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Decision tree analysis calculator

Paste or type a tree. You get the expected value of every option, the recommended choice, the range of outcomes and the working written out step by step, like a textbook solution. Change any number and everything updates.

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Best optionLaunch nationallyExpected value 42,000 · 6,500 ahead of Pilot in one city first
Best option
Launch nationally – expected value 42,000, 6,500 ahead of Pilot in one city first. It stays the best choice unless the chance of strong demand under Launch nationally falls below 36.4%, when Pilot in one city first wins.
What would change the answer · sensitivity analysis, switch points
Launch nationallyPilot in one city fir…020k40k60k80k056,500100,000

Under 56,500, Launch nationally wins. Above it, Pilot in one city first.

Everything else in the tree stays as written.

Launch the new product?−50k40%60%−15k50%−45k70%30%50%−45k10%90%Launch the newproduct?EV 42,000→ Launch nationallyLaunch nationallyEV 92,000Strong demand200,000Weak demand20,000Pilot in one city firstEV 50,500Pilot succeedsEV 101,000→ Roll out nationallyRoll out nationallyEV 146,000Strong demand200,000Weak demand20,000Stop after pilot0Pilot failsEV 0→ Stop after pilotRoll out anywayEV 38,000Strong demand200,000Weak demand20,000Stop after pilot0Don't launch0

The working, step by step

Start at the outcomes and work back to the question. Where chance decides, take the weighted average; where you decide, take the best option; subtract costs on the way.

  1. 1Launch nationally depends on chance, so it is worth the probability-weighted average of its outcomes: 40% × 200,000 + 60% × 20,000 = 92,000.
  2. 2Roll out nationally depends on chance, so it is worth the probability-weighted average of its outcomes: 70% × 200,000 + 30% × 20,000 = 146,000.
  3. 3Pilot succeeds is your choice, so it is worth its best option: Roll out nationally = 101,000 (146,000 − 45,000 cost); Stop after pilot = 0. Best: Roll out nationally at 101,000.
  4. 4Roll out anyway depends on chance, so it is worth the probability-weighted average of its outcomes: 10% × 200,000 + 90% × 20,000 = 38,000.
  5. 5Pilot fails is your choice, so it is worth its best option: Roll out anyway = −7,000 (38,000 − 45,000 cost); Stop after pilot = 0. Best: Stop after pilot at 0.
  6. 6Pilot in one city first depends on chance, so it is worth the probability-weighted average of its outcomes: 50% × 101,000 + 50% × 0 = 50,500.
  7. 7Launch the new product? is your choice, so it is worth its best option: Launch nationally = 42,000 (92,000 − 50,000 cost); Pilot in one city first = 35,500 (50,500 − 15,000 cost); Don't launch = 0. Best: Launch nationally at 42,000.
  8. ✓So the whole decision is worth 42,000, and the recommendation is Launch nationally.

How the math works

  1. 01

    Expected monetary value

    An uncertain outcome is worth its probability-weighted average. A 40% chance of 200,000 and a 60% chance of 20,000 is worth 0.4 × 200,000 + 0.6 × 20,000 = 92,000. Subtract what it costs to get there: launching nationally costs 50,000, so the branch is worth 42,000.

  2. 02

    Rollback

    Start at the outcomes and work backwards. Every point where chance decides becomes its expected value. Every point where you decide becomes the value of its best option, because you will choose it. When you reach the question at the top you have the value of the whole decision and the choices that get you there. The steps above show it for your tree.

  3. 03

    Range of outcomes (risk profile)

    The expected value hides the spread. The range of outcomes lists everything you could end up with if you follow the recommendation, and how likely each one is, so you can see the chance of a loss and the worst case before you commit.

  4. 04

    What would change the answer (sensitivity)

    Your numbers are estimates. Move one of them across a range and watch the value of the best option. Where the recommended option changes is the switch point. If the switch point is close to your estimate, the decision is fragile and worth more research. On the example, piloting beats a national launch below a 36.4% chance of strong demand.

  5. 05

    Worth finding out (value of information)

    Imagine you could learn an uncertain outcome before deciding. The value of that knowledge, the expected value with the information minus the value without it, is the most you should pay for the study, pilot or expert who could tell you.

Longer explanations with a different worked example: Expected value and decision trees, explained. New to the format? How to make a decision tree.

Questions

What is decision tree analysis?
A way to value a decision under uncertainty. You lay out the options, the chance events and the outcomes as a tree, put probabilities and payoffs on them, and roll the tree back to find the expected value of each option and the best one.
What is rollback?
It's how a decision tree gets its numbers: start at the outcomes and work back to the question. Where chance decides, take the probability-weighted average; where you decide, take the best option; subtract costs on the way.
What is a switch point?
The value of an input at which the recommended option changes. If your estimate is close to a switch point, the decision is fragile and worth more research.
Is this the same as EMV?
Yes. Expected monetary value is expected value when the payoffs are money. The calculator works for any unit.

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