgar is the ONLY woman to EVER break the top 100 in statistical elo rankings. Obviously there were a lot of barriers against women throughout history, but there haven't been barriers for women in chess for several decades. If women and men had equal skill at chess we would expect at least a handful of women to bump into the top 100.

I'm not sure how many different people have dipped into the top 100 rankings over that time, but suffice to say that it is several hundred people. And yet only one women has made it in.

I'm sure that men participate in chess more than women, but I do not believe they participate more than 500 times (or even more probably) than women!

The data seems to imply an innate difference or a heavily culture influenced difference.

For accuracy's sake, let me say that I was wrong. Susan Polgar, Judit's sister, also made the top 100 at one point. So two women in the past couple decades where it is relevant.

I have already explained why, Bort. Because you can't get better by playing only your equals or your inferiors, which is what all women international players (except Judit Polgar) do. Women-only tournaments are the cause of this problem. A 2500 can play in a ton of tournaments full of 2400 players, and you can't expect to get the same strength as you would from exercising with the 2700 titans.

THIS is the difference. THIS is why only 2 women have broken into the top 100. And notice, Zsuzsa (Susan) Polgar did this during a time when she was playing in NON-WOMEN-ONLY TOURNAMENTS.

I can't understand why people keep acting like this is a difficult thing to understand, or how this study could be so abysmally and drastically devoid of any mention of the real issue. You can't get to be a world-class weightlifter if you're only lifting 5 pound weights!!

By Smyslov Fan (not verified) on 30 Jan 2007 #permalink

Hi. Interesting debate. We brought chess into our local school cluster. 243 students attended our major tournament, and our program included over 300 primary school aged kids. In our tournament play we were awarded 38 scholarships twenty six went to boys.Many of the boys who excelled were performing poorly in other intellectual areas. For example many boy who were doing poorly at maths excelled at chess. We think one reason for this is the maths they do involves rote learning and times tables (verbal based). When given a competitive game, where there is the possibility of solving problems immediately-not process based but product based, and involves 3d problem solving, hands on kinetic learning, and the opportunity to move about and actively engage boys performance levels sky rocketed.
Bear in mind many of our chess successes were boys who suffered from disability like autism, disaffectedness,and were intellectually below their peers, as well as behavourial problems.
I think the bloggers here are under-estimating female success in the Maths and Sciences today. They are surpassing males in these areas in Australia. It is only at the elite level where they thin out.
The largest marginalised group in education in the western world today is 'males in general' and black males in particular. The fact that they are still numerically strong at the top 1% is irrelevent.
The question encompasses general intellectual achievement and university results clearly place women at the apex of achievement. They make up 62% of university graduates today and are beginning to numerically dominate the maths sciences. Some sources say in the western world only 38% of males meet the university entrance standard but the universities bolster male attendance by bringing them through the back door.
Given women excell everywhere else academically how come they are not doing it at chess???

The Polgars are in fact a complete study in themselves. They were never told they couldn't play chess at the top levels, so they have (all three of them!). They were never told fairy tales, and never went to school, their father believing home tutoring to be both more effective and productive for, and less destructive to the creativity of, his three lovely girls (and if you ever get to meet any of them, you would have to say he made his point rather elegantly). Thus these girls are very real and hard evidence for the social discrimination hypothesis, since their pre-teen years were relatively free - of the imaginings and views of others their own age, and of adults who had been conditioned into thinking what was culturally acceptable for girls.
The Polgars are also evidence against the theory of a discrepancy in ability in favour of males. Father Polgar was not the strongest chessplayer himself, yet through a series of tutors 2 of his girls make top 100 and the third is >2000, Judit breaking the record until then held by R.J.Fischer for the youngest IGM (not WGM) ever at age 15 and a handful of months.
The Polgars also smash the personality traits theorem for the same reasons already stated: they are elegant, well-mannered women, all three of them, and no-one who has met them would say they are anything less than ladies, yet they compete without being or even seeming any less lady-like (or any more competitive, or any less agreeable) than Her Majesty Beatrix, the Queen of the Netherlands. Yet they haven't had what would be considered a traditional, nor an expected, upbringing.
All of this points to nurture. The sisters obviously have the talent to match any male on the planet, and they were kept away from negative cultural influences such as school classrooms and the associated playgrounds. In a study that speculated, based on numbers, about the participation rates of women, culture seems the only logical explanation if the Polgars are to be taken as an example in chess.

