- Choose an Odds Format and enter Bet Odds and Stake.
- Choose a Fair Value Format and enter Fair Odds (or fair probability).
- Optionally enter Bankroll for Kelly sizing.
- Read the output. EV $, EV %, Recommended (¼) Kelly Stake, and Full Kelly Stake.
Expected Value Calculator
An expected value calculator for sports betting. Enter American odds and your estimated true probability to see whether a bet is positive EV.
How to Use This Calculator
What is an expected value calculator?
An expected value calculator for sports betting tells the bettor the average amount they can expect to win or lose per wager over the long run. A positive expected value (+EV) bet is profitable over time. A negative expected value (-EV) bet loses money over time.
Almost every bet placed at a sportsbook is -EV, because the sportsbook bakes a commission (the vig) into the odds. +EV betting is the practice of finding the exceptions and placing only those bets.
Formula
\[
\begin{aligned}
\text{EV} &= (P_{win} \times \text{Win Profit}) - (P_{loss} \times \text{Loss Amount})
\end{aligned}
\]
Worked example
A moneyline is offered at -110 on a $100 bet. The sportsbook is pricing the side at roughly 52.4% implied probability. The bettor estimates the true probability is 55%.
\[
\begin{aligned}
\text{EV} &= (0.55 \times \$90.91) - (0.45 \times \$100) \\[6pt]
&= \$50.00 - \$45.00 = +\$5.00
\end{aligned}
\]
That is a +5% EV bet. Over hundreds of similar bets, the average profit per $100 wagered is $5. Any single bet can still lose. The edge plays out only over volume.
Why +EV matters for sports bettors
Expected value is the foundation of every profitable sports betting strategy. Matched betting, arbitrage, and +EV betting are all applications of the same underlying math: only place bets where the price beats the true probability.
The challenge is determining true probability. For a coin toss it is 50%. For an NFL spread it is much harder. The DarkHorse Odds +EV Bet Finder estimates true probability by comparing the line being bet against the consensus pricing across 50+ sportsbooks. Any time a book offers a meaningfully better price than the market average, the difference is surfaced as a +EV bet.
Start with our Intro to +EV Sports Betting guide. Pair this calculator with the No Vig Calculator to find consensus fair odds and the Kelly Criterion Calculator for proper bet sizing.
Common +EV mistakes
- Confusing one bet with the long run. A +EV bet can still lose. EV is about average outcomes across many bets, not certainty on any single one.
- Overestimating your edge. If your estimated probability is wrong, the EV calculation is wrong. Sharp pricing tools are more reliable than gut estimates.
- Ignoring bet sizing. Even profitable +EV bets can bust your bankroll if you wager too much per bet. Pair this calculator with the Kelly Criterion Calculator for proper sizing.
- Account limits. Consistent +EV betting attracts sportsbook restrictions over time. Read our Don't Get Limited guide for risk management tactics.
Frequently Asked Questions
What is an expected value calculator?
An expected value calculator computes the average return a sports bet will produce over the long run. Inputs are the sportsbook's odds, the bettor's estimated true probability of winning, and the stake. The output is the expected value in dollars and as a percentage of the stake. Positive EV means the bet is profitable over time; negative EV means it is not.
How do you calculate an expected value?
Multiply the probability of winning by the profit on a win, then subtract the probability of losing multiplied by the stake.
\[
\begin{aligned}
\text{EV} &= (P_{win} \times \text{Win Profit}) - (P_{loss} \times \text{Loss Amount})
\end{aligned}
\]
For example, a 55% chance to win $90.91 minus a 45% chance to lose $100 produces an EV of +$5.00.
How do you calculate the EV of a bet?
Convert the sportsbook's American odds to potential profit per dollar staked, estimate the true probability of winning, then apply the EV formula. A $100 bet at -110 with an estimated 55% win probability produces +$5.00 EV. A $100 bet at +200 with an estimated 35% win probability produces +$5.00 EV. The math is identical; only the inputs change.
How do I determine the true probability of a sports bet?
True probability is rarely known exactly. The most reliable estimate comes from the consensus market price across many sportsbooks, with the vig removed. Sharp books like Pinnacle and Circa are widely treated as the closest available proxy. Use the No Vig Calculator to find the consensus fair odds.
What is a good EV percentage to target?
Any positive EV is mathematically profitable in the long run. In practice, most bettors target +2% or higher to overcome modeling error and variance. The higher the EV, the larger the sample size of bets needed to confidently realize that edge.
Can a bet be +EV and still lose?
Yes. Expected value is an average across many trials. Any one bet can lose even if it is mathematically profitable in the long run. Variance is the cost of admission to +EV betting.
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