Introduction
The Expected Value (EV) Calculator helps you find the average outcome of a random event. Expected value is a key idea in statistics. It tells you what result you can expect over time if you repeat something many times. To find it, you multiply each possible outcome by its chance of happening, then add all those results together. This tool does that math for you quickly and easily. Whether you are working on a homework problem, studying probability distributions, or making decisions based on data, this calculator saves you time and reduces mistakes. Just enter your values and their probabilities, and the calculator gives you the expected value right away.
How to Use Our EV Calculator
Enter your bet details and your estimated win probability below. The calculator will tell you the expected value (EV) of your bet in dollars and as a percentage, show whether the bet is worth making, and give you a full breakdown of the math.
Stake ($): Type in the amount of money you plan to bet. This is the dollar amount you are putting at risk on this wager.
Odds: Enter the odds offered by the sportsbook. You can type American odds (like -110 or +150), decimal odds (like 1.91), or fractional odds (like 3/2). Use the dropdown next to the odds field to pick which format you are using, and the calculator will convert between formats automatically.
Odds Format: Select whether your odds are in American, Decimal, or Fractional format. If you switch formats, the calculator will convert your current odds to the new format for you.
True Win Probability (%): Enter what you believe the real chance of your bet winning is, shown as a percentage between 0.1% and 99.9%. This is your own estimate, not the probability implied by the sportsbook's odds. For example, if you think a team has a 55% chance of winning, type 55. You can also drag the slider below the input to adjust this value quickly.
What Is Expected Value (EV) in Betting?
Expected value (EV) is a statistics concept that tells you how much money you can expect to win or lose on average each time you place a bet. It combines two things: the probability of each outcome and the amount you stand to win or lose. A positive EV (+EV) means the bet is profitable over time, while a negative EV (−EV) means you'll lose money in the long run.
How Expected Value Is Calculated
The formula for expected value in betting is simple:
EV = (Win Probability × Profit if You Win) − (Loss Probability × Stake)
For example, say you bet $100 at American odds of −110, and you believe the true win probability is 55%. The odds imply you'd profit $90.91 on a win. The math looks like this:
- EV = (0.55 × $90.91) − (0.45 × $100) = $50.00 − $45.00 = +$5.00
That +$5.00 means you'd expect to gain $5 per bet on average if you made this same wager many times.
Implied Probability vs. True Probability
Every set of odds has a built-in win percentage called the implied probability. This is the breakeven point — the win rate you'd need just to avoid losing money. For −110 American odds, the implied probability is about 52.38%. If you believe the real chance of winning is higher than that, you have an edge. The gap between your estimated probability and the implied probability is what creates positive or negative EV. You can use our No Vig Calculator to remove the sportsbook's margin and find the true implied probabilities from a two-way market.
Why Expected Value Matters
A single bet can go either way regardless of its EV. You can lose a +EV bet and win a −EV bet. But over hundreds or thousands of bets, the math takes over. Bettors who consistently find +EV opportunities will be profitable over time, while those who place −EV bets will lose money. This is the same principle that keeps casinos profitable — every game they offer has a negative expected value for the player. Understanding the normal distribution can help you appreciate how results cluster around the expected value as your sample size grows.
Key Terms to Know
- ROI (Return on Investment): The expected value expressed as a percentage of your stake. An EV of +$5 on a $100 bet is a +5% ROI. For broader investment analysis, you might also explore our Margin Calculator.
- Edge: The difference between your estimated win probability and the implied probability from the odds, measured in percentage points. You can think of this like a percent change in your favor.
- Breakeven Probability: The exact win rate at which EV equals zero. Betting above this rate produces +EV; below it produces −EV. Our Break Even Calculator applies this same concept to business scenarios.
Understanding Odds Formats
This calculator supports three common odds formats. American odds use positive numbers (like +150) for underdogs and negative numbers (like −110) for favorites. Decimal odds (like 1.91) show your total return per dollar wagered. Fractional odds (like 10/11) show your profit relative to your stake — if you need help working with fractions in general, try our Fraction Calculator. All three formats are just different ways to express the same payout, and the calculator converts between them automatically.
Tips for Using This Calculator
The most important input is your estimated win probability. The odds are set by the sportsbook, but the probability is your judgment. Be honest and realistic with this number. If your probability estimates are accurate over time, the EV calculation will reliably guide you toward profitable bets. Use the sensitivity table to see how small changes in your estimated probability affect the expected value — it shows just how much your edge depends on getting that number right. For deeper statistical analysis of your results over time, tools like the Standard Deviation Calculator, Z Score Calculator, and Confidence Interval Calculator can help you determine whether your observed results are statistically significant or simply due to variance. You may also find the Combination Calculator and Permutation Calculator useful when evaluating parlay-style bets or multi-outcome scenarios.