Skip to content
Thinking in Diagrams

Decision tree

Strategy & decisionsField guide · Strategy & decisions · 2 of 6

Which choice, given the chances of what follows each?

A decision tree branches left to right from a choice: a square where someone decides, a circle where something beyond their control turns out one way or another, and a branch for each choice or outcome, each path ending in the value of its result.

Marks

Section titled “Marks”
MarkDrawn asStands forSource
decision nodea small squarea point where the decision maker chooses one of several courses of actionHarvard, Decision node; Middleton §14.1
A decision tree's decision node The words cut today?, then a small square, the decision. cut today?
chance nodea small circlea point where one of several events beyond the decision maker’s control takes place, or becomes knownHarvard, Chance node; Middleton §14.1
A decision tree's chance node A small circle, a chance point, with two branches leaving it to the right: rain on the cut hay, probability 0.4; and no rain, probability 0.6. No branch has an arrowhead. rain on the cut hay (0.4) no rain (0.6)
enda small triangle, or a branch’s bare end when drawn by handthe end of one path of decisions and eventsHarvard, Terminal node; Middleton §14.1
A decision tree's end A branch, wait, ending at a small triangle. The branch has no arrowhead. wait
brancha line with its choice or event written on it, and a probability on each chance branchone choice or one event; a node’s branches exclude one another and cover every caseMiddleton §14.1
A decision tree's branches Read left to right. A small square, the decision, and a branch, cut, running to a small circle, a chance point; from the circle, a branch, no rain, probability 0.6. No branch has an arrowhead. cut no rain (0.6)
payoffa number or words at a path’s endthe value of that path’s resultMiddleton §14.2
A decision tree's payoff A small triangle, a path's end, beside the words about 22% lost, poorer feed. about 22% lost, poorer feed

A line with an arrowhead

Section titled “A line with an arrowhead”

No line on a decision tree has an arrowhead: each branch is one choice or one outcome, read left to right in the order the decision maker learns of them, not necessarily the order in which events happen. An effect produces a change in the variable at its head; a branch leads to the next node and changes nothing, and the probabilities on a circle’s branches add up to one. Howard and Matheson’s influence diagram, from decision analysis, shows the same decisions and chances as boxes and circles in one graph without loops; its lines into a chance node need not mean cause, and it is not the influence map.

Cutting hay before forecast rain

Section titled “Cutting hay before forecast rain”
A farmer deciding whether to cut hay before forecast rain, as a decision tree Read left to right. The words cut today?, then a small square, the decision. Two branches leave it. The upper branch, cut, runs to a small circle, a chance point, with two branches of its own: rain on the cut hay, probability 0.4, ending at a small triangle beside the words about 22% lost, poorer feed; and no rain, probability 0.6, ending at a small triangle beside the words about 6% lost. The lower branch, wait, ends at a small triangle beside the words cut after the rain, the crop a few days older. No branch has an arrowhead. cut today? cut rain on the cut hay (0.4) about 22% lost, poorer feed no rain (0.6) about 6% lost wait cut after the rain,the crop a few days older

The farmer’s question is Rankin and Undersander’s: the hay is ready to cut, but rain is forecast. In Collins’s Wisconsin trial, alfalfa rained on after a day’s curing lost 22% of its dry matter, against 6.3% for hay cured dry, and rained-on hay can lose 6 to 40% of its digestibility. The probabilities and the waiting branch’s end are illustrative.

When to draw one

Section titled “When to draw one”

Draw one where a choice leads to uncertain events, or to further choices, and each path’s result can be valued: ACCA teaches the tree for a series of business decisions, and Harvard’s School of Public Health for clinical ones.

When not to draw one

Section titled “When not to draw one”

Where the better choice is plain once the paths are written down, a sentence states it. Where no one can estimate the probabilities, which ACCA lists among the method’s limits, a tree’s expected values rest on guesses. Howard and Matheson found the tree’s order rarely the order in which a decision maker’s information is best assessed, and drew an influence diagram instead.

Reasoning and polish

Section titled “Reasoning and polish”
  • Reasoning5 of 5
  • Polish4 of 5choice sketch → quantified decision model
  1. One decision with distinct outcomes
  2. Chance nodes, probabilities, costs and payoffs
  3. Expected values, sensitivity, information value and staged options
Section titled “Related types”

No type is listed as related to this one.

Sources

Section titled “Sources”
  • Harvard T.H. Chan School of Public Health, Glossary, teaching pack Building Decision Trees, on the decision tree and its decision, chance and terminal nodes.
  • Mike Middleton, “Introduction to Decision Trees”, chapter 14 of his text on decision analysis with TreePlan (2007), §§14.1–14.2, on nodes and branches, their order, and terminal values.
  • ACCA, “Decision trees”, technical article, on drawing left to right, when to draw one, and estimating probabilities.
  • Ronald A. Howard and James E. Matheson, “Influence Diagrams”, Decision Analysis 2, no. 3 (2005): 127–143, §§7 and 10, on the decision tree’s order and the influence diagram.
  • Mike Rankin and Daniel Undersander, “Rain Damage to Forage During Hay and Silage Making”, Focus on Forage 2, no. 4 (University of Wisconsin, 2000), for the figure’s decision and losses, as read on 10 October 2026.