Hey, Smyslov fan, what are you talking about? There are plenty of women playing chess against men. I was just in Holland at the Corus tournament, one of the most prestigious tournaments in the world. And guess what? I saw at least 4 women playing in the class B and C groups. And not a single Polgar to be seen.

Regarding the main article and the response "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."

I don't see any evidence to back this statement up. This is your opinion and you write it down as fact. I don't think that makes for good, scientific writing.

Or this statement: "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." Care to back this up with some evidence?

I have already explained why, Bort. Because you can't get better by playing only your equals or your inferiors, which is what all women international players (except Judit Polgar) do.

No, you didn't "explain it," you just made a claim based on admittedly one example and no other evidence.

On one hand your theory makes some sense, but on the other chess software is more than available to let people play against higher levels and women are not barred from men's tournaments. There is an open tournament that women can compete in and then a women's only tournament.

Another problem with your theory is that plenty of chess people have gotten stronger than their opponents. Bobby Fischer as a young teenager was much stronger than anyone he was playing, for example.

Thus these girls are very real and hard evidence for the social discrimination hypothesis, since their pre-teen years were relatively free - of the imaginings and views of others their own age, and of adults who had been conditioned into thinking what was culturally acceptable for girls.

You are leaving out one crewcial component in your painting of the Polgar family. That is, their father had a theory that geniuses could be raised and recruited a wife to check out his theories and then raised all of his daughters to be chess players from birth. I'm sure that their father wans't a tryant and didn't force them to be chess players, but it was something he raised them to do and being raised from brith to excell at something is a special situation.

The Polgars seem more like outliers than anything else.

The Polgars also smash the personality traits theorem for the same reasons already stated:

I'm sorry Rob, but you just don't seem to understand said theorem. We are talking in generalizations and it is expected and implied that SOME people will break the generalizations. Put it this way: I can say that men are on average taller than women. Does this mean that every single man is taller than every single women? No, it only means that on average they are.

Pointing to a really tall woman and saying that she "smashes the male height theorem" is just silly.

The sisters obviously have the talent to match any male on the planet,

Why haven't they then? Look, both sisters are amazing chess players, far better than I am, but if both sisters could match any man on the planent in chess then they would be world champions. Or at lest would have gotten close. Judti has never been considered one of the top 5 players, though she did break the top 10 for a period, and Susan was never even close to challanging the world championship throne.

Nothing wrong with that. 99.9999% of chess players don't come close to winning the WC. But let's not get too hyperbolic.

Because you can't get better by playing only your equals or your inferiors,

One last thing on this. If this statement was true, that no one would ever be the best at anything and no one would ever raise the bar for anything. If you could never get better than your equals, you would never be superior to anybody.

But the fact is Paul Morphy WAS superior to other chess players in his day, despite only playing inferiors. Same with Bobby Fischer. Same with Casablanca. Same with Micheal Jordon for that matter (or an even better example, same for people liek Lebron James and other elite atheletes when they were in college. In college they were already playing at NBA levels, despite only getting to practice against inferiors.)

The real question is why it is, that while apparently, the women that chose to play chess have a distribution of talent similar or equal to that of chessplaying men, there are so few chessplaying women.
My explanation is that evolution tend to make females less prone to take risks. To fight or not fight amongst mammals is a matter of death and reproduction. Females breed even if they are low-ranked so they dont tend to risk their lives to improve their status. In the evolution game a man without status is a complete loser and hence fighting to gain status and killing some competitors is a good idea.
So the balance between fear of losing (think dying) and joy of winning (think sex) tend to make females more cautious and men more aggressive.

