Fair qualifying times give all athletes an equal opportunity to compete, regardless of sex. If an age group has twice as many girls than boys, then a fair event would qualify twice as many girls than boys in that age group. Conversely, an event that qualifies equal numbers of girls and boys in an age group can only be fair if that age group includes equal numbers of girls and boys. In this post, we analyze the fairness of the 11-12 50m backstroke qualifying times in the 2019 Eastern Zone Long Course Age Group Championships (EZ2019L). Girls and boys aged 11 to 12 both need a 34.59L to qualify for this event. No converted or non-conforming times are accepted, so the only way to qualify for this event is to swim the 50m backstroke in a 50m pool in the past year, and finish in 34.59 seconds or less. We report that the Eastern Zone currently has 1.3 times as many girls as boys, but the aforesaid qualifying times admit 1.3 to 1.7 times as many boys as girls. These two imbalances combine multiplicatively to give a boy 1.8 to 2.3 times greater opportunity to swim the 11-12 50m backstroke than a girl. Since there are more girls than boys in the Eastern Zone 11-12 age group, but fewer are likely to qualify for 50m backstroke, we conclude that the qualifying times for this event discriminate against girls to the benefit of boys. ## Data Sources.Our analysis of EZ2019L qualifying time fairness uses both historical and current data. For historical data, we’ll use our database of 23 million USA-S age group swims in over 15,000 meets across 14 years. The data was collected from eighteen USA-S LSCs and one Zone. It has been analyzed and reported on at http://www.swimtheory.com/home/001-lifecycle For current data, we’ll use swimmingrank.com. Swimmingrank.com is arguably the top internet source of current USA-S age group swimming data. It publishes the top 1000 times achieved in the current competition year in every age group event by every Zone and LSC, along with full team rosters for all fifty nine LSCs. The remainder of this post consists of five sections. In the first section, we estimate the ratio of girls to boys in the 11-12 age group. In the second section, we estimate the ratio of boys to girls in the 11-12 age group who will qualify for the 50m backstroke at EZ2019LC. In the third section, we combine our estimates into an overall assessment of the fairness of this event. In the fourth section we explain how to recast our analysis in probabilistic terms. The fifth section demonstrates that USA Swimming’s AAA motivational times for the same event qualify comparable numbers of 11-12 athletes but are significantly fairer than the EZ2019LC cuts. ## Step 1: Age Group Population.The first step in our analysis is to estimate the ratio of girls to boys in the Eastern Zone 11-12 age group, using both historical and current data. As summarized in the following table, we estimate that the 11-12 age group contains 1.28 to 1.49 times more girls than boys. “Historical” is from our database of 23 million age group swims. An athlete is included if they swam at least one event in an age year without being disqualified. “Historical LCM” is from the same data, but restricted to those athletes who swam a LCM event in their 11th or 12th year. “Current US” is from all USA-S club rosters posted on swimmingrank.com as of 2019-05-02. “Current EZ” is from the subset of Eastern Zone club rosters posted on swimmingrank.com. This table reports the breakdown of “Current EZ” by LSC. Every Eastern Zone LSC has more girls than boys in the 11-12 age group. “Current EZ Stratify” is a stratified sample of the clubs with the most 11-12 athletes for each of the twelve LSCs in the Eastern Zone, in alphabetical order. It includes two clubs from Niagara Swimming (NI) because they are tied for the greatest number of 11-12 athletes in that LSC. We include this stratified sample so that the reader can manually verify our athlete counts on swimmingrank.com. “Current EZY Sample” provides the current roster of the ten clubs with the most swims at the 2019 Eastern Zone Short Course Age Group Championships. Again, we include this sample so that the reader can manually verify our athlete counts on swimmingrank.com. We’ve learned that the 11-12 age group in the Eastern Zone includes 1.3 to 1.5 times more girls than boys. Next we’ll estimate how many of those athletes can swim the 50m backstroke in 34.59L or less. ## Step 2: Qualified Population.The second step in our analysis is to estimate the ratio of qualified boys to qualified girls in the Eastern Zone 11-12 age group, using both historical data and current data. As summarized in the following table, we estimate that the 11-12 age group contains 1.26 to 1.71 times as many qualified boys than qualified girls. “Historical” is from our database of 23 million USA-S age group swims. “US 2019-05-18” is from the top 1000 current season USA-S swims on swimmingrank.com as of 2019-05-18. This count may be verified via archived links for the boys and girls. “EZ 2019-05-18” is from the top 1000 current season Eastern Zone swims on swimmingrank.com as of 2019-05-18. This count may be verified via archived links for the boys and girls. As of this writing, the 2019 Eastern Zone Long Course Age Group Championships is a few months away. No one -- including the Eastern Zone technical committee -- knows for sure how many boys