DecisionBranch
Build a tree

Calculator

Decision tree analysis calculator

Paste or type a tree. You get the expected value of every option, the recommended choice, the risk profile and the rollback written out step by step, like a worked textbook solution. Change any number and everything recomputes.

Open the full editorJust need an expected value?
Your tree
Outline is valid.
RecommendedLaunch nationallyExpected value 42,000 · 6,500 ahead of Pilot in one city first
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 new product?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

Step-by-step rollback

Work from the outcomes back to the root. Chance nodes average, decision nodes choose, branch costs come off on the way.

  1. 1Launch nationally is a chance node. Its value is the probability-weighted average of its branches: 40% × 200,000 + 60% × 20,000 = 92,000.
  2. 2Roll out nationally is a chance node. Its value is the probability-weighted average of its branches: 70% × 200,000 + 30% × 20,000 = 146,000.
  3. 3Pilot succeeds is a decision. You would pick the best branch: 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 is a chance node. Its value is the probability-weighted average of its branches: 10% × 200,000 + 90% × 20,000 = 38,000.
  5. 5Pilot fails is a decision. You would pick the best branch: 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 is a chance node. Its value is the probability-weighted average of its branches: 50% × 101,000 + 50% × 0 = 50,500.
  7. 7Launch the new product? is a decision. You would pick the best branch: 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 maths works

1. 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. Rollback

Start at the outcomes and work backwards. Every chance node becomes its expected value. Every decision node becomes the value of its best branch, because you will choose it. When you reach the root you have the value of the whole decision and the policy that achieves it. The steps above show it for your tree.

3. Risk profile

The expected value hides the spread. The risk profile lists every outcome you can end up with under the recommended policy and how likely each one is, so you can see the chance of a loss and the worst case before you commit.

4. Sensitivity and switch points

Your numbers are estimates. Sweep one of them across a range and watch the root value. 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. 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?
Working from the outcomes back to the root. Each chance node becomes the probability-weighted average of its branches. Each decision node becomes the value of its best branch. Costs on branches are subtracted 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.