# Expected Value (EV) Calculator

## How to Use Our Expected Value Calculator

Here's how to use our expected value calculator:

- Select your odds format (American, decimal, fractional, etc.)
- Enter the odds of your bet in your chosen format.
- Enter your bet amount.
- Enter your win probability.

After you enter valid values in all inputs, the calculator will automatically output your Expected Value (EV) and the Expected ROI of your bet.

## What is Expected Value (EV)

In sports betting, **expected value (EV)** is the average profit you expect to make from a wager if you could bet the same odds and amount an infinite number of times at the same expected win probability. A positive expected value bet (+EV) implies it will win over time, and a negative expected value bet (-EV) implies it will lose over time.

Win probability can be derived from a betting model or the no-vig odds from a sharp sportsbook. Because it's impossible to predict sports betting outcomes perfectly, win probability is an estimate, and thus, the expected value and expected ROI are also estimates.

## Why Use An Expected Value Calculator

Let's say you've built a predictive model for assigning probabilities of a baseball team beating their opponents. Your model predicts that the New York Yankees have a 60% chance of beating the Los Angeles Dodgers. The best odds for the New York Yankees to win are -120. By entering the -120 odds, $100 bet amount, and a 60% win probability into the expected value calculator, you can see that your bet is expected to make $10 of profit (10% ROI), given your estimated win probability.

For those without the ability to accurately model sports outcomes, a common tactic is to use the vig-free odds of a sharp sportsbook (such as Pinnacle or Circa) to assign probabilities to an event. If you see that the Circa odds are -134 on the Yankees to beat the underdog Dodgers at +162, you can calculate the vig-free odds to estimate that the Yankees have a 60% chance of winning. If a less sharp sportsbook has the Yankees' odds at -120, we can use the EV calculator to see a $100 bet has an expected value of $10 and an expected ROI of 10%.

## How to Calculate Expected Value

Here's the formula for expected value:

Win Probability As a Decimal * Profit If Win - Loss Probability As a Decimal * Bet Amount

Using our bet calculator, we can see that a $100 bet at -120 odds will profit $83.33 if the bet wins. If we predict the win probability as 60% (40% loss probability), we can use the formula above to calculate our EV:

0.60 * 83.33 - 0.40 * 100 = 50 - 40 = $10 Expected Value