Anchors beat arithmetic

Anchors beat arithmetic

Good estimates do not start with a calculation. They start with something you already know the size of, and a count.

The problem with working it out

Ask someone how tall the Eiffel Tower is and watch what happens. Most people try to compute. They reach for a formula, find no numbers to put in it, and produce a guess that could be off by a factor of ten in either direction.

The tower is 300 metres. Nobody arrives there by arithmetic. The people who get close do something else: they picture a building they know, and they stack it.

What an anchor actually is

An anchor is a length you carry around without effort. A credit card is 8.6 cm on its long side. A shipping container is 6 metres. A London double-decker is 11.3 metres. None of those are facts you revised for. They stuck because you have stood next to them.

The useful part is what happens when you count them.

27

double-deckers, end to end

That is the Eiffel Tower, near enough. 300 divided by 11.3 is 26.5, and that miss is smaller than the one you would have made by guessing.

Bus and tower from the How big? data set, both sourced.

Two anchors, four orders of magnitude

The distance between the smallest and largest object in the How big? set is a factor of nineteen thousand. A golf ball is 4.3 cm. The Burj Khalifa is 828 metres. Between those two sit thirty-two things you can picture, and any of them will do as a stepping stone.

AnchorSizeWhat it gets you
Credit card8.6 cmAnything on a desk
A4 sheet29.7 cmScreens, books, small animals
Shipping container6.06 mVehicles, rooms, large animals
Double-decker11.3 mBuildings up to about ten storeys

The people who estimate well are not doing more mathematics than everybody else. They are doing less of it, on better numbers, and they stop as soon as the order of magnitude is right.

The objection, and it is a fair one

You do not know the length of a blue whale. That is true, and it does not matter. You know a bus. A blue whale is 30 metres, which is two and a half buses, and once you have made that link once you will never lose it.

This is how the reveal in every round is written: the answer, the truth, the miss as a factor, and then the chain that would have got you there.

A good estimate is not a lucky number. It is a chain of two or three things you already know. Enrico Fermi, on order-of-magnitude reasoning

Four anchors worth carryingDouble-decker11,3 mShipping container6,06 mGiraffe5 mConcert grand piano2,74 mBasis: Four of the 34 objects in the How big? data set
Sourced from Wikipedia and Wikidata.

Where anchors fail

Anchors break when nothing in your life resembles the thing. Nobody has stood next to the Saturn V, so 110.6 metres arrives as a number and stays one. The fix is not a better anchor. It is a chain: the rocket is roughly a football pitch stood on end, and a pitch is something you have walked across.

They also break in the other direction. Below a centimetre your hands stop being a reference, and above a kilometre your eyes do.

What the miss tells you

  • A factor under 1.5 means the anchor was right and the count was close.
  • A factor near 10 means the anchor was right and the count was wrong.
  • A factor over 100 means you never had an anchor at all.
The direction matters more than the size of the miss.

How to build one

  1. Pick something you see every week and look up its size once.
  2. Count it into three things you cannot measure.
  3. Check the three, and keep the anchor if it held.

Before your next guess

  • Name the anchor out loud.
  • Round it hard, then count.
  • Say the order of magnitude before the number.

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