Right off the start let me clarify that I’m not talking about civil rights: those must be equal. What I’ll be talking about is the difference between the two genders in the Boston qualifying (BQ) standards. It’s not a new topic, it comes back over and again at least once a year, but the unprecedented closing of the registration for the Boston Marathon had spurred many pundits to discuss the topic once again. One of the punchlines was: women should have tougher qualifying times.

As it stands now, men younger than 34 have to run, in order to qualify for Boston, a marathon in 3:10:59 or faster, while women 3:40:59 or faster. The Wall Street Journal wrote an article suggesting that, because the difference between the two world records is closer to 20 minutes than to 30 minutes, so should the qualifying times. The topic is obviously delicate, since we all (repeat with me, we all) want equality between genders, but at the same suggesting a strict equality in sports, and track and field in particular, would create an unfair disadvantage for women; men and women are different, and it’s not surprise that not even Paula Radcliffe can outrun Haile Gebrselassie.
Running Times rebuked the WSJ article with a well-rounded discussion on how different is different, and how 30 minutes difference in the BQ’s is probably fair.
I really liked the Running Times article, but I’m accustomed to do things my way, in particular I wondered why nobody had ever done a statistical analysis of the problem; it’s nothing hard and it took me no more than half an hour (most of which was dedicated to make cool graphs).

I’ll discuss a bit about the data before drawing my conclusions.
Everyone who’s ever run a race knows that every race is different: there are fast races and slow races, good running weathers and bad running weathers … The variable are so many that I had to be careful into trying to find the most homogeneous of data; I ended up deciding not to average over different races, but to pick up one single race in one single year. The best choice, I think, is to take a good Boston qualifier, that is, a marathon that is sanctioned to be a qualifier and that is considered fast enough (no hills, mostly dry, cool weathers); I went for the Chicago Marathon, which is known for its flat, fast course, and for its 2009 edition. The year was chosen because the weather was almost perfect and Sammy Wanjiru set the course record. I then went online and downloaded the entire male 30-34 and female 30-34 field divisions: Chicago is big enough a race that both divisions have around 3000 participants, so the sample should be statistically significant.
The following is the plot of the histogram of the men data and interpolating Gaussian curve of average, 4 hours 14 minutes, and standard deviation, 50 minutes.

Average: 4 hours 14 minutes; Standard Deviation: 50 minutes

For the women, the average was 4 hours 39 minutes and the standard deviation 48 minutes.

Average: 4 hours 39 minutes; Standard Deviation: 48 minutes

I was surprised to find the two standards deviations very similar, 50 minutes vs 48 minutes. I was expecting a larger spread for the women; the reason of the bias is that, because women are slower, they should be more effected by race traffic than men (by the way, the WSJ argues that the reason of a larger spread in women times would be that they are more social than men). The similarity in the two curves can be more easily seen when plotted together:

Blue curve and data: men; Red curve and data: women

The BQ times were thought to create a challenge high enough to limit the field and easy enough not to destroy the field. And it’s pretty interesting that the time of 3:10 for men is 1.25 standard deviations away from the average; if we believe that the natural predisposition should fall in a bell curve, around 10% of the population should be able to qualify. (By the way, I tested the Gaussian distribution assumption with the standard χ² test and found a 99.9% of agreement.)
An analogous BQ time for women should be 1.25 of their standard deviations faster than their average, which gives … 3:39, just 1 minute shy of their current BQ, 3:40.

This, for me at least, closes the discussion and suggests that women BQ’s are not easier than men.

Advertisements