Expected Opportunity Loss (EOL) Calculator
Use this tool to calculate the Expected Opportunity Loss (EOL) for two competing actions (Action 1 and Action 2) based on two possible uncertain outcomes (Outcome A and Outcome B). EOL helps you choose the action that minimizes the potential "regret" from not having chosen the best possible option for each outcome.
Enter the probability of Outcome A occurring, and the numerical result (either payoff or cost) for each combination of Action and Outcome. Specify whether the results are payoffs (higher is better) or costs (lower is better). The calculator assumes the probability of Outcome B is 1 minus the probability of Outcome A.
Input Decision Details
Probability of Outcome B will be 1 - P(A).
Results for Each Scenario
Enter the numerical result (e.g., profit, loss, cost) for each cell.
Understanding Expected Opportunity Loss (EOL)
What is Opportunity Loss?
Opportunity Loss (sometimes called Regret) is the difference between the result you *did* get by choosing a certain action and the best result you *could* have gotten if you had known the outcome in advance and chosen the optimal action for that specific outcome. It's the "cost" or "loss" associated with not making the perfect decision for a given situation.
For a specific outcome:
- If results are **Payoffs** (maximize): Opportunity Loss = (Best Payoff for that Outcome) - (Actual Payoff for chosen Action in that Outcome)
- If results are **Costs** (minimize): Opportunity Loss = (Actual Cost for chosen Action in that Outcome) - (Best Cost for that Outcome)
Opportunity loss is always a non-negative value.
What is Expected Opportunity Loss (EOL)?
Expected Opportunity Loss is the weighted average of the opportunity losses for each possible outcome, where the weights are the probabilities of those outcomes occurring. It represents the average amount of "regret" you would expect to experience over the long run if you repeatedly made the same decision under similar uncertain conditions.
Formula:
EOL (for an Action) = (Opportunity Loss for Outcome A * P(Outcome A)) + (Opportunity Loss for Outcome B * P(Outcome B))
Why use EOL? (EOL vs EMV/EV)
Minimizing EOL is equivalent to maximizing Expected Monetary Value (EMV) or Expected Value (EV). The action that minimizes EOL is always the same action that maximizes EMV. However, EOL is useful because it frames the decision in terms of potential regret, which can sometimes align better with a decision-maker's intuition or risk attitude. If you want to minimize how bad things *could* be compared to the ideal, EOL is a good metric.
Expected Opportunity Loss Examples
Click on an example to see the step-by-step EOL calculation:
Example 1: Investment Decision (Payoffs)
Scenario: You have $1000 to invest. You can invest in Stock A or a Bond. The market can either go Up or Down.
- Action 1: Invest in Stock A
- Action 2: Invest in Bond
- Outcome A: Market Goes Up
- Outcome B: Market Goes Down
Known Values (Payoffs - higher is better):
- P(Market Up) = 0.7 (70%)
- Result (Stock A, Market Up) = $1300
- Result (Stock A, Market Down) = $900
- Result (Bond, Market Up) = $1050
- Result (Bond, Market Down) = $1050
1. Probabilities: P(A=Up) = 0.7, P(B=Down) = 1 - 0.7 = 0.3.
2. Best Outcome Values (Payoffs):
- Best for Outcome A (Up): max($1300, $1050) = $1300 (from Stock A)
- Best for Outcome B (Down): max($900, $1050) = $1050 (from Bond)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $1300 - $1300 = $0
- OL (Action 1, Outcome B): $1050 - $900 = $150
- OL (Action 2, Outcome A): $1300 - $1050 = $250
- OL (Action 2, Outcome B): $1050 - $1050 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = (OL A1, A * P(A)) + (OL A1, B * P(B)) = ($0 * 0.7) + ($150 * 0.3) = 0 + 45 = $45
- EOL (Action 2) = (OL A2, A * P(A)) + (OL A2, B * P(B)) = ($250 * 0.7) + ($0 * 0.3) = 175 + 0 = $175
5. Optimal Action: The action with the lowest EOL is Action 1 (Stock A) with EOL = $45.
Conclusion: Investing in Stock A is expected to result in less opportunity loss ($45) compared to investing in the Bond ($175).
Example 2: Production Decision (Costs)
Scenario: A factory needs to decide whether to use Machine X or Machine Y for a product. Demand can be High or Low.
