Estimation questions in job interviews

I had heard about those questions in job interviews where you are asked to estimate on the spot something, though having no real data about it.

There was some example about estimating the quantity of gas stations on the whole USA; I seem to remember that was for a Google job application. The guy had the guts to throw up numbers in a hunch with the handwaviest idea of how they could be good numbers… and, luckily, at the end the result was even not a bad approximation.

I realize now that at the moment, when I read that, the “luckily” part is what stuck on me. While it’s true that the guy had the wit to back the numbers and/or the chutzpah to pick them out of thin air, and even though he also had some brillian moments to just turn around and cross-check some imagined number by using another set of assumptions… the thing is that finally he was near the true number.

It was fascinating, and rather intimidating. How in hell would I be able to do something like that?

So, when in a recent job interview I was asked point-blank for such an estimation, I was totally caught off-guard. I was rather well prepared technically, if only because I had been kind-of-practicing lately - but I wasn’t really expecting any more technical questions that day (it was late after work!), and certainly no estimations. But here I was, with the interviewer just charmingly dropping the question and handing me a piece of paper.  Something like, “how many tumbles do together all the martial art practitioners in Kyoto on one given day?”.
Oh god oh god oh god. WTF. Wasn’t this the HR part of the interview??

Well, who would have thought. I had never practiced for such a thing (how?), but suddenly I was throwing up numbers all the same. Adrenaline, I guess. One factor, two, a third one, of course this is approximate but we can consider it’s good enough because of blah, … a big multiplication of it all, it’s done.

The interviewer looked at me kind of blankly. Then at the piece of paper.

“Are you sure?”, I think he asked.

I took another look at the numbers and crossed over one number and fumbled a bit with another and mumbled something but the final result stayed more or less where it was already. Which had to be a good sign, since the interviewer had started saying that just getting in the order of magnitude would be OK.  “Yes, I think that has to be something like this”.

“Oh, I wonder what would the real number be. Hehe”. Change of subject.

What… the … fuck?

You don’t even have it? What kind of dumbness is this? What use is to come up with all kind of assumptions if you are not checking the results?

How can then we know if I was lucky or not??

Yep, I remembering even getting annoyed for a moment. Are we playing job interviews or what?

I only managed to understand how wrong I was about it all when I talked to my interviewers some time afterwards. Luck? Numbers? Who cares? The important thing is the process, and if you can assure yourself and others about how the assumptions are the best than can be had.

I knew that the process was important; what I didn’t get earlier was that the process was the only important thing.

The Google interviewee who explained his assumptions to come up with an approximation of the number of gas stations in the USA took advantage of things he knew about geography and population, about his own driving and mileage per gallon, about… whatever. Probably in fact that is what stroke me as brilliant, maybe just because I rarely drive so I wouldn’t have probably had the feeling for that kind of data; seeing him conjure numbers was amazing.

And I did the same! For my assumptions I had the advantage of having lived most of my life in touristic places and the knowledge of how people flock there (and the difference between a concrete event or a seasonal thing). I knew how different martial art practitioners are more or less prone to be tumbling around (say, Aikido all the time, Karate rarely :P). I knew how an average tatami looks like, how many people can be training in it at once, how they behave - because I spent a lot of time in them.
I remember the feeling of flow while I was stringing all the numbers one after another, realising how in fact I could give solid estimates for every factor. I was pulling it off!

... in my head, at least. Because turns out that I barely explained any of the reasonings behind each number. I just wrote, wrote, crossed out something, started again, mumbled, wrote. I just wanted to be fast and get a lucky result.

So, one ends, feeling even smug about it. Fuck yeah, I aced it. The other looks blankly, not knowing what to do with a number. “…heh. Yeah, well. OK, let’s move on.”
(looking back, maybe they should have also re-stated the goals, since clearly they were more expecting a rather longish string than a number :P. I can only assume that we cross-guessed each other. Also funny that I could sense his awkwardness but didn't know what to do of it... way to waste a pretty nice hint!)

An even more interesting take is that it is not even about having the background / experience to imagine the correct numbers. I should have been able to sell him on my numbers, even if they had been pulled straight out of my ass in real time. Because if they are right that’s nice, but no one is going to notice because he didn’t have anything to compare to. Which means that this is not only about “reasoning being more important than data”, but that it’s about communication being even more important than reasoning. That might be even arguable, and probably for an engineer is a tad too much (as opposed, say, to a sales guy); but anyway for sure we all would prefer working with someone who communicates his idea (maybe to the point of unduly pulling you into it, Reality Distortion Field style) than with someone who can’t / doesn’t bother to explain what is going on in his head, where he’s the primadonna to an audience of 1.

Yes, that was a shocking thing to realize. Partly because it sounds so logical now, in hindsight.

And, of course, even the Google interview guy did it. After all, I had been able to glimpse (... or, had been shown) his brilliance. And that was it. The result being “correct” was icing on the cake, because he was already communicating it.

And now I am doing it, too. :P

One lingering question is, why was I so fixated with getting a number? First thing I though is that the style of other programming tests had put me on that frame of mind. But there’s a more insidious possibility: what comes to my mind when I think about solving a math problem is to tidily frame the final result, making it stand out from all the noise of the process. That’s what I guess we all did in exams. And I guess that’s even good presentation of the result, which should always be good. Only that in this case the result to be presented was not the final number, but… everything else. I was framing the unimportant part, and not bothering with the rest.

So, one other thing to learn is: make sure to check a couple of times at least if the question is being answered or not… another oh-so-logical tip, huh?

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