Decision Tree Analysis
Decision tree analysis helps you compare choices when you do not know exactly what will happen next. It maps the possible paths, adds the probability and value of each outcome, and helps you choose between competing options.
See how a decision tree is built
Follow the example from the first decision through to expected monetary value.
How the tree is built
- Define the decision. Start with the question you need to answer.
- Add the choices. Show each realistic course of action as a separate branch.
- Add uncertainty. Mark the point where you cannot be certain what will happen next.
- Add possible outcomes. Show the possible results and estimate the probability of each one.
- Add financial values. Give each final outcome a cost, reward or other measurable value.
- Calculate expected monetary value. Multiply each outcome by its probability, then add the results together.
Table of Contents:
- What is decision tree analysis?
- When should you use a decision tree?
- The parts of a decision tree
- How to carry out decision tree analysis
- What is expected monetary value?
- Worked decision tree example
- Working backwards through a decision tree
- Decision trees and risk management
- Real-world decision tree example
- Advantages of decision tree analysis
- Limitations of decision tree analysis
- Tips for using decision trees
- Summary
What is decision tree analysis?
A decision tree is a diagram that shows a decision, the choices available and what could happen after each choice.
You start with the decision you need to make. Branches then show the available options. Further branches show uncertain events or outcomes. The end of each path shows the final result.
You can also add the probability, cost or reward associated with each outcome. This lets you compare different choices using expected monetary value (EMV).
Decision tree analysis in simple terms
A decision tree asks: What can we do, what might happen next, how likely is it, and what would the result be worth?
The aim is not to predict the future perfectly. It is to make uncertainty visible and compare your choices in a structured way.
When should you use a decision tree?
Decision tree analysis is useful when a decision has several possible outcomes and you cannot be certain which one will happen.
You might use a decision tree when you have:
- two or more possible courses of action;
- uncertainty about what will happen after each choice;
- reasonable estimates of the probability of different outcomes;
- costs, savings or rewards that you can attach to those outcomes; and
- later decisions that depend on what happens first.
Project managers can use decision trees for procurement, investment, product development, risk responses and business case decisions.
For example, you might need to decide whether to:
- repair or replace equipment;
- build software or buy an existing system;
- use one supplier or another;
- carry out more testing;
- accept a project risk; or
- pay for a risk response.
The parts of a decision tree
A decision tree normally contains decision points, chance events and final outcomes.
Decision point
A decision point is where you choose between two or more alternatives. It is normally shown as a square. Branches from the square lead to the available choices, such as Option A and Option B.
Chance event
A chance event is where the outcome is uncertain. It is normally shown as a circle. Branches from the circle show the possible outcomes and their probabilities, for example a 70% chance of high demand and a 30% chance of low demand.
Outcome
An outcome is the final result at the end of a path. It usually has a value attached to it, such as a cost, benefit, profit or loss.
How to carry out decision tree analysis
Start with the decision you need to make. Then build the tree from left to right.
- Define the decision. Be clear about the question you are trying to answer.
- List your choices. Draw a branch for each realistic option.
- Add uncertain events. Show what could happen after each choice.
- Estimate the probabilities. Give each possible outcome a probability.
- Add costs and rewards. Give each final outcome a financial value where possible.
- Calculate expected values. Multiply each outcome by its probability.
- Work backwards through the tree. Compare the expected values of the available choices.
- Make the decision. Use the result alongside judgement, risk appetite and other factors.
What is expected monetary value?
Expected monetary value, or EMV, combines the probability of an outcome with its financial value.
EMV = Probability × Financial value
If an outcome has a 30% chance of creating £100,000 of value: 0.30 × £100,000 = £30,000 EMV.
Where several outcomes can follow the same decision, calculate the EMV of each outcome and add them together.
This gives you the expected value of that branch of the decision tree.
Worked decision tree example
Imagine a company is deciding whether to develop a new software product. Developing the product will cost £40,000.
The company estimates that there are two main outcomes:
| Outcome | Probability | Revenue | Net value after development cost |
|---|---|---|---|
| Strong sales | 60% | £100,000 | £60,000 |
| Poor sales | 40% | £20,000 | -£20,000 |
The alternative is not to develop the product. For this simplified example, we will give that choice a value of £0.
Calculate the value of strong sales
There is a 60% chance of making £60,000 after the development cost.
0.60 × £60,000 = £36,000
Calculate the value of poor sales
There is a 40% chance of losing £20,000.
0.40 × -£20,000 = -£8,000
Calculate the total expected monetary value
£36,000 - £8,000 = £28,000
Expected monetary value: £28,000
On financial value alone, developing the product is better than the £0 expected value of doing nothing.
This does not mean the company will make £28,000. The actual outcome could still be a £60,000 gain or a £20,000 loss.
EMV gives you a way to compare uncertain choices. It does not remove the uncertainty.
Working backwards through a decision tree
More complicated decision trees may contain several decisions and chance events.
In these cases, start at the far right of the tree and work backwards towards the first decision.
At each chance point, multiply each outcome by its probability and add the results together.
At each decision point, compare the values of the available choices.
Think right to left
Draw the decision tree from left to right, but calculate it from right to left.
This process is sometimes called rolling back the decision tree.
Decision trees and risk management
Decision tree analysis can be useful when a project team needs to choose between different ways of dealing with a risk.
Suppose a risk could cost a project £200,000 if it happens. The team might have three choices:
- accept the risk;
- pay to reduce the probability of the risk; or
- buy insurance or transfer part of the financial impact.
