Calculate the weighted average of possible outcomes.
Understanding Expected Value
Expected Value (EV) is a fundamental concept in probability and statistics that represents the average outcome of a random variable over a large number of trials. It's a weighted average where each possible outcome is multiplied by its probability of occurrence. In simpler terms, it tells you what you can expect to gain or lose on average if you were to repeat an event or decision many times.
The formula for Expected Value is:
E(X) = Σ [ x * P(x) ]
Where:
E(X) is the Expected Value of the random variable X.
Σ represents the sum of all possible outcomes.
'x' is the value of a specific outcome.
P(x) is the probability of that specific outcome occurring.
How the Calculator Works:
This calculator allows you to input multiple possible outcomes for an event and their corresponding probabilities.
Outcome Value: The numerical result (gain or loss) associated with a specific scenario.
Probability (%): The likelihood of that specific outcome occurring, expressed as a percentage (e.g., 25% for a 1 in 4 chance). The calculator will convert this to a decimal for calculation (e.g., 25% becomes 0.25).
The calculator then applies the Expected Value formula: it multiplies each outcome's value by its probability and sums up these products to give you the overall Expected Value.
Use Cases for Expected Value:
Expected Value is a powerful tool used across various fields:
Finance and Investment: Evaluating the potential profitability of different investment options. A positive EV suggests an investment is likely to be profitable on average, while a negative EV indicates an expected loss.
Gambling and Gaming: Determining the fairness of games or the long-term profitability of a strategy in casino games or lotteries. A fair game has an Expected Value of zero.
Decision Making: Assessing the potential consequences of different choices under uncertainty. For example, a business might use EV to decide whether to launch a new product.
Insurance: Insurance companies use EV to set premiums. They calculate the expected payout for a policy and add administrative costs and profit margin.
Project Management: Estimating the potential risks and rewards of different project approaches.
A positive Expected Value suggests that, on average, you can expect a favorable outcome over the long run, while a negative Expected Value indicates an unfavorable average outcome. Understanding EV helps in making more informed and rational decisions when faced with uncertainty.
var outcomeCount = 2;
function addOutcomeField() {
outcomeCount++;
var outcomesContainer = document.getElementById('outcomes-container');
var newOutcomeGroup = document.createElement('div');
newOutcomeGroup.className = 'input-group probability-group';
newOutcomeGroup.innerHTML = `
`;
outcomesContainer.appendChild(newOutcomeGroup);
}
function removeOutcome(id) {
var outcomeGroupToRemove = document.querySelector(`.probability-group input[id="outcomeValue${id}"]`).closest('.input-group');
if (outcomeGroupToRemove) {
outcomeGroupToRemove.remove();
}
// After removal, we might want to re-evaluate the total probabilities
// or just var the user proceed. For simplicity, we won't re-index here.
}
function calculateExpectedValue() {
var totalProbability = 0;
var weightedSum = 0;
var isValid = true;
var resultDiv = document.getElementById('result');
resultDiv.innerText = "; // Clear previous result
for (var i = 1; i <= outcomeCount; i++) {
var outcomeValueInput = document.getElementById(`outcomeValue${i}`);
var probabilityInput = document.getElementById(`probability${i}`);
// Check if elements exist before trying to access their values
if (!outcomeValueInput || !probabilityInput) {
continue; // Skip if this outcome number doesn't exist (e.g., after removal)
}
var outcomeValue = parseFloat(outcomeValueInput.value);
var probabilityPercent = parseFloat(probabilityInput.value);
// Validate inputs
if (isNaN(outcomeValue)) {
resultDiv.innerText = 'Error: Please enter a valid number for all Outcome Values.';
isValid = false;
break;
}
if (isNaN(probabilityPercent) || probabilityPercent 100) {
resultDiv.innerText = 'Error: Probabilities must be numbers between 0 and 100.';
isValid = false;
break;
}
var probabilityDecimal = probabilityPercent / 100;
weightedSum += outcomeValue * probabilityDecimal;
totalProbability += probabilityDecimal;
}
// Final check for total probability if we have at least two outcomes
// Allowing for minor floating point inaccuracies
if (isValid && outcomeCount >= 2 && Math.abs(totalProbability – 1.0) > 0.0001) {
resultDiv.innerText = 'Error: Probabilities must sum to 100%. Current sum: ' + (totalProbability * 100).toFixed(2) + '%';
isValid = false;
}
if (isValid) {
var expectedValue = weightedSum;
resultDiv.innerText = `Expected Value: ${expectedValue.toFixed(2)}`;
resultDiv.style.backgroundColor = 'var(–success-green)';
} else {
resultDiv.style.backgroundColor = '#dc3545'; // Red for errors
}
}