Enter the optimal expected payoff (the best available expected payoff) and the expected payoff of the option you chose into the calculator to determine the expected opportunity loss (expected regret). This calculator can also evaluate the optimal expected payoff and the chosen expected payoff amounts if given the other variables.
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Expected Opportunity Loss Formula
The following equation is used in this calculator to compute expected opportunity loss from two expected payoffs (the best available expected payoff minus the chosen expected payoff).
EOL = OP - AP
- Where EOL is the expected opportunity loss ($)
- OP is the optimal expected payoff amount ($)
- AP is the chosen option’s expected payoff amount ($)
To calculate the expected opportunity loss in this simplified form, subtract the chosen option’s expected payoff from the optimal expected payoff. (In general decision analysis with multiple states of nature, expected opportunity loss is the expected value of “regret” across states using their probabilities.)
What is an Expected Opportunity Loss?
Definition:
Expected opportunity loss (also called expected regret) is the difference between the expected payoff of the best available alternative and the expected payoff of the alternative you choose.
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 × $5,000) + (0.90 × $0) = $500
Expected payoff (B) = $1,200
The optimal expected payoff is $1,200 (Option B). If you choose Option A, the expected opportunity loss is EOL = $1,200 − $500 = $700. (If you choose Option B, EOL = $0 because it is the best option by expected payoff.)
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.
