How Many Piano Tuners Are There In New York City?

Why this isn’t such an irrelevant question to be asked in an interview after all, and how to solve it

Interviewer — “How many piano tuners are in New York City?”
You — “… is this really relevant to working for a travel advertiser?”

I’m sure plenty of you have been asked similar quirky interview questions that left you scratching your head. “How much would you charge to wash all the windows in Chicago?”, “How much money does your local cinema make in a week?” or “How many cups of coffee does Starbucks serve in London each year?”. These type of questions often elicit a deer-in-the-headlights look, and leave you scrambling to figure out how exactly you are supposed to know the answer.

Of course the truth is that you aren’t supposed to know the answer — the interviewer often just wants to see how you react to the question and handle the pressure of being put on the spot. This can give useful information about a candidate, but it strikes most people as an unfair and innacurate way to judge, given the candidate might think you really do expect an accurate answer. This slightly gimmicky tactic could diminish the chances of otherwise stellar potential employees that get caught off-guard by the seemingly irrelevant question.

What most people don’t realise is that there truly is a real method to answering these questions, and that developing this ability can be incredibly beneficial in the workplace. These types of questions are called “Fermi Problems” — after the famous engineer Enrico Fermi who used them to estimate the strength of atomic blasts, deduce the circumference of the Earth and determine the likelihood of aliens existing in our universe. Surprisingly Fermi’s method was remarkably accurate — he once estimated the strength of a nuclear blast (top secret at the time) by measuring the distance pieces of paper travelled when dropped from his hand during the blast!

How does he do it?

It might seem like magic, but it’s actually relatively simple to answer these questions using the following method: A) break it down into a series of smaller questions B) use common-sense and make educated guesses C) use your assumptions to calculate the answer. For example:

  1. Roughly how many people live in New York City? — 8,000,000
  2. Does every person own a piano? — no
  3. Can we assume that families own pianos, not individuals? — yes
  4. How large is the average family? — 5 people
  5. So how many families are there in NYC? — 1,600,000
  6. Does every family own a piano? — no… perhaps one in ten does
  7. So how many pianos are there in NYC? — 160,000
  8. How often per year do pianos need to be tuned? — once per year
  9. How many piano tunings can one piano tuner do? — let’s say 4 per day, so if there’s 200 working days in a year, that’s 800 per year
  10. So how many piano tuners could NYC support?— 160,000/800 = 200 piano tuners

Is this accurate?

Looking on Yelp for Piano tuners in New York City I can see 24 listings — if our estimate is correct we’re talking about 8 piano tuners per company… maybe too high but if you figure that many piano tuners won’t be listed on Yelp, we’ve actually arrived at a pretty reasonable number! The reason the number can come out so accurately after all those wild guesses, is that the guesses are likely to cancel themselves out — sometimes we would have guessed too low, other times we would have guessed too high, so in the end we’re likely to land on a fairly accurate number, despite knowing little about piano tuning.

Additionally, we can later come back to the assumptions we made to update them, say if we find out piano tuners can handle 1000 tunings a year, or that there are actually 10,000,000 people living in NYC. Either way, 100% accuracy isn’t the point here — the aim is to get the answer within an order of magnitude. We know there are probably more than 100 piano tuners in NYC, but almost definitely less than 1000. This information alone is enough for you to make a decision on whether to go further with whatever plans you had for the piano tuning market.

So why is this useful?

The benefit of Fermi’s method is that it allows you to rapidly size up an opportunity to a reasonable degree of accuracy, without investing much time or effort in finding an accurate answer. Sometimes called ‘back-of-the-napkin’ or ‘back-of-the-envelope’ calculations, the ability to make these estimates can come in handy, particularly in negotiations, brainstorming sessions and when setting priorities.

If you can rapidly estimate the size of the piano tuning market in New York to be less than the 1000 people you need to run a profitable piano tuner training school, you can quickly abandon your plans and move onto a business idea with more potential. Following a brainstorming session you could use this method to quickly build a rough business case for each idea, allowing you to rank them from biggest to smallest opportunity without expending too much effort. If you model it in excel you can even go back to the model to update your assumptions as you gather more data. If that section of the website turns out to have 20,000 visits a month, not 15,000 — just update your model in excel and straight away you’ve got a more accurate estimate.

Real world marketing example

You are in a meeting with your boss and a large publisher, where you are negotiating to buy some advertising on their website. The publisher tells you the CPM (cost per thousand impressions, or views of your Ad) they charge is £10. To effectively negotiate you need to know the maximum CPM you can afford, given your goal of collecting email addresses for potential new customers. You know that the CTR (click-through rate, clicks / impressions) of your Ad in the past has been around 1%, and your conversion rate (email sign ups / clicks) is historically averaging 10%. If you can afford to pay £5 per email you acquire (CPA, cost per acquisition), is £10 CPM a good price?

Assumptions: CPM = £10, CTR = 1%, Conv. Rate = 10%, CPA goal = £5
CPA = CPM / ((CTR*1000)*Conv. Rate)
CPA = £10 / ((1%*1000)*10%)
CPA = £10 / (10*10%)
CPA = £10 / 1, so the CPA is equal to £10

We can see that this price would leave us double our CPA target. You should at least be able to work this out in excel after the meeting (before you sign anything), but extra kudos if you can figure this out in your head and bust it out in the middle of the meeting, rain-man-style, impressing your boss and putting the publisher on the back foot!

While the publisher may argue that they are giving you ‘premium’ inventory that is more likely to click and convert, it could also go the other way and perform worse than average. Either way, the chances of the publisher performing twice as good as your other sources of traffic are pretty slim. If they could offer a £5 CPM, or offer significantly better placement (above the fold) then maybe you could consider it.

Note: in scenarios like this, where the publisher is adamant they can deliver a higher CTR or Conversion rate, you might ask them to consider a CPC or CPA agreement. This way they only charge you per click (transferring the risk of a low CTR to them) or only charge you per email sign up (they’re taking all the risk here — you can’t lose, but volume can be low/unpredictable).

Contact me on Twitter with any questions / feedback @2michaeltaylor