Expected value and sensitivity analysis

Expected value converts uncertain outcomes into a probability-weighted planning estimate. Sensitivity analysis then tests how strongly the decision depends on assumptions that may prove wrong. Used together, they replace a single confident forecast with a more transparent view of uncertainty.

When to use it

• Use expected value for discrete, consequential outcomes such as winning a major contract, obtaining approval or renewing a large lease. It is especially useful when a small number of “yes or no” events drive the result.
• Use sensitivity analysis in every material investment appraisal, whether or not expected values are part of the base case.

Origins

Expected value emerged from the development of probability theory by Blaise Pascal, Pierre de Fermat and Christiaan Huygens, including work on how to divide the stakes of an unfinished game. Decision theory later connected probability-weighted outcomes with choices under uncertainty. Sensitivity analysis developed across applied mathematics, economics and operations research as a complementary discipline: vary an important assumption and observe whether the result or preferred decision changes.

What it is

For a set of mutually exclusive outcomes, expected value is the sum of each outcome multiplied by its probability. In a contract pipeline, that means weighting every opportunity by its estimated chance of success and adding the weighted amounts.

The result is an average over repeated comparable situations, not a prediction that the portfolio will produce that exact amount. A single large contract will still be won or lost. Expected value is therefore most useful for planning a portfolio of uncertain events and understanding the central case across them.

Sensitivity analysis asks “what if?” It changes one or more uncertain inputs—probability, price, volume, cost or timing—and recalculates the outputs. The analyst learns which assumptions drive the model, where downside threatens cash or capacity, and whether a decision remains attractive across a credible range.

The two methods work together: expected value supplies a probability-weighted base case, and sensitivity analysis describes the range and fragility around it.