- Action 1: Use Machine X
- Action 2: Use Machine Y
- Outcome A: High Demand
- Outcome B: Low Demand
Known Values (Costs - lower is better):
- P(High Demand) = 0.6 (60%)
- Result (Machine X, High Demand) = $5000 (Cost)
- Result (Machine X, Low Demand) = $3000 (Cost)
- Result (Machine Y, High Demand) = $4000 (Cost)
- Result (Machine Y, Low Demand) = $3500 (Cost)
1. Probabilities: P(A=High) = 0.6, P(B=Low) = 1 - 0.6 = 0.4.
2. Best Outcome Values (Costs):
- Best for Outcome A (High): min($5000, $4000) = $4000 (from Machine Y)
- Best for Outcome B (Low): min($3000, $3500) = $3000 (from Machine X)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $5000 - $4000 = $1000
- OL (Action 1, Outcome B): $3000 - $3000 = $0
- OL (Action 2, Outcome A): $4000 - $4000 = $0
- OL (Action 2, Outcome B): $3500 - $3000 = $500
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = (OL A1, A * P(A)) + (OL A1, B * P(B)) = ($1000 * 0.6) + ($0 * 0.4) = 600 + 0 = $600
- EOL (Action 2) = (OL A2, A * P(A)) + (OL A2, B * P(B)) = ($0 * 0.6) + ($500 * 0.4) = 0 + 200 = $200
5. Optimal Action: The action with the lowest EOL is Action 2 (Use Machine Y) with EOL = $200.
Conclusion: Using Machine Y is expected to result in less opportunity loss ($200) compared to Machine X ($600).
Example 3: Marketing Campaign (Payoffs)
Scenario: Launching a new product, choosing between online ads or print ads. Success depends on whether the target audience is primarily online or offline.
- Action 1: Online Ads
- Action 2: Print Ads
- Outcome A: Audience is Online
- Outcome B: Audience is Offline
Known Values (Expected Profit - Payoffs):
- P(Audience Online) = 0.8
- Result (Online Ads, Online Audience) = $15000
- Result (Online Ads, Offline Audience) = $3000
- Result (Print Ads, Online Audience) = $4000
- Result (Print Ads, Offline Audience) = $10000
1. Probabilities: P(A=Online) = 0.8, P(B=Offline) = 1 - 0.8 = 0.2.
2. Best Outcome Values (Payoffs):
- Best for Outcome A (Online): max($15000, $4000) = $15000 (Online Ads)
- Best for Outcome B (Offline): max($3000, $10000) = $10000 (Print Ads)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $15000 - $15000 = $0
- OL (Action 1, Outcome B): $10000 - $3000 = $7000
- OL (Action 2, Outcome A): $15000 - $4000 = $11000
- OL (Action 2, Outcome B): $10000 - $10000 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($0 * 0.8) + ($7000 * 0.2) = 0 + 1400 = $1400
- EOL (Action 2) = ($11000 * 0.8) + ($0 * 0.2) = 8800 + 0 = $8800
5. Optimal Action: The action with the lowest EOL is Action 1 (Online Ads) with EOL = $1400.
Conclusion: Based on the probabilities, the Online Ads campaign has a significantly lower expected opportunity loss.
Example 4: Supplier Choice (Costs)
Scenario: A company needs to choose between Supplier X and Supplier Y. Delivery time depends on whether the shipping route is Clear or Delayed.
- Action 1: Choose Supplier X
- Action 2: Choose Supplier Y
- Outcome A: Shipping Route Clear
- Outcome B: Shipping Route Delayed
Known Values (Total Cost including penalties - Costs):
- P(Route Clear) = 0.9
- Result (Supplier X, Route Clear) = $10000
- Result (Supplier X, Route Delayed) = $15000
- Result (Supplier Y, Route Clear) = $11000
- Result (Supplier Y, Route Delayed) = $12000
1. Probabilities: P(A=Clear) = 0.9, P(B=Delayed) = 1 - 0.9 = 0.1.
2. Best Outcome Values (Costs):
- Best for Outcome A (Clear): min($10000, $11000) = $10000 (Supplier X)
- Best for Outcome B (Delayed): min($15000, $12000) = $12000 (Supplier Y)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $10000 - $10000 = $0
- OL (Action 1, Outcome B): $15000 - $12000 = $3000
- OL (Action 2, Outcome A): $11000 - $10000 = $1000
- OL (Action 2, Outcome B): $12000 - $12000 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($0 * 0.9) + ($3000 * 0.1) = 0 + 300 = $300
- EOL (Action 2) = ($1000 * 0.9) + ($0 * 0.1) = 900 + 0 = $900
5. Optimal Action: The action with the lowest EOL is Action 1 (Supplier X) with EOL = $300.
Conclusion: Despite potential delays costing more with Supplier X in that specific outcome, Supplier X is the better choice overall given the high probability of a clear route.
