What are the odds of finding love in the universe? Revisited.

I revisit the paper “Why I Don’t Have a Girlfriend” and figure out what’s missing from the equation.


As I started to develop the algorithm behind Nanaya, I wanted to make sure I wasn’t reinventing the wheel. I found all sorts of personal stories about people doing their own calculations of whether or not they’ll find love – but only one actually described what he did. Dr. Peter Backus, then a graduate student at University of Warwick studying economics, wrote a joke paper “Why Don’t I have a Girlfriend.” He used an equation near and dear to my heart to figure out the chances of finding love in the UK: the Drake Equation.

The Drake Equation has been around for a bit. It gives us an estimate of the chances that there are alien races populating the galaxy. In Backus’s version, he’s figuring out the chances there’s an ideal match he’ll run into in the UK. Maybe it’s another way of saying women really are from Venus?

So he has an equation of all these factors multiplied together which gives him the probability of finding a match. His factors are:

  • The rate of formation of people in the UK (i.e. population growth).
  • The fraction of people in the UK who are women
  • The fraction of women in the UK who live in London.
  • The fraction of the women in London who are age appropriate.
  • The fraction of age appropriate women in London with a university education.
  • The fraction of university educated, age appropriate women in London who I find physically attractive.
  • The length of time in years that I have been alive thus making an encounter with a potential girlfriend possible.

With some estimates and a few additional factors he comes to about 1/285,000. Is this reasonable?

The answer is no. Those few additional factors he assumes are “1 in 20 of the women find me attractive, half are single and I get along with 1 in 10.” Well that’s a big deal! In fact, that multiplier is bigger than any of the factors in his equation!

A part of what’s going on is that he assumes there’s linear independence involved in all of those answers. That is to say, there’s a relationship between “university educated women” and “women who find him attractive” so you can’t look at the odds of each one independently. For instance, women who are university educated, just by being in the same culture, will be more attractive to him and vice versa. By treating all these factors independently poor Peter is really making his odds worse for himself.

We can all do what Peter did for ourselves pretty quickly but it takes a lot of work to get the rest of the way. Figuring out what traits and cultural values are independent of others is the major problem. If you want to take it to the next level, the problem becomes how much that answer changes in time. The Nanaya algorithm solves both of these problems – no one else has done that.

Even if the chances seem bleak, one shouldn’t despair! Something like the birthday paradox comes around to help people. I’ll be writing on that later. Even at Peter’s self-reported odds of 1/285,000 he still found a wife. Congrats, Peter!

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