Decisions
45 min

Expected value of information

Compute what a piece of research is worth by asking how often it would change your decision, and by how much.

Time cost
45 min
Output
A value ceiling for the proposed research.
Steps
5
Run it — Expected value and decision tree →

Use when

  • Someone proposes more analysis and you want to know whether to fund it.
  • You are tempted to delay a decision to learn more.
  • A study, pilot or trial has a price attached and no stated benefit.

Do not use when

  • The information is free and immediate. Just get it.
  • You would not change course whatever it said — which is the finding, and it means the answer is zero.

Inputs required

  • The decision as it stands
  • The best option’s current expected value
  • What the information could reveal, and how likely each result is

Procedure

  1. 01

    Compute the decision without new information

    Best expected value under current beliefs. This is the baseline.

  2. 02

    Ask what the information could say

    Enumerate the possible findings and how likely each is. If there is only one plausible finding, the information is worth nothing.

  3. 03

    Decide what you would do under each finding

    For each possible result, what becomes the best option? If the answer is the same option every time, stop — the value is zero regardless of cost.

  4. 04

    Compute the informed expectation

    Weight the value of the best action under each finding by the probability of that finding, and sum.

  5. 05

    Subtract and compare

    The difference between the informed and uninformed expectation is the value of perfect information — a ceiling. Real, imperfect research is worth less. If the ceiling is below the price, do not buy it.

Characteristic failure mode

Buying information that cannot change the decision. It feels responsible, it produces a document, and its value was zero before it was commissioned.

Worked example

A £15,000 market study is proposed before a product decision.

  1. 01Current best option has an EV of £180k.
  2. 02The study could come back favourable (65%) or unfavourable (35%).
  3. 03Under favourable, the same option is chosen. Under unfavourable, a different option worth £140k is chosen instead of one that would have returned £95k.
  4. 04EVPI = 0.35 × (£140k − £95k) = £15.75k.

Result

Perfect information is worth £15.75k. The study is imperfect and costs £15k. It is not worth buying, and the arithmetic says so before the money is spent.

Where to go next

Also cited by
Fermi estimation