and girls in the 11-12 age group will ultimately qualify for the 50m backstroke in that meet. Our estimates of the ratio of qualified boys to girls are credible, transparent, and verifiable, and they all predict that substantially more boys than girls will qualify for this event, even though the 11-12 age group includes substantially more girls than boys. ## Step 3: Qualifying Time Advantage.The third and final step of our analysis is to multiply the population ratio and the qualification ratio to arrive at an overall fairness ratio. This fairness ratio is 1.0 when the event is perfectly fair. It is greater than 1.0 when the event favors boys, and less than 1.0 when the event favors girls. Below we’ll prove that the fairness ratio is mathematically equivalent to the boy’s likelihood of qualifying divided by the girl’s likelihood of qualifying. In step 1, we provided six estimates for the girls-to-boys population ratio in the Eastern Zone 11-12 age group, ranging from 1.28 to 1.49. These estimates appear on the left edge of the following table, highlighted in red. In step 2, we provided three estimates for the boys-to-girls qualification ratio for the 11-12 50m backstroke, ranging from 1.26 to 1.71. These estimates appear on the top edge of the following table, highlighted in blue. Multiplying the six population ratios by the three qualification ratios gives us eighteen possible fairness ratios, which range from 1.61 to 2.54. These fairness ratios appear in the center of the table, highlighted in purple. Thus we estimate that a boy has 1.61 to 2.54 times greater opportunity to compete in the 11-12 50m backstroke than a girl. The most consistent estimates are where both ratios are calculated using the same data. When using the same data for population and qualified ratios, we see that a boy has 1.81 to 2.28 times greater opportunity to compete in this event than a girl. ## Technical Note: The Duality of Ratios and Probabilities.In step 1, we calculated the girls-to-boys population ratio ng/nb using two numbers: ng - the number of girls in the athlete population; and nb - the number of boys in the athlete population. In step 2, we calculated the boys-to-girls qualified ratio qb/qg using two additional numbers: qg - the number of girls who qualified; and qb - the number of boys who qualified. In step 3, we multiplied these two ratios (qb/qg)(ng/nb) = ((qb/nb)/(qg/ng)) to arrive at the fairness ratio. This algebraic equivalence proves that the fairness ratio is mathematically equivalent to the likelihood qb/nb that a boy qualifies divided by the likelihood qg/ng that a girl qualifies. While the population and qualified ratios are easy to understand, the likelihoods are easier to work with. As shown in previous posts, we can roll up the event qualifying likelihoods to calculate the overall fairness of an age group or an entire meet. For completeness, this table reports the four qualifying likelihoods for boys and girls in the “Likelihood” columns. The boys-to-girls fairness ratio appears in the rightmost column, highlighted in purple; it ranges from 1.81 to 2.28, meaning that a boy has a 1.81 to 2.28 times greater likelihood of qualifying than a girl. ## AAA Motivational Times are Much Fairer.Previously we’ve seen that the AAA motivational times used by the Central Zone for it’s age group championships are remarkably fair. For this reason, on April 11 2019 we proposed to the Eastern Zone Technical Planning Committee that they use the AAA motivational times instead of their draft cuts, which were demonstrably unfair to girls. Accordingly, it is instructive to compare the fairness of the EZ2019L qualifying times and the AAA motivational times for this event. The AAA motivational times for the 11-12 50m backstroke are 34.79L for girls and 34.09L for boys. Under those times, more girls than boys qualify under all estimates (Historical, Current US, Current EZ). The fairness ratio ranges from 0.97 for Current EZ data to 1.15 for Historical LCM. Thus, the AAA motivational times qualify similar numbers of athletes but are vastly fairer than the EZ2019L qualifying times. This chart plots the fairness ratios of the EZ2019L cuts and the AAA motivational times for the 11-12 50m backstroke. It clearly shows that the AAA times are vastly fairer than the EZ2019L cuts, for all four data sources. Recall that a perfectly fair event has a fairness ratio of 1.0. ## Conclusion.No matter whether we use historical data or current data, the picture remains the same. The qualifying times for the 11-12 50m backstroke in the 2019 Eastern Zone Long Course Age Group Championships appear to greatly disadvantage girls to the benefit of boys. We have also seen that USA Swimming’s AAA motivational times are significantly fairer for this event. The likelihood of an athlete qualifying for an event measures the opportunity afforded to that athlete by the meet’s organizers. Swim meets have a limited amount of pool time. Therefore athletes with greater qualifying likelihoods are afforded greater opportunity to compete at the expense of those athletes with lesser qualifying likelihoods. In this case, it appears that the Eastern Zone gives a boy nearly double the opportunity to compete in the 11-12 50m backstroke than a girl. Revision History. 2019-05-06 Published. 2019-05-18 Updated US and EZ qualified counts. 2021-04-01 Corrected typos, added links. |