Imagine where you work, the median women earns 33% less than the median man. Although your workplace is gender balanced with 50:50 men:women, the pay gap exists because 1 in 4 of managers and 3 in 4 of the lowest paid admin staff are women. How long will it take for the pay gap to disappear assuming that all future recruitment at all levels have 50:50 candidate pools with men and women equally likely to be appointed to the role?

**Up to 25 years i.e. a generation**

When I point this out to people, I get a variety of reactions ranging from disbelief, despair and discouragement. I am not surprised by these sentiments because when I hear and read what others have to say about the gender pay gap, too often I get the sense that people think it can be solved with a 5 year project plan and the only reason it doesn’t happen is because people don’t want to make the effort. In part, this might be because some people still confuse gender pay gaps with unequal pay when in fact they have nothing to do with each other but if you do think this, even subconciously, then of course you will tend to think resolution is simple because all you have to do is give women a pay rise which can be done tomorrow.

I will first demonstrate why closing a gender pay gap is a 25 year generational project with a simple example of an employer with 16 male and 16 female employees. This demonstration will be backed up with a more sophisticated analysis using a simulation model in a spreadsheet which can be downloaded. Finally I will explain how the timeframe can be shortened if you adopt the mindset of a card counter playing blackjack in a casino.

**5050 STEM Ltd Today**

My fictional company 5050 STEM Ltd is so-called because it has the same number of male and female employees (16 of each) covering 4 types of jobs of which 2 (Engineers and Analysts) are STEM related. There are 8 employees in each job type and men and women are paid the same for doing the same type of job i.e. there is no equal pay issue. As highlighted in the graphic, the median man earns £30 an hour and is an Engineer whilst the median woman is an Analyst earning £20 an hour. So for every £1 earned by the median man, the median woman earns 33p less i.e. the official median gender pay gap that would have to be reported to the government would be +33%.

The reason for this pay gap is obvious. Men are more likely to be Managers & Engineers and women are more likely to be Analysts & Administrators. To eliminate a pay gap, the first step is ensure that each job type has the same gender ratio. Since 5050 STEM Ltd’s gender ratio is 1:1 that means our goal is transform this company so that each of the 4 job types has 50% men and 50% women. To achieve this, 6 employees need to change gender with 2 Managers & 1 Engineer becoming female and 1 Analyst & 2 Administrators becoming male.

*Important! When I say that the first step to eliminating a gender pay gap is to have the same gender ratio in each job type, the gender ratio does not have to be 50:50. An employer with a 90% male workforce can eliminate their gender pay gap if wherever you look in that employer boardroom, shop floor, department, location, pay grade, etc, you always see a 9:1 male:female ratio.*

**5050 STEM Ltd – Recruiting for the future**

When I state that closing a gender pay gap takes a generation, I am making three major assumptions.

- The total number of employees remains unchanged.
- For all future recruitment, on average, the gender ratio of candidates will be 50:50 for all job types.
- Both male and female candidates for all job types are equally qualified and the probability of a vacancy being filled by a woman is equal to a man’s i.e. 50%.

My more sophisticated model which can be downloaded later on allows you to modify these assumptions and see what the effect is but I will be using these for 5050 STEM Ltd.

I want to emphasise assumption 3 now because this implies no sex discrimination at the recruitment stage. One obvious way to shorten the timeframe to closing the pay gap is to only appoint women to senior roles and only appoint men to junior roles. I am working on the understanding that this is illegal under British law and even if it is not, it not something I can ever endorse. Equality in my view is about men and women having equal chances to work wherever they wish and you cannot fight discrimination of one kind by replacing it with a different kind of discrimination. Any employer violating assumption #3 would leave themselves open to charges of discrimination either in a court of law or the court of public opinion.

If 5050 STEM Ltd wishes to change its gender ratio for all 4 job types through recruitment and promotion and not through growth (assumption 1), the first thing that has to happen is that jobs have to become vacant due to existing employees leaving the company. It should be obvious that an employer with high turnover of employees can achieve its desired gender ratio much quicker than an employer with low employee turnover which raises an interesting paradox. I think most people would agree that employers with low turnover are more likely to be desirable places to work than places with high turnover. Yet it would appear that high turnover employers can achieve the kudos for closing their pay gaps simply by being a horrible place to work at.

