Expected Value (EV) in Sports Betting, Explained
What a +EV bet is, how to calculate it from fair odds, and why even good bets lose often in the short run.
The Smart Lines teamOctober 20265 min read
What expected value means
Expected value (EV) is what a bet is worth on average if you could place it thousands of times. A bet with positive expected value (+EV) pays more than its chance of winning is worth. A bet with negative expected value (−EV) pays less. Most bets at a sportsbook are −EV, because the book builds a margin into every price.
EV says nothing about whether one particular bet wins. A +EV bet on an underdog will still lose more often than it wins. What EV tells you is whether the price is good for the risk you take, which is the only part of a bet you control.
How to calculate EV
For a bet that either wins or loses, EV as a percentage of your stake is:
EV % = (win probability × decimal odds − 1) × 100
Decimal odds are the total you get back per $1 staked, stake included (American +150 is 2.50 in decimal; see how to read betting odds). If the result is above zero, the bet is +EV.
Example 1
A fair coin flip at +110
A coin lands heads 50% of the time. If someone offers you +110 (2.10 in decimal) on heads, then on a $100 bet:
- Win probability
- 50%
- Decimal odds
- 2.10
- EV = 0.50 × 2.10 − 1
- +5.0%
On average you make $5 per $100 bet. You’ll still lose half the flips; the edge only shows up over many of them.
Where the “true” probability comes from
The formula needs the real chance of the bet winning, and nobody knows that exactly. The practical answer is to borrow it from the most accurate prices available: a sharp sportsbook, or a consensus of many books, with their margin removed. Those are called fair or no-vig odds, and they’re the most reliable public estimate of the true probability that exists. Our guide to no-vig odds shows how to remove the margin yourself.
At The Smart Lines, the fair price for a line is Pinnacle’s price with its margin removed when Pinnacle quotes that exact line. Otherwise it’s the median fair price of at least three other independent books. The book you’re looking at never counts toward its own fair price.
Example 2
Same team, two sportsbooks
Say the fair probability of Team A winning is 42%, which is fair odds of about +138. Sportsbook X offers +150 and sportsbook Y offers +130:
- Sportsbook X at +150 (2.50): 0.42 × 2.50 − 1
- +5.0%
- Sportsbook Y at +130 (2.30): 0.42 × 2.30 − 1
- −3.4%
It’s the same team in the same game. One price is a good bet and the other is a bad one, and the only difference is where you place it.
Why +EV bets still lose: variance
A bet at +150 with a 42% chance of winning loses 58% of the time, even though it’s +5% EV. Over a small number of bets, luck swamps the edge. Here’s what to expect betting $100 a time on bets exactly like the one at sportsbook X:
| Bets placed | Expected profit | Chance you’re still behind |
|---|---|---|
| 100 | +$500 | about 34% |
| 500 | +$2,500 | about 18% |
| 1,000 | +$5,000 | about 10% |
| 5,000 | +$25,000 | under 1% |
That’s with a real, correctly measured 5% edge. In practice the fair probability is an estimate, so your true edge is less certain than this. Judge your betting by whether you consistently get good prices, not by last week’s results.
Why +EV prices exist, and why they don’t last
Sportsbooks set and move thousands of prices at once. Some react to news or sharp action more slowly than others, and some shade prices to attract customers. For a few minutes a book can be noticeably out of line with the market. That gap is the +EV opportunity, and it usually closes as the book catches up.
- Prices move. Check the price is still there before you bet; the edge you saw a minute ago may be gone.
- Books limit winners. Many sportsbooks cut the maximum stake of customers who consistently beat their prices.
- Small edges need volume. A 3–5% edge only matters over hundreds of bets, which is why bet sizing matters as much as bet selection.
How much to stake on a +EV bet
Even a good bet can be too big. The Kelly criterion sizes each bet in proportion to its edge, and most bettors stake only a fraction of what full Kelly suggests to keep the swings survivable. You can try both with the expected value calculator and the Kelly calculator.
The short version
- EV % = win probability × decimal odds − 1.
- The best estimate of win probability is a sharp, no-vig price.
- The same bet can be +EV at one book and −EV at another, so compare prices.
- Expect long losing stretches even with a real edge, and size bets so you can ride them out.
The Smart Lines is an analytics tool: we don’t take bets or place them for you. Use the numbers with your own judgment, and only bet what you can afford to lose.