Expected Value
List the important outcomes, estimate how likely each one is, multiply probability by value, then add the results. This turns uncertainty into a clearer comparison.
Expected value is the probability-weighted average of possible outcomes.
What is this option worth once likelihood and impact are considered together?
Investments, experiments, product bets, forecasts and repeated uncertain choices.
Fast overview
An attractive upside is not enough. A frightening downside is not enough either. Expected value forces both magnitude and probability into the same calculation.
For monetary choices, value can be money. For broader decisions, define a consistent scoring unit. Do not mix incompatible units casually.
Mental Model Compass
Learn it progressively
1. Define the options
Compare choices using the same time horizon and value measure.
2. List meaningful outcomes
Include gains, losses and neutral results that materially affect the choice.
3. Estimate probabilities
Use data, base rates or calibrated judgment. Make uncertainty explicit.
4. Assign comparable values
Use the same unit across outcomes and include relevant costs.
5. Multiply, add, then stress-test
Calculate the probability-weighted result. Change uncertain assumptions to see whether the preferred option remains preferred.
Try the calculation
Enter a probability and two net outcomes. The second probability is calculated automatically.
See it in practice
Product experiment
A small test can be compared with its possible learning value, upside and cost of failure.
Hiring
A high-upside candidate with wider uncertainty can be compared with a steadier candidate, while keeping hard constraints separate.
Operations
Preventive maintenance can look expensive until the probability and cost of downtime are included.
Worked application
Run a ₱200,000 pilot or skip it
Outcome A: 30% chance the pilot identifies an opportunity worth ₱1,000,000 net of later implementation costs.
Outcome B: 70% chance it does not, leaving the ₱200,000 pilot cost as the loss.
Illustrative expected value: (0.30 × ₱1,000,000) + (0.70 × -₱200,000) = ₱160,000.
Interpretation: The probability-weighted average is positive. This does not mean this one pilot will earn ₱160,000.
Next check: Stress-test the success estimate and payoff. If modest changes reverse the conclusion, the decision is assumption-sensitive.
Expected value is not the whole decision
Two choices can have the same expected monetary value but very different downside risk. Risk tolerance, liquidity, survival, irreversibility and non-monetary consequences can matter. Expected utility extends the idea by weighting outcomes according to utility rather than simply money.
Common mistakes
Using one best case
A large payoff can dominate attention even when its probability is tiny.
Inventing precise probabilities
Use ranges and sensitivity checks when estimates are weak.
Forgetting net value
Count relevant costs, not only gross upside.
Ignoring ruin
Positive expected value does not justify a bet that can threaten survival or violate a hard constraint.
When not to use it
Do not rely on simple expected monetary value when outcomes involve catastrophic downside, strong risk aversion, ethical constraints, incomparable values or probabilities too weak to estimate responsibly. Use it as one input and add the decision rules the situation requires.
Related mental models
Bayesian Updating
Improve probability estimates as evidence arrives.
Opportunity Cost
Compare the chosen option with the best alternative use of resources.
Reversibility
Determine how much downside can be tested before a large commitment.