Calculate Expected Value

Expected Value Calculator

Enter the value and probability for each possible outcome.

function calculateExpectedValue() { var outcome1Value = parseFloat(document.getElementById('outcome1Value').value); var outcome1Probability = parseFloat(document.getElementById('outcome1Probability').value); var outcome2Value = parseFloat(document.getElementById('outcome2Value').value); var outcome2Probability = parseFloat(document.getElementById('outcome2Probability').value); var outcome3Value = parseFloat(document.getElementById('outcome3Value').value); var outcome3Probability = parseFloat(document.getElementById('outcome3Probability').value); var resultDiv = document.getElementById('expectedValueResult'); var warningDiv = document.getElementById('probabilityWarning'); warningDiv.style.display = 'none'; // Hide previous warnings // Input validation if (isNaN(outcome1Value) || isNaN(outcome1Probability) || isNaN(outcome2Value) || isNaN(outcome2Probability)) { resultDiv.innerHTML = 'Please enter valid numbers for at least the first two outcomes.'; resultDiv.style.color = '#dc3545'; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.borderColor = '#f5c6cb'; return; } // Handle optional third outcome if (isNaN(outcome3Value)) outcome3Value = 0; if (isNaN(outcome3Probability)) outcome3Probability = 0; // Probability validation if (outcome1Probability 100 || outcome2Probability 100 || outcome3Probability 100) { resultDiv.innerHTML = 'Probabilities must be between 0% and 100%.'; resultDiv.style.color = '#dc3545'; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.borderColor = '#f5c6cb'; return; } var totalProbability = outcome1Probability + outcome2Probability + outcome3Probability; if (totalProbability > 100.001 || totalProbability < 99.999) { // Allow for minor floating point inaccuracies warningDiv.innerHTML = 'Warning: The sum of probabilities is ' + totalProbability.toFixed(2) + '%. For a complete analysis, probabilities should sum to 100%.'; warningDiv.style.display = 'block'; } // Calculate Expected Value var expectedValue = (outcome1Value * (outcome1Probability / 100)) + (outcome2Value * (outcome2Probability / 100)) + (outcome3Value * (outcome3Probability / 100)); resultDiv.innerHTML = 'Expected Value: ' + expectedValue.toFixed(2) + ''; resultDiv.style.color = '#28a745'; resultDiv.style.backgroundColor = '#e9f7ee'; resultDiv.style.borderColor = '#d0ecd7'; } // Run calculation on page load with default values window.onload = calculateExpectedValue;

Understanding Expected Value

The Expected Value (EV) is a fundamental concept in probability theory and statistics, widely used in decision-making, finance, gambling, and risk assessment. It represents the average outcome of a random variable over a large number of trials. In simpler terms, it's what you can expect to happen on average if you repeat an event many times.

How is Expected Value Calculated?

The formula for Expected Value is straightforward:

EV = (Outcome₁ Value × Probability₁) + (Outcome₂ Value × Probability₂) + … + (Outcome_n Value × Probability_n)

Where:

• Outcome Value: The numerical value associated with a specific event (e.g., profit, loss, points, monetary gain). This can be positive or negative.
• Probability: The likelihood of that specific outcome occurring, expressed as a decimal (e.g., 0.5 for 50%) or percentage.

Our calculator simplifies this by allowing you to input probabilities as percentages, converting them to decimals for the calculation.

Why is Expected Value Important?

Expected Value is a powerful tool for making informed decisions under uncertainty:

• Risk Assessment: It helps evaluate the potential gains or losses of a decision or investment.
• Strategic Planning: Businesses use EV to assess the potential profitability of projects, marketing campaigns, or product launches.
• Gambling and Games: Professional gamblers and game designers use EV to determine the fairness or profitability of a game. A positive EV suggests a favorable long-term outcome, while a negative EV indicates an unfavorable one.
• Insurance: Insurance companies use EV to set premiums, ensuring they cover potential payouts and make a profit.

How to Use This Calculator

1. Identify Outcomes: Determine all possible outcomes of the event or decision you are analyzing.
2. Assign Values: For each outcome, assign a numerical value. This could be a monetary gain (positive), a monetary loss (negative), points, or any other quantifiable metric.
3. Determine Probabilities: Estimate the probability of each outcome occurring. These probabilities should ideally sum up to 100% (or 1.0 if using decimals) to represent all possible scenarios.
4. Input into Calculator: Enter the value and probability for each outcome into the respective fields. The calculator provides fields for up to three outcomes, but you can use fewer if needed (just leave the optional fields at 0).
5. Calculate: Click the "Calculate Expected Value" button to see the result.

Example Scenarios

Example 1: Simple Coin Flip Game

Imagine a game where you flip a coin. If it lands on heads, you win $100. If it lands on tails, you lose $50.

• Outcome 1: Win $100 (Heads) – Probability: 50%
• Outcome 2: Lose $50 (Tails) – Probability: 50%

Using the calculator:

• Value of Outcome 1: 100, Probability: 50
• Value of Outcome 2: -50, Probability: 50

Expected Value = (100 × 0.50) + (-50 × 0.50) = 50 – 25 = $25

This means, on average, you can expect to gain $25 per flip if you play this game many times.

Example 2: Business Project Decision

A company is considering a new project with three possible outcomes:

• Outcome 1: Great Success – Profit of $1,000,000 (Probability: 20%)
• Outcome 2: Moderate Success – Profit of $200,000 (Probability: 50%)
• Outcome 3: Failure – Loss of $500,000 (Probability: 30%)

Using the calculator:

• Value of Outcome 1: 1000000, Probability: 20
• Value of Outcome 2: 200000, Probability: 50
• Value of Outcome 3: -500000, Probability: 30

Expected Value = (1,000,000 × 0.20) + (200,000 × 0.50) + (-500,000 × 0.30)

= 200,000 + 100,000 – 150,000 = $150,000

The expected value of $150,000 suggests that, on average, this project is expected to be profitable.

Limitations of Expected Value

While powerful, Expected Value has limitations:

• Risk Aversion: EV doesn't account for an individual's or organization's attitude towards risk. A high EV project with a small chance of catastrophic loss might be avoided by a risk-averse entity.
• Single Event: EV is most meaningful over many repetitions. For a single, one-off event, the actual outcome will be one of the discrete possibilities, not the average.
• Accuracy of Probabilities: The accuracy of the EV depends heavily on the accuracy of the estimated probabilities. Poor probability estimates lead to misleading EV calculations.