From Philip Tetlock’s “Superforcasting”
What is the Fermi Method?
Enrico Fermi was a physicist who helped invent the Atomic Bomb. He was also famous for answering seemingly impossible questions with little data. (During a time before the internet was invented.)
“Fermi was renowned for his estimates. With little or no information at his disposal, he would often do back-of-the-envelope calculations like this to come up with a number that subsequent measurement revealed to be impressively accurate.” (p. 113)
For example, Fermi would ask his students, “How many piano tuners are there in Chicago?”
Students didn’t have the internet to search for the answer, and they couldn’t use the yellow pages.
Fermi taught his students the “Fermi” method of thinking, to come up with a reasonably accurate answer.
How many piano tuners are there in Chicago?
This is how Fermi would solve this problem:
“the key was to break down the question with more questions like “What would have to be true for this to happen?” Here, we can break the question down by asking, “What information would allow me to answer the question?”
“So what would we need to know to calculate the number of piano tuners in Chicago? Well, the number of piano tuners depends on how much piano-tuning work there is and how much work it takes to employ one piano tuner. So I could nail this question if I knew four facts
1. How many pianos in Chicago?
2. How often pianos are tuned each year?
3. How long it takes to tune a piano?
4. How many hours a year the average piano tuner works?
How Many Pianos in Chicago?
“I have no idea. But just as I broke down the first question, I can break this down by asking what I would need to know in order to answer it.”
How many people are there in Chicago?
“I’m not sure, but I do know Chicago is the third-largest American city after New York and Los Angeles. And I think LA has 4 million people or so. That’s helpful. To narrow this down, Fermi would advise setting a confidence interval—a range that you are 90% sure contains the right answer.”
“So I’m pretty sure Chicago has more than, say, 1.5 million people. And I’m pretty sure it has fewer than 3.5 million people. But where is the correct answer within that range? I’m not sure. So I’ll take the midpoint and guess that Chicago has 2.5 million people.”
What percentage of people own a piano?
“Pianos are too expensive for most families—and most who can afford one don’t really want one. So I’ll put it at one in one hundred. That’s mostly a black-box guess but it’s the best I can do.”
“How many institutions—schools, concert halls, bars—own pianos? Again, I don’t know. But many would, and some, like music schools, would own many pianos. I’ll again make a black-box guess and say that it’s enough to double the per person number of pianos to roughly two in one hundred. With those guesses, I can do some simple math and conclude that there are fifty thousand pianos in Chicago.”
Now we can move on to answer the three other questions.
How Often Are Pianos Tuned?
“Maybe once a year. That strikes me as reasonable. Why? I don’t know. It’s another black-box guess.
How Long Does it Take to Tune a Piano?
“I’ll say two hours. Again, it’s a black-box guess.”
How Many Hours a Year Does the Average Piano Tuner Work?
“This one I can break down. The standard American workweek is 40 hours, minus two weeks of vacation. I don’t see any reason why piano tuners would be different. So I’ll multiply 40 hours by 50 weeks to come up with 2,000 hours a year. But piano tuners have to spend some of that time traveling between pianos, so I should reduce my total by that much. How much time do they spend between jobs? I’ll guess 20% of their work hours. So I conclude that the average piano tuner works 1,600 hours a year.”
Final Answer:
“Now I’ll assemble my guesses to make a final calculation: If 50,000 pianos need tuning once a year, and it takes 2 hours to tune one piano, that’s 100,000 total piano-tuning hours. Divide that by the annual number of hours worked by one piano tuner and you get 62.5 piano tuners in Chicago.”
“So I will estimate that there are sixty-three piano tuners in Chicago.”
“The yellow pages shows that there was 84 piano tuners in Chicago.”
“What Fermi understood is that by breaking down the question, we can better separate the knowable and the unknowable. So guessing—pulling a number out of the black box—isn’t eliminated. But we have brought our guessing process out into the light of day where we can inspect it. And the net result tends to be a more accurate estimate than whatever number happened to pop out of the black box when we first read the question.” (p. 111)
Example 2:
- “Consider Peter Backus, a lonely guy in London, who guesstimated the number of potential female partners in his vicinity by starting with the population of London (approximately six million) and winnowing that number down by the proportion of women in the population (about 50%), by the proportion of singles (about 50%), by the proportion in the right age range (about 20%), by the proportion of university graduates (about 26%), by the proportion he finds attractive (only 5%), by the proportion likely to find him attractive (only 5%), and by the proportion likely to be compatible with him (about 10%).”
- “Conclusion: roughly twenty-six women in the pool, a daunting but not impossible search task.”