Expected Value: How to Calculate and Interpret It
Expected Value: How to Calculate and Interpret It
Plain-Language Definition
Expected value is a probability-weighted average of possible outcomes. Instead of just looking at the best-case or worst-case payoff, it accounts for how likely each outcome is, giving you a single number that represents the average result if a decision were made repeatedly under the same conditions.
Why It Matters
Picking the alternative with the single best possible payoff is tempting but often wrong — a low-probability, high-payoff option can be a worse bet than a moderate, more-likely one. Expected value is what lets you compare alternatives fairly, accounting for both size and likelihood of outcomes.
The Calculation
Expected value = (Probability of Outcome A × Payoff A) + (Probability of Outcome B × Payoff B) + …
For each alternative, multiply every possible payoff by its probability of occurring, then sum those weighted values.
Worked Example (Fictitious Company)
Alderbrook Coffee Roasters is evaluating its “develop new product” alternative:
- Probability of low demand: 0.30, with a payoff of $780.00
- Probability of high demand: 0.70, with a payoff of $2,600.00
Calculation: (0.30 × $780.00) + (0.70 × $2,600.00) = $234.00 + $1,820.00 = $2,054.00
This $2,054.00 is the expected value — not a guaranteed outcome, but the probability-weighted average result if this decision were made repeatedly under these same conditions. Compare this number across every alternative, and the highest expected value is generally the mathematically preferred choice.
Key Takeaways
- Expected value weights outcomes by their probability, not just their size — a big payoff with a small probability doesn’t automatically win
- Always show the full calculation (each payoff × its probability, then summed) rather than just presenting the final number
- Expected value is an average across many hypothetical repetitions, not a promise about what will happen this one time
- Comparing expected values across alternatives is how you translate a decision tree into an actual recommendation
Related Content
- C207 Course Roadmap
- C207 QUM3 Task 2 Guide: Decision Tree Analysis
- Decision Tree Analysis, Explained
References & Further Reading
- Lee, C. S., Cheang, P. Y. S., & Moslehpour, M. (2022). Predictive Analytics in Business Analytics: Decision Tree. Advances in Decision Sciences, 26(1), 1–29. — A peer-reviewed paper covering the expected-value calculation as the core mechanism for comparing alternatives in decision tree analysis.