Calculate EVPI, EVwPI, or EMV by entering any two values to find the missing expected value in decision analysis and risk planning.
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EVPI Formula
The EVPI calculator uses the relationship between expected value with perfect information, expected monetary value without perfect information, and the expected value of perfect information.
EVPI = EVwPI - EMV
- EVPI = expected value of perfect information
- EVwPI = expected monetary value with perfect information
- EMV = expected monetary value without perfect information
If you need to solve for a different missing value, the same formula can be rearranged:
EVwPI = EMV + EVPI
EMV = EVwPI - EVPI
The calculator accepts any two of the three values and calculates the missing one. If EVwPI and EMV are known, it calculates EVPI. If EMV and EVPI are known, it calculates EVwPI. If EVwPI and EVPI are known, it calculates EMV.
EVPI Result Interpretation
EVPI tells you the most you should be willing to pay for perfect information before making a decision.
| EVPI result | Meaning | Decision use |
|---|---|---|
| 0 | Perfect information adds no expected value. | Do not pay for more information based on expected value alone. |
| Positive value | Perfect information improves the expected outcome. | The value is the maximum amount worth paying for perfect information. |
| Negative value | Usually indicates an input or calculation issue, since perfect information should not reduce the best expected value. | Check the EVwPI and EMV values. |
Common inputs used with EVPI are shown below.
| Term | What it represents | How it is found |
|---|---|---|
| EMV | The best expected payoff when you must choose without perfect information. | Multiply each possible payoff by its probability, then choose the best expected option. |
| EVwPI | The expected payoff if you knew the future state before choosing. | For each state, choose the best payoff, multiply by that state’s probability, then add the results. |
| EVPI | The value gained from having perfect information. | Subtract EMV from EVwPI. |
Example
Example 1: Calculate EVPI
Suppose the expected monetary value with perfect information is 12,000, and the expected monetary value without perfect information is 9,500.
EVPI = 12000 - 9500 = 2500
The EVPI is 2,500. This means perfect information is worth up to 2,500 in expected value.
Example 2: Calculate EVwPI
Suppose the EMV is 18,000 and the EVPI is 4,000.
EVwPI = 18000 + 4000 = 22000
The expected monetary value with perfect information is 22,000.
FAQ
What does EVPI measure?
EVPI measures the expected value of knowing the future state of nature before making a decision. It shows the maximum amount you should pay for perfect information. If the information costs more than the EVPI, it is not worth buying based on expected monetary value.
Can EVPI be negative?
In a standard decision analysis problem, EVPI should not be negative. Perfect information should allow you to make at least as good a decision as you would make without it. A negative EVPI usually means EVwPI or EMV was entered incorrectly.
Is EVPI the same as EMV?
No. EMV is the expected monetary value of a decision made without perfect information. EVPI is the added expected value that perfect information provides. The formula is EVPI = EVwPI – EMV.