By Tomas Pettersson (not verified) on 30 Jan 2007 #permalink

"The sisters obviously have the talent to match any male on the planet,

Why haven't they then?"
You might be willing to take into account that Judit is mother of 2 children as far as I know for example.

Agree entirely with Smyslov fan. A few comments.

People who are great in their field are not born great and do not become great overnight. They work bl00dy hard at it for years and years before they appear on the scene. They learn from their elders and betters and never stop learning. They appear to have natural talent, because they make a difficult game look easy, but it is because they have put themselves in this position hundreds of times in training and just know what to do. This applies to Woods, Federer, Schumacher and other once in a lifetime "talents". Saying someone beat me because he/she is naturally talented is a get out clause because I can�t be bothered to do the work.

Bobby Fischer worked very hard as a kid and through the sixties (to the extent that he had no life outside chess), but it was only from 1970 that he could be considered the best in the world. He got there by playing, losing to and learning from the Soviets, learning Russian, to read their books, magazines and analysis. You can see his results against the likes of Tal, who he couldn't beat for love or money at the start of his career, but who he learned to beat at the end.

A measure of true greatness in any sport is when a player can reach the top and stay there despite playing inferior opposition. They are there as the target and many people will raise their game and have a chance to win a one-off event. To consistently, beat them down suggests mental strength as well as the ability in the discipline.

Fischer didn't manage this, whereas Karpov and Kasparov took on all-comers and beat them over a period of over 10 years. I'm not belittling Fischer's achievement, he overcome a Soviet system that was designed to keep him from winning which is something that nobody has done before or since. Fischer did play at a level not seen before or since for a short time, but he couldn't sustain it, he realised it and couldn�t handle it.

Lebron James has potential, is posting excellent individual figures but he won't be great until he has a number of Championship rings. Look at Michael Jordan, Hakeem the Dream, Tim Duncan, (Joe Montana, Steve Young, Tom Brady in gridiron). Together with a great coach they built a team around them and realised that the reason you play sport is not to be the MVP, but to win championships and rings. That's what I like about The Pistons- they realise that basketball is a team game, nobody cares about the individual stats and they are without doubt a team that has been greater than the sum of their parts. None of those players are marquee players but they sat down, worked out a system that played to their strengths and stuck to it, and always played for each other. It wasn�t always pretty to watch, but it certainly was effective.

Women who compete against men generally will exceed potential when competing against women. Another example is Danica Patrick, who learned how to manoeuvre a car in pressure situations, driving at her extreme limit which just wouldn�t occur in a women only race. She was bound to improve. Finally in supreme endurance events (ironman is entry level), women are narrowing the gap in such a way that they compete on equal terms with men.

There is a difference betweeen getting better and getting a better rating.

(1) It is impossible to improve your rating beyond a certain level if you play only in a pool with rating that max out at around that level. (If the strongest player in a restricted pool of this sort had a 3 to 1 win ratio agains the next best player, the strongest player's rating would not be much more than 100pts higher on any of the standard rating alogorithms). What it takes to increase one's rating is to beat players with a significantly higher rating.

(2) Getting better at the activity may result from being stretched by exposure to stronger players, and typically is. But this is neither a necessary (Fischer) nor a sufficient condition for sustained rating improvement (me).

By growltiger (not verified) on 31 Jan 2007 #permalink

There's an assumption here that I can't see anyone bringing up: Do we know that chess skill is transitive? If A mostly beats B, and B mostly beats C, does it follow that A mostly beats C? It seems this way in practice... but I'd be suprised if the rules of chess didn't allow for at least _some_ different ways of being good at it, so that for some A B and C, A beats B, B beats C, C beats A.

Does this matter?

Just wanted to point out that the theory that Americans are bad at "soccer" because their best athletes play other sports is intuitively appealing but most likely wrong.

Soccer is not a sport such as track and field where the best athlete is the best at the sport. It is about having a ball, controlling it and doing the right thing with it. In fact, if you look at the American national team, their athleticisim appears to be superior to most European teams. What Americans lack is exactly what somebody said female chess players need, it is a surrounding level of play. It is a much greater problem in a true team sport like soccer.

