Expected Value
Expected Value Calculator: Is This Bet +EV Over the Long Run?
Expected value (EV) is the average profit or loss you would make if you placed the same bet an unlimited number of times. The formula is EV = p × stake × (odds − 1) − (1 − p) × stake. A positive EV bet (+EV) builds profit over time and a negative one loses, whatever happens in a single game. The expected value calculator takes your win probability and the sportsbook's price and returns the average dollar result per bet and the EV as a percentage of stake.
Expected Value Calculator
Expected ValueThe one number that says whether a bet wins or loses over time
EV = p × S × (O − 1) − (1 − p) × Sp = your estimated win probability, S = stake, O = decimal odds. Break-even win rate = 1 ÷ O.
How to use the expected value calculator
Enter your win probability, the odds and the stake, and the calculator returns the expected value in dollars and as a percentage. The percentage is the most useful number: +5% means that for every $100 you bet, you earn $5 on average over the long run; −5% means you lose $5.
Watch the break-even win rate too. It equals 1 ÷ odds, the market's implied probability including vig, and your estimate has to beat it for the bet to be +EV. At -105 (1.95) the break-even rate is 51.3%; at -133 (1.75) it is 57.1%; at standard -110 (1.91) it is 52.4%. The shorter the price, the higher the bar.
With multiple legal sportsbooks in most states, you have two levers: estimate the probability accurately and shop for the best price. The same 55% estimate is +EV at -105 and barely break-even at -125 (1.80), so check the line at more than one book before you bet.
A +EV bet is not a bet that will win
Positive expected value is a long-run average; any single bet can lose. A 55% bet loses three in a row about 9% of the time, so you will hit a few of those streaks in every hundred bets. Doubting the EV and changing strategy after a losing streak is the most common beginner mistake.
That is why EV needs a bet log. Record the win probability, the odds and the result for every bet, and after a few hundred bets compare your estimated win rate with your actual hit rate. If bets you rated 55% land 48% of the time, the problem is your estimation method, not luck. The Mysports.AI bet tracker is built for this comparison.
Expected value and the Kelly criterion together
Expected value tells you whether to bet; the Kelly criterion tells you how much. The workflow is: confirm EV is positive with this calculator, size the bet with the Kelly criterion calculator, then verify the results in your bet log. All three tools use the same probability and odds inputs, so you estimate once.
A bet with tiny EV, say +1%, produces a tiny Kelly stake, often well under one unit (1% of bankroll). That is the math telling you the edge is not worth the variance; passing beats forcing a minimum bet.
Example: 55% win probability, -105 (1.95), $100 stake
- When the bet wins you profit $100 × (1.95 − 1) = $95, with probability 55%; when it loses you lose $100, with probability 45%.
- EV = 0.55 × $95 − 0.45 × $100 = $52.25 − $45.00 = +$7.25, or +7.25% of stake.
- Break-even win rate = 1 ÷ 1.95 = 51.3%; your 55% clears it, so the bet is +EV.
If the line moves to -125 (1.80), EV = 0.55 × $80 − $45 = −$1, and the same 55% estimate becomes −EV. Recalculate whenever the price changes instead of relying on yesterday's number.
FAQ
What does positive expected value mean?+
A positive expected value (+EV) bet earns money on average when repeated many times. The test is simple: your estimated win probability has to be higher than the probability implied by the odds, which is 1 ÷ decimal odds, or 52.4% at -110 (1.91).
How do you calculate expected value in sports betting?+
EV = win probability × stake × (decimal odds − 1) − (1 − win probability) × stake. With a 55% win probability, -105 (1.95) odds and a $100 stake, EV = 0.55 × $95 − 0.45 × $100 = +$7.25 per bet.
How much EV makes a bet worth placing?+
There is no fixed threshold, but the EV percentage has to cover the error in your win-probability estimate. Many bettors treat +3% to +5% as a minimum; below that range a small misjudgment of the probability flips the bet negative.
Why do my +EV bets keep losing?+
Two possibilities: the sample is still too small, or your win-probability estimates run high. After one or two hundred logged bets, compare the average estimated probability with the actual hit rate and you will see which one it is.
Can the expected value calculator handle a parlay?+
Yes. Enter the parlay's total decimal odds as the price and your estimate of the chance every leg hits as the win probability. Get the total odds from the parlay calculator first.
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A calculator answers the formula; the AI answers the game. Mysports.AI compares model win probability against market odds every day and flags the prices that look mispriced.
For informational purposes only. Sports betting is legal in 39 states and D.C.; rules and minimum age vary by state. 21+. Gambling problem? Call 1-800-GAMBLER.
Odds and vig conventions follow standard US sportsbook pricing (-110 on spreads and totals). The tax line is based on IRS Topic 419 and the Form W-2G instructions (rev. 01/2026); it is not tax advice.