Expected Value (EV) Calculator

This calculator turns your estimated win probability and the American odds into an expected value, shown in percent and dollars, so you can see whether a betting line is a long-run winner before you ever place a wager.

What Is Expected Value?

Expected value is the single most important number in serious betting: it is the average result you would get if you could place the same bet thousands of times. A positive expected value, or +EV, means the price is a long-run winner. A negative one means it bleeds money no matter how any single game turns out.

EV depends on two things the price alone cannot tell you. The first is the payout, which the odds set. The second is the true win probability, which is your job to estimate, since no sportsbook publishes it. The odds only tell you the implied probability baked into the price, and that already includes the book’s margin, so it is never a neutral estimate of the real chance.

When your estimate of the real chance beats the chance the odds imply, the bet is +EV and worth making. When your estimate falls short of that implied chance, the bet is -EV, and taking it repeatedly is a losing strategy even if it wins occasionally. This is why the calculator asks for your own probability rather than pulling one from the market: EV is only meaningful when the probability you enter reflects genuine research.

How Expected Value Is Calculated

The formula is: expected value per $1 staked equals your win probability multiplied by the decimal odds, minus 1. Multiply that per-dollar figure by your stake to get the EV in dollars. Written another way, EV equals the probability of winning multiplied by the profit if you win, minus the probability of losing multiplied by the stake. Both versions produce the same answer; the calculator shows the result in percent and dollars.

American odds have to be converted to decimal odds before this formula works, and that conversion always runs through 100. For a plus-money price like +120, add 100 to the odds and divide by 100, which gives a decimal price of 2.20. For a minus-money price like -110, divide 100 by the odds and add 1, which gives 1.91. Once you have the decimal odds, plug in your win probability. Take the +120 example with a 52% win probability: multiplying 52% by the 2.20 decimal odds, then subtracting 1, leaves an expected value of 14.4% per dollar staked. On a $50 bet, that scales up to $7.20 in expected profit. A result of exactly zero means the price and your probability agree perfectly. Anything above zero is +EV; anything below zero is -EV, and repeating it will cost you money over time even though any individual bet can still win.

What the Calculator Shows You

The calculator returns four figures once you enter the American odds and your estimated win probability. First is the implied probability the price itself represents, which is what the sportsbook needs to be true for the bet to break even on their side. Second is the expected value per unit, shown as a percentage, which tells you the average return per dollar staked if the bet were repeated many times over. Third is the expected value in dollars, which scales that percentage up to your actual stake size. Fourth is the verdict: whether the bet is +EV, break-even, or -EV. Together these figures let you judge a price on its own merits rather than on gut feel alone.

Worked Example

Take a $50 bet on an underdog moneyline priced at +120, where you estimate the true win chance at 52%. The first step is converting +120 to decimal odds, which comes out to 2.20. The price itself implies a win probability of 45.5%, meaning the sportsbook only needs the underdog to win 45.5% of the time for the price to break even on their side.

Your own estimate of 52% is well above that 45.5% implied number, a 6.5-point edge in your favor. Plugging both figures into the formula, multiplying 52% by the 2.20 decimal odds and subtracting 1, gives an expected value per unit of 14.4%. That 14.4% is the average return per dollar staked if this exact bet were placed over and over with the same true 52% win rate.

Scaled up to the actual $50 stake, that 14.4% becomes $7.20 in expected profit. In other words, if you could rewind this exact matchup thousands of times and bet $50 on the underdog at +120 every single time, your average result across all of those repeated bets would be a profit of $7.20 per bet, even though any one instance of the bet either wins outright or loses the full $50 stake.

This is the core value of running the numbers instead of trusting instinct: the price alone told you nothing about whether +120 was a good bet to begin with. It was only by comparing the sportsbook’s implied 45.5% to your own researched 52% that the 14.4% edge, and the $7.20 in expected dollar value, became visible in the first place. Without running that comparison, a bettor could just as easily take a -EV price because it “felt right.”

EV per $50 Bet at +120 by Your Estimated Win Probability

The table below holds the odds and implied probability fixed at +120 and 45.5% and varies only your own estimated win probability, so you can see how sensitive the expected value is to that one input. Notice that even a probability just half a point below the 45.5% break-even mark turns the bet slightly negative, while an estimate several points above it produces a meaningfully larger dollar edge on the same $50 stake.

Break-Even Win Probability by American Price

Every American price has a break-even win probability built into it: the exact win rate at which betting that price forever would leave you with neither profit nor loss. The table below lists that break-even percentage alongside the decimal odds for a handful of common American prices, from a heavy favorite at -200 down to a longshot at +300. Your estimated win probability needs to clear the listed break-even number for a bet at that price to be +EV.

How Sensitive EV Is to Your Probability Estimate

EV lives or dies on the probability you feed it, and that number is an estimate, not a fact. Change 52% to 48% on the +120 example and the bet swings from +14.4% to only +5.6%; drop to 45% and it turns slightly negative. The break-even point, where EV is exactly zero, is just the implied probability of the price: 45.5% at +120.

This is why sharp bettors obsess over accurate probabilities rather than gut feel. A small error in the estimate can flip a winning bet into a losing one, and the +120 example makes that concrete: the gap between a 45% estimate and a 52% estimate is a small one, yet it is the entire difference between a bet worth avoiding and one worth making repeatedly. The formula treats your input as exact, so the quality of that input is the quality of the whole calculation.

EV also says nothing about variance. A +EV bet can lose many times in a row before the edge shows up over a large sample, purely because a 52% chance still means the underdog fails to win 48% of the time. That gap between the math and any single result is exactly what bankroll management exists to survive: it keeps a bettor in the game long enough for a genuine edge to play out.

When Expected Value Makes Sense

Expected value is the right tool whenever you have a genuine, researched view on a game’s true probability that differs from what the market is pricing in. It suits bettors who track team and player data closely enough to form their own probability estimate, then compare it against the American odds on offer, rather than betting on hunches or team loyalty. Used this way, EV becomes a filter: it screens out prices that only look attractive and confirms the ones that are mathematically attractive as well.

It makes the most sense as an ongoing, repeated practice rather than a one-off check. A single +EV bet, like the $50 wager at +120 above, can still lose, because expected value describes an average across many repetitions, not a guarantee on any one outcome.

EV makes less sense when the probability being entered is not genuinely researched, since a guessed probability produces a meaningless figure that looks precise but is not. It also is not the right tool if the goal is guaranteed profit on a single event; an approach like arbitrage or matched betting, which locks in a result across multiple outcomes, fits that goal better than a probability-based edge that only pays off statistically over time. EV is best treated as one input in a broader staking and bankroll strategy, not a green light on its own.

Common Mistakes

Trusting a gut-feel probability is the most common error, since EV is only as good as the number entered into it. Some bettors also confuse a positive EV reading with a guaranteed win on that specific bet, when it only describes an average across many repeated bets. Others make the mistake of using the odds’ own implied probability as their estimate, which mathematically always produces an EV of zero and defeats the purpose of the calculation. Finally, ignoring variance is a persistent trap: even a genuinely +EV bet still needs a properly sized bankroll to survive the losing streaks that will happen along the way.

Reading the EV Result

Once the calculator returns a number, the sign of that number is what matters: positive, zero, or negative. Each outcome points to a different conclusion about the price and a different action to take, summarized in the table below.