The athletic traits that make a good basketball player (seen any soccer players over 6'3'' lately?), football players (over 250 pounds?) or baseball player are mostly unrelated to soccer-playing ability.

Transitivity holds in a weak large numbers sense, despite the phenomenon of temporary non-transitivity at the micro level. A ratings difference of 200 points implies that the higher-rated player will almost always beat the lesser-rated. But style difference, particularly in blitz chess, mean that we are all likely to meet the occasional Nemesis with a much lower rating. On the whole, a Nemesis of this sort will be a weak player with a few trick openings. The resolution of the transitivity paradox is that the stronger player will work out the trick openings over some modest number of losing plays, after which they no longer succeed. (This is what happened, on a macro level to most of the sharp gambit openings after the rise of "positional" type play).

By growltiger (not verified) on 31 Jan 2007 #permalink


Obviosly no one becomes great overnight and no one is born great. But if you are implying there is no such thing as natural talent I totally disagree. If the only factor involved was hard work, then why is there still such huge gaps between athletes and chess players?

Are we going to say that the only reason Kasporav was better than Karpov was because Kaprov slacked off more?

No one gets to be a world class champion at anything without tons of practice and hard work. However, no one gets to be world class champion at something without a lot of natural talent as well.

Donald, interesting point, but I think that each worked as much as the other (i.e. excluded all non-chess things from their lives).

IMHO, the difference in favour of Kasparov was that he worked smarter - he probably gained more per unit work, at least in part because all who went before him (especially including Karpov) had done the hard yards. It seems daft not to make use of your predecessors work and expertise. Indeed, Kasparov pays tribute to all of them in his My Great Predecessors series.

Also Kasparov had a computer to do a lot of the administrative work for him (maintaining databases, searches etc.), whereas Karpov never really got to grips with using the computer as a tool (This was really apparent in an advanced Chess match vs Anand in Leon in 1999 which the latter won 5-1). I think Karpov's decline coincided with the rise of the computer generation (Anand, Kramnik etc.). Karpov could still teach them a lesson on some of the less glamorous and more subtle aspects of the game, but too often he ran into superior opening preparation.

The main reason Kramnik is World champion today is that he alone of the top players is aware of this. Other players use brute force alone to calculate variations and prepare great novelties. The Kramnik-Topalov match showed this at work- Topalov's team worked hard at brute force and opening innovations. He often found the first novelty of the game and had a slight advantage on the board and a large one on the clock. However, when they got out of charted waters, Kramnik's superior feel for the game took over and he was often able to equalise or even gain the upper hand and he ended up with a deserved match victory.

However, from the evidence of the Fritz match, the day when the brute force generation moves ahead, may not be too far ahead.

growltiger makes a lot of valid points regarding transitivity.

In addition, the colour matters an awful lot, especially as the standard increases to grandmaster level. A could be 100 points above B. A reasonable expectation may be that A would win with white and draw with black in a 2-game match. However in a single game in a tournament where B was white, all three results would be possible.

As some purely anecdotal evidence, I've played one player of a similar rating 7 times all with white and lead 6-1 (I don't consider to be better, just lucky with the colour draw. Conversely my bete-noire as a child was someone of a lower rating who was an excellent defender and counter-puncher (rope-a-dope, I guess). He had something like a 7-3 record and almost all wins on both sides were black.

The beauty of the rating system is that all games are treated as equal and statistically, as the sample size rises, they should even out.

"You can see his results against the likes of Tal, who he couldn't beat for love or money at the start of his career, but who he learned to beat at the end."

al, i think this whole topic is like chess itself! that is, there are lots and lots of possibilities to consider before making a move! i think it should be mentioned that even though Fischer did finally best Tal, Misha was very sick for the latter part of his career with chronic kidney disease! so, IMHO it's not entirely just a matter of Fischer's strength that allowed Fischer to best Tal!

