5 Quantitative Risk Analysis

What quantitative risk analysis supports

Quantitative risk analysis uses numerical estimates to examine how uncertainty may affect project objectives, including cost, schedule, and performance. It can help teams compare alternatives, estimate exposure, and focus responses on the risks that matter most.

Because it can require more data and effort than qualitative assessment, it is commonly applied to significant or high-priority risks.

Calculating expected monetary value

Expected monetary value (EMV) is the probability-weighted average of possible outcomes. Multiply each outcome's monetary value by its probability, then sum the products:

Here, $p_i$ is the probability of outcome $i$, and $x_i$ is its monetary value. For threats, record impact as a loss; for opportunities, record it as a gain. If the outcomes are exhaustive, their probabilities should sum to $1$.

EMV is an average across possible outcomes, not a prediction of what will happen in a particular case. For example, a supplier delay with a $30\%$ probability of causing a $\$50{,}000$ loss has an EMV of:

This indicates an expected loss of $\$15{,}000$ from the risk; it does not mean the project will necessarily lose that amount. The result can inform a contingency estimate or help compare responses.

When combining several risks, add their EMVs only when the estimates use a consistent scope and time frame. Dependencies between risks can make a simple sum misleading.

Comparing choices with decision trees

A decision tree represents choices and uncertain outcomes as branches. A decision node marks a choice, a chance node marks possible outcomes and their probabilities, and terminal branches show the resulting payoff or cost. Calculate the EMV at each chance node, then work backward toward the decision node. Choose the alternative with the best expected result, such as the highest expected payoff or lowest expected cost.

In a supplier comparison, a standard supplier costs $\$100{,}000$ and has a $30\%$ chance of causing a delay cost of $\$50{,}000$:

A more reliable supplier costs $\$112{,}000$ and has a $5\%$ chance of the same delay cost:

On these assumptions, the more reliable supplier has the lower expected cost by $\$500$. The tree makes assumptions and outcomes visible so stakeholders can check whether the probabilities, costs, and alternatives are reasonable.

Testing sensitive assumptions

Sensitivity analysis tests how much an estimate or decision changes when an input changes. Analysts vary one factor at a time while holding other assumptions constant, then compare the results. Factors might include event probability, impact, duration, labor rates, or supplier costs.

A tornado chart can rank factors by how much they change the result. Input ranges should be supported by evidence or documented assumptions rather than arbitrary adjustments.

For the supplier comparison, the standard supplier's expected cost is its $\$100{,}000$ cost plus the delay probability multiplied by $\$50{,}000$. If the delay probability rises from $30\%$ to $40\%$, the expected cost rises from $\$115{,}000$ to $\$120{,}000$. This shows how sensitive the comparison is to the probability estimate. If a small change reverses the preferred option, investigate that assumption or plan for the possibility that it is wrong.

Applying and updating the analysis

Use quantitative results alongside project objectives and informed judgment. EMV supports comparisons, but it does not describe the full range of possible outcomes or how much risk an organization is willing to accept. A low-probability, severe loss may deserve attention even if its EMV is modest. Estimates are only as reliable as their underlying data and assumptions.

Record important assumptions, probabilities, impacts, response costs, and analysis dates. As the project progresses, compare estimates with actual results, update the risk assessment when conditions change, and reassess whether planned responses remain worthwhile. Quantitative analysis supports risk-informed decisions; it does not remove uncertainty.