A decision tree can compare the expected cost of each choice.
This gives the project team more information than simply classifying a risk as Low, Medium or High.
Decision tree analysis is particularly useful for major risks where there is enough information to estimate probabilities and financial impacts.
For broader risk assessment, see our risk assessment guide . You can also see how risks are recorded and managed in our risk register guide .
Published case application: choosing a project risk response
Decision tree analysis has been applied to a real project as part of a published research case study.
In the study, Prasanta Dey applied a structured risk management method to a US$600 million cross-country petroleum pipeline project in India. The project was about 1,300 kilometres long and included pipeline laying, river crossings, pumping stations, delivery stations and other infrastructure.
A risk management group was formed for the case application, with representatives from several project disciplines. The group worked with experienced project staff to identify and assess risks, develop possible responses and compare the alternatives using expected monetary value (EMV).
Decision tree for pipeline-laying risk
For the pipeline-laying work package, the risk management group considered five possible responses.
| Risk response | Response cost | Probability of failure | Delay if failure occurs | Cost overrun if failure occurs | EMV |
|---|---|---|---|---|---|
| Do nothing | $0m | 31.7% | 12 months | $22m | $35.5m |
| Carry out an additional detailed survey | $12m | 15.8% | 2 months | $4m | $15.0m |
| Use superior technology | $3m | 15.8% | 12 months | $22m | $21.0m |
| Engage an expert project team | $22m | 31.7% | 2 months | $4m | $28.0m |
| Use all the proposed risk responses | $56m | 5.0% | 2 months | $2m | $56.9m |
How was the expected cost calculated?
The study valued a month of delay at about $7.5 million. This allowed the analysis to combine the financial effect of a possible delay with any direct cost overrun.
For example, carrying out an additional detailed survey cost $12 million. After this response, the study estimated the probability of failure at 15.8%.
Response cost: $12m
Expected delay cost: 15.8% × 2 months × $7.5m = $2.37m
Expected cost overrun: 15.8% × $4m = $0.63m
EMV = $12m + $2.37m + $0.63m = approximately $15m
Lowest expected cost: additional detailed survey
In the case analysis, the detailed survey had the lowest expected cost at about $15 million. Doing nothing had an expected cost of about $35.5 million.
The case illustrates why the response that reduces risk the most is not automatically the best financial choice. Using every proposed response reduced the estimated probability of failure to 5%, but the responses themselves cost $56 million. This resulted in the highest EMV.
Decision tree analysis allowed the study to compare the cost of reducing the risk with the expected financial effect of the risk that remained.
Where did the probabilities come from?
The probabilities were not calculated from a large historical dataset. They were produced as part of the case study's structured risk analysis, using the judgement of experienced project specialists and brainstorming.
The analysis also used information from recently completed projects and quotations from contractors and vendors when estimating costs.
What this means for your own decision tree
Use reliable historical data where it is available. Where it is not, expert judgement can be used, but record where your probabilities and cost estimates came from and test how changes to them affect the result.
Reference
Dey, P. K. (2001). Decision support system for risk management: a case study. Management Decision, 39(8), 634-649. DOI: 10.1108/00251740110399558 .
See the publication record at Aston University .
Advantages of decision tree analysis
One of the biggest strengths of a decision tree is that it makes the logic behind a decision visible.
A decision tree can help you:
- show the available choices clearly;
- make uncertainty visible;
- combine probabilities with costs and rewards;
- compare alternatives consistently;
- show the possible consequences of a choice;
- support a project business case;
- challenge assumptions; and
- show how one decision may lead to another.
Limitations of decision tree analysis
A decision tree can look impressively precise. That does not mean its assumptions are precise.
Probabilities may be based on estimates rather than hard evidence. Costs and benefits may also change.
This means the quality of the answer depends heavily on the quality of the information you put into the tree.
EMV is not a prediction
An EMV of £28,000 does not mean you will receive £28,000. It is a weighted average used to compare uncertain choices.
Decision trees can also become difficult to use if there are too many branches.
Some important factors are difficult to turn into money. These can include:
- safety;
- reputation;
- customer satisfaction;
- staff morale;
- environmental impact;
- legal obligations; and
- strategic fit.
Include these factors in the final decision even if they do not appear in the EMV calculation.
Tips for using decision trees
Keep the first version simple
Start with the choices and outcomes that could change the decision. Add detail only when it is useful.
Make your assumptions visible
Record where your probabilities and financial estimates came from. This makes it easier for other people to challenge or update them.
Check your probabilities
The probabilities that follow the same chance point should add up to 100%.
Include the cost of taking action
Do not just record the value of the final outcome. Include the cost of the action needed to reach it.
Test uncertain assumptions
If a probability is uncertain, run the calculation more than once. For example, test success rates of 40%, 50% and 60%.
If the preferred choice changes when you make a small adjustment, the decision is sensitive to that assumption.
Do not let the calculation make the decision for you
The option with the highest EMV is not automatically the right option. Consider risk appetite, safety, strategy and other non-financial factors as well.
Decision tree analysis summary
Decision tree analysis helps you compare choices where future outcomes are uncertain.
A decision tree shows:
- the decision you need to make;
- the choices available;
- what might happen after each choice;
- the probability of each uncertain outcome; and
- the cost or reward associated with the final results.
Expected monetary value then gives you a consistent way to compare the financial value of different paths through the tree.
A decision tree cannot tell you what will happen. What it can do is make the uncertainty, assumptions and trade-offs visible before you commit to a decision.
Related project management guides
Continue with these related StakeholderMap guides: