Expected Value Calculator
Understanding Expected Value (EV)
Expected value is a fundamental concept in probability and statistics used to determine the average outcome of a random event if it were repeated many times. In simple terms, it tells you the "long-run" average of a set of possibilities.
The Expected Value Formula
The mathematical formula for Expected Value (EV) is:
Where:
- xi represents the value of a specific outcome.
- P(xi) represents the probability of that outcome occurring.
- Σ indicates the sum of all such products.
Real-World Example: Business Investment
Imagine a company is deciding whether to launch a new product. They estimate the following scenarios:
| Scenario | Profit/Loss | Probability |
|---|---|---|
| High Success | $50,000 | 20% |
| Moderate Success | $10,000 | 50% |
| Failure | -$20,000 | 30% |
Calculation:
(50,000 * 0.20) + (10,000 * 0.50) + (-20,000 * 0.30)
10,000 + 5,000 – 6,000 = $9,000
The Expected Value is $9,000. This positive result suggests that, on average, the investment is profitable.
Why Is Expected Value Important?
Expected value is used by professional gamblers, insurance companies, and financial analysts to make objective decisions. If an EV is positive, the action is generally considered "good" in the long run. If the EV is negative, the action will result in a loss over time, even if you win occasionally in the short term.