Giving a toss: probability, sexism and the endless queue.

I was thinking about sexism the other night. I hadn’t planned to be, but I was pootling around on Facebook and started reading a post about the recent Southwest Airlines incident where an engine failure led to the death of a passenger and a well flown single engine diversion and landing by pilot Tammie Jo Shults.

The thrust of the post was that the main reason the event was getting so much media coverage was that the pilot was woman, and that this was a bad thing.

This got my goat. I’ve been in aviation since I was a teenager and it was sexist then and it’s sexist now. Female pilots are still the exception. So, I decided to say something about it, based on my own experience.

I posted that when I graduated from RNZAF pilot training in 1988 we had one woman on our graduating course – Angie Dickinson, our first ever female pilot. Fast forward almost 30 years to last year’s graduating class and there were none. Just eight blokes. I said that I thought this was a bad thing, and that anything that attracted women to follow a career in aviation – like telling the story of a woman who did her job well and saved 150 lives – was a good thing.

This wasn’t universally well received.

The main argument was, “shouldn’t the RNZAF just get the best available pilots and not worry whether or not any of them are women?”

This got me thinking, and that led to this. My Endless Queue Theory of Why Sexism Is Bad for Business.

The Endless Queue Theory of Why Sexism Is Bad for Business.

It goes like this. (We’ll stick with the pilot thing, as it’s what I know. But I’m sure you can apply it to whatever it is you do for a job too.)

Imagine we could line up all the people who could possibly become air force pilots, rated from the very best, then the second best, all the way down to the most useless.

In an endless queue – or even a decent-sized one – half of the potential pilots would be men and the other half would be women (give or take people who identify as neither or both).

It wouldn’t be boy-girl-boy-girl like a dinner party seating plan, but over the length of the queue it would even out.

Now let’s say it’s your job to get the 8 best people in the queue to join the air force.

Assuming that a person at any point in the endless queue is equally likely to be a guy or a girl, we can do some pretty easy maths if we just treat gender likelihood for any spot in the queue like it was a coin toss. (The fancy term is a binomial distribution.)

If we decide to just hire one trainee pilot this year, there’s an equal chance that the best possible candidate – the one at the front of the queue – is a guy.

As the number of pilots we hire increases, while the chance of each individual in the queue being a guy is still 50%, the chance of everyone being a guy plummets. Binomial distribution tells us that by the time we get to the 8th person in the queue, as the air force did, the chance of them all being guys is 1 in 128, or 0.7%.

It’s far more likely that we’re just missing out on the best talent.

Since when has gender equality been the RNZAF’s job?

Good point. It isn’t. All the RNZAF should care about is protecting our borders, supporting our foreign policy around the globe and playing beach volleyball with their Ray Bans on. But to do that well, you need the best possible talent. And you just can’t get that if you’re only hiring every second person in the queue.

But what if there really are more guys in the queue?

Another good point. I expect there probably are. The real-world queue isn’t filled with every possible RNZAF pilot; it’s filled with everyone who applied. 30 years after this career choice has been open to women, though, you’d think the RNZAF would be doing a better job of attracting and recruiting them.

My old flying buddy Tony would get this maths. We flew the C130 Hercules together when he was a captain and I was still a copilot, and he was well known for discussing logic puzzles as we flew across the Pacific. The good news is that Tony runs the air force these days, so he’s in a good position to do something about it.

And you know what, he is. The RNZAF now runs school holiday programmes targeted at young women, giving them the opportunity to experience life on an RNZAF Base, meet women already serving and hopefully increase the chances they’ll join that queue. I think that’s a great idea but, as last year’s graduating class shows, there’s a huge job to do here.

How about a gender quota then?

Depends on what you’re trying to achieve. If your single-minded job is to hire the very best talent, you have evidence that there’s no gender bias in your hiring practices and you still end up hiring more men, you probably have a supply problem. The job then is to do what the RNZAF is doing (but probably a bit better, going by the numbers) and work hard to attract whatever minority you’re missing to consider your sector as a career.

If diversity of thought is important to your business (which it almost certainly is) then there’s a strong business case for looking further down the queue (without falling below whatever hiring standards you have set) to improve the mix.

But I don’t hire pilots

Fair enough. Like I said earlier (excuse the long post), the endless queue theory applies to any profession where gender doesn’t affect performance (spoiler: pretty much all of them). Take a boardroom, for instance. If there are 12 people on your board and all of them are men, you’ve probably hired half of the top 24 potential candidates, not the top 12. What are the chances you really have the best talent, let along the diverse range of life experiences that good decision-making needs?

Boards, businesses and air forces aren’t here to make life better for women. They’re here to do a job. But to do those jobs well and deliver the goods for the shareholders and taxpayers they serve, they owe it to us to have the best possible talent. And they’re not going to do that by only picking every second person in the queue.