Value of Perfect Information
How much better decisions become with full information.
Formula
Live Calculator
MembersVariables
Example
VPI caps what you should pay for research or a forecast.
How it works
The value of perfect information measures how much extra expected payoff you gain if you could know the uncertain outcome before choosing what to do. It works by comparing two expectations: the best average payoff you can achieve after seeing the truth, versus the best average payoff you can achieve when you must commit without that knowledge. Because extra information can only help you choose better actions, this difference is never negative; if it is zero, the uncertainty is irrelevant to your decision. In decision analysis, it quantifies the maximum rational amount to pay for a perfectly accurate forecast or test about the uncertain event.
When to use it
Use this when a decision depends on an uncertain state of the world and you want to know the upper bound on the worth of learning that state first. It is common in economics, operations, risk analysis, medical testing, and strategic planning under uncertainty.
Worked example, step by step
A manufacturer must choose one production plan before knowing whether next quarter’s demand will be High or Low. Payoffs (in $000s): - Plan A: 90 if High, 40 if Low - Plan B: 70 if High, 55 if Low Probability of High demand = 0.6, Low demand = 0.4 Step 1: Compute EV without information for each plan. Plan A: EV = (0.6)(90) + (0.4)(40) = 54 + 16 = 70 Plan B: EV = (0.6)(70) + (0.4)(55) = 42 + 22 = 64 Best EV without info = 70 Step 2: Compute EV with perfect information. If demand is High, choose Plan A because 90 > 70. If demand is Low, choose Plan B because 55 > 40. So EV_info = (0.6)(90) + (0.4)(55) = 54 + 22 = 76 Step 3: Subtract to get VPI. VPI = EV_info - EV_no info = 76 - 70 = 6 Final answer: VPI = 6 ($000s), so perfect information is worth up to $6,000 to this manufacturer.
Common mistakes to avoid
- Subtracting the payoff of the currently chosen action instead of the best expected payoff without information
- Using impossible probabilities or forgetting to weight each state by its probability
- Treating perfect information as guaranteed profit rather than the expected gain in decision quality
Did You Know?
VPI sets a rational ceiling on consulting fees — never pay more for data than the better decisions are worth.
Share this formula
More in Game Theory & Decision
View allExpected Value
BasicProbability-weighted average outcome of a decision.
Kelly Criterion
AdvancedOptimal fraction of bankroll to bet for long-run growth.
Expected Utility
AdvancedWeighted average of the utility of outcomes, not just their cash value.
Payoff Comparison
IntermediateOne strategy dominates another if its payoff is always higher.
Minimax Value
AdvancedBest worst-case payoff a player can guarantee.
Mixed Strategy (Indifference)
AdvancedProbability that makes an opponent indifferent between their options.