The Expected Value Formula
Expected value (EV) measures the average outcome of a bet placed repeatedly over time. A positive EV means you make money long-run; negative EV means you lose to the house.
Example: +EV bet — $100 on +150 (decimal 2.50) where you estimate 48% win probability
Net profit if win: $100 × (2.50 − 1) = $150
EV = (0.48 × $150) − (0.52 × $100) = $72 − $52 = +$20
EV% = +20% → For every $100 wagered, you expect to earn $20 on average.
Example: −EV bet — $100 on -200 (decimal 1.50) where you estimate 55% win probability
Net profit if win: $100 × (1.50 − 1) = $50
EV = (0.55 × $50) − (0.45 × $100) = $27.50 − $45 = −$17.50
EV% = −17.5% → You lose $17.50 per $100 wagered on average.
Why Most Bettors Lose
The average recreational bettor doesn't think in terms of EV. They pick favorites because they're "safe," chase parlays for the payout, and bet on gut feelings about matchups. All of these lead to negative expected value — and long-run losses.
Sportsbooks are designed to offer -EV bets. Every standard -110 line has 4.76% vig built in. The book doesn't need to be smarter than you on every game — it just needs you to keep taking -EV propositions and the law of large numbers does the rest.
The Only Long-Run Edge Is +EV
Over 1,000 bets, luck evens out. A bettor running at +5% EV will show a profit of roughly $5,000 on $100 average stakes. A bettor at −5% will lose the same amount. Short-term variance is noise — EV is signal.
How to Find +EV Bets
- Build or use a model — Estimate true win probabilities from historical data, team stats, matchup trends, and situational factors. If your probability exceeds the book's implied probability, the bet is +EV.
- Remove the vig first — Compare your estimate against the no-vig fair probability, not the raw posted line. Use the No-Vig Calculator to strip the juice before comparing.
- Shop for the best line — Even a +EV model bet becomes more +EV at better odds. Always take the best available price across sportsbooks.
- Track your EV, not your win rate — A 48% win rate at +200 average odds is more profitable than a 55% win rate at -110. Focus on EV, not record.
Sample Size Is Everything
A +EV bet can and will lose short-term. In a coin-flip with 53% win probability, you'll lose more than you win roughly 35% of the time over 20 flips. Variance is large at short sample sizes. Profitable bettors think in thousands of bets and grade their system on EV, not recent wins and losses.
If your true win probability consistently exceeds the book's no-vig implied probability, you are a profitable bettor — even during losing streaks. The money follows the edge, not the result.
Sibyl Calculates EV on Every Line, Every Day
Our AI models estimate true win probabilities for every game across MLB, NFL, NBA, NHL, WNBA, and Golf — surfacing only the bets with measurable positive edge.
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