Example 5: Project Management Strategy (Payoffs)
Scenario: Choosing between two development methodologies (Agile vs Waterfall). Success depends on project Scope Stability (Stable or Changing).
- Action 1: Use Agile Methodology
- Action 2: Use Waterfall Methodology
- Outcome A: Scope is Stable
- Outcome B: Scope is Changing
Known Values (Project Value/Success Score - Payoffs):
- P(Scope Stable) = 0.4
- Result (Agile, Stable Scope) = 70
- Result (Agile, Changing Scope) = 90
- Result (Waterfall, Stable Scope) = 85
- Result (Waterfall, Changing Scope) = 50
1. Probabilities: P(A=Stable) = 0.4, P(B=Changing) = 1 - 0.4 = 0.6.
2. Best Outcome Values (Payoffs):
- Best for Outcome A (Stable): max(70, 85) = 85 (Waterfall)
- Best for Outcome B (Changing): max(90, 50) = 90 (Agile)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): 85 - 70 = 15
- OL (Action 1, Outcome B): 90 - 90 = 0
- OL (Action 2, Outcome A): 85 - 85 = 0
- OL (Action 2, Outcome B): 90 - 50 = 40
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = (15 * 0.4) + (0 * 0.6) = 6 + 0 = 6
- EOL (Action 2) = (0 * 0.4) + (40 * 0.6) = 0 + 24 = 24
5. Optimal Action: The action with the lowest EOL is Action 1 (Agile) with EOL = 6.
Conclusion: Agile is the preferred methodology as it minimizes the expected opportunity loss, particularly valuable given the higher probability of changing scope.
Example 6: Personal Finance - Insurance (Costs)
Scenario: Deciding whether to buy extended warranty (Warranty) for a new appliance or not (No Warranty). The appliance can either break down or not break down during the warranty period.
- Action 1: Buy Extended Warranty
- Action 2: Do Not Buy Extended Warranty
- Outcome A: Appliance Breaks Down
- Outcome B: Appliance Does Not Break Down
Known Values (Total Cost - Cost of Warranty + Repair Costs - Costs):
- P(Breaks Down) = 0.1
- Cost of Warranty = $100
- Repair Cost (No Warranty) = $400
- Result (Warranty, Breaks Down) = $100 (Warranty cost, repair is covered)
- Result (Warranty, Does Not Break Down) = $100 (Warranty cost)
- Result (No Warranty, Breaks Down) = $400 (Repair cost)
- Result (No Warranty, Does Not Break Down) = $0
1. Probabilities: P(A=Breaks Down) = 0.1, P(B=No Break Down) = 1 - 0.1 = 0.9.
2. Best Outcome Values (Costs):
- Best for Outcome A (Breaks Down): min($100, $400) = $100 (Warranty)
- Best for Outcome B (No Break Down): min($100, $0) = $0 (No Warranty)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $100 - $100 = $0
- OL (Action 1, Outcome B): $100 - $0 = $100
- OL (Action 2, Outcome A): $400 - $100 = $300
- OL (Action 2, Outcome B): $0 - $0 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($0 * 0.1) + ($100 * 0.9) = 0 + 90 = $90
- EOL (Action 2) = ($300 * 0.1) + ($0 * 0.9) = 30 + 0 = $30
5. Optimal Action: The action with the lowest EOL is Action 2 (Do Not Buy Warranty) with EOL = $30.
Conclusion: Based on this low probability of breakdown, not buying the warranty has a lower expected opportunity loss.
Example 7: Pricing Strategy (Payoffs)
Scenario: A new product launch needs a pricing decision: High Price or Low Price. Success depends on customer Price Sensitivity (Sensitive or Not Sensitive).
