Positive Expected Value (+EV)
Updated May 13, 2026 by Sam Smith
Positive expected value (+EV) is the long-run profit a bet returns when the bettor's estimated probability of winning is higher than the probability implied by the offered odds. It is the mathematical condition that separates profitable sports bettors from losing ones over a large enough sample.
The expanded definition
Every set of odds posted by a sportsbook carries an implied probability — the probability the book is offering at those odds, before factoring in its margin. A +110 underdog implies a 47.6% win probability. If the bettor's model puts the same outcome at 52%, the expected value of a $100 stake is:
(0.52 × $110) − (0.48 × $100) = +$9.20 per $100 staked.
Any single bet at +110 is still 47.6% to lose at the book's price. The +$9.20 is the average return across many independent bets at that same edge. The size of the edge matters more than any single outcome — variance shrinks as the sample grows, and the expectation is what shows up in the bottom line.
Why +EV matters
Sportsbooks profit by pricing every market with a built-in margin. The only way to beat that margin over time is to take bets where the offered price is longer than the outcome's true probability. Recreational bettors try to find that edge by handicapping individual games. Long-term winners use tools that quantify +EV across thousands of markets at once — comparing soft sportsbooks against the sharp-book consensus — and bet the mispriced lines without trying to predict every outcome themselves.
Related terms
- Closing line value (CLV) — the standard scoreboard for whether a bettor is consistently finding +EV.
- No-vig odds — the fair odds implied by a sharp book after removing its margin; the benchmark a +EV bet is measured against.
- Kelly criterion — the bet-sizing formula that translates a known edge into an optimal stake size.
- Hedging — taking the opposite side of an existing position to lock in profit or limit risk; usually reduces expected value in exchange for variance.
Frequently Asked Questions
What is a +EV bet?
A +EV bet is one where the bettor's estimated probability of winning is higher than the probability implied by the sportsbook's odds. The bet has positive expected return per dollar staked, even though any individual wager can still lose. Over a large enough sample, the bankroll grows on average — that's the mathematical definition of beating the market.
Is +EV betting profitable?
Yes, +EV betting is profitable over a sufficiently large sample, provided the bettor's probability estimates are accurate and bet sizing is disciplined. Short-term variance can still produce losing weeks or months. The strategy depends on tracking closing line value and avoiding bets where the edge is smaller than the sportsbook's vig.
How is expected value calculated in sports betting?
Expected value = (probability of winning × profit on a win) − (probability of losing × amount staked). For a $100 bet at +120 odds with a 50% estimated win probability, EV = (0.50 × $120) − (0.50 × $100) = +$10. A positive number indicates a +EV bet; a negative number indicates the book has the edge.
What tools help find +EV bets?
OddsShopper's +EV betting tools surface positive expected value bets automatically by comparing soft-book lines against a sharp-book consensus and computing the no-vig fair odds. Portfolio EV extends this with bet-sizing guidance via a modified Kelly criterion. Manual bettors can replicate the process with a public odds aggregator and a spreadsheet.
Sam Smith
Sam Smith is a writer and editor with Stokastic and OddsShopper. He has been immersed in the world of professional sports data since 2015 while also writing extensively on the NFL for a multitude of blogs and websites. With OddsShopper, Sam looks to blend his sports and editorial expertise with OddsShopper's data to bring you the best betting information possible.
