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WZ2019L-50FR

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 freestyle qualifying times in the 2019 Western Zone Long Course Age Group Championships (WZ2019LC).  Girls and boys aged 11 to 12 both need a 29.39L, a 28.59S, or a 25.69Y to qualify for this event.  Since SCM swims are so rare in the USA-S, our analysis will be limited to the 29.39L and 25.69Y cuts.


We report that the Western Zone currently has 1.3 times as many girls as boys, but the aforesaid qualifying times admit 2.0 to 6.8 times as many boys as girls.  These two imbalances combine multiplicatively to give a boy 2.8 to 10.2 times greater opportunity to swim the 11-12 50m freestyle than a girl. Since there are more girls than boys in the Western Zone 11-12 age group, but far fewer are likely to qualify for 50m freestyle, we conclude that the qualifying times for this event manifestly discriminate against girls to the benefit of boys.

Data Sources.

Our analysis of WZ2019L 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 freestyle at WZ2019LC. 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 are significantly fairer than the WZ2019L cuts.

Step 1: Age Group Population.

The first step in our analysis is to estimate the ratio of girls to boys in the Western 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 1.31 to 1.49 times more girls than boys.


11-12 Age Group

Girls

Boys

Girls/Boys

Historical

158,628

110,193

1.44

Historical LCM

73,937

49,662

1.49

Current US

41,124

30,362

1.35

Current WZ

20,180

15,446

1.31


“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 age year.


“Current US” is from all USA-S club rosters posted on swimmingrank.com as of 2019-05-02.  


“Current WZ” is from the subset of Western Zone club rosters posted on swimmingrank.com.  This table reports the breakdown of “Current WZ” by LSC; it shows that every Western Zone LSC has more girls than boys in the 11-12 age group.


LSC

11-12 Girls

11-12 Boys

Girls/Boys

AK

238

166

1.43

AZ

544

305

1.78

CA

2,341

1,994

1.17

CC

151

99

1.53

CO

1,113

735

1.51

HI

312

229

1.36

IE

171

135

1.27

MT

146

88

1.66

NM

229

148

1.55

OR

770

545

1.41

PC

1,672

1,366

1.22

PN

837

718

1.17

SI

457

340

1.34

SN

296

223

1.33

SR

141

78

1.81

UT

492

436

1.13

WY

180

118

1.53

Total

10,090

7,723

1.31


We’ve learned that the 11-12 age group in the Western 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 freestyle in 29.39L or the 50yd freestyle in 25.69Y 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 the Western 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 2.12 to 6.83 times more qualified boys than qualified girls.


11-12 50m Freestyle

Qualified Girls

Qualified Boys

Boys/Girls

Historical

1,711

3,625

2.12

USY 2015-05-17

280

660

2.36

WZY 2015-05-17

74

152

2.05

USL 2019-05-17

42

155

3.69

WZL 2019-05-17

6

41

6.83


“Historical” is from our database of 23 million USA-S age group swims.


“USY 2019-05-17” and “USL 2019-05-17” are from the top 1000 current season USA-S SCY and LCM swims respectively on swimmingrank.com as of 2019-05-17.  These counts may be verified via archived links for the boys (SCY; LCM) and girls (SCY; LCM).


“WZY 2019-05-17” and “WZL 2019-05-17” are from the top 1000 current season Western Zone SCY and LCM swims respectively on swimmingrank.com as of 2019-05-17.  These counts may be verified via archived links for the boys (SCY; LCM) and girls (SCY; LCM).


As of this writing, the 2019 Western Zone Long Course Age Group Championships is more than  two months away. No one knows for sure how many boys and girls in the 11-12 age group will ultimately qualify for the 50m freestyle 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 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 a boy’s likelihood of qualifying divided by a girl’s likelihood of qualifying.


In step 1, we provided four estimates for the girls-to-boys population ratio in the Western Zone 11-12 age group, ranging from 1.31 to 1.49.  These estimates appear on the left edge of the following table, highlighted in red.


In step 2, we provided five estimates for the boys-to-girls qualification ratio for the 11-12 50m freestyle, ranging from 2.05 to 6.83.  These estimates appear on the top edge of the following table, highlighted in blue.


Multiplying the four population ratios by the five qualification ratios gives us twenty possible fairness ratios, which range from 2.68 to 10.17. These fairness ratios appear in the interior of the table, highlighted in purple.


11-12 50m Freestyle

Qualified Boys/Girls

Historical

USY 2015-05-17

WZY 2015-05-17

USL 2019-05-17

WZL 2019-05-17

Population Girls/Boys

2.12

2.36

2.05

3.69

6.83

Historical

1.44

3.05

3.39

2.96

5.31

9.84

Historical LCM

1.49

3.15

3.51

3.06

5.49

10.17

Current US

1.35

2.87

3.19

2.78

5.00

9.26

Current WZ

1.31

2.77

3.08

2.68

4.82

8.93


Thus we estimate that a boy has 2.7 to 10.2 times greater opportunity to compete in the 11-12 50m freestyle 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 3.0 to 8.9 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 3.05 to 8.93, meaning that a boy has 3.05 to 8.93 greater likelihood of qualifying than a girl.


11-12 50m Freestyle

Girls (29.39L/25.69Y)

Boys (29.39L/25.69Y)

Boys/Girls

Population

Qualified

Likelihood

Population

Qualified

Likelihood

Fairness

Historical

158,628

1,711

0.0108

110,193

3,625

0.0329

3.05

Historical LCM

73,937

1,711

0.0231

49,662

3,625

0.0730

3.15

Current US

41,124

42

0.0010

30,362

155

0.0051

5.00

Current WZ

20,180

6

0.0003

15,446

41

0.0027

8.93


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, we propose to the Western Zone Technical Planning Committee that they adopt the AAA motivational times instead of their current cuts, which are demonstrably unfair to girls.  Accordingly, it is instructive to compare the fairness of the WZ2019L qualifying times and the AAA motivational times for this event.  The AAA motivational times for the 11-12 50m freestyle are 30.49L/26.79Y for girls and 29.39L/25.59Y for boys. Under those times, more girls than boys qualify under all estimates (Historical, Current US, Current WZ).  The fairness ratio ranges from 0.79 for Historical data to 0.91 for Current US, which affords a girl 1.10 to 1.27 times greater likelihood of qualifying than a boy. Thus, while the AAA motivational times are not entirely  fair for this event, they are nonetheless vastly fairer than the WZ2019L qualifying times.


11-12 50m Freestyle

Girls (30.49L/26.79Y)

Boys (29.39L/25.59Y)

Boys/Girls

Population

Qualified

Likelihood

Population

Qualified

Likelihood

Fairness

Historical

158,628

6,260

0.0395

110,193

3,454

0.0313

0.79

Historical LCM

73,937

6,260

0.0847

49,662

3,454

0.0696

0.82

Current US

41,124

231

0.0056

30,362

155

0.0051

0.91

Current WZ

20,180

66

0.0033

15,446

41

0.0027

0.81


This chart plots the fairness ratios of the WZ2019L cuts and the AAA motivational times for the 11-12 50m freestyle. It shows that the AAA times are vastly fairer than the WZ2019L 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 freestyle in the 2019 Western 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 Western Zone gives a boy more than triple the opportunity to compete in the 11-12 50m freestyle than a girl.