Gender equity in sports; Is equal prize money at equivalent events fair?

Since the last century sports have taken a crucial place in our society, mostly because they turned out into a profitable business for people around them. But also, because sports have become a tool to shape society. A great example of this occur when the equity gender concept started to grow during the 70’s, at that time society (or who was in charge to assign salaries) thought that women should earn less than men because they weren’t ‘as good’ as their male peers. To proof this idea wrong, a tennis court turned out to be the perfect arena; the ‘Battle of sexes” in 1973 was a tennis match between Bobby Riggs and Billy Jean King that proved to million viewers that women were as capable as men performing athletic skills. That day Billy Jean King won and started a fight for equal pay for men and women on sport events.

Nowadays most of the sports still have an unequal pay, just think at soccer or golf, (the gap is insane!!!) but some other sports as tennis, badminton or squash are trying to close this gap providing in some events same prize money for men and women.

Even though this should look like an effort unanimously celebrated, not everyone agrees with it; a couple of weeks ago Novak Djokovic said that men should earn more money than women players at because they attracted more people to watch the sport.

The logic of Djokovic might be right for a salesman or a pop singer, but not for professional athletes, as a tennis player he is sort of a ‘contractor’ of the ATP, and his pay is according to the place he finishes at competitions, not how many people watch him smiling at the camera or wiping his face with a giant towel. (Sponsors are the ones that should pay for that.)

I beleive that equity gender should fight for equal prize rewards for men and women according to their effort. To ensure that, you need to consider the differences that each athlete faces, and this doesn’t mean that equal pay at tournaments is the way to go.

To explain why equal pay at tournaments is not entirely fair I decided to use data from the PSA (Professional Squash Association)  to find out what is an equivalent pay for men and women. The analysis can be extended to similar sports with similar format and ranking systems

Analysis

For the analysis below I decided to use  data from the 2017 April PSA Rankings assuming two things:

  • Is equally difficult to be No 1 in the men’s rankings as in the women’s rankings.
  • Being last on the rankings requires no effort.

The rankings are assigned according to the average points earned during the last 12 months. Is natural to use the standardized average points as a measurement of effort. The following charts shows the effort required to be at a certain ranking for men and women. The logarithmic transformation chart shows the same information but emphasising the difference on crucial sports.Effort

From this chart, we can see that it requires almost the same amount of effort to be at the top positions, but as soon as the ranking start dropping, the effort required for men is higher. This happens mainly because there are more men than women in the rankings. This fact is crucial but doesn’t tell the whole story.

Assigning an effort to each ranking is what I consider the best method with the avaliable data to find equivalent rankings, although is not the only one.

On the chart below I want to show 3 methods that could be used to find equivalent rankings between both genders.

  • Effort. This method matches the effort required for every ranking according to the previous analysis.
  • Naïve. This method assumes parity between both rankings, although this is unrealistic due different population sizes it a useful reference tool.
  • Active players.  This method divides the rank according to the number of active players.

Equivalent

The left chart shows that the effort and the active players methods are almost equivalent, but the way they compare the top 10 is not the same. The right chart zoom in at the Top 10 ranking positions, you can see that the closer it gets to the No 1 the active player method gets closer to the Naïve method. This means that for the number of players in both rankings, women are more competitive on the race to the top than men.

The table below shows the ranking equivalency for men and women according to each method.

Women Rank Equivalent Men Rank
Effort(%) Active Players Naive
1 1 1 1
2 2 3 2
3 4 5 3
4 6 8 4
5 8 10 5
6 11 12 6
7 13 14 7
8 15 16 8
10 20 21 10
20 38 42 20
26 50 56 26
46 100 100 46
50 109 108 50
90 200 196 90
100 220 216 100

Since the Effort matching method captures better the relationship on the top 10 than the Average Players method (in which most of the money is distributed) I will use for the rest of the analysis.

If the goal is to make sure that you get paid properly despite the gender then prizes should be assigned in a way that players with equivalent rankings make the same amount of money in a whole year. To ensure that, it is important to find if players with equivalent rankings participate on similar amount of tournaments (assuming that every tournament pays exactly the same amount of money), that way they can make almost the same amount of money.

Tournam played

Looking at the chart above is possible to see the difference of tournaments played by athletes with equivalent rankings. Performing a linear regression is possible to find that a woman plays 14% less tournaments than a man with an equivalent ranking.

This means that to make sure players with equivalent rankings make the same amount of money in a year is important to provide prizes for women 16% bigger than men so at the end of the year they can make similar amount of money.

This might lead you to think that women tournaments need to award more money than men tournaments, but that is not the case, remember that there are less women players.

To make things clear let’s take as an example the PSA World Series Final Tournament, In this tournament only the best 8 players on tour are allowed to play and the prize money breakdown for men and women is as follows:

 Winner 30%
 Runner-up 20%
 Semi-finalist 12.5%
5/6 7.5%
 7/8 5%

The total awarded prize for men and women is the same, this is a great idea towards equity pay but it is not fair, unless you think that the Naïve matching method is the way to match rankings and you have rules that encourage men and women with equivalent rankings to play the similar amount of tournaments.

So, considering that women play 14% less tournaments than men, and the Effort (%) matching method an equivalent prize money breakdown would be:

Men Women
 Winner 30% 35%
 Runner-up 20% 23%
 Semi-finalist 12.5% 11.5%
5/6 7.5% 4.5%
 7/8 5% 3%

With this breakdown, you still have a 4% from the women prize unassigned, why? Because according to the equivalent rankings the effort of being rank between 3 to 8 is bigger for men than for women.  Then the prize money for women should be 4% smaller than for men and the breakdown should end up like this.

Men Women
 Winner 30% 37%
 Runner-up 20% 24%
 Semi-finalist 12.5% 12%
5/6 7.5% 4.5%
 7/8 5% 3%

This approach might not look as appealing as the strategy of giving the same amount of money for men and women, but the biggest problem with equal pays is that the lady ranked as number 1 will make less money than the male athlete ranked as number 1 (assuming both were undefeated during the whole season) because she will play less tournaments.

If you have different rules and population sizes, you need different prize breakdowns to make sure you reward the effort equally regardless the gender no matter the sport. This shows that the fight should not be only about being paid equally but also about bringing more women to the world of professional sports.

Note: This analysis might turn out more accurate if data of previous ranking months were available.

Check the code on GitHub.

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