- Action 1: Set High Price
- Action 2: Set Low Price
- Outcome A: Customers are Price Sensitive
- Outcome B: Customers are Not Price Sensitive
Known Values (Expected Revenue - Payoffs):
- P(Price Sensitive) = 0.5
- Result (High Price, Sensitive) = $5000
- Result (High Price, Not Sensitive) = $12000
- Result (Low Price, Sensitive) = $8000
- Result (Low Price, Not Sensitive) = $9000
1. Probabilities: P(A=Sensitive) = 0.5, P(B=Not Sensitive) = 1 - 0.5 = 0.5.
2. Best Outcome Values (Payoffs):
- Best for Outcome A (Sensitive): max($5000, $8000) = $8000 (Low Price)
- Best for Outcome B (Not Sensitive): max($12000, $9000) = $12000 (High Price)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $8000 - $5000 = $3000
- OL (Action 1, Outcome B): $12000 - $12000 = $0
- OL (Action 2, Outcome A): $15000 - $4000 = $11000
- OL (Action 2, Outcome B): $12000 - $9000 = $3000
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($3000 * 0.5) + ($0 * 0.5) = 1500 + 0 = $1500
- EOL (Action 2) = ($0 * 0.5) + ($3000 * 0.5) = 0 + 1500 = $1500
5. Optimal Action: Both actions have the same EOL ($1500). The choice is indifferent based on this calculation.
Conclusion: When P(A) = 0.5, both pricing strategies yield the same expected opportunity loss. Other factors might influence the final decision.
Example 8: Inventory Management (Costs)
Scenario: A retailer needs to decide how much of a seasonal item to order (High Stock or Low Stock). Demand will be either High or Low.
- Action 1: Order High Stock
- Action 2: Order Low Stock
- Outcome A: High Demand
- Outcome B: Low Demand
Known Values (Total Cost - Purchase Cost + Holding Cost + Stockout Cost - Costs):
- P(High Demand) = 0.7
- Result (High Stock, High Demand) = $1000 (Cost)
- Result (High Stock, Low Demand) = $1500 (Cost)
- Result (Low Stock, High Demand) = $1800 (Cost)
- Result (Low Stock, Low Demand) = $800 (Cost)
1. Probabilities: P(A=High) = 0.7, P(B=Low) = 1 - 0.7 = 0.3.
2. Best Outcome Values (Costs):
- Best for Outcome A (High): min($1000, $1800) = $1000 (High Stock)
- Best for Outcome B (Low): min($1500, $800) = $800 (Low Stock)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $1000 - $1000 = $0
- OL (Action 1, Outcome B): $1500 - $800 = $700
- OL (Action 2, Outcome A): $1800 - $1000 = $800
- OL (Action 2, Outcome B): $800 - $800 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($0 * 0.7) + ($700 * 0.3) = 0 + 210 = $210
- EOL (Action 2) = ($800 * 0.7) + ($0 * 0.3) = 560 + 0 = $560
5. Optimal Action: The action with the lowest EOL is Action 1 (Order High Stock) with EOL = $210.
Conclusion: Ordering High Stock is the better strategy to minimize expected opportunity loss, especially with a high probability of high demand.
Example 9: Hiring Decision (Payoffs)
Scenario: A manager is hiring for a crucial role. Candidate A is promising but unproven; Candidate B is experienced but perhaps less innovative. The key outcome is the success of a new project (Succeed or Fail).
- Action 1: Hire Candidate A
- Action 2: Hire Candidate B
- Outcome A: New Project Succeeds
- Outcome B: New Project Fails
Known Values (Contribution to Project Value - Payoffs):
- P(Project Succeeds) = 0.6
- Result (Candidate A, Succeeds) = $100000
- Result (Candidate A, Fails) = $20000
- Result (Candidate B, Succeeds) = $70000
- Result (Candidate B, Fails) = $30000
1. Probabilities: P(A=Succeeds) = 0.6, P(B=Fails) = 1 - 0.6 = 0.4.
2. Best Outcome Values (Payoffs):
- Best for Outcome A (Succeeds): max($100000, $70000) = $100000 (Candidate A)
- Best for Outcome B (Fails): max($20000, $30000) = $30000 (Candidate B)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $100000 - $100000 = $0
- OL (Action 1, Outcome B): $30000 - $20000 = $10000
- OL (Action 2, Outcome A): $100000 - $70000 = $30000
- OL (Action 2, Outcome B): $30000 - $30000 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($0 * 0.6) + ($10000 * 0.4) = 0 + 4000 = $4000
- EOL (Action 2) = ($30000 * 0.6) + ($0 * 0.4) = 18000 + 0 = $18000
5. Optimal Action: The action with the lowest EOL is Action 1 (Hire Candidate A) with EOL = $4000.
Conclusion: Hiring Candidate A minimizes the expected opportunity loss, suggesting this candidate is the better choice given the project's importance and likelihood of success.
