Fermi estimation, scored the way traders think about it

Estimation questions come up in trader and quant phone screens and as the opening of a make-a-market exercise: how many piano tuners work in Chicago, how many litres of water are in an Olympic pool, how many flights take off in the US each day. Nobody expects the exact number. The interviewer is checking whether you can break the question into parts you can reason about, keep the arithmetic straight under time pressure, and say honestly how sure you are.

Each question in this game gives you 60 seconds to enter a low and a high estimate: a range you think has a 90% chance of containing the answer. Points come from two parts. Accuracy is scored on a log scale from the geometric middle of your range, so being 3 times too high costs the same as being 3 times too low. The range part pays only if the answer lands inside it, and pays more for a tight range. After every question you see the answer on a log ruler next to your range, the factor you were off by, and a worked estimate that shows one sensible way to break the question down.

At the end you get a score out of 100, a calibration check (how many of your 90% ranges caught the answer), how far off you were on facts versus guesstimates, and the full list of worked estimates to review.

What is a Fermi question in a trading interview?

A question with a numeric answer you cannot know exactly, such as the number of golf balls that fit in a school bus. You are expected to split it into quantities you can estimate, multiply them through, and give a range or a market around your answer.

How is the Fermi game scored?

Each question is worth 100 points: up to 60 for accuracy, measured on a log scale from the geometric middle of your range, and up to 40 if the answer falls inside your range, more for tighter ranges. A hint costs 10 points. Unanswered questions score 0.

Why use a log scale for estimation?

Estimation errors are multiplicative. Saying 300 when the answer is 100 is the same size of mistake as saying 33, and a log scale scores them the same.

Is the Fermi estimation game free?

There is a free sample run with no signup: 8 questions at 60 seconds each, scored, with the worked estimate after every answer. Medium and Hard question sets, point-estimate mode, longer runs and your history are part of QuantVault Pro.

Related: Kelly criterion guide · Fermi estimation questions · Probability interview questions · SIG betting and market-making round · All trading games