12 August 2008

Variance in Olympic events

It's often claimed that the reason that there are many more men than women in certain academic disciplines (mathematics is one, but that's not the point of this post) is not that men and women have different mean abilities, but rather that the standard deviation of male ability is larger than the standard deviation of female ability. (Of course, it is unwise to espouse these views publicly, for political reasons; that's what got Larry Summers in a lot of trouble.)

It occurs to me, having watched lots of the Olympics in the last few days, that something similar might be true in athletic events. I'm not claiming that men and women are physically identical (I'm not blind), or that their average performance in physical feats is the same. But it may be the case that the difference between the very best men and the very best women in physical feats (say, times in some sort of race, because these are the most easily quantified) is larger than the difference between the average man and the average woman, because there could be more variance among men than women.

Is there any evidence for this? I'm obviously not a student of this sort of thing (in fact, I don't even know what "this sort of thing" is called, although it's clearly some subfield of biology or medicine).

Oh, and Jordan Ellenberg wrote an explanation of why the new gymnastics scoring system is good. I'm glad he did, because I'd had a feeling it was better than the old system but was having trouble articulating why.

10 comments:

Anonymous said...

A difference in variance between sexes could also be more perceived than real: if a greater percentage of men can pursue athletics, then we can encounter more impressive outliers among them.

Yes, the new scoring system seems to make more sense.

unapologetic said...

Actually the first place I ever heard of differing variances was to explain racial disparities in physical performance.

MikeWebkist said...

I don't even know what "this sort of thing" is called, although it's clearly some subfield of biology or medicine

I think you're looking for Kinesiology.

John said...

I wrote a post this afternoon to explore your question assuming male and female performance are normally distributed.

Variation in male and female Olympic performance.

Loz said...

I've read that female hips are slightly less efficient for running than male hips. No idea how it's measured or whether there's anything to concrete back it up. If it's true it might suggest different means.

Blake Stacey said...

It's not even a well-established claim with regard to academic or mathematical performance. Setting aside a whole host of other problems, which gender has the larger variance changes from country to country.

Anonymous said...

I do wish people would stop with the myth that Larry Summers' main problem was that he once espoused an unpopular political view. While that's a convenient version of the history for many with an axe to grind, the truth of it was he was just a bad manager and leader, and this incident (one in a long series) provided an excuse for all his detractors to call him out.

Blake Stacey said...

Stephen Jay Gould wrote a whole bunch about baseball statistics, proposing an answer to the "where are the .400 hitters?" question; one upshot, I recall, was that distributions of quantities of interest are not Gaussian, being squeezed by an effective "wall" on one side or the other. So, you'd probably have to look at higher cumulants to compare any two populations and figure out what's going on.

It's also possible, hypothetically, that some athletic performance quantifier is normally distributed in the general population, or among the total population of players, but the selection process skews the distribution. Suppose that for the set of all Centrifugal Bumble-Puppy players, the number of fizzbins scored per year follows a Gaussian distribution. Only the best Centrifugal Bumble-Puppy player in each regional league can compete in the National Championship. What, then, is the probability distribution for fizzbins per year among National Championship contestants? The answer won't be a Gaussian, but rather an extreme-value distribution, an asymmetric curve not at all well characterized by its mean and variance.

I'm far too ignorant about sports to speak of the issue in less hypothetical terms.

Anonymous said...

I do wish people would stop with the myth that Larry Summers' main problem was that he once espoused an unpopular political view. While that's a convenient version of the history for many with an axe to grind, the truth of it was he was just a bad manager and leader, and this incident (one in a long series) provided an excuse for all his detractors to call him out.

I don't want to turn this into a discussion of Larry Summers, but let me say that he is often underestimated, and I consider him in no way a bad leader. A lot of people think a president's job is to raise as much money as possible while not taking any position that could possibly upset a faculty member. Instead, Summers actually tried to use the position to do some good for Harvard. Some things he did were almost universally viwed as good (such as massively increasing financial aid for low-income students). Many were probably good for Harvard overall but caused some faculty to hate him. (Think Allston expansion or tightening law school tenure standards or making science a higher priority for Harvard.) Eventually, too many people felt that they could benefit by replacing Summers with somebody spineless. Maybe it was a failure of leadership that he pushed too hard, but if so that was his main failing.

If it hadn't been for the Cornell West situation (which he was 100% right about) and the women in science comments (which he was perhaps 25% right about), he would probably still be president now. He didn't lose his job because of those comments, strictly speaking - the faculty were upset with him over other issues (and the students were never particularly upset with him). However, these situations caused enough embarrassment to Harvard to push the corporation to go along with his enemies on the faculty.

jd2718 said...

Thanks for the link, nice piece. Has anyone tried rescoring those 10s using the new scoring system?

(inherently unfair, as those gymnasts were performing against the 10 scale, but still interesting)

Jonathan