Ian Hargreaves.
Rigour for strategic decisions
Companion № 03 · Distributions
№ 03
Companion
guide
A plain guide for Elicit & Simulate

Which shape?

The tools ask you to pick a distribution for each uncertain input. Here is what each one means, in plain terms, and how to choose without any statistics.
Ian Hargreaves Companion to: Elicit & Simulate Reading ~5 min Annotated, plain-language

A “distribution” is just a shape for how an uncertain number is likely to land: where the common values cluster, and how far the rare ones stray. You don’t need the maths; you need to match the shape to the kind of quantity you’re guessing. Five cover almost everything you’ll meet in a commercial decision. Each one below leads with what it is for, so you can see every type at a glance, then opens to its picture and the fine print. The five marketing examples below are one story: a single product launch, its campaign, and the numbers you would have to put on it.

01

A number that could land either side of your best guess

Normal
The classic bell. Values sit symmetrically around your best guess, as likely to land a bit above as a bit below, with big misses either way rare. If that is your input, choose Normal in Elicit or Simulate.
see shape →
The shape, an example, and when not to use it
Use it for
Symmetric errors and estimates: a forecast that could be out either way by a similar amount.
Marketing example
The uplift a change might deliver, plus or minus a few points either way.
Watch out
It allows negative values, so don’t use it for things that can’t go below zero.
02

Money or time: positive, usually modest, sometimes much bigger

Log-normal
Like the bell, but squashed up against zero with a long tail to the high side, so most values are modest and now and then one is much larger. The natural shape for money and time. If that is your input, choose Log-normal in Elicit or Simulate.
see shape →
The shape, an example, and when not to use it
Use it for
Positive amounts that can occasionally be much bigger than usual.
Marketing example
Deal size or average order value: most orders modest, a few large ones pull the average up.
Watch out
Needs all-positive numbers (low, centre, high > 0).
03

Counts in a period, or the wait between events

Gamma
A close cousin of log-normal, positive and skewed to the high side, but the natural fit for counts of things in a period and the waiting time between them. If that is your input, choose Gamma in Elicit or Simulate.
see shape →
The shape, an example, and when not to use it
Use it for
Events per period, or the time between events.
Marketing example
Leads per week, support tickets per day, time between sign-ups.
Watch out
Positive only. If you can’t decide between this and log-normal, it rarely matters much.
04

A rate or share, held between 0% and 100%

Beta
For a rate or share, a number that cannot fall below 0% or rise above 100%. It bends to sit naturally inside those walls instead of spilling past them. If that is your input, choose Beta in Elicit or Simulate. The A/B test runs on this shape.
see shape →
The shape, an example, and when not to use it
Use it for
Proportions, rates, and shares bounded between 0 and 1.
Marketing example
Conversion rate, click rate, the share of a market you’ll take.
Watch out
Only for things genuinely capped at 0% to 100%.
05

Just three guesses: lowest, most likely, highest

Triangular
The simplest shape, and a fair choice when you have no data at all. You give the lowest, most likely, and highest it could be, and it draws a plain tent between them, with nothing assumed beyond the three numbers you gave: straight sides, and no chance outside your bounds. If that is your input, choose Triangular in Simulate.
see shape →
The shape, an example, and when not to use it
Use it for
Quick back-of-envelope work from three honest guesses.
Marketing example
A new product’s first-year sales: worst, likely, and best case.
Watch out
Crude (straight sides). Fine for rough work; for careful judgement, Elicit fits a smoother shape.
Quick pick
A number that could be out either way by a similar amount
Normal
Money or time, positive, occasionally much bigger
Log-normal
Counts of events in a period
Gamma
A rate or %, capped at 0% to 100%
Beta
Just three guesses, no data
Triangular
Genuinely not sure
Normal or Triangular
Now pick one in the toolsBoth instruments let you choose a shape per input. This guide is one click from each shape picker.
Open Elicit → Open Simulate →

A note on the pictures. The pictures are deliberately schematic: they show the kind of shape (symmetric, skewed, bounded, a tent), not exact curves. The five here cover the vast majority of commercial inputs; a count-of-successes shape (Binomial) could follow if the tools ever need it. Picking the shape is the easy half; how to get three honest numbers in the first place is its own guide: elicitation methods.