What Marketers Can Learn From Enrico Fermi

Fermi problems, Fermi decomposition, and making better estimates.

There’s a degree of uncertainty in any business problem.

The goal of data analysis is to reduce uncertainty, not eliminate it.

Elimination of uncertainty is a pipe dream.

An illusion.

Instead, marketers and growth professionals must be comfortable making decisions where using estimation is the best way to minimize uncertainty.

This article will show you my favorite technique for doing that.

Fermi problems

For the 5% of you that like textbook definitions, a Fermi problem is:

“an estimations problem designed to teach dimensional analysis or approximation of extreme scientific calculations, and such a problem is usually a back-of-the-envelope calculation.”

For the rest of us, think of a Fermi problem as a question that seems to be impossible to answer (e.g., how many sponges are in the state of California), but isn’t impossible to estimate if you break the problem down into small pieces.

Fermi decomposition

Fermi decomposition is the term used to describe the approach to solving Fermi problems.

To teach Fermi decomposition, Enrico Fermi (the originator of the Fermi problem) asked his students to estimate the number of piano tuners (i.e., people who tune pianos) in Chicago.

The only information he’d give them was the population size of Chicago.

Here’s the explanation of the problem (thank Nasa):

As a lecturer, Enrico Fermi used to challenge his classes with problems that, at first glance, seemed impossible. One such problem was estimating the number of piano tuners in Chicago, given only the city’s population.When the class returned a blank stare at their esteemed professor, he would proceed along these lines:

From the almanac, we know that Chicago has about 3 million people.

Now, assume that an average family contains four members. That means the number of families in Chicago must be about 750,000.

If one in five families owns a piano (Note: More on this below!), there will be 150,000 pianos in Chicago.

If the average piano tuner

• serviced four pianos every day of the week for five days

• rested on weekends, and

• had a two-week vacation during the summer,

Then in one year (52 weeks), he would service 1,000 pianos. 150,000/(4 x 5 x 50) = 150, so there must be about 150 piano tuners in Chicago.
This method does not guarantee correct results; but it establishes a first estimate which might be off by no more than a factor of 2 or 3–certainly well within a factor of, say, 10.

We know, for example, that we should not expect 15 piano tuners, or 1,500 piano tuners. (A factor of 10 error, by the way, is referred to as being ‘to within cosmological accuracy.’ Cosmologists are a somewhat different breed from physicists, evidently!!!)

Reasonable estimation

In the classic Fermi problem described above, you may have caught that 1 in 5 families owning a piano was an estimate.

We have to use our intuition here and ask, “Is this a reasonable estimate?” We probably know that 1 in 2 is probably too small, but 1 in 100 is too large. So what’s a reasonable minimum and maximum value here? Maybe 1 in 4 and 1 in 20?

Selecting a min and max creates lower and upper bounds for our estimation. It may be a wide range, but that’s accurately describing the uncertainty we have in approaching the problem.

It’s the truth.

Don’t be the marketer who builds a revenue forecast that shows conversion rate doubling next year to hit the revenue target the CEO tasked you to hit.

How the heck are you going to do that?

There’s nothing wrong with having revenue goals, but you need to have a clear path to getting there. If you just fiddle with numbers in a spreadsheet until the model looks how the CEO wants, the year will pass, the CEO will be unhappy, and you probably won’t have a job.

Applying Fermi decomposition to marketing

I use Fermi decomposition every week in marketing and business.

It’s just “back of the napkin math” that helps your most important marketing tool (your brain) make better decisions.

Here are some examples of when you could use this mindset:

• Forecasting revenue

• Calculating your SOM

• Estimating content marketing ROI

• Estimating the CAC payback of a distribution channel you can’t track (e.g. podcast, organic social)

• Building a growth model

Final thoughts

Learning to think like Enrico Fermi is an incredibly valuable skill to have as a marketer and it’s really not difficult. It just takes some practice and a little bit of creativity.

Until next time.

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