The ratings gap and gender: Analyzing U.S. Chess Championships (Part II)

by Alexey Root
4/18/2021 – Comparing the average ratings of the U.S. Championships and U.S. Women’s Championships from 1972–2000 shows a 300+ point difference between the former and the latter, as detailed in part one of this two-part series. In this part two, Ashley Yan and Alexey Root offer a possible explanation for this gender-based ratings gap.

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Ratings Gap

For each year between 1972–2000, the average USCF rating of the overall U.S. Championship was always more than 300 points greater than the average rating of the U.S. Women’s Championship.

Although the rating differences are already apparent, Ashley Yan conducted an independent samples t-test to compare the means. The results confirmed a statistically significant difference between the average ratings of overall U.S. Championship participants and U.S. Women’s Championship participants. Since the resulting p-value was much less than 0.05, which is the standard threshold for statistical significance, it’s highly likely that the average rating differences are influenced by an external factor.

Given these results, one might conclude that there is a significant difference in skill between men and women. But other explanations are possible.

Participation Hypothesis

We hypothesize that the difference in ratings between the U.S. Women’s Championship and the overall U.S. Championship is expected due to the small numbers of girls and women with USCF memberships. This conclusion remains valid under two assumptions: that women made up 5% of the total USCF membership, and the rating distribution for all female USCF members was relatively the same as the rating distribution for all male USCF members.

Due to the lack of data available to us, the exact percentage of female USCF members between 1972–2000 remains unknown, and the rating distributions based on gender are also unknown. Given that 5% of USCF players were girls or women in April 2000, as mentioned in part one, one might speculate that the percentage was even lower in the years before 2000. Indeed, for the datapoint of 1993, the percentage was lower (4.65%). Further data points may or may not be available from the US Chess. Requesting a data search would require staff hours and thus an outside funding source to pay for US Chess staff time.

If a funded study were conducted, and data points of girls/women in various years from 1972 to 1993 were uncovered (since we already have the 1993 and 2000 data points), these additional data points might demonstrate a substantial participation gap between men and women.

In addition, assuming the rating distributions for men and women were relatively equal, it is expected that the highest ratings for men would be higher than those for women. More specifically, when comparing two distributions with the same average value and variability, the distribution with the larger sample size will logically have greater representation on both ends of the distribution curve.

Extreme Values

When this logic is applied to the U.S. Championships’ rating differences, the difference between the average ratings of the overall and women’s championships would be expected due to a smaller sample size of total female USCF members. The participants in both championships have ratings in the top percentile for their corresponding gender, so the championships’ ratings are the highest or most extreme values in the rating distributions of all USCF players. Since there are substantially more male USCF players than female, the male USCF player distribution would not only have a greater magnitude of players in the top percentile, but the highest ratings would also be greater than those for female USCF players. Extreme values explain why the participants in the overall U.S. Championships generally have much higher ratings than those in the U.S. Women’s Championships.

Chess Life  magazine, March 1996 (from the Chess Life and Chess Review Archives)

Graphs and Conclusion

Based on the graph illustrating the average ratings of the U.S. Championships and U.S. Women’s Championships, the rating difference has generally decreased over 1972–2000. Due to the proportion of female USCF members possibly increasing over this period, this trend is statistically expected: The extreme values of the two distributions become more similar as the distributions’ size difference decreases. That the proportion of female USCF members increased between 1972–2000, though, is another assumption we make as we do not currently have much gender-based data for those years.

We conclude that the gender participation gap influences the average rating differences between the U.S. Championship players and the U.S. Women’s Championship players, and, therefore, the difference would be expected. However, our conclusions and the insight we can draw from the given data are limited. There may or may not be available rating distributions from 1972–2000, and overall USCF membership during those years perhaps did not include sufficiently accurate gender coding.

Future Research

In 2001, there was no women’s tournament. In 2004, there was a seven-player U.S. Women’s Championship but no corresponding U.S. Championship. That is, the 2004 U.S. Championship was named the 2005 championship for legal reasons and was a mixed-gender Swiss system. In 2002 (56 players), 2003 (58 players), 2005 (64 players), and 2006 (two 32-player Swiss systems), the women and men played in combined U.S. championships.

The comparison chart found in part one could resume in 2007, with the caution that, for several of those years, the U.S. championships’ averages would be depressed due to large numbers of players competing in the U.S. Championships. 

Starting in 2014, both the U.S. Women’s Championship and the U.S. Championship were round robins of smaller sizes. Comparisons would again be possible, as they were for 1972–2000, the focus of this two-part series. A future article could analyze those more recent years, 2014–2020, when the percentage of US Chess female members is above 10%, to see if the rating gap is closing between the U.S. Women’s and the U.S. Championship fields. Also possible is a second historical article, about the years 1950 to 1972 and the average ratings for those years for the U.S. Women’s and U.S. Championships.

