Guide · 6 min read
Expected value in sports betting: how to calculate EV
Expected value (EV) is the single most useful number in betting maths: it tells you what a bet is worth on average, not what will happen next. Here is the formula, a worked example, a step-by-step way to calculate it yourself, and the reason a positive EV still says little about your next hundred bets.
Updated 22 October 2026
Contents
EV in one sentence
Expected value is the average profit or loss per unit staked if you could place the same bet under the same conditions a very large number of times. It does not describe the next bet; it describes what a bet is worth on average.
A positive expected value (+EV) means the odds are higher than the probability of the outcome justifies. A negative one (−EV) means you are paying more than the bet is worth. Most bets are −EV, because the bookmaker builds a margin into its prices.
The formula
With p as the probability that your bet wins and decimal odds:
EV = p × (odds − 1) − (1 − p)
The first term is the net win per unit, weighted by the chance of winning; the second is the lost unit, weighted by the chance of losing. Simplified, it becomes the shorter form:
EV = p × odds − 1
An outcome has fair odds of 2.00, so p = 0.5. A bookmaker offers 2.10.
EV = 0.5 × (2.10 − 1) − 0.5 = 0.55 − 0.50 = +0.05, that is +5% per unit staked.
The same outcome at 1.90: EV = 0.5 × 0.90 − 0.5 = −0.05, or −5%.
The odds at which EV is exactly zero are the fair odds, 1 ÷ p. If the offer is above them, EV is positive; below them, negative.
Where p comes from
The formula is easy. The hard part is p. There are three common approaches:
- Fair odds from a sharp market. Take the prices of a bookmaker with a low margin and high limits and remove the margin, as shown in no-vig fair odds. This is the most common method, because such markets absorb a lot of information. Why those markets are more accurate is explained in sharp vs soft bookmakers.
- An average of many bookmakers. The margin-free average across many operators is a usable estimate when no sharp market is available.
- Your own model. For example, one built on goal statistics. It is a lot of work, and a model that is worse than the market only produces bets that look +EV.
A hunch is not a probability. The same example shows how sensitive EV is to errors in p: if the true probability behind odds of 2.10 is not 50% but 48%, EV shrinks to +0.8%. At 47% it is −1.3%. An estimate that is three percentage points off wipes out the whole edge.
EV in percent and in euros
EV in percent applies per unit staked. For the amount in euros, multiply by the stake: EV in € = stake × (p × odds − 1).
| p | Fair odds | Offered | EV in % | EV on €10 |
|---|---|---|---|---|
| 0.50 | 2.00 | 2.10 | +5.0% | +€0.50 |
| 0.50 | 2.00 | 1.90 | −5.0% | −€0.50 |
| 0.60 | 1.67 | 1.75 | +5.0% | +€0.50 |
| 0.25 | 4.00 | 4.40 | +10.0% | +€1.00 |
Over 100 bets of €10 at +5%, that is an expected +€50 on €1,000 of turnover. It is an average over all possible paths, not an amount you will have in your account after 100 bets.
EV is not a result: the spread
Stay with 100 bets of €10 at odds of 2.10 with p = 0.5. Each bet returns either +€11 or −€10. The expectation is +€50, but the standard deviation is about €105.
- In roughly two out of three paths you end somewhere between −€55 and +€155.
- With 47 or fewer winners you are down. The probability of that is about 31%.
- After 1,000 such bets the expectation is +€500 with a standard deviation of about €332. You would still be down in roughly 7% of cases.
So your balance after a few dozen bets tells you almost nothing about whether those bets were +EV. A better early indicator is how your odds compare with the closing price, explained in closing line value. More on losing runs in betting variance, on sizing your money to survive them in bankroll, and on stake size in the Kelly criterion.
Assumptions: independent bets, p known exactly, every bet accepted at the stated odds, no betting fee. A worked example, not a forecast. Real results vary and can be negative.
Calculate EV yourself, step by step
If p comes from fair odds, the calculation gets even shorter, because p = 1 ÷ fair odds:
EV = offered odds ÷ fair odds − 1
- Find the fair odds. For example, from a low-margin market with the margin removed: 2.00.
- Find your effective odds. The offered odds, after any betting fee the bookmaker passes on: 2.10, or 2.10 × 0.95 = 1.995 if 5% is deducted from the payout.
- Divide and subtract 1. 2.10 ÷ 2.00 − 1 = +5%. With the fee: 1.995 ÷ 2.00 − 1 = −0.25%.
- Multiply by the stake. +5% × €10 = +€0.50 expected value.
The Austrian case in step 3 shows why fees matter: a passed-on 5% fee is as big as the entire edge of a typical +EV bet. Details in our guide to the Austrian betting tax.
EV, sure bets and ArbVantage
A sure bet does not need p. Because you cover every outcome, the margin is fixed once all legs are accepted at the shown odds and stand. The risk there lies in execution, not in estimation. Value bets, by contrast, live on EV: you back one outcome because its odds are above the fair price, and you accept the spread. The difference is explained in value betting.
Today ArbVantage finds sure bets, converts free bets and shows middles. Value bets are coming soon.
Frequently asked questions
What does +EV mean?
+EV stands for positive expected value: the offered odds are higher than the fair odds, so higher than the estimated probability justifies. Averaged over a very large number of similar bets, the result would be positive, provided the estimate is right.
Can a +EV bet lose?
Yes, every single one can. A bet at 2.10 with a 50% chance loses every other time. Even after 100 such bets of €10, you are down in about 31% of cases, although the expected value is +€50.
How accurate does the probability p need to be?
More accurate than most people think. At odds of 2.10, a true probability of 47% instead of 50% is enough to turn +5% into about −1.3%. That is why p is usually taken from the margin-free odds of a sharp market rather than from gut feeling.
Does ArbVantage offer value bets?
Not yet. Value bets are coming soon. Today ArbVantage finds sure bets, converts free bets and shows middles.
Sources
- Štrumbelj (2014): On determining probability forecasts from betting odds, International Journal of Forecasting 30(4)
- Clarke, Kovalchik, Ingram (2017): Adjusting Bookmaker's Odds to Allow for Overround, American Journal of Sports Science 5(6)
- Kaunitz, Zhong, Kreiner (2017): Beating the bookies with their own numbers, arXiv:1710.02824
- Unternehmensserviceportal (USP, Austria): Wettgebührenabrechnung
As of October 2026. Probabilities of losing runs are calculated with the binomial distribution.
Betting involves risk, sure bets included: odds change, bets get voided and accounts get limited. Only bet money you can afford to lose. Our responsible gambling page lists free help.
Not betting, legal or tax advice. 18+. As of October 2026. See our disclaimer.