I think what is missing from the study is an understanding of what it takes to become one of the best players in the world in chess. What it takes is some inate characteristics (probably), but more importantly massive amount of work. Now almost all excellence requires that, but in chess it has the following characteristics:

1) start at very young age. There are very few GMs who learned to play chess seriously as adults. Most GMs (I think)played chess seriously from age 9 at the latest.

2) the work is essentially all done alone. There is coaching, but most of chess learning is dne alone; the drudgery of working through chess problems and replaying and analysing games. For hours a day.

3) There is no real chance of serious financial reward. Yes the top 5 players in the world might make a good living, but almost everyone else makes peanuts. Unlike music (which can lead to scholarships at least) or sports.

4) Unlike sports practice, chess preparation is probably useless for anything but chess. It does not lead to physical fitness or involve friends (like team sports for eg.) It seems to me that even music "genius" has more side benefits than chess "genius"

So the real question is who in their right mind would put all of that effort into becoming a chess GM? I think your answer will largely help explain the lack of top female players.

Well, one of the strongest reasons is that:
- motivation to play chess is much less for girls. They face often strong discouraging comments from their closest families, friends and sociaty in general.

- female player if gets to stronger level of play becomes isolated and her feelings can be similar to a prisoner that is alone in his cell, but she didn?t commit worse crime than to become a chessplayer
--social point: female player of certain age is often watched badly if talking to males even if her intentions are totaly the same as by male players in the tournaments: who likes to spend all time alone???
Plus young girls more often cann?t travel to the tournaments alone.
-- proffessional point: it?s often hard to find a partner for analyses and free games- planty of male strong players are not able to accept a lady as normal chess partner (bit improved by internet, ICC great place). For sure the main work of studying needs to be done individually, but it?s hard to imagine that one will never speak about his or her work exept on the chessboard while playing tournaments.

- competition among girls is much less, it?s relatively easy to get to national team... from that point is the goal to get to the world elite too far away.

-life time of female chessplayers is much shorter. Very often strongly limited by her partner and babies. Female player is often not expected to play longer when her marriage comes, so why should she spend hours in something that will be after few years thrown out of the window??

Well, for sure there are planty of other reasons but I wanted to mention at least some of them.

By Lenka Ptacnikova (not verified) on 31 Jan 2007 #permalink

I'm curious to know why they assume that there is no discrimination in chess just because ratings are an objective measure. Didn't Susan Polgar have some odd discrimination things happen to her when she tried to be the first to play in "Men's Tournaments"? I recall that FIDE decided to raise all the other women's ratings EXCEPT for Susan, which had the effect of closing the gap between her and the #2 player. That sounds like discrimination by rating manipulation, doesn't it?

I choose that example, because presumably the ordinary discrimination that happens during tournaments (I've heard plenty of lewd or sexual comments from men directed at women during matches) is one of the driving forces for lower participation. But it seems even the rating can be a weapon of discrimination.

1. I suppouse that the chess level at a certain comunity (country, city, zip code, etc.) is more determined by the general level than by the top level. If general level is low, then you need lesser effort to got up to it. That comunity then will have a lesser number of GMs.

2. From that point on, the reasoning also aplies to women-onlu tournments.

3. To suppouse that someone's life ends in a marriage and children... that says a lot about internalized predjuices. So, can we seriously think about a "objective" judgment of this things, that are on the "social" side more than on the "phisical" side of things?

(I hope my english will be understandable).

By Nimzowitsch fan (not verified) on 31 Jan 2007 #permalink


You make some good points, but I think the fault lies with me for a bad example. Kasporov and Karpov were near equals and most of their matches were much closer than people (I think kasporov kept his title on a tie once or twice).

My point though is just that it seems a bit insulting to say that of the top chess players (the ones as you correctly say exclude everything but chess from their life) that the reason one person is #1 and the next 100 points lower is merely that one studies more than the other. Natural talent must play a role.

Or to use a reductio ad absurdum, do you believe that anyone could be raised to be a chess grandmaster with enough work? Could mentally retarded people become Grandmasters? If not natural talent per se, at least a certain level of mental power in certain realms must be needed as a base to build on.

