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What the maths of dating can tell you about how to recruit

By Brendan O'Donovan, Group Data Marketing Director, Hays

The challenge of dating is that you can’t know for certain whether your current date is going to be the best suitor you’ll ever find. Settle down too quickly, and you might never meet Mr or Mrs Perfect, get too picky and you may end up rejecting someone who is highly suitable for you. Replace the word “suitor” with “the perfect job candidate”, and you will see that there are in fact many parallels between trying to find love and trying to find the best talent for your organisation, albeit with very different judging criteria.

Now, according to plus.maths.org the strategy is simple: “Out of all the people you could possibly date, see about the first 37 per cent. Then after you have dated the first 37 per cent, settle for the first person who’s better than the ones you saw before.” In other words, multiply the number of different dates you go on each year by the maximum number of years before you’d want to settle down, date 37 percent of this number, pick your best date from the 37 percent (let’s call them person a), and then continue the date the remaining 63 per cent until you find someone better than person a.

The problem with the 37 per cent theory when hiring

Unfortunately, while this simplified problem has a very elegant mathematical solution, it isn’t a lot of help in the real world of hiring, as there are three big issues with the way it’s set up:

1. No search costs – For dating, it might not matter if you spend the whole of your twenties working your way down the list to the magic 37 per cent, but in a real business there are time costs involved in recruiting, both the time taken away from the hiring manager for each interview, and the cost of leaving a vacancy open longer than needed (during which time customers are getting poorer service, sales aren’t being made, overtime is being paid to overstretched staff, etc.)

2. Focus on perfection – As presented, the only thing that the 37 per cent rule cares about is maximising your probability of landing the single best person in your potential dating pool. The rule doesn’t care if the best person turns up in the first 37 per cent. In fact it specifically states you should still reject them, using this person only as a benchmark for the next 63 per cent of people you date.

In the real world, failing to fill a role can be very damaging, and we know that of all the account directors or software developers in the world, it’s not realistic to try to find the single best one, so a more realistic objective might be to maximise the probability of hiring someone in the top 10 per cent of performance for that role.

3. No going back – In dating, the idea that you usually can’t go back makes some sense (soap opera plots aside), but in recruitment, the idea that you would interview and then accept or reject people precisely in sequence is clearly unrealistic. In the real world, candidates are interviewed in parallel, and you can compare them against each other during a well organised interviewing process, before choosing.

An alternative strategy

Fixing these limitations means that rather than creating an elegant mathematical solution, we need to rely on brute force simulation to get an answer, but in return the strategies coming out at the end are much more likely to tell us something useful in the real world.

So using the 37 per cent rule as a guide, we’ll keep the rules simple – “Interview candidates for the first X weeks, then as soon as you have a candidate available who is at least as good as the Nth best candidate you’ve seen already, hire them.”

What do the results of this modelling look like? The two outcomes we’ll keep an eye on are quality (the probability of hiring someone in the top 10 per cent of performance) and time (the number of weeks taken on average to fill the role, ignoring cases where the role never gets filled). Figure 1 shows the results for the case where two candidates are interviewed per week, and we assume that candidates remain generally available for a fortnight after you interview them.

 

As you would expect, when we look at the quality side of the equation, it pays to look for a long time and to be choosy (picking the 2nd best candidate you’ve seen after 10 weeks gives you an 84 per cent chance of hitting a top 10 per cent candidate), but interestingly, not too choosy (if you hold out for someone better than the best person you’ve seen after waiting 10 weeks, then the possibility of never finding the right person changes.)

On the other side of the equation though, the need for an efficient and rapid hire will push in the opposite direction – to interview for as few weeks as possible and accept anyone (although if you’re only interviewing for as long as your first candidate stays available, you can afford to pick the best person you’ve seen).

How should you balance these two opposing drivers?

One answer would be to express them both in financial terms – the cost of spending longer hiring (which will be related to the cost of the interviewer’s time, and the penalty for leaving a vacancy open) versus the value of hiring a candidate who is great rather than ok (which will depend on the extra business benefit the best hire can bring, as well as the typical tenure for a person in the role.)

The tables in figure 2 below show the “true cost” of hiring using each interviewing strategy, combining the cost of interviewing, holding a vacancy open, and the opportunity cost of not hiring the best person. The purple cell shows the lowest cost and hence “optimal” strategy, for three different “quality of hire” premiums.

Applying this evaluation approach to the model gives the intuitive result – the more impactful or important a role is for your business, the longer you should spend hiring for it, although it also suggests that for the longest searches, you might not get the best result by holding out for the single best candidate, but might need to accept #2 if you’ve left it too long to hire the best person you’ve seen.

How should we apply the lessons of this model to real-world hiring decisions?

Although we have added some realism to these calculations beyond the very abstract 37 per cent rule we started with, the real world is definitely messier – candidates don’t arrive in a neat queue and wait a fixed time before they accept an alternative job.

As such, rather than try to extract exact strategies from the model, it’s better to think in terms of the more general lessons it highlights:

  • You need a wide net – the optimal hiring approaches suggested by the model generally involve interviewing a much larger number of candidates than a typical recruitment process might include. If you interview four candidates, your probability of not having seen a top ten per cent candidate is 66 per cent, whereas after ten this chance has dropped, but only to 35 per cent. The best way to get a top ten per cent candidate will often be to outsource a first phase of interviewing to a recruiter, who can talk to tens or even hundreds of potential candidates to assess their fit, before narrowing it to a shortlist for you.
  • Pace of interviewing matters – Although in the real world, you may be able to reserve candidates for more than the fortnight used in the model above (particularly if a recruiter is helping you to access people who are not actively job-seeking), a drawn out process will mean that you lose potential hires, as they are snapped up by competitors, or lose enthusiasm due to the wait. All things being equal, it will be much better to interview five people over a week, than to interview the same number over a month.
  • In long searches, you might not get your top pick – a long time spent interviewing candidates can sometimes elicit a tendency to expect a better candidate in return for that time investment. This is particularly likely to happen if you’ve seen a great candidate early in the process who you failed to hire, perhaps because you didn’t move onto a final round of interviews soon enough. In these situations, it can be necessary to ask yourself whether the best person available at that moment is good enough. If you’ve spent months looking, and they are clearly at least the second best person you’ve interviewed, well ahead of the general standard, they might be the right person to hire. On the other hand, if they’re still not the person you want to hire, you may need to revisit your search parameters, whether in terms of skills, experience, sourcing approach or salary.

In summary, although the strategy for a perfect hire in the real world is no more solvable with a spreadsheet than the quest for perfect love, maths can provide a window into new ways of thinking about the process, challenge our intuitions and beliefs, and perhaps even improve the outcomes.

About this author

Brendan O’Donovan is the Group Data Marketing Director at Hays, responsible for setting the strategy and developing the capabilities to allow marketing teams across our countries of operation to gain more value from data. Brendan brings over a decade of experience in data-driven customer marketing, gained through a mix of senior marketing and strategy roles at a global loyalty marketing company.

Brendan has a degree in Engineering from Cambridge University, and stayed on to complete a PhD in Engineering Design, focusing on how large teams organise innovation. After university, Brendan worked in strategy consulting for a mix of transport, financial services and private equity clients, before joining the start-up which had just launched the Nectar loyalty card.

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