Expected value is the one number that tells you whether a bet is worth making at a given price. This guide walks through the formula with American and decimal odds, shows worked examples, and covers the mistakes that make EV numbers lie.
If you just want the answer for a specific bet, use the free EV calculator.
The EV formula
For a bet with stake S:
where p is the true probability of the bet winning. It is cleaner in decimal odds (D), where profit = S × (D − 1):
and the edge (EV per $1 staked) is simply:
That last line is all you need. Multiply the true win chance by the decimal price and subtract one.
Converting American odds to decimal
- Positive odds (+150): D = 1 + 150/100 = 2.50
- Negative odds (−150): D = 1 + 100/150 = 1.667
Our odds converter does this instantly, and the American odds guide explains the logic.
Worked example 1: an underdog
A book offers +165 on an underdog. You estimate its true chance at 40%.
- D = 2.65
- Edge = 0.40 × 2.65 − 1 = 0.06 → +6%
- On a $50 bet: EV = $50 × 0.06 = +$3.00
Worked example 2: a favorite
A book offers −120 (D = 1.833). True chance: 52%.
- Edge = 0.52 × 1.833 − 1 = −0.047 → −4.7%
Even though the team is more likely to win than lose, the price is too short. Favorites are not "safe" bets; they are just expensive ones.
Worked example 3: a player prop
Over 6.5 strikeouts at +105 (D = 2.05). Fair probability of the over from a sharp market: 51.5%.
- Edge = 0.515 × 2.05 − 1 = +5.6%
Where does "p" come from?
The formula is trivial. The hard part is an honest estimate of p. You have three choices:
- Your own model. Possible, but most handmade models are worse than the market.
- Gut feeling. This is how most people lose money while believing they are +EV.
- The sharp market. Take a price from a sharp book or exchange, strip out its vig, and use the result as p. This is what nearly every serious +EV bettor does. (How to devig odds.)
Example: the sharp book has −140 / +120. Implied probabilities are 58.33% and 45.45%, totaling 103.8%. Divide each by 1.038 and the fair chances are 56.2% and 43.8%. Now compare those to every other book.
EV in dollars vs EV in percent
Use the percentage to decide whether to bet and the dollar figure to understand how much you expect to gain. A 2% edge on $500 (+$10 EV) is worth more than a 10% edge on $20 (+$2 EV), but the 10% edge may be suspect. Stake size should come from your bankroll rules, not from EV alone. (Bankroll management.)
Common EV mistakes
- Forgetting the vig. Using the sharp book's raw implied probability instead of the devigged one overstates the win chance of both sides. Always remove the margin first.
- Using a stale fair line. If the sharp price moved five minutes ago and you compare against the old number, your "edge" is just the book being correct.
- Ignoring limits and voids. An obvious error line (+900 on a −300 favorite) is often voided. The EV of a voided bet is zero.
- Adding up EV across correlated bets. Two bets on the same game are not independent, so their risk does not diversify.
Quick reference table
| Decimal price | Break-even probability | Edge if true chance is 55% |
|---|---|---|
| 1.80 (−125) | 55.6% | −1.0% |
| 1.91 (−110) | 52.4% | +5.0% |
| 2.00 (+100) | 50.0% | +10.0% |
| 2.10 (+110) | 47.6% | +15.5% |
Frequently asked questions
What is a good EV percentage in sports betting?
On main markets at legal US books, 1–4% is a realistic, trustworthy edge. Props and alternate lines can be higher. Edges above about 10% are often stale or erroneous lines.
Is EV the same as ROI?
EV is what you expect to earn before the bet settles. ROI is what you actually earned. Over a large sample, a bettor's ROI should drift toward the average EV of the bets they placed.
Do I need to calculate EV by hand?
No. The math is a single multiplication, but finding fair odds across every book and market is tedious. An odds screen with +EV detection does it continuously.