003.004 The Fairness of Championship Meets

In the previous post, we explained how to analyze the fairness of an individual event in a recent elite age group championship meet (link).  We saw that the 13-14 year old 200 LCM breastroke event was fair to women and men. In this post, we’ll analyze the remaining events in that championship meet.  We’ll also explain how to roll up the analysis of individual events to an assessment of the meet as a whole. Again, we won’t name the meet because our goal is to develop our analytical technique, not criticize this particular meet or its organizers.

The Event Most Favorable to Women.

Let’s first consider the 13-14 200 LCM IM, which is the event whose qualifying times most favor women over men.  The women’s qualifying time for that event was 2:34.59; the men’s was 2:23.19. The Recent Swim metric in the following plot reports that slightly more women swam this event in their 13th or 14th year, while the Qualifying Time metric reports that 8.53% of the eligible women and 6.37% of the eligible men achieved the qualifying time in their 13th or 14th year. Thus women are 0.0853/0.0637 = 1.34 times as likely as men to achieve a qualifying time for this event in a recent swim.

Here is the log-ratio plot, which reports the logarithm of the men’s likelihood divided by the women’s likelihood.  Recall that positive log-ratios indicate that the men’s likelihoods are greater than the men’s, while negative values indicate the opposite.  Larger values indicate greater differences. The log-ratio reduces the magnitude of very large differences.

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This log-ratio plot shows that (1) women are slightly more likely than men to have swum the the 200m IM in their 13th or 14th year (”Recent Swim”); (2) women are significantly more likely than men to make the qualifying time in this event (“Qualifying Time”); and therefore (3) women are significantly more likely than men to qualify for this event (“Accepted”).

The Event Most Favorable to Men.

The event most favorable to men in this championship meet is the 11-12 100 LCM breastroke. The women’s qualifying time was 1:24.59; the men’s was 1:25.39.  Yes, the men’s qualifying time for this event was slower than the women’s. As a result, 11-12 men are 2.2 times as likely to achieve the qualifying time, and 2.0 times as likely to be accepted to the event even though the 11-12 women are 1.1 times more likely to have swum the event recently.

This extreme mismatch of opportunity is summarized in the following log-ratio plot.

Women are More Prepared.

The following graph plots the Recent Swim log-ratio for all events in the meet.  Recall that positive values indicate that men are more likely than women to have swum the event recently, while negative values indicate the opposite.  This graph shows that -- with the notable exception of the 13-14 year old 1500 LCM Free, which is by far the most rare LCM event -- women are more likely to have recently swum championship events than men.

Men’s Qualifying Times are Much Easier.

The following graph plots the Qualifying Time log-ratio for all the events in the meet.  Again, positive values indicate that men are more likely to have made the qualifying time recently, while negative values indicate the opposite.  This graph shows that it’s easier for women to qualify in only 8 of the 39 events, and often only by a little bit. Conversely, it’s easier for men to qualify in 31 of the 39 events, often by an enormous amount.  Men have at least 1.5x the likelihood of qualifying in 12 of the 39 events.

It’s Much Easier for Men to Enter Events.

Now let’s combine the Recent Swim and Qualifying Time likelihoods into an overall likelihood of being accepted to the event.  Again, even though women are more likely to swim championship events than men, the imbalance in qualifying times results in an imbalance in the overall likelihood of being able to enter an event in this meet. It’s easier for men to enter 32 of the 39 events, often by a large amount.

This conclusion is even more stark when we roll up the age groups for each event.  After the rollup, only one event -- the 400m IM, which is only offered to 13-14 year olds in this meet -- is favorable to women.  It’s easier for men to enter the other 16 events, often by a large margin.

Every Age Group is Gender-Unfair.

Finally, we’ll roll up the meet events by age group.  We’ll jump right to the log-ratio plot, which shows that the 13-14 age group is the most fair while the 11-12 age group is the least fair.  

In the 11-12 age group, men had a 1.55 times greater opportunity to enter events than women.  Overall, men aged 9 to 14 had a 1.23 times greater opportunity to enter events in this meet than women.

Conclusion.

To recap: we’ve seen that the qualifying times in this elite championship meet are remarkably unfair to women.  With a small number of exceptions, it’s much easier for men aged 9 to 14 to qualify for events in that meet than women.  In subsequent posts, we’ll examine the recent history of Zone- and LSC-level age group championship meets. We’ll discover that the qualifying times in these meets are also consistently biased against women athletes.