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Expected Value

Weigh each possible outcome by its probability to compare uncertain options.

Use it whenoutcomes are uncertain but you can estimate the odds.

Origin
Blaise Pascal and Pierre de Fermat, 1654
Time
15 to 30 min
Works
Solo or group
Loading the workspace
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Abstract

When outcomes are uncertain, it's tempting to judge an option by its best case or its most likely case. Expected value multiplies each possible outcome by its probability and adds them up. It's what the option is worth on average, if you could take the same bet many times.

An average can hide a lot of risk, so this workspace also shows the best case, the worst case and how widely the results spread. A higher expected value isn't worth a downside you couldn't survive.

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Method

  1. 01

    Frame the choice

    Name the decision and pick one unit to measure value in, such as money or hours.

  2. 02

    List the outcomes

    For each option, write down the different ways it could turn out. Include doing nothing as an option.

  3. 03

    Estimate the probabilities

    Give each outcome a probability. Within one option they have to add up to 100%.

  4. 04

    Estimate the values

    Put a value on each outcome, with negative numbers for losses.

  5. 05

    Compare value and risk

    Compare the expected values, then look at the worst case and the spread. Drop any option whose downside you couldn't afford.

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When to use it

  • You're choosing between options with uncertain payoffs, such as two product bets.
  • A safe option is up against a risky one that might pay off much more.
  • A team keeps arguing about what's likely versus what's possible.
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Common pitfalls

  • False precision. The probabilities are estimates, so check whether a small change would flip the answer.
  • Ignoring ruin. A small chance of a catastrophic loss can matter more than a high average.
  • Leaving out the option of doing nothing, which has an expected value too.
  • Counting only money when the outcome also costs time or reputation.
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Origin and references

Attributed to Blaise Pascal and Pierre de Fermat (1654).

  1. von Neumann, J., & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
  2. Bernoulli, D. (1954). Exposition of a new theory on the measurement of risk (L. Sommer, Trans.). Econometrica, 22(1). (Original work published 1738)
  3. Hacking, I. (1975). The Emergence of Probability. Cambridge University Press.
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