How to Calculate Expected Value

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Expected Value Calculator

Enter the numerical outcomes and their associated probabilities (0 to 1 or percentage).

Calculated Result:

What is Expected Value?

Expected Value (EV) is a fundamental concept in probability and statistics that represents the long-term average outcome of a random variable. Whether you are analyzing stock market investments, poker hands, or business decisions, EV helps you determine the average return you can expect if an action is repeated many times.

E(X) = Σ (xᵢ * P(xᵢ))

How to Calculate Expected Value

To calculate the expected value of a discrete random variable, follow these steps:

  1. Identify all possible outcomes: List every potential result of the event (denoted as x).
  2. Assign probabilities: Determine the likelihood of each outcome occurring (denoted as P(x)). The sum of all probabilities must equal 1 (or 100%).
  3. Multiply: Multiply each outcome value by its corresponding probability.
  4. Sum: Add all those products together to find the Expected Value.

Practical Example: The Coin Toss Game

Imagine a friend offers you a game: If a coin lands on heads, you win $10. If it lands on tails, you lose $5.

  • Outcome 1: +10 (Probability 0.5)
  • Outcome 2: -5 (Probability 0.5)

Calculation: (10 * 0.5) + (-5 * 0.5) = 5 – 2.5 = 2.5.

In this scenario, the Expected Value is $2.50. This means that while any single flip results in a win or loss, if you play this game 1,000 times, you should expect to average a profit of $2.50 per flip.

Why EV Matters in Business

Decision-makers use EV to choose between different strategies. If a project has a 20% chance of making $1,000,000 and an 80% chance of losing $100,000, the EV is $120,000. Even though there is a high chance of loss, the positive expected value suggests it might be a risk worth taking in a diversified portfolio.

function addRow() { var container = document.getElementById('evRows'); var newRow = document.createElement('div'); newRow.className = 'ev-row'; newRow.innerHTML = '
'; container.appendChild(newRow); } function calculateEV() { var valInputs = document.getElementsByClassName('val-input'); var probInputs = document.getElementsByClassName('prob-input'); var errorBox = document.getElementById('errorBox'); var resultContainer = document.getElementById('resultContainer'); var evResult = document.getElementById('evResult'); var evInterpretation = document.getElementById('evInterpretation'); var totalEV = 0; var totalProb = 0; var isValid = true; errorBox.style.display = 'none'; resultContainer.style.display = 'none'; for (var i = 0; i 1, assume it's a percentage unless the user actually meant a value > 1 (unlikely for basic EV) // However, standard math expects decimals. Let's check total. totalEV += (val * prob); totalProb += prob; } if (totalProb === 0) { errorBox.innerText = "Error: Total probability cannot be zero."; errorBox.style.display = 'block'; return; } // Normalizing logic: if sum is roughly 100, they used percentages. // If sum is roughly 1, they used decimals. // To be precise, we divide totalEV by totalProb if they didn't normalize. // But mathematically, EV = Sum(x*p) / Sum(p) is the weighted average. var finalEV = totalEV / totalProb; evResult.innerText = finalEV.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}); if (finalEV > 0) { evInterpretation.innerText = "This result indicates a positive long-term average outcome."; } else if (finalEV 0.001 && Math.abs(totalProb – 100) > 0.1) { errorBox.innerText = "Note: Probabilities sum to " + totalProb.toFixed(2) + ". The calculator has treated this as a weighted average."; errorBox.style.display = 'block'; errorBox.style.color = '#f39c12'; // Warning color } else { errorBox.style.color = '#e74c3c'; // Reset to error color } }

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