Masahiro Yoshida

Masahiro Yoshida

Arts & Sciences: Economics, PhD

Scholar Highlight

Predict the World in One Minute

I begin by asking 3 HARD questions for you to answer.

  1. How many cats are there in the U.S.?
  2. How many delivery pizza shops are there in Missouri?
  3. How many Airbnb hosts are there at Washington University?

It turns out that an extremely effective way to respond to such out-of-the-blue questions is to calculate the answers by using the method of “Fermi-estimation”. This makes it feasible to get an approximate estimate that is as precise as possible in one minute. I’ve continuously used this method for my research in economics, business, and daily life for almost seven years.

Why is the Fermi estimation such an effective exercise to develop our scientific thinking to predict the world within one minute? Consider five cookbook steps to answer the first question: How many cats are there in the U.S.? By doing so you can see that the essence of scientific thinking is condensed in each step.

  • Step one: ASSUME. When the problem is complicated, it’s a good idea to narrow the scope of the problem. I assume most of the cats in the U.S. are pets because of the highly organized public hygiene system to accommodate homeless cats.
  • Step two: MODEL. We have to break down the problem into several manageable elements, so I divide it into 3 parts:
  1. The number of households x
  2. The proportion of households that own cats x
  3. The average number of cats per household
  • Step three: SUBSTITUTE. In each part, if you know the number, put the number into the element or construct the number with some assumptions and logic. We can model (A) as:

a.  The population of the U.S. ÷ the average household size

I know that the population in the U.S. is about 300 million and I estimate that each household consists of three people.

Next, for (b), I estimate that the maximum is 30%, and the minimum is 10%. So I take the intermediate number of 20%. And last, (c) is set as 3.5 because I estimate the maximum number of cats is six (cats bear many babies) and the minimum is one.

  • Step four: CALCULATE. 100 million HHs × 20% × 3.5 = 70 million
  • Step five: VERIFY. Compare your estimate and actual data. According to the latest survey, the correct number of cats in the U.S. is 74.06 million, which is almost the same figure as the human population in Turkey. Surprisingly, this is 95% accurate.

By way of historical background, the name “Fermi” in the Fermi estimation comes from a legendary physicist Enrico Fermi, a Nobel Prize winner in physics in 1938. He was also known as a master of quick estimation. His approach has been implicitly used for a long time in science, and currently the method is spreading into the fields of social science and business. Furthermore, it has often been used for job interviews in U.S.-based firms such as Google and Microsoft.

Let me share my personal history with the Fermi estimation. My first encounter was not so romantic. About 7 years ago, I was looking for a job at consulting firms and had to prepare a crazy exercise for job interviews, which led me to the Fermi estimation. I formed a study group with my geek friends, and we surprisingly got hooked. Eventually, we solved more than 1,000 questions.

So our natural next step was to write a handbook about the Fermi-estimation. I co-authored it with a friend, and it was published in 2009 in Japan. So far, more than 60,000 copies have been sold. It has also been translated into Korean.

Not surprisingly, we were curious about why. Our natural concern is how the estimation yields such accurate results. In trying to answer this question, we quickly (within 5 minutes) solved 20 target problems in Japan, such as estimating the number of utility poles or the annual consumption of disposable chopsticks quickly within 5 minutes. The result was that in 15 out of 20 examples cases we came within a 50% error range. This is not between 1000% and 10%, indicating that we can at least capture the order of magnitude of any target problem.

So far, we have implicitly assumed that there are always data to use as a check. In reality however, we have to admit that the data we could obtain is quite limited. We can export GDP and population data from the IMF database, for example, but we struggle hard when trying to construct the country-level indexes of corruption or freedom in media, which are not directly observable in raw data. In business, we can search the latest market size in industries by Bloomberg, but it’s very challenging to predict the future market size of Apple watch five years from now.

In the public sector, imagine when a war or natural disaster happens. We can look up the geographic or weather information by GPS, but it might be crucial to calculate the amount of food, shelter, and medicine that needs to be delivered to refugee camp locations. Nobody knows these precise figures. Wikipedia doesn’t know either. This is where Fermi-estimation works. It empowers us with unique insights to predict the world in one minute.