Links

The ratings gap and gender: Analyzing U.S. Chess Championships (Part I)


Alexey was the 1989 U.S. Women's Chess Champion and is a Woman International Master. She earned her bachelor’s degree in History at the University of Puget Sound and her doctoral degree in Education at The University of California, Los Angeles. She has been a Lecturer in Interdisciplinary Studies at UT Dallas since 1999 and is a prolific author.
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Longhorn Longhorn 4/30/2021 07:18
Adbennet wrote, "Your suggested plan above sounds like a necessary condition for improvement, but is it a
sufficient condition?"

In Scottsdale AZ and Beverly Hills CA, female realtors are as interested, involved, educated, and successful
as men. Highly competent and motivated. If you Google '22 Best Scottsdale Real Estate Agents' 11/22 are women.
I know many other Scottsdale female millionaire realtors. On Yelp, 'Best Real Estate Agents Beverly Hills CA'
I found 6/10 were female. Adding a couple, it was 7/11. The interest, Professionalism, and Success of Women
in the field of Real Estate demonstrates that in that subject - Real Estate - that the qualities that produce success
in that field - including INTEREST and DEVOTION - is a sufficient condition. Parity at the top in Scottsdale and Beverly Hills shows what interest in a subject produces.

In contrast, although about 70 percent of US women cook, in the US Cooking industry, there are 392,000
Male Chefs and Head cooks. 114,000 female. Thus, 77.4% male.
In the famous 'Bocuse d'Or' (World Cooking Contest) held every 2 years (since 1987), 16 men have won and 1
female (Lea Lindster, 1989). In the '100 best chefs in the World' by Lissa Poirot 3/22/21, 5 are female.

Relative to other successful career pursuits, women aren't as interested in Professional cooking as are men.

In chess women aren't interested in the game much. Otherwise they would comment here in numbers similar
to their supposed USCF membership totals. Instead comments are near 0. If they have a 12% membership rate, every 7-8 players on the FIDE/USCF top player ratings lists would be female. In the end, perhaps women underestimate the value of a 2400+ Trainer.

In this brief study, women are successful in Real Estate because it attracts them.
adbennet adbennet 4/26/2021 03:50
Longhorn wrote: "The point is that there's no substitute for reading Classical chess books, studying a 1000 games, frequency of play, playing actively in strong tournaments, and obtaining a Trainer."

Yes, agreed. Couple of counterpoints though. (1) _Why_ were women in 1974 playing so infrequently? And still after all this time? We should ask women this question and not shut them down when we don't like their answer(s). Because maybe women need to do something different, _or_ maybe men need to do something different. (2) Your suggested plan above sounds like a necessary condition for improvement, but is it a sufficient condition? If there are other conditions, are they outside of the player's control? Are the conditions different for women than for men?

I don't pretend to know the answers.
Longhorn Longhorn 4/23/2021 07:08
"Women made up 5 percent of the total USCF membership."
I played in 500-600 USCF rated games from 1972 thru 1988. (Peak rating 2110 Summer 1987). Most games were played in Massachusetts. The Boston area had strong players, often approaching those
in CA and NY.

From 1972 thru 1976, I rarely saw more than 1 or 2 women playing in a 100+ person tournament.
Be it the Open section, under 1800 sections, etc. If female membership was 5 percent, participation
was half that.

Moreover, when a few more women eventually participated, they often had a master or GM husband/boyfriend.
ie Anna Akhsharumova (Gulko), Esther Epstein (Ivanov), Natasha Us (Christiansen).

In the December 1974 Chess Life & Review magazine Annual rating list, US Women's Champion Mona Karff
leads the Women's rating list at 2011 USCF rating. Number 12. is 1806. The average for the top 12 women is 1879.
Contrast this with top 13 and 14 year old boy ratings from 12/74. 2289, 2109, 2034, 1983, 1934, 1932, 1925, 1902,
1867, 1848, 1841, 1838, Average for 13 & 14 year olds: 1958.

On the December 1974 list there are 175 masters (US citizens) and 23 like Senior Masters (2400+) 203 players.
(this does not include the hundreds of male experts 2000-2199). This contrasts sharply with the Womens list
of 2011, 1919, 1917, 1898 and so on.

47 years later, the Top 10 US women average 2430. Led by Irina Krusch at 2521 (FIDE 2429). She is ranked 72
on the Overall April 2021 USCF list, This 2430 average is on par with that of the top ten 17 year olds (2465 average)
along with the 16 year olds (2423).

What counts here is not that US top female players have moved on from 13-14 year old parity of strength
comparisons to those of 16 - 17 year boys (Sophomore/Juniors in HS).