For my demonstration, I will assume for each round of recruitment, 1 in 8 employees within each of the 4 job types leave the company. I will also assume that every employee (male and female) has an equal chance of leaving. That means the probability that the employee leaving is a man is 3 in 4 for Managers, 5 in 8 for Engineers, 3 in 8 for Analysts and 1 in 4 for Administrators. By assumption 3 above, there is a 1 in 2 chance that they will be replaced by a woman and 1 in 2 chance they will be replaced by a man. Therefore we have 4 possible scenarios that can happen in a single round of recruitment which are –

- Man replaced by a womaen
- Man replaced by a man
- Woman replaced by a woman
- Woman replaced by a man

Scenarios 2 & 3 do not change the gender ratio. Scenario 1 improves the gender ratio if it occurs among Managers & Engineers and worsens the gender ratio if occurs among Analysts and Administrators. Scenario 4 is the reverse of scenario 1. Whilst the probability of the new employee being female is the same for all 4 job types, the probability of the leaving employee being female is different and hence the probabilities of each scenario are different for the 4 job types as shown below.

For Managers, scenario 4 (Man to Woman) is desirable but the left hand crosstab table tells us the chances of this happening without discriminatory behaviour (assumption 3) and a gender balanced candidate pool (assumption 2) is 3 in 8 (=0.75 x 0.5). There is a 50% chance nothing changes and a 1 in 8 chance (=0.25 x 0.5) of a regression whereby a female manager is replaced by a male manager. Therefore the net probability that the number of female managers will increase by 1 in the next recruitment round is 25% (=37.5%-12.5%).

That tells us that on average it will take more than 1 recruitment round to achieve an increase in female representation among managers. The expected number of recruitment rounds is easy to calculate as it’s equal to 1 divided by the net probability of there being an additional female manager (0.25) which equals 4 recruitment rounds. It should be obvious that some employers will be unlucky and will take more than 4 rounds to improve female representation among managers even if they are genuinely non-discriminatory in their recruitment practices and others will be lucky and get there in 1 round.

If it take 4 recruitment rounds on average to increase the number of female managers by 1 , you should be able to see why employee turnover determines the timeframe to undertake 4 rounds of recruitment. A good employer with a loyal workforce might have to wait 10 years whilst a bad employer might achieve that within 2 years. Exactly the same applies to Administrators except this time the goal is to increase male representation so it will take on average 4 rounds of recruitment to increase the number of men by 1. But of course, this is not our end goal. All 5050 STEM Ltd has managed so far is to change the gender ratio from 1 in 4 women/men for Managers/Administrators to 3 in 8 men/women. In other words, after 4 rounds, Managers and Administrators will be in the same position that Engineers and Analysts started out with.

**Narrowing a pay gap makes it harder to close it!**

In the graphic above, the same calculation of the probabilities of the 4 scenarios shows that for Engineers and Analysts, it will take an average of 8 rounds of recruitment to change the gender of an employee. For Managers & Administrators who needed 4 rounds to put themselves in the same position as Engineers and Analysts, that adds up to 12 rounds of recruitment that is needed to eliminate the gender pay gap.

Here is the key point that I think those who imagine closing the gender pay gap to be a relatively simple exercise are missing. When a role is very gender dominant, you can make rapid changes to the gender ratio with gender balanced recruitment simply because the employee that leaves is much more likely to be of a particular gender. But when a role is nearly but not quite gender balanced then the probability that the employee that leaves is of the gender you want to see more of is much higher. Consequently, the 4 scenarios become much more equal in their probabilities and it becomes largely a matter of luck as to which non-discriminatory employer ends up making progress in the desired direction. For many such employers they will end up regressing in the “wrong” direction and having to start all over again.

This is not an esoteric mathematical point, there is real data to back up this contention. In my post “*Did the UK gender pay gap narrow in 2019?*“, I showed this chart for small employers (less than 500 employers) split into 3 groups based on the years they had reported data for. A point I didn’t comment on was that the Triangles (reported in 2018 & 2019 only) had the largest gender pay gap of the 3 groups in 2018 but made more progress on closing it in 2019 than the Squares (reported in all 3 years). Triangles narrowed their median pay gap by 1.6p from 14.7 pence in the pound against women to 13.1p whilst Squares only narrowed their median pay gap by 0.5p from 11 pence in the pound to 10.5p. The progress for Triangles is 3 times that of Squares which is a similar order of magnitude to the fact that it takes twice as many recruitment rounds to increase the number of Engineers by 1 women in 5050 STEM Ltd as it does for Managers.

