Fermi Decomposition
Break an unknowable question into smaller quantities that can be estimated
- Difficulty
- Easy
- Time to result
- ~days to results
- Steps
- 6
- Confidence
- 97%
Fermi decomposition tackles an apparently intractable quantity by translating it into a chain of smaller estimates. Rather than guessing the number of piano tuners in Chicago directly, a forecaster estimates the population, the proportion of households with pianos, tuning frequency, and the workload one tuner can serve. Multiplying those quantities produces a plausible answer and, more importantly, exposes every source of uncertainty. Teammates can then challenge specific assumptions instead of debating an opaque intuition. Ranges should be used where inputs are uncertain, followed by a sanity check against known constraints. The method does not promise exactness; it converts ignorance into a transparent model that can be researched, corrected, and progressively narrowed.
Origin
Extracted from Masters in Business, where Philip Tetlock described Enrico Fermi's practice of teaching students to estimate seemingly impossible quantities.
Core principles
- 01An unknown whole may contain estimable parts
- 02Approximate inputs can still produce a useful range
- 03Decomposition exposes ignorance instead of concealing it
- 04Independent assumptions can be challenged and improved
- 05A reasoned estimate is often better than an unsupported shrug
How to run it
- 1
Specify the target
Write the exact quantity, geography, population, and time period being estimated. Decide whether the useful output is a point estimate, range, or order of magnitude.
Pro tip Include units in the question to prevent dimensional mistakes.
Watch out A loosely defined target will produce an answer that cannot be checked.
- 2
Build the decomposition
Express the target as smaller quantities connected through multiplication, division, or addition. Choose components that are easier to estimate than the original question.
Pro tip Draw the equation before assigning any numbers.
Watch out Do not merely replace one unknowable quantity with several equally unknowable ones.
- 3
Estimate component ranges
Assign low, central, and high estimates to uncertain inputs using general knowledge and relevant base rates. Record why each range seems plausible.
Pro tip Use orders of magnitude first, then narrow them only when justified.
Watch out Avoid anchoring the entire model on the first number that comes to mind.
- 4
Invite assumption-level criticism
Let collaborators inspect and correct individual inputs. Focus discussion on the assumptions with the widest uncertainty or greatest effect on the result.
Pro tip Ask each reviewer which single input they would research first.
Watch out Group discussion is unhelpful if participants only debate the final number.
- 5
Calculate and sanity-check
Compute the range and compare it with physical, economic, or demographic constraints. Revise assumptions when the output implies something implausible.
Pro tip Translate the result into an intuitive ratio, such as tuners per thousand pianos.
Watch out Arithmetic consistency does not guarantee that the model structure is valid.
- 6
Reduce the largest uncertainty
Identify the input that contributes most to the output range and seek better evidence for it. Recalculate and repeat until further research is not worth the cost.
Pro tip Use sensitivity analysis to prioritize research effort.
Watch out Do not spend equal effort refining inputs that barely affect the result.
In the wild
Estimate Chicago's population, the share of households owning pianos, how often each piano is tuned, and the number of appointments one tuner can complete annually. Divide annual tuning demand by annual tuner capacity, then test the result against plausible employment levels.
→ An initially unknowable quantity becomes a transparent estimate whose assumptions can be checked and improved.
A software company estimates monthly active customers, support-contact frequency, average handling time, and productive hours per agent. Multiplying expected ticket volume by handling time and dividing by available capacity yields a staffing range.
→ Management receives a defensible hiring range and knows which demand assumptions to monitor.
Common mistakes
Guessing the whole directly
A direct intuition hides assumptions and gives collaborators no specific component to challenge.
Using unsupported point estimates
Single numbers create false confidence when the inputs are uncertain; ranges preserve and expose that uncertainty.
Skipping the constraint check
A tidy calculation may still conflict with known limits such as population, capacity, or total spending.
Is it for you?
Best for
It is best for ambiguous quantitative questions that can be decomposed into populations, rates, frequencies, capacities, or other estimable components.
Not ideal for
It is not ideal when the target cannot be decomposed causally or when correlated assumptions make the arithmetic misleading.
From the transcript
“He what do he wanted to the students to do was to take an seemingly intractable problem and break it down into parts or components…”
“What you're doing in the process is you're revealing sources of ignorance, and your colleagues on your team, for example, if it's because our forecasters…”
“It's it's a lot better than simply shrugging your shoulders and saying I have no idea.”
From the episode
Barry Ritholtz's Masters in Business: Philip Tetlock Interview
Philip Tetlock