Decision Tree Analysis Calculator
Decision AnalysisAdvanced decision analysis with expected monetary value and risk assessment
Multiple outcome evaluation
EMV calculations
Probability analysis
Best path identification
Decision Parameters
For present value calculations
Analysis time period
Decision Options
Likelihood of success
Expected financial result
Likelihood of success
Expected financial result
What is Decision Tree Analysis?
Decision tree analysis is a quantitative risk analysis technique recognized by the PMBOK Guide as a core tool within the Perform Quantitative Risk Analysis process. It uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility values. Each branch represents a decision path, and each node represents either a decision point where you choose an action or a chance point where probability governs the outcome.
The foundation of decision tree analysis is Expected Monetary Value (EMV), which multiplies the probability of each outcome by its financial impact. By calculating EMV for every branch and summing across chance nodes, project managers can identify the decision path that maximizes expected value. This technique is particularly powerful when you face multiple decision alternatives with uncertain outcomes, such as choosing between building a custom solution versus buying an off-the-shelf product.
Decision trees connect directly to sensitivity analysis because they reveal which probability or outcome variable has the greatest effect on the final EMV. When you adjust a single probability or outcome value and observe how the optimal decision changes, you are performing a sensitivity analysis on your decision tree. This connection is frequently tested on the PMP exam and is a hallmark of rigorous project risk management.
Decision Tree EMV Formula Explained
Probability is expressed as a decimal between 0 and 1, representing the likelihood of a specific outcome occurring. Financial Outcome is the monetary value associated with that outcome -- positive for gains, negative for losses. The Expected Monetary Value for a decision branch is simply the product of these two values.
For decisions with multiple possible outcomes on a single branch, you sum the EMV of each outcome: EMV(total) = (P1 x O1) + (P2 x O2) + ... + (Pn x On). The decision with the highest total EMV is mathematically optimal when you are risk-neutral. Present value adjustments can be applied using the discount rate and time horizon to account for the time value of money.
Step-by-Step Guide to Decision Tree Analysis
Define the decision clearly and identify all viable alternatives. Each alternative becomes a major branch emanating from the root decision node.
Identify the chance events (uncertainties) that affect each alternative and assign probabilities. Ensure probabilities at each chance node sum to 1.0.
Estimate the financial outcome for each end branch. Include all relevant costs, revenues, and intangible benefits converted to monetary terms.
Calculate the EMV for each branch by multiplying probability by outcome. Roll up values through chance nodes by summing EMVs, then compare decision branches.
Select the alternative with the highest EMV as your optimal decision. Document assumptions, validate with sensitivity analysis, and present to stakeholders for approval.
Real-World Example
Scenario: A project manager must decide whether to build a custom analytics platform or license an existing SaaS solution
• Build Custom: 60% probability of success, $200,000 outcome if successful, -$50,000 if it fails
• License SaaS: 85% probability of success, $120,000 outcome if successful, -$20,000 if integration fails
• Build Custom EMV: (0.60 x $200,000) + (0.40 x -$50,000) = $100,000
• License SaaS EMV: (0.85 x $120,000) + (0.15 x -$20,000) = $99,000
Result: Build Custom has a marginally higher EMV ($100,000 vs. $99,000), but the SaaS option has far less downside risk. A risk-averse organization would choose SaaS despite the $1,000 EMV difference.
Common Mistakes to Avoid
- Confusing decision nodes with chance nodes -- Decision nodes (squares) represent points where you make a choice; chance nodes (circles) represent points where probability determines the outcome. Mixing these up leads to fundamentally flawed trees.
- Probabilities not summing to 1.0 -- At every chance node, the probabilities of all branches must total exactly 1.0. Leaving probability gaps or double-counting outcomes invalidates your entire EMV calculation.
- Ignoring opportunity costs -- Each decision branch should include the opportunity cost of not choosing the alternative. Omitting this biases the tree toward options that appear cheaper but sacrifice hidden value.
- Using EMV alone for risk-averse decisions -- EMV assumes risk neutrality. In reality, most organizations are risk-averse for large losses. Always pair EMV analysis with a risk attitude assessment for high-stakes decisions.
PMP Exam Tips
Decision tree questions on the PMP exam almost always involve calculating EMV. You will typically see a scenario with two or three alternatives, each with stated probabilities and financial outcomes. Work through each branch methodically: multiply probability by outcome for each path, sum the EMVs at each chance node, and compare across decision alternatives. The highest EMV wins unless the question specifies risk aversion.
Watch for questions that combine decision trees with contingency reserves. Remember that the contingency reserve is based on the EMV of identified risks. If a risk has a 30% probability and a $100,000 impact, the contingency reserve allocation would be $30,000 (the EMV). This connection between decision tree analysis and reserve analysis is a favorite exam topic.
Finally, know that decision trees are a tool of the Perform Quantitative Risk Analysis process, not Qualitative Risk Analysis. Qualitative analysis uses probability-impact matrices and risk categorization, while quantitative analysis uses numeric techniques like decision trees, Monte Carlo simulation, and sensitivity analysis to calculate specific risk exposures.