Obviously one way 5050 STEM Ltd can speed up the process is to prevent female Engineers, say, from leaving in the first place. If the probability was reduced from 3/8 to 1/4 then the crosstab table for Engineers would be same as for Managers and the extra female Engineer can be expected after 4 rounds of recruitment rather than 8. I have seen plenty of employer activity aimed at female retention e.g. family friendly policies, part time working, but is it a good thing for female employees to be encouraged to remain at their existing employer?

Other HR professionals can answer this better than me but these days I think it is unusual for men to reach senior positions such as director or CEO without having changed employer at some point in their career. I am not sure if treating women differently in this regard is helpful to their career prospects. In any event, at an industry sector level, a gain for one employer is a loss for another employer. In sectors like airlines where the gender pay gap is driven almost entirely by the lack of female pilots across the industry, the challenge for the sector to increase the number of women becoming pilots rather than retaining or poaching existing female pilots.

**Using Simulation to measure time to close a pay gap.**

If you’re not convinced by my simple demonstration for 5050 STEM Ltd, then you should download my **Recruitment Simulation Spreadsheet** and check it for yourself. In this spreadsheet, you can enter a variety of parameters including –

- Total number of employees
- Number of female employees
- Expected % of employees who will leave in each recruitment round
- Expected % of recruited employees who are female

Using something known as the Binomial Distribution at each recruitment round, a random number of employees will leave the employer and the same number of employees will be recruited to replace them. As explained with the simple demonstration earlier, the gender ratio of those leaving will depend on what the existing gender ratio was at the start of each recruitment round whereas the ratio of those recruited will on average be 50:50 but can vary according to the laws of chance as defined by the Binomial Distribution. The two charts below are two separate simulations for the Manager roles at 5050 STEM Ltd. The first assumes there are 8 staff in all, the second assumes there are 10 times more staff.

With only 8 staff in all for the left chart, it is possible to reach 50:50 men:women in very few rounds whereas with 80 staff in all for the right hand chart, it needs more rounds to get there. As I say these are just one simulation and in the spreadsheet, I can run as many simulations as I want. I’ve chosen to run 1000 simulations and for each simulation I record 2 numbers. The first is how many recruitment rounds are needed to get the % managers that are female up from 25% (1 in 4) to 37.5% (3 in 8). I call this threshold 1 or T1. The second is how many recruitment rounds are needed to get the %managers that are female from 25% to 50% which I call threshold 2 or T2.

Having recorded these two numbers for 1000 simulations I can then calculate summary statistics and create box plots (see my post on Gender Pay Fingerprints for an explanation of how box plots are interpreted). 3 box plots are shown here representing the distribution of the simulated number of recruitment rounds needed to reach T1 and T2 for Managers at 5050 STEM Ltd assuming there are 8, 80 and 800 managers respectively.

Two observations stand out from these box plots.

- For Threshold 1 (3 in 8 women), this can be achieved within 5 or 6 rounds of recruitment. As the number of employees goes up, the variation in possible outcomes reduces so that by the time you get to 800 employees, you are almost certain to reach this within 10 recruitment rounds.
- For Threshold 2 (1 in 2 women), on average this is achieved in 10 rounds with 8 employees, 18 rounds with 80 employees and 27 rounds with 800 employees. Not only does the average number of rounds increase with more employees but so does the variation in possible outcomes.

This is why I say at the very beginning we are looking at a whole generation to achieve gender balance. It also validates my other observation that making quick progress when you have a large imbalance is quite feasible, making small progress when you have a slight imbalance is remarkably difficult if men and women are equally likely to leave their employer. The last few steps turn out to be mountains.

**How to climb the last mountain quicker**

Three options are unlikely to be desirable and have already been mentioned

- A –
**Recruit more frequently**by implementing a hire and fire culture. The faster you get through your employees, the quicker you can go through a large number of recruitment rounds and eliminate your gender pay gap. - B –
**Discriminate in favour of women**at each recruitment round and run the risk of being sued by men for sex discrimination. - C –
**Do what you can to keep existing senior women.**As I said earlier, it may be better a woman’s career prospects to move on. Also a focus on female retention and not male retention could lead to an unequal pay situation where a woman is offered pay rises to keep her there and ends up earning more than her male peer.

Two other options that my Recruitment Simulator spreadsheet will demonstrate for you are both quicker to close a pay gap and I think more equitable.

