Expected Value (EV) Calculator

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How to Use Our Expected Value Calculator

Here's how to use our expected value calculator:

  1. Select your odds format (American, decimal, fractional, etc.)
  2. Enter the odds of your bet in your chosen format.
  3. Enter your bet amount.
  4. 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