Expected Value Analysis

Expected value (EV) is the probability-weighted average of an option's possible outcomes: multiply each outcome's value by its probability and sum. It turns "which gamble is better?" into arithmetic, and it is the right default when a decision will be repeated many times or when no single loss would be ruinous. Its weakness is that the inputs are estimates, and a single average hides risk. So the discipline is as much about stating the uncertainty as about the number.

Input required

• The options, including doing nothing.
• The possible outcomes of each, with a value (money, hours, points) for each.
• Probability estimates, with the basis for them (data, base rates, judgment).
• Costs and timing, and the discount rate if the payoffs are spread over years.
• Risk tolerance — what loss would be intolerable.

If details are missing, state assumptions or ask the questions below once, then proceed.

Questions to ask first

Ask in one batch of at most five questions, skipping any already answered, then proceed:

1. What are the options, and what does each cost up front?
2. What are the realistic outcomes of each (best, typical, worst), in one unit such as dollars?
3. How likely is each, and what is that based on: data or gut?
4. Is this a one-off bet or one of many similar ones?
5. Is there any loss large enough that you must avoid it regardless of the average?

Method

1. Choose one unit of value and use it for every outcome.
2. List mutually exclusive outcomes for each option, covering all the possibilities (so probabilities total 100%). Include the bad ones; groups of three to five are usually enough.
3. Estimate probabilities from base rates or reference classes first (how often does this kind of thing succeed?), then adjust for the specifics. Avoid starting from optimism.
4. Value each outcome net of cost, including the up-front spend, and discount future values when timing differs.
5. Compute EV = Σ (probability × value) for each option.
6. Examine the spread. Report the best case, worst case, and probability of a loss. Two options with the same EV can differ greatly in risk.
7. Run sensitivity analysis. Change the most uncertain probability and payoff and find the break-even probability: how likely success must be for the option to beat the alternative.
8. Apply the risk filter. For one-off or ruinous downside, prefer the option that survives the worst case, even with a lower EV.
9. Price the value of information. If a cheap test or study could sharpen a key estimate, say whether it is worth more than it costs.

Output format

| Option | Outcome | Probability | Net value | Weighted | |---|---|---|---|---| | A: Launch now | Strong uptake | 25% | +$400k | +$100k | | | Modest uptake | 45% | +$60k | +$27k | | | Flop | 30% | –$150k | –$45k | | | EV | | | +$82k |

Then provide, per option: EV, range, probability of loss, and break-even probability. Finish with:

• Recommendation — the preferred option and why.
• Key assumptions — the two or three estimates the answer depends on.
• What would change the answer.
• Cheapest way to improve the estimates.

Ground rules

• Probabilities are estimates. Present them as ranges when unsure and show how conclusions change.
• No false precision. Round; "about $80k" is more honest than "$82,350".
• Never report EV alone. Always include spread and worst case.
• Keep outcomes exhaustive. Missing the catastrophic branch inflates EV.
• Money is not always the unit. If value is not linear (a loss that ends the business), say so and adjust.

Self-check before answering

• Do the probabilities for each option sum to 100%?
• Are costs included in the net values, and is timing handled?
• Was the break-even probability and sensitivity reported?
• Was the worst case checked against what is survivable?

Common pitfalls

• Optimism bias — success probabilities taken from the pitch deck.
• Ignoring tail risk — rare, severe losses dominate repeated bets.
• Double-counting — the same upside appearing in two outcomes.
• Treating one-off bets as averages — you live one outcome, not the mean.
• Precise-looking nonsense — decimals on guesses.
• Anchoring on the first estimate — gather ranges from more than one person.

Example prompt

We can spend $50k on a pilot with maybe a 30% chance of landing a $400k contract, or spend nothing. Do an expected value analysis, show the break-even probability, and tell me how sensitive the answer is to my estimates.

Learn more

• Decision Tree for sequences of decisions and chances.
• Bayes Theorem Analysis for updating probabilities with evidence.
• Break-Even Analysis for the volume or price at which an option pays off.
• Weighted Decision Matrix when criteria are not all monetary.
• Decision Journal to record your probabilities and check your calibration later.