Example 10: Event Planning (Costs)
Scenario: Planning an outdoor event. Decision is whether to rent a large tent (Rent Tent) or not (No Tent). The outcome is whether it Rains or Stays Dry.
- Action 1: Rent Large Tent
- Action 2: Do Not Rent Tent
- Outcome A: It Rains
- Outcome B: It Stays Dry
Known Values (Total Event Cost - Costs):
- P(It Rains) = 0.2
- Result (Rent Tent, Rains) = $10000 (Tent cost + regular event costs)
- Result (Rent Tent, Stays Dry) = $8000 (Tent cost + regular event costs)
- Result (No Tent, Rains) = $15000 (Regular event costs + losses due to rain disruption)
- Result (No Tent, Stays Dry) = $7000 (Regular event costs)
1. Probabilities: P(A=Rains) = 0.2, P(B=Stays Dry) = 1 - 0.2 = 0.8.
2. Best Outcome Values (Costs):
- Best for Outcome A (Rains): min($10000, $15000) = $10000 (Rent Tent)
- Best for Outcome B (Stays Dry): min($8000, $7000) = $7000 (No Tent)
3. Opportunity Loss (OL) Calculations:
- OL (Action 1, Outcome A): $10000 - $10000 = $0
- OL (Action 1, Outcome B): $8000 - $7000 = $1000
- OL (Action 2, Outcome A): $15000 - $10000 = $5000
- OL (Action 2, Outcome B): $7000 - $7000 = $0
4. Expected Opportunity Loss (EOL) Calculations:
- EOL (Action 1) = ($0 * 0.2) + ($1000 * 0.8) = 0 + 800 = $800
- EOL (Action 2) = ($5000 * 0.2) + ($0 * 0.8) = 1000 + 0 = $1000
5. Optimal Action: The action with the lowest EOL is Action 1 (Rent Large Tent) with EOL = $800.
Conclusion: Renting the tent is the decision that minimizes the expected opportunity loss, reflecting protection against the high cost of rain disruption.
Frequently Asked Questions about Expected Opportunity Loss
1. What is Opportunity Loss?
Opportunity Loss (or Regret) is the difference between the best possible outcome you could have achieved for a specific situation and the outcome you actually got with your chosen action. It quantifies the cost of not having made the optimal choice *after* the uncertainty is resolved.
2. What does Expected Opportunity Loss (EOL) mean?
EOL is the average opportunity loss you would expect over many repetitions of the same decision problem. It's calculated by summing the possible opportunity losses for each outcome, weighted by the probability of that outcome occurring.
3. How do I calculate Opportunity Loss for a specific outcome?
First, identify the best possible result for that outcome (highest payoff or lowest cost). Then, subtract your actual result from the best result (for payoffs) or subtract the best result from your actual result (for costs). The result is always non-negative.
4. How is EOL calculated for an action?
For a given action, you calculate the Opportunity Loss for each possible outcome. Then, you multiply each opportunity loss by its corresponding outcome probability and sum these values up. EOL(Action) = (OL for Outcome A * P(A)) + (OL for Outcome B * P(B)).
5. What's the relationship between EOL and Expected Monetary Value (EMV)?
Minimizing EOL is mathematically equivalent to maximizing EMV. The action that gives the minimum EOL is the same action that gives the maximum EMV. They are two sides of the same coin in decision analysis under uncertainty.
6. Why would I use EOL instead of EMV?
While mathematically equivalent, EOL focuses on minimizing potential regret, which can sometimes be a more intuitive way for decision-makers to think about risk and uncertainty compared to maximizing expected gain.
7. How many actions and outcomes can this calculator handle?
This specific calculator is designed for the simplest case: exactly two actions and exactly two possible outcomes. The principles of EOL can be extended to problems with more actions and outcomes, but that requires a more complex calculator.
8. What units should I use for the results?
Use consistent units for all your result inputs (e.g., all in dollars, all in points, all in hours). The calculated EOL will be in the same units. The calculator performs no unit conversions.
9. Does the probability of Outcome B need to be entered?
No, you only need to enter the Probability of Outcome A. The calculator automatically assumes P(Outcome B) = 1 - P(Outcome A), because the probabilities of all possible outcomes must sum to 1.
10. What does a low EOL value mean?
A lower EOL value means that, on average over many similar situations, the chosen action is expected to result in less "regret" compared to not choosing the best possible action for each outcome. The action with the *minimum* EOL is considered the optimal decision based on this criterion.
