Expected Value Calculator
Is this bet worth placing?
Enter the odds, your estimated win probability, and your stake. The calculator shows your edge, expected value per bet, and projected return over 100 bets — with the full formula so every number is verifiable.
Calculator inputs
Negative = favourite. Positive = underdog.
Enter a valid American odds value (not 0).
Your model's estimate — not the implied probability in the odds (1–99).
Enter a win probability between 1 and 99.
Leave blank to see percentages and ratios only.
Results
Enter the odds and your win probability,
then click “Calculate expected value”.
The formula explained
What is expected value in sports betting?
Expected value (EV) is the average outcome of a bet if it were placed an infinite number of times. A positive EV bet returns more than you risk over a large enough sample. A negative EV bet does the opposite. It is the single most important concept in systematic betting.
Every bet you place has an expected value, whether you calculate it or not. Bookmakers set their lines so that the implied probabilities sum to more than 100% — the overround, or vig. This means the default EV on any randomly selected bet is negative.
Positive expected value only exists when your estimated probability of winning exceeds the bookmaker's implied probability at the offered odds. That gap is your edge. Without an independent probability estimate, you cannot know whether any bet is +EV or −EV.
EV does not predict the outcome of any individual bet. A +EV bet loses sometimes. A −EV bet wins sometimes. EV tells you what happens over a large sample of similar bets — which is the only timeframe that matters for a systematic betting approach.
Expected value formula
EV = (p × W) − (q × L)- EV = expected value per unit staked
- p = your estimated win probability
- W = net profit per unit on a win (decimal odds − 1)
- q = probability of losing (1 − p)
- L = stake lost on a loss (typically 1 unit)
A positive EV result does not guarantee profit on any individual bet or even over a short run. Sports betting involves variance. The EV framework is meaningful only when applied consistently across a large sample — typically 500+ bets for the results to approach the expected average.
Scenario: NFL game, odds −110 (American). Your model estimates a 57% win probability. Stake: $110.
−110 → 100/110 + 1 = 1.909Net win per unit (W):
1.909 − 1 = 0.909p = 0.57 | q = 0.43 | L = 1EV = (0.57 × 0.909) − (0.43 × 1)EV = 0.518 − 0.43 = +0.088Scenario: Same −110 odds, but your win probability is 50% (below the 52.38% break-even).
EV = (0.50 × 0.909) − (0.50 × 1)EV = 0.455 − 0.50 = −0.045Break-even reference
Break-even win rate by odds
These are the win rates required to break even at each set of odds — before any edge is generated. Your estimated win probability must exceed this figure for the bet to have positive expected value.
| American odds | Decimal odds | Break-even win rate | At 55% win rate | At 50% win rate |
|---|---|---|---|---|
| +200 | 3.00 | 33.33% | +EV Edge: +21.7pp | +EV Edge: +16.7pp |
| +150 | 2.50 | 40.00% | +EV Edge: +15.0pp | +EV Edge: +10.0pp |
| +110 | 2.10 | 47.62% | +EV Edge: +7.4pp | +EV Edge: +2.4pp |
| -100 | 2.00 | 50.00% | +EV Edge: +5.0pp | Break-even |
| -110 | 1.909 | 52.38% | +EV Edge: +2.6pp | −EV Gap: −2.4pp |
| -120 | 1.833 | 54.55% | +EV Edge: +0.5pp | −EV Gap: −4.6pp |
| -130 | 1.769 | 56.52% | −EV Gap: −1.5pp | −EV Gap: −6.5pp |
| -150 | 1.667 | 60.00% | −EV Gap: −5.0pp | −EV Gap: −10.0pp |
| -200 | 1.500 | 66.67% | −EV Gap: −11.7pp | −EV Gap: −16.7pp |
pp = percentage points of edge or gap relative to break-even. Edge columns assume a flat win rate across all odds; real edge is bet-specific.
FAQ
Frequently asked questions
What does positive expected value mean in sports betting?
A positive expected value (positive EV, or +EV) bet is one where your estimated probability of winning is higher than the probability implied by the bookmaker's odds. Over a large sample, +EV bets produce a profit. A single +EV bet can still lose — EV is a long-run average, not a prediction of any individual outcome.
How do I get an accurate win probability estimate?
Your win probability must come from an independent source — not from the bookmaker's odds you are evaluating. Common methods include: stripping the vig from sharp-market odds (Pinnacle, Circa), using a statistical model calibrated to historical results, or comparing multiple independent sportsbooks to find a consensus. If you use the implied probability of the odds you are evaluating, the EV calculation is circular and produces zero edge by definition.
What is the break-even win rate for −110 odds?
At −110 American odds (1.909 decimal), you need to win 52.38% of bets to break even before generating positive expected value. This is the standard vig on most point spread and totals markets in the US. Winning exactly 50% of bets at −110 produces a −4.5% expected loss per bet — not a break-even result.
How many bets do I need to confirm positive EV?
A meaningful sample requires at minimum 500 bets to begin separating edge from variance, and 1,000+ to approach statistical confidence at a 5% edge. Smaller samples are dominated by luck. A 10-bet or 50-bet winning run tells you almost nothing about whether your process is genuinely +EV. The EV guide includes a sample size table by edge level.
What is the difference between EV and ROI in sports betting?
Expected value is a pre-bet calculation based on probability and odds. ROI (return on investment) is a post-bet measurement of actual results. A positive EV process should produce positive ROI over a large sample, but short-term ROI can diverge significantly from EV due to variance. Use EV to evaluate individual bets before placing them; use ROI to track whether your overall process is working over time.
Should I use expected value or Kelly Criterion for bet sizing?
These tools answer different questions. The EV Calculator tells you whether a bet is worth placing at all. The Kelly Criterion Calculator tells you how much of your bankroll to stake on a bet you have already identified as +EV. A complete decision process uses both: EV to filter bets, Kelly to size them.
Need probability estimates to plug in?
EV calculation requires an independent win probability. ZCode System uses AI and historical data across 80+ parameters for NFL, NBA, MLB, NHL, and soccer — generating the probability estimates this calculator needs as inputs.
Affiliate disclosure: we earn a commission if you sign up via this link, at no extra cost to you. We recommend ZCode because it provides probability-based analysis, not because of commission rate.
Responsible gambling notice. Expected value is a mathematical framework, not a guarantee of profit. Sports betting involves variance — even correctly identified +EV bets lose. Never bet money you cannot afford to lose. If gambling is causing harm: NCPG | BeGambleAware | Gambling Therapy