003.006 The Fairness of Equal Acceptances

In previous posts, we learned how to quantify the sex-fairness of event qualifying times.  We saw that championship events are sex-fair if and only if their qualifying times accept male and female athletes at similar rates.  Thus, a sex-fair age group championship event admits boys and girls in proportion to their representation in USA-S age group swimming.


Our analysis based on qualifying times applies to most -- but not all -- USA-S age group championships.  The Southern Zone long course age group championship does not have qualifying times.  And prior to 2018, the Eastern Zone short course age group championships did not have qualifying times.  These championships accept equal numbers of male and female athletes from their constituent LSCs.


This post will explore whether this approach produces fairer entry opportunities than the more common method based on qualifying times.  We’ll learn that such meets are sex-fair only if the underlying athlete population has equal numbers of male and female athletes.

From Gender Distribution to Acceptance Ratios.

Let pf be the fraction of female athletes in a USA-S age group and pm= 1-pf be the fraction of male athletes in that age group.  In an age group event that accepts equal numbers of men and women, the ratio of their acceptance rates is pf / (pf-1).  When the sexs are balanced, pf = pm=0.5 and the acceptance ratio is 0.5/0.5 = 1, ie., perfectly fair. As the fraction of female athletes increases, pfgrows larger than pmand the acceptance ratio grows larger than 1, ie., increasingly unfair.


Previously we learned that 56.3% of USA-S age group athletes are female (pf=0.563).  And therefore, the acceptance ratio for events that accept equal numbers of men and women is 0.563/0.437 = 1.29, meaning that men have 1.29 times the likelihood of being accepted.

The following chart plots the sex distribution of USA-S athletes by age group.  It shows that there are more female than male athletes in every age group, with the smallest difference in the 15/Over group.

From this information, and the formula above, we can infer that any meet that accepts identical numbers of men and women by age group will be unfair to women to the degree shown by the following plot.  

It shows that in any event that accepts identical numbers of men and women, the men have 1.39 times the likelihood of qualifying in the 10/Under age group, 1.44 times in the 11-12 age group, 1.36 times in the 13-14 age group, and 1.03 times in the 15-18 age group. In other words, since more women compete in USA-S age group swimming, it is only fair that they be allotted more berths in USA-S age group championships. 

Discussion.

The athlete sex distribution is nearly identical for long- and short-course.  Nonetheless, we can refine our analysis by using the SCY sex distribution to derive acceptance ratios for SCY meets, and the LCM sex distribution to derive acceptance ratios for LCM meets.


We can combine these generic acceptance ratios with the “expected recent swims” values for a given meet to calculate the qualifying time likelihood ratios for that meet.  Since women typically swim slightly more championship events than men, this will tend to result in increasingly unfair qualifying time likelihood ratios.

Conclusion.

We’ve seen that meets which accept equal numbers of men and women are sex-fair only when the athlete population contains equal numbers of men and women.  Since USA-S age group swimming contains more female than male athletes, such meets are unfair to female athletes.


Revision History.


Published

2021-02-18

Added links. Replaced “gender” with “sex”.