I also think that the rise of prodigies like Fischer show how much natural talent helps. Although Fischer did learn chess at a young age (6), he tought himself and didn't have a tutor until 13. At 13 he also beat DOnald Byrne, one of the strongest US chess players in the famous "game of the century." Byrne was 26 or 27 and had almost certainly practiced, studied and played far more chess than Fischer yet still lost.

Chess is something that requires a lot of memorization of opening moves and such to be skilled so in that respect it isn't the best area to judge natural talent perhaps. But I think if we look at something like the arts we find plenty of artists/writers/painters/etc whose first books or works are considered excellent. People who never wroter creativly until they were old can suddenly produce masterpieces.

Didn't Susan Polgar have some odd discrimination things happen to her when she tried to be the first to play in "Men's Tournaments"? I recall that FIDE decided to raise all the other women's ratings EXCEPT for Susan, which had the effect of closing the gap between her and the #2 player. That sounds like discrimination by rating manipulation, doesn't it?

It does, but it wasn't discrimination AGAINST female players, it was discrimination FOR all women players against Susan Polgar. It was also unprecendented and hasnt' been repeated. It was also done in the 80s when political pressure was huge re: Soviet Union and was a move forced by the Soviet Union who didn't want a non-soviet player at the top.

I'd also note that this is really an argument against the earlier claim of women's ratings being deflated because of playing only against women, since this was the Soviet Union's claim which has been widely disputed and shown (in the specific claim by the Soviet Union at the time) to be based on faulty statistics.

Doesn't anyone want to admit that men and women are different; not lesser or better, just different?

'Given women excell everywhere else academically how come they are not doing it at chess???'
Posted by: Harry January 31, 2007 12:19 AM

Your three question marks imply that you think there is a contradiction between woman 'excelling' in some areas but not equalling men at chess. There isn't. Being a high-achiever in, say, law or medicine is different to BEATING an opponent in a COMPETITIVE environment. In actual fact there is scarcely ANY competitive area where women can compete on equal terms with men.

By Charles Tudor (not verified) on 01 Feb 2007 #permalink

For me this is very clear.

Men will statistically be more extreme (wider spread of talent) if you look at a fairly narrow skill like playing chess. This is due to pure genetics: Men have more recessive genes being expressed, since we have one x and one y chromosome. This means more men then women have the extreme talent for chess. More men than women also totally lack talent for chess, but most of these would quit playing very early.

This is true in many areas of life of course but most clearly if isolating a very specific attribute (like more men are color blind). In a skill where many talents have to be combined, like most science, it is less clear. But statisticaly the most extreme specimens of humans are more likely to be men.


This is a good discussion. I guess that it comes down to the old argument about whether chess is an art, a science or a sport. I appreciate your argument if you consider chess as an art, but in the context of this debate, we are talking about ratings and the sporting aspect of the game.

The examples you gave again lead to the working smarter approach. Take two players, one (who is typical of lower rated players) who spends 80% of his chess time (20 hours a week) and budget on opening materials and 20% on tactics. Another who spends 25% of 10 hours a week on each of openings, tactics, endings and the games collections of the greats (I mean really read and study the books, not buy them to flick through or to look good on the bookshelf when a friend comes round). Which one will be the more rounded and better player? The former will be in book for longer and may win the odd game through traps, but will not know how to convert any advantage gained by the superior opening knowledge.

It definitely comes down to good coaching and an excellent setting of goals and targets. You also need the tools to do the job. Two different people with different toolsets will achieve different results. Often the person with the more limited toolset will become more ingenious through necessity and keep things working very well within the limits and budget, but the one with the better tools will be able to create something new and move ahead of the game (again we are talking intelligent use of tools- I work in software and see 90% of users using 10% of the application).

Also, you can't ignore psychology. In the example you gave, the teenaged Fischer probably felt invincible and backed himself to navigate through the minefield whereas at Byrne's age you would probably have other non-chess baggage.

