The anatomy of a tree
A decision tree contains two kinds of node. Decision nodes (conventionally drawn as squares) are points where you choose; chance nodes (circles) are points where the world chooses, with a probability attached to each branch. Each path terminates in an outcome value. The tree is solved by rolling back from the right: at each chance node, compute the probability-weighted average of the branches; at each decision node, take the branch with the best expected value. The result is not a prediction but a consistent way of comparing options whose risks differ.
A worked branch, kept honest
Suppose a product team is choosing between a full launch and a staged pilot. The illustrative numbers below are inputs a team might debate; the point is the structure of the comparison, not the figures.
| Path |
Probability |
Outcome value |
Contribution to expected value |
| Full launch: strong adoption |
50% |
+€8m |
+€4.0m |
| Full launch: weak adoption |
50% |
-€3m |
-€1.5m |
| Full launch: expected value |
|
|
+€2.5m |
| Pilot first (costs €1m): pilot succeeds, then launch |
60% |
+€7m net |
+€4.2m |
| Pilot first: pilot fails, stop early |
40% |
-€1m |
-€0.4m |
| Pilot: expected value |
|
|
+€3.8m |
What the example shows
The pilot wins not because its best case is bigger (it is smaller, since the pilot costs money and delays revenue) but because it converts a coin-flip on a €3m loss into a cheap early exit. That is the recurring lesson of tree analysis: options that buy information or preserve the ability to stop are systematically undervalued by teams comparing only headline upsides. The tree makes the value of reversibility visible.
Decisions where trees are worth building
- Sequenced commitments where an early, cheaper step can resolve the biggest uncertainty: pilots, options to expand, staged acquisitions with earn-outs.
- Litigation, regulatory and negotiation decisions, where settle-versus-fight choices have estimable probabilities and sharply different payoffs.
- Any decision where the team keeps arguing about "risk" in the abstract, and needs the disagreement converted into a specific probability someone must defend.
How trees mislead
The framework has failure modes that are worth knowing before trusting any expected value.
- The probabilities are invented to make the preferred branch win. A tree is only as honest as its least honest probability, and there is rarely evidence behind "70 per cent likely to succeed" beyond the sponsor's optimism.
- Expected value hides ruin. An option with a small chance of a company-ending loss can still show the best average; a 10 per cent probability of catastrophe does not average away for an organisation that only gets to play once.
- The tree stops one level deep, at the point convenient to the argument: the full-launch branch above assumes no competitor response on any path.
- False precision creeps in: three invented probabilities multiplied together produce a number with impressive decimals and no more truth than the guesses underneath.
- Continuous uncertainty gets forced into two branches, "success" and "failure", when the realistic outcome is a distribution. The middle of that distribution is where most projects actually land.
Getting probabilities that deserve the name
The remedy for invented probabilities is reference: what happened in comparable cases, not what the room feels. Senior operators who have run similar launches, entered similar markets or fought similar disputes hold exactly that reference class. Putting your tree's key probabilities to selected senior operators through a confidential client brief converts the most fragile inputs from advocacy into evidence before the expected values are quoted to the board as though they were facts.
