Calculate expected opportunity loss by subtracting your chosen expected payoff from the expected payoff with perfect information. A separate task compares the chosen payoff with the best fixed choice.

Compare your choice with the perfect-information benchmark.

Probability-weighted best payoff in each state; not the best fixed choiceโ€™s expected payoff.

Related Calculators

Expected Opportunity Loss Formula

The following equation computes expected opportunity loss from two averages: the expected payoff with perfect information minus the chosen choiceโ€™s expected payoff. Perfect information permits choosing the best action separately in each state.

EOL = OP - AP
  • Where EOL is the expected opportunity loss ($)
  • OP is the expected payoff with perfect information ($)
  • AP is the chosen optionโ€™s expected payoff amount ($)

To calculate expected opportunity loss, subtract the chosen choiceโ€™s expected payoff from the expected payoff with perfect information. Equivalently, weight each stateโ€™s regret by its probability and sum. The gap to the best fixed choiceโ€™s expected payoff is a different quantity.

What is an Expected Opportunity Loss?

Definition:

Expected opportunity loss (expected regret) is the probability-weighted difference between the best payoff in each state and the payoff of the fixed choice you make. It need not be zero for the choice with the highest expected payoff.

For example, suppose you are choosing between two alternatives. Option A has a 10% chance of a $5,000 payoff and a 90% chance of a $0 payoff. Option B has a guaranteed payoff of $1,200.

First, calculate the expected payoff for Option A:

Expected payoff (A) = (0.10 ร— $5,000) + (0.90 ร— $0) = $500

Expected payoff (B) = $1,200

With perfect information, choose A in the 10% state and B in the 90% state: expected payoff = 0.10 ร— $5,000 + 0.90 ร— $1,200 = $1,580. Thus EOL(A) = $1,580 โˆ’ $500 = $1,080, and EOL(B) = $1,580 โˆ’ $1,200 = $380. The $700 gap between A and Bโ€™s expected payoffs is distinct. B minimizes expected regret, and the $380 minimum is the expected value of perfect information.

You should not expect to realize exactly this amount in any single outcome; it is an average based on the stated probabilities and is used for comparing choices under uncertainty.