Mentally retarded is a very ugly term and I don't really know what you mean. I think that Fischer probably had a form of autism and other current players including David Navara (currently ranked #14 in the world) is known to be autistic. A more mannerly and pleasant GM than Navara it would be hard to meet. Are they retarded?

It comes down to the fact that the study is limited because it only looks at one aspect of a player's development. I still maintain that what appears to be "natural talent" relies on being given good direction by a mentor (to get the pupil to concentrate on what is really important and make maximum use of the "ability" and time available) and . Beyond this and having sufficient tools to do the job, the differential is hard work.



"The examples you gave again lead to the working smarter approach."

Uh, no they don't. You didn't give any evidence, nor I"m sure do you have any (since it is impossible to know), that my examaples were cases of people who worked "smarter."

I appreciate your argument, but I hope you can understand how it reads like a bit of a cop out. There are no examples I can ever bring up to prove natural talent plays a role when you can claim, without any evidence, that any person who is better just worked "smarter" instead of was smarter.

To be honest, the way you are phrasing it sounds like circular logic. You take as a priori the belief that natural talent doesn't exist and the player who is better is the player who works harder and smarter. Any person who does well must have studied smart and anyone who plays bad must have studied dumb. Circular argument.

I think that Fischer probably had a form of autism and other current players including David Navara (currently ranked #14 in the world) is known to be autistic.

Do you have any sources for those two?

Beyond this and having sufficient tools to do the job, the differential is hard work.

Ah... but maybe this is just a semantic disagreement, because what when I talk about "natural skill" I'm talking about good mental tools with which to build your chess house with.

Psychology is the reason an unfortunate number of people come to hate science, and why so many scientists in turn hate psychology.

Thanks for posting this. This sounds more like a beginning to a field of study than a series of bankable conclusions.
It's important to do such studies, and to learn from them and refine them, as they are a window to a world of gender issues and answers.

'Given women excell everywhere else academically how come they are not doing it at chess???'
Posted by: Harry January 31, 2007 12:19 AM

To answer Harry's question...
Most women are not interested in i'm not interested in why would i "excell" in rugby! The few that are intersted, do excell..take our best female players, take those who are really interested... if more women/girls can get an interest in chess, you will see more of us excell in chess! I think it's more a case of interest and not more a case of men are better... you can't force someone to take part in a sport... i have no interest in hockey, so why will i be forced to take part JUST to show that i'm part of the human race (females) that can "excell"...earlier years, - that's when i was little - chess was seen as a game/sport for boys..well, that was at my school... I didn't play chess at school as I was stared at by the boys as if...i was an alien!

I found this a very interesting post, because I have been mulling over this same issue as it pertains to competitive Scrabble. Recently, our National Champs (I live in New Zealand) were won by a woman, and someone said to me that this particular person was the first female to win our National Champs in 25 years. This surprised me, since I play competitive Scrabble, and know that most of the players are female. So I looked at the current National ratings, and this is what I found:

1. There are 278 ranked Scrabble Players in NZ of whom 62 are Male (22%)
2. The top 100 players contain 36 men (36%)
3. The Top 50 players contain 23 men (46%)
4. The top 20 players contain 13 men (65%)
5. The top 10 players have 9 men (90%) plus our current national champ, Joanne.

I thought this inverted pyramid was pretty astonishing - only 22% of Competitive Scrabble players in NZ are men, yet they dominate the top echelons of the game. And I think the same applies internationally (I know that a woman has not won the world champs yet).

I'm not aware that there is any discrimination operating in Scrabble, but the sheer number of women playing the game should produce more top ranked players - unless there are other factors prevailing.

But in this case participation levels can hardly be the culprit.

By Peter Johnstone (not verified) on 16 Jun 2009 #permalink

@Peter look at scrabble and say the top positions belong to men! haha...women have better things to do than playing scrabble my friend. It shows again...interests are different...women don't always have the same interests as men and...women have so many tasks to fulfil at home! and around home..not time for sitting playing all sorts of games all the time.