Expected Monetary Value Calculator
Calculate probability-weighted expected outcomes
EMV Formulas
Understanding Expected Monetary Value
Expected Monetary Value (EMV) is the probability-weighted average of all possible outcomes. It represents the 'average' result if the decision were made many times. EMV is fundamental to decision analysis under uncertainty.
EMV is calculated by multiplying each possible outcome by its probability and summing the results. If a project has 30% chance of $1M and 70% chance of -$200K, EMV = 0.3×$1M + 0.7×(-$200K) = $160K.
EMV helps compare alternatives with uncertain outcomes. The rational choice is typically the option with highest EMV, though risk tolerance may modify this for extreme outcomes.
EMV in Decision Making
Project Selection
Compare projects by EMV. Higher EMV = better expected outcome.
Bid Decisions
Calculate EMV of bidding: probability of winning × profit.
Risk Response
Compare EMV of risk mitigation options vs accepting risk.
Decision Trees
EMV at each node enables complex multi-stage decisions.
EMV Examples
| Scenario | Outcomes | Probabilities | EMV |
|---|---|---|---|
| New Product | +$5M, -$1M | 40%, 60% | $1.4M |
| Expansion | +$3M, +$1M, -$500K | 30%, 50%, 20% | $1.3M |
| Litigation | Win $2M, Lose $800K | 25%, 75% | -$100K |
| Investment | +50%, +10%, -30% | 20%, 60%, 20% | +10% |
| Insurance | $0, -$100K | 98%, 2% | -$2K |
Using EMV Effectively
Estimate Probabilities Carefully
EMV is only as good as probability estimates. Use data, expertise, and multiple perspectives.
Consider Multiple Scenarios
Three scenarios (optimistic, likely, pessimistic) is minimum. More scenarios = better accuracy.
Watch for Black Swans
EMV may miss rare but catastrophic outcomes. Consider worst-case scenarios separately.
Update with New Information
Revise probabilities as you learn more. EMV should be dynamic, not static.
Frequently Asked Questions
When shouldn't I use EMV?
EMV assumes you can 'play' many times and average out. For one-time, high-stakes decisions, also consider worst-case impact. If worst case is catastrophic, EMV alone isn't sufficient.
How do I estimate probabilities?
Use historical data if available, expert judgment, market research, or analogies to similar situations. Delphi method (averaging expert estimates) often works well.
EMV vs Expected Utility—what's the difference?
EMV uses monetary values directly. Expected Utility adjusts for risk tolerance—a risk-averse person values a certain $1M more than a 50% chance at $2M, even though EMV is the same.
Can EMV be negative?
Yes. Negative EMV means expected loss on average. This might still be acceptable if it reduces a larger risk (like insurance) or enables other opportunities.
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