The point is that there's no substitute for reading Classical chess books, studying a 1000 games, frequency
of play, playing actively in strong tournaments, and obtaining a Trainer.
abdekker abdekker 4/20/2021 04:19
Agree with @Leavenfish. A good path forward is to de-segregate and combine everyone into one championship. Then the rop-ranked player is the "US Open champion", and the top-ranked woman is the "US Woman champion". And if the US gets their own Judit Polgar, and she wins the Open...awesome!

Chess is an aggressive war-simulation game. Or more simply, its just a game. Are we *really* surprised when us daft, one-track-minded males with our egos and bravado and loutish behaviour push girls out of the game?

TFor me, Judit Polgar and Alexendra Kosteniuk and Hou Yifan (and others) prove beyond doubt that this notion that men are somehow innately "better" at chess is just nonsense. Sure, maybe male brains have evolved to be a minute fraction better at 3D visualisation or whatever, but any of those players would beat 99% of males with their eyes shut!

The authors are right. The rating difference is cultural and down primarily to participation levels.

Show kindness and respect to all your opponents. And let us de-segregate tournaments.
adbennet adbennet 4/20/2021 04:05
"We hypothesize that the difference in ratings between the U.S. Women’s Championship and the overall U.S. Championship is expected due to the small numbers of girls and women with USCF memberships." .. "We conclude that the gender participation gap influences the average rating differences between the U.S. Championship players and the U.S. Women’s Championship players, and, therefore, the difference would be expected."

The hypothesis is plausible, but when stated as hypothesis and conclusion like this, the conclusion is unfounded. It would be unfounded even if all USCF participation and USCF ratings numbers were available for all years. The authors need to devise a comparison across *two* (or more) *large* data sets with different participation ratios that would confirm (or not) the hypothesis. They would also need to control for other mitigating factors which might differ between men and women and explain (or not) any statistically measured differences.
fgkdjlkag fgkdjlkag 4/20/2021 03:07
Maybe the locus of control is very important for gender differences in chess. It takes tremendous psychological toughness to be a strong chess-player. If you believe in the victim narrative, it is probably already too late. But if you do not consider it (eg, Judit Polgar), then you can play on an equal level.

There was a famous study that took place online and women were not told their opponent but was told the gender. When they were told they were playing a male (but in actuality they were playing a female), they played worse, compared to if they were told they were playing a female. They also found stylistic differences, females played more aggressively when they were told they were playing females. At least this study indicates psychological factors as a component.
fgkdjlkag fgkdjlkag 4/19/2021 09:49
This sort of analysis based on participation numbers does not prove anything, as what if fewer women play chess because they are worse at it?

@Leavenfish, that is the format of the Spanish championship and I agree with it. It was done once in the US Championship. Also why not lump the US Junior and US Girls championships into it as well. I proposed that grouping the Open and Women's be done at the US Championship and the response I got was that the results would be less accurate. Although that it true, I think the pros outweigh the cons.
MrSnrub MrSnrub 4/19/2021 08:54
Typically, the authors seem hold it as axiomatic that women can't possibly be be less talented in chess than men, despite a mountain of evidence to the contrary. While other factors certainly play a role, the simplest and most probable explanation remains differences in cognition. Is it really so terrible if men are better at some things and women better at others? Must we blind ourselves to reality in service of some simplistic notion of equality?
Leavenfish Leavenfish 4/18/2021 08:37
I think the answer is painfully simple and requires no ‘funding for studies’: a much larger percentage of women do not care for the mental combat of chess compared to men. If it’s genetics, so be it; if it’s “male white corporate oppression” (nod to Sonic Youth), so be it…

For space limitations, I cite the (pre-COVID) 1998 winners. Go to uschess.org and you see Paikidze played in no other tourney that year. Sam Shankland – Open winner, played in 8. You get rating increases by being a bit better than those you play and if you don’t play or largely play in ‘gender specific tourneys with their smaller ratings, well…

To address what the author notes – an obvious answer: DESEGREGATE and combine the two ‘Championships’ and let the highest scoring female player be the ‘Women’s Champion’. I know that would never fly with those who have a vested interested in continuing to SEGREGATE the sexes…but it would get the better female players out of the kiddie rating pool which had 3 U 2300 and 7 U 2400 players by putting them into a pool of higher rated players. The lowest in the Open section was 2552…over 100 rating point higher than the highest rated player in the women’s only section.

Math…does not have to be that hard people.
BeFreeBusy BeFreeBusy 4/18/2021 05:17
If only men would compete with women, then women`s ratings would obviously get higher and men`s lower. Now that men players play only with other men (sexist or misogynistic agenda), things probably will not change so easily. I think one explanation is men are afraid of women.
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