Expected Value in Sports Betting: Formula and Examples

Expected value (EV) in sports betting is the average amount a bet wins or loses per wager if it were repeated many times at the same price and the same true win probability. For a bet that risks a stake to win a profit, EV = (probability of winning × profit) − (probability of losing × stake). At -110, a bet that truly wins 50% of the time has an EV of -$5.00 per $110 risked, which is about -4.55% of the stake.

The result depends on two inputs: the price, which is printed on the line, and the true probability, which is never printed anywhere and can only be estimated. Because the price includes the operator’s margin, a bet needs a true win probability above the break-even point before its EV turns positive. At -110 that threshold is 52.38%.

This guide gives the EV formula with every symbol defined, works through -110 and +150 examples with hypothetical win probabilities, shows how EV changes as the probability changes, and explains why an average says little about any short run of bets. No line here is a pick or a prediction.

What Expected Value Means for a Single Bet

Think of a bet as a small business transaction with two outcomes. You either win a profit or lose your stake, and each outcome has a probability. Expected value weights each outcome by how likely it is, then adds the results. It is a long-run average, not a forecast of the next bet.

A bet is called positive EV when its average result is above zero and negative EV when it is below zero. Positive EV requires a true probability above the break-even probability, which is 1 ÷ D at decimal odds D. Since each price embeds a margin (see overround), the true probability would have to be better than the market’s own implied estimate.

That is a demanding condition, and it is worth stating plainly: the true probability is an estimate, not a known number. Two people can compute different EVs for the same line simply because they hold different estimates. The calculation is exact; the input is not.

EV also differs from the result of any one bet. A -110 bet resolves to either +$100 or -$110, and the average of -$5.00 is a value it can never actually produce. The average only appears across many repetitions, which is the point of the law of large numbers.

The Sports Betting EV Formula

Write the stake as S, the profit if the bet wins as W, and the probability of winning as p. The probability of losing is then 1 − p.

For a result per $1 staked, use decimal odds D, where profit per $1 is D − 1:

where:

p = the true probability the bet wins (an estimate).
W = the profit paid if it wins.
S = the amount risked.
D = decimal odds, equal to 1 + W ÷ S.
EV = the average result per bet, in the same units as W and S.

The second form follows from the first. Total return is D per $1 when the bet wins and 0 when it loses, so the expected return is p × D, and subtracting the $1 staked gives p × D − 1. At -110, D = 1 + 100 ÷ 110 ≈ 1.9091, so the break-even probability is 1 ÷ 1.9091 ≈ 52.38%.

These formulas assume a single bet with two outcomes, no push (tie), and a stake that is returned only on a win. Pushes, fees and alternative payout rules change the numbers and must be added as extra outcomes.

Worked Example: A Hypothetical -110 Bet

Suppose a bet is priced at -110: risk S = $110 to win W = $100. Compute EV at two different estimated win probabilities.

Case 1, p = 50%.

Step 1. Win part: 0.50 × $100 = $50.00.

Step 2. Loss part: 0.50 × $110 = $55.00.

Step 3. EV = $50.00 − $55.00 = -$5.00 per bet.

Step 4. As a share of stake: -5.00 ÷ 110 ≈ -4.55%.

Case 2, p = 55%.

Step 1. Win part: 0.55 × $100 = $55.00.

Step 2. Loss part: 0.45 × $110 = $49.50.

Step 3. EV = $55.00 − $49.50 = +$5.50 per bet, or +5.00% of stake.

Check with the second formula: 0.55 × 1.9091 − 1 ≈ 0.0500. A five-point change in the estimated probability swung the EV by $10.50, which is why the quality of the probability estimate matters far more than the arithmetic.

How EV Changes With Probability and Price

Each percentage point of win probability is worth $2.10 on a $110 bet at -110, because the gap between winning ($100) and losing (-$110) is $210. EV rises in a straight line with the probability, crossing zero at 52.38%.

The same method works for any price. A hypothetical +150 bet risks $100 to win $150, so D = 2.50 and the break-even probability is 1 ÷ 2.50 = 40%. At a true probability of 45%, EV = 0.45 × $150 − 0.55 × $100 = $67.50 − $55.00 = +$12.50 per $100 risked. At 38% it would be 0.38 × $150 − 0.62 × $100 = $57.00 − $62.00 = -$5.00.

Averages hide swings. A -110 bet at p = 50% has a standard deviation of about $105 per bet, so over 100 such bets the expected total is -$500 while the standard deviation of the total is about $1,050. As a rough normal approximation, about 95% of 100-bet totals fall within two standard deviations, roughly -$2,600 to +$1,600. The approximation is imperfect, but it shows why a good or bad run proves little. The size of a stake against those swings is a separate question, discussed in the Kelly criterion guide.

Common Mistakes With Betting EV

The most common error is treating the implied probability as the true probability. A -110 price implies 52.38%, but that figure already includes the margin. If an estimate equals the implied probability, EV is exactly zero, so any positive EV needs an estimate above it.

The second is reading positive EV as a likely win. A bet with +5.00% EV still loses 45% of the time in the example above. EV describes the average over many bets, not the next outcome.

The third is using a probability from a small sample. Ten wins in fifteen bets does not establish a 67% win rate; the sampling error at that size is large enough to cover the entire range between a losing and winning edge.

The fourth is ignoring pushes and fees. Both alter the outcome set, and the EV formula must include them as separate outcomes with their own probabilities.

Quick Reference and Check Your Answer

Check the result against the break-even point: if p is above 1 ÷ D, EV must be positive, and if it is below, negative. Then run the second formula, p × D − 1, and confirm it equals the dollar EV divided by the stake. Always state the rounding and the assumed probability next to any EV figure.

Related Concepts and Next Steps

The general method for any bet, including casino bets, is set out in the expected value formula guide. To find the probability a price needs, use the break-even win rate calculation, and to see how the margin inside a price is built, read about overround.

It is also worth noting the contrast with casino games. In standard casino bets the payout is set below fair odds, so EV is negative for the player on every bet and no stake pattern changes that. In betting markets any positive result depends entirely on an uncertain probability estimate, and the margin works against it.