Even the very best recruiters are going to make a mistake from time to time. And even a razor-thin margin of error can have a big effect on making sure your company is identifying top talent. Here's the math to prove it.

This logic problem comes from the forthcoming book from Harvard Business Review Press, written by executive search expert Claudio Fernández-Aráoz, It's Not the How or the What but the Who. It goes a little something like this...

Imagine you are able to correctly gauge talent 90 percent of the time. Fernández-Aráoz writes that this would basically be impossible--even the best interviewers and recruiters hit about 70 percent of the time--but for the sake of argument, let's say you are just spectacular.

And let's say you're interviewing 100 people for a position. You probably don't have the time for that, but again: sake of argument.

So what percentage of those candidates will you correctly identify as top talent?

"I've done this exercise hundreds of times, all over the world, with thousands of students, professionals, and executives," Fernández-Aráoz writes. "The responses I typically get from a large crowd usually range from 9 percent to 90 percent. Very few people give the right answer intuitively, and not many more can calculate it.

Wait, what?

Stick with me. If you're interviewing 100 people, 10 of those people will necessarily represent the top 10 percent of talent in that larger pool. Of those 10, you will choose nine to pass on to the next round, and wrongly dismiss one.

You will then have 90 other candidates who are not top talent. You will rightly dismiss most of them. However, since you are only right 90 percent of the time, that 10 percent margin of error will lead you to incorrectly pass 10 percent of that group on to the next round.

So in the end, you'll have nine people who are top performers and nine lesser candidates moving on to the second round of interviews. That's a sobering showing to come from your 90 percent rate.

(Did I mention, Fernández-Aráoz is also a former industrial engineer?)

Okay, now that you're adequately shocked, here's the good news. Just because the numbers work out this way, it doesn't mean you'll be hiring all those people and wind up with nine less-than-ideal hires. (Unless, I guess, if you have 18 spots open for people with similar qualifications and experiences and don't plan on doing any further vetting.)

Instead, the numbers really drill down the importance of the second and third interview process, and making sure your colleagues conducting those are also strong judges of talent. This kind of "filtering" process, as Fernández-Aráoz puts it, should ultimately widdle things down to the right candidate.

If you, a second interviewer, and a third interviewer are all very skilled at gauging talent, by the end, there's only a 1 percent chance that you'll wind up with a low performer in the pool when it's time to make a decision, Fernández-Aráoz writes. That suddenly doesn't look so scary.