- D –
**Grow your workforce**. If your employer is in growth and needs to keep recruiting more and more staff, then that means the legacy staff which might be male dominated will become a smaller proportion of the total and the new staff which we assume are being recruited in 1:1 ratio will start to dominate the workforce. - E –
**Be a Blackjack Card Counter**. In Blackjack, there is a well known method of counting the cards being played in all the hands. When the count reaches a favourable number, you double your bet because you are more likely to win. The equivalent situation in recruitment occurs when you have a larger turnover of staff than usual in a recruitment round. In that instance you go all out to get as many female candidates as possible.

The simulation box plots for options D (middle plot) & E (right hand plot) are shown for the scenario of where we start with 80 managers in a 3:1 male:female ratio along with the same box plot (left hand plot) from the previous section for 80 employees. The average number of recruitment rounds needed from left to right is respectively 18, 12.5 and 14.3 rounds. If both options D & E occur at the same time, the average number of rounds drops to 10.

Why option D (growth) works should be easy to understand but how does option E (card counting) speed up the process? In a way, option E is about using options A & B at the same time as a one off event rather than a continuous policy. Suppose on average you are recruiting 5 men and 5 women every year but then in one year, you find you need to recruit 20 employees instead. This equates to option A of large turnover and it is a golden opportunity to bring in a lot more women.

What you don’t want to do is end up recruiting say 15 men and 5 women because that will set you back a long way. Instead it is a time to explicitly load up your candidate pool with more women so that you perhaps end up recruiting 8 men and 12 women. That is in fact option B, discrimination in disguise but notice in this situation you are still recruiting more men than average (8 instead of 5) so it would be harder to claim men are being discriminated against in this situation.

**A recruitment strategy for a generation**

I hope by now that I have convinced you that closing a gender pay gap is not a 5 year project. It is a project that will take a generation and thus one must set reasonable expectations along the way and accept you will have setbacks along the way. I’ve demonstrated that making good initial progress should be straightforward when you have a large gender disparity but the hardest work comes when you are trying to close the smaller gap at the end. Because such a strategy is so long term, it is essential that fatigue with the strategy is avoided especially a feeling of “why bother, we do all this work for no reward”.

That’s why I recommend the card counting strategy since it demands an all out focus on the occasions you have large employee turnover but conversely it also means that when turnover is low, you don’t need to focus as much on gender balance in recruitment especially if finding female candidates is hard in the first place. Effectively card counting is about saving your energy for the times when you make the largest impact otherwise it will become a long slog that runs the risk of people becoming disheartened.

I should remind you that every scenario I explored in this post was based on the assumption that from today, your candidate pool of future employees will be 50:50 male:female. In many industries, this will not be the case and it will take a long time before even that situation can be achieved. Only then can the generational project I’ve laid out here get going.

The other implication of my work here is that ranking employers on speed of progress can be misleading. I’ve demonstrated that an employer who rapidly closes a gap might be a bad place to work and is only able to make good progress because they’ve expanded their workforce rapidly, they have a hire and fire culture or they had a very large gender imbalance in the first place. This is yet another demonstration of why gender pay gap analytics is not about and can never be about the one number i.e. the pay gap. The whole exercise is inherently multivariate and requires expertise in statistical thinking to appraise whether you are in a good or bad situation. Obviously this is a service I offer so please do get in touch using the link below if you would like to find out more.

**— Need help with understanding your pay gap? —**

I offer the following services.

**Analysis**– I can dig deep into your data to identify the key drivers of your pay gaps. I can build a model using a large number of variables such as pay band, seniority, job function, location, etc and use this to identify the priority areas for closing your gaps.**Training**– I run training courses in basic statistics which are designed for non-statisticians such as people working in HR. The courses will show you how to perform the relevant calculations in Microsoft Excel, how to interpret what they mean for you and how to incorporate these in an action plan to close your gaps.**Expert Witness**– Has your gender pay gap data uncovered an issue resulting in legal action? Need an expert independent statistician who can testify whether the data supports or contradicts a claim of discrimination? I have experience of acting as an expert witness for either plaintiff or defendant and I know how to testify and explain complex data in simple language that can be easily understood by non-statisticians.

If you would like to have a no-obligation discussion about how I can help you, please do contact me.

**— Want to know more about pay gaps? —**

I have written a number of articles about pay gaps. You can find the full list of my articles grouped by theme here.

I also comment on pay gaps on my Twitter thread. Some notable tweets are here.

- My complaint about comments made by the head of the TUC on the 2018 pay gap.
- Some observations on the government’s guidance to producing gender pay gap statistics and the numerous deficiencies in these.
- My comments on why incorrect gender pay gap data is being submitted.
- At last, the BBC publishes a good article on gender pay gaps!

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