Expected value (EV) in sports betting explained
By the Match Tail team ·
Expected value, or EV, is the one number that separates a good bet from a bad one before the game is played. It does not tell you whether a bet will win. It tells you whether the price is worth taking. This guide shows the EV formula, how the sportsbook margin fits in, how to remove it, and why a good bet can still lose.
What is expected value in sports betting?
Expected value is the average profit or loss a bet would make per bet if you could place it many times at the same odds. A positive EV bet makes money on average. A negative EV bet loses money on average. EV depends on two things: the price you get and the real chance of winning.
The formula is short. EV = (chance of winning × profit if it wins) − (chance of losing × stake). The profit comes from the odds. The chance of winning is your own estimate, or a fair estimate taken from the market, which we cover below.
A bet with positive EV can lose, and a bet with negative EV can win. EV is about the price, measured over many bets, not about the next result.
How do you calculate the EV of a bet?
Multiply the profit by your chance of winning, then subtract the stake times your chance of losing. For $100 at +150 with a 45% chance of winning, EV is 0.45 × 150 − 0.55 × 100 = +$12.50 per bet. At a 38% chance, the same bet has an EV of −$5.00.
| Win chance | Calculation | EV per bet |
|---|---|---|
| 35% | 0.35 × 150 − 0.65 × 100 | −$12.50 |
| 40% | 0.40 × 150 − 0.60 × 100 | $0.00 |
| 45% | 0.45 × 150 − 0.55 × 100 | +$12.50 |
| 50% | 0.50 × 150 − 0.50 × 100 | +$25.00 |
The break-even point is 40%, which is exactly the implied probability of +150: 100 ÷ (150 + 100) = 40%. That is the general rule. A bet has positive EV when your chance of winning is higher than the implied probability of the odds. Our guide on how to read American betting odds shows how to find the implied probability of any price.
$110 to win $100, true chance 50%: 0.50 × 100 − 0.50 × 110 = −$5.00
As a share of the stake: −5.00 ÷ 110 = −4.55%
True chance 55%: 0.55 × 100 − 0.45 × 110 = +$5.50
What is the vig, and how does it affect EV?
The vig, or juice, is the sportsbook’s margin built into the odds. At -110 on both sides of an even game, each side implies 52.38%, adding up to 104.76%. If the game really is a coin flip, both bets have negative EV. The vig is why a bettor who wins half of their -110 bets still loses money.
One bettor stakes $110 on each side: $220 taken in
The winner is paid $110 + $100 = $210
Kept: 220 − 210 = $10, so 10 ÷ 220 = 4.55% of all money staked
Same result from the odds: 1 − 1 ÷ 1.047619 = 4.55%
That 4.55% is the house edge on a balanced -110 market. To beat it, you need to win more than 52.38% of -110 bets, not just more than half.
How do you remove the vig to find fair, no-vig odds?
Convert both sides to implied probability, add them up, then divide each side by the total. The results add up to 100% and estimate the fair chance of each side. For a -150 favorite against a +130 underdog, the fair chances are 57.98% and 42.02%, which convert to fair odds of -138 and +138.
| Side | Odds | Implied | No-vig chance | Fair odds |
|---|---|---|---|---|
| Favorite | -150 | 60.00% | 57.98% | -138 |
| Underdog | +130 | 43.48% | 42.02% | +138 |
| Total | 103.48% | 100.00% |
Fair favorite: 60.00 ÷ 103.48 = 57.98%. Fair underdog: 43.48 ÷ 103.48 = 42.02%
Fair odds for the favorite: −(57.98 ÷ 42.02) × 100 = -138
Fair odds for the underdog: (57.98 ÷ 42.02) × 100 = +138
Another book offers the underdog at +150
Exact fair chances: 0.6 ÷ (119/115) = 69/119 and (10/23) ÷ (119/115) = 50/119
EV of $100 there: (50/119) × 150 − (69/119) × 100 = 600 ÷ 119 = +$5.04
This proportional method is the simplest way to strip the vig, and it assumes the sportsbook spreads its margin evenly across both sides. Other methods shift more of the margin onto the underdog, so treat a no-vig price as an estimate. It is only as good as the market you took it from.
How can you tell a good bet from a bad one?
A good bet is one where your best estimate of the win chance is higher than the implied probability of the price you can get. Compare the two numbers before every bet. If you have no estimate of your own, compare the price with a fair, no-vig price from another market. If the edge is not there, skip it.
- Write down your win chance before you look at the odds.
- Convert the odds to implied probability.
- Bet only when your chance is clearly higher, not just a point or two.
- Shop for the best price; a better price raises EV on the same pick.
- Note the closing price. If you bet +150 and it closes at +130, the market moved toward your side, from 100 ÷ 250 = 40.00% to 100 ÷ 230 = 43.48% implied.
Regularly beating the closing price is widely treated as a sign that your estimates are good, even during a losing run. The same logic decides between bet types, as in our guide to moneyline vs spread vs total.
Why can a positive EV bet still lose?
A positive EV bet loses whenever the losing outcome happens, and that can be the more likely outcome. A 45% bet at +150 loses 55% of the time. Over ten such $100 bets, the average profit is 10 × $12.50 = $125, yet if the bets are independent you finish behind about a quarter of the time. That is variance.
Expected profit: 10 × (0.45 × 150 − 0.55 × 100) = +$125
Four wins break even: 4 × 150 − 6 × 100 = $0
Treating the ten bets as independent, the win count is binomial (n = 10, p = 0.45)
P(X ≤ 3) = Σ (k = 0 to 3) C(10, k) × 0.45^k × 0.55^(10 − k) = 0.2660 = 26.6%
Chance of losing all ten: 0.55^10 × 100 = 0.25%
Small, steady stakes let the average show up over time. Big stakes on a few good bets can still wipe you out first. Our guide to bankroll management and betting units covers how to size bets for that. Parlays are the clearest case of EV working against you, explained in our parlay odds math guide. If you would rather follow bets than price them, Match Tail lets you copy the bets we place and tells you when to open or close each one.
What else should you know?
What does +EV mean?
+EV means positive expected value: at the odds offered, the bet makes money on average over many repeats, because its real chance of winning is higher than the implied chance.
Is a heavy favorite a safer bet?
It wins more often, but that does not make it a better bet. A -400 favorite breaks even at exactly 400 ÷ (400 + 100) = 80%. It needs to win more than 80% of the time for positive EV, so it can easily be negative EV.
How big an edge is worth betting?
Any positive EV is worth having in theory. In practice your win chance is an estimate, so a tiny edge can disappear if the estimate is slightly off. Bigger gaps between your chance and the implied chance leave more room for error.
Only bet money you can afford to lose. If betting stops being fun, call or text the National Problem Gambling Helpline at 1-800-MY-RESET (1-800-697-3738).