The Size Instinct: Numbers Without Denominators

All courses / Landscape / Module 2 / Chapter 10

Learning objectives

After the lesson the participant can:

• Explain the three reasons the size instinct misleads in this landscape.
• Restate a lone count with its denominator, its comparison and its definition, or say that none exists.
• Distinguish one fact measured against several denominators from two different facts.
• Assign a reach class to a unit by counting people and write down who was counted.

Key concepts

The size instinct

The habit of being impressed by a large number on its own, without the denominator, the base rate or the comparison that would tell us whether it is large. Rosling's cure is to divide.

Count and share

ICT specialists in the EU27 rose from 5,681.3 thousand in 2011 to 10,450.8 thousand in 2025, and from 3.0 to 5.0 per cent of total employment. Both are true; the habit is to look for each beside the other.

Three denominators to ask for

People: how many people's work or outcomes does this touch? Deployments: out of how many comparable systems, users or decisions did this happen? Time: over what period, and against what period before it?

Reach class

The area of a mark encodes the people the unit's actions touch in a year, in four fixed sizes: S under 100, M 100 to 999, L 1,000 to 9,999, XL 10,000 and more. It is never a count of transactions.

Rule of thumb: never a number alone

Never accept a number alone; ask what it is divided by and compared with. A denominator corrects the size of a thing and does not excuse a harm: divide to see the size, not to see whether it matters.

Interactive exercises

Do them here and get feedback at once. Choose a card and then where it belongs, or drag it.

Teaching plan

Discussion

1. A journalist may write that most companies now use AI, which is true of large enterprises and false of the population. Which denominator do the numbers about AI in your own organisation's papers usually carry, if any?
2. The author declines to compute a rate of harm per deployment because no public dataset counts deployments. What is gained by naming the gap instead of estimating across it?
3. Hansa Mutual's claims-triage agent is the same size as the embedded workplace assistants. What would your board be shown about each today, and what would drawing both by people touched change?

Written exercise

Self-test

Choose an answer to see whether it is right, or open the answer below each question.

1. A unit handles 400,000 transactions a year for 12,000 people. Which reach class does Contour give it?

   1. L, because it falls between 1,000 and 9,999 people
   2. It has no reach class until the transactions have been divided by the people they concern
   3. XL, because it touches 10,000 or more people, whatever the number of transactions
   4. XL only if the transactions rise to four million
   Show the answer

   C. XL, because it touches 10,000 or more people, whatever the number of transactions
   Reach is a count of people, not of transactions. A unit that handles 400,000 transactions for 12,000 people is XL by people, and it would be XL at four million transactions.

2. Why can ENISA's 4,875 incidents for the twelve months to June 2025 not be read as a fall from 11,079 the year before?

   1. Because the later report covers only public administration
   2. Because the two reports cover different member states
   3. Because the earlier count included incidents outside Europe
   4. Because the counts were produced under different versions of ENISA's methodology
   Show the answer

   D. Because the counts were produced under different versions of ENISA's methodology
   The 2025 report states that it used the agency's updated methodology of August 2025, so the later count is no baseline for the earlier one. Two numbers are comparable only when the thing counted, the way of counting and the period are the same.

3. Where does the chapter say the rule of dividing stops applying?

   1. At the top row of the landscape: one irreversible outcome for one person is not made small by a rate
   2. In the bottom row, where everything is reversible at once
   3. For official statistics, which need no denominator
   4. For any unit of reach class S, because fewer than 100 people a year are too few to give a meaningful rate
   Show the answer

   A. At the top row of the landscape: one irreversible outcome for one person is not made small by a rate
   A denominator corrects the size instinct; it does not excuse a harm. The reversibility rows exist so that irreversible outcomes are seen by position and not lost in a rate.