Expected Value for Two Uncertain Options

Multiply each supported outcome by its probability, but keep affordability, constraints, and non-monetary consequences outside the average.

Define consistent outcomes

Use the same unit and time horizon for both options. Include all material outcomes rather than listing only the upside for one and the downside for the other.

Define every outcome over the same period and in the same unit before multiplying. Include the cost of reaching the outcome and avoid mixing revenue for one option with profit for the other. If an outcome has several material effects, show them separately. A clean number built from unlike definitions is less useful than a partial calculation with clear boundaries.

Use defensible probabilities

Prefer observed frequencies or a documented forecast. When evidence is weak, use a range and report how the result changes rather than presenting a single guess as precise.

Use probabilities that have a stated basis, such as relevant historical data, a bounded estimate, or a scenario range. Keep source conditions beside the number. When evidence is weak, calculate several plausible probabilities and find the switching point. Do not use an exact percentage simply because the formula requires an input.

If one probability estimate drives the result, compare the options with scenario analysis instead of reporting one fragile average.

Calculate the weighted result

Multiply each outcome by its probability, then add the products for each option. Show the components so a reader can inspect the assumptions.

For each option, multiply every outcome value by its probability and add the products. Check that the listed outcomes cover the same decision period and that probabilities are internally consistent. Keep the unrounded result for review but present a sensible level of precision. Extra decimal places do not improve uncertain inputs.

Check whether the average is tolerable

An option can have higher expected value and still be unsuitable if one loss exceeds available cash, safety limits, or recovery capacity. Repeated small bets and a single irreversible choice are not equivalent.

Inspect the full outcome list after calculating the average. Ask whether the household or organization can survive the largest credible loss, how long recovery takes, and whether repeated opportunities exist. Expected value is most informative across repeatable choices with tolerable downside. A positive average does not make a one-time harmful outcome acceptable.

If later actions depend on which outcome occurs, map the choices and uncertain events in a decision tree before calculating averages.

Keep non-monetary outcomes visible

Expected value can use time, output, or another consistent unit, but many consequences should not be forced into money. Safety, dignity, privacy, trust, and legal compliance may act as constraints or separate criteria. Show them beside the calculation.

When outcomes use different units, calculate only the part that can be supported and then use a multi-criteria comparison for the rest. A partial transparent calculation is more credible than a complete total built from invented conversion rates.