Expected Value Calculator
Expected Value (EV) is the mathematical foundation of profitable sports betting. A +EV bet is one where the odds you're receiving are better than the true probability of the outcome — over enough repetitions, these bets make money. A -EV bet is a tax on overconfidence. Use this calculator to instantly evaluate any wager before you place it.
What Does EV Tell You?
EV converts your probability estimate and the bookmaker's odds into a single number: the average amount you'll win or lose per unit wagered if you placed this bet many times under identical conditions.
EV Formula:
EV = (Your Probability × Profit on Win) − (Loss Probability × Stake)
In its most practical form:
EV = (P × (Odds − 1) × Stake) − ((1 − P) × Stake)
A positive EV (+) means the bet is profitable over time. A negative EV (−) means the bookmaker's margin is working against you. The size of the EV (as a % of stake) tells you how strong the edge is — a +5% EV is significantly more attractive than a +0.5% EV.
The Calculator
Worked Examples
Example 1: Premier League — Liverpool to Win
You analyse Liverpool vs. Everton and estimate Liverpool have a 60% chance of winning. The bookmaker offers odds of 2.00 (implied probability 50%). You plan to stake €100.
- Your probability: 60%
- Implied probability: 50%
- EV = (0.60 × (2.00 − 1) × 100) − (0.40 × 100) = (0.60 × 1.00 × 100) − 40 = 60 − 40 = +€20
- EV as % of stake: +20%
- Verdict: Strong +EV bet. This is worth taking.
Example 2: NBA — Lakers vs. Warriors Spread
You estimate the Lakers have a 52% chance of covering -5.5. Sportsbook offers odds of 1.91 (implied probability 52.4%). Stake: €100.
- Your probability: 52%
- Implied probability: 52.4%
- EV = (0.52 × (1.91 − 1) × 100) − (0.48 × 100) = (0.52 × 0.91 × 100) − 48 = 47.32 − 48 = −€0.68
- EV as % of stake: −0.68%
- Verdict: Small -EV. The odds aren't in your favour. Pass or find a better line.
Example 3: Tennis — Underdog with Big Odds
You're betting on a tennis player at odds of 5.50. You estimate they have a 25% chance of winning (based on head-to-head data, surface records, and recent form). Stake: €50.
- Your probability: 25%
- Implied probability: 18.2%
- EV = (0.25 × (5.50 − 1) × 50) − (0.75 × 50) = (0.25 × 4.50 × 50) − 37.50 = 56.25 − 37.50 = +€18.75
- EV as % of stake: +37.5%
- Verdict: Significant +EV. Despite lower win probability, the generous odds make this a profitable bet if your 25% estimate is accurate.
How to Estimate Your Own Probability
The EV calculator is only as good as your probability estimate. If your estimate is wrong, the EV output is meaningless. Developing accurate probability estimates is the core skill of sports betting. Here's how sharp bettors approach it:
- Statistical models: The most rigorous approach uses historical data, matchup stats, and predictive algorithms to generate probability estimates. Even simple models (e.g., Poisson distribution for soccer goals) outperform gut feeling significantly.
- Form analysis: Recent performance, home/away splits, injury status, head-to-head records. This is the minimum baseline for any bet.
- Gut + calibration: Intuition informed by experience. The key is calibration — track how often outcomes you estimated at X% actually occurred. If you said 60% thirty times, did they happen roughly 18 times? Calibration corrects overconfidence.
- Line shopping as a signal: If one sportsbook offers significantly better odds than another, that line movement may reflect information you're missing. Compare across books before dismissing a price.
Limitations of EV
EV is a powerful tool, but it has important limitations:
- EV doesn't predict single results. A +20% EV bet can still lose. EV only describes the expected average over many repetitions. Never use a single EV calculation to justify recklessly large stakes. Once you've identified a +EV bet, use Kelly Criterion staking to determine the optimal amount to wager — sizing bets proportionally to your edge rather than betting on instinct.
- Probability estimates drive everything. Bad inputs = bad outputs. If your probability assessment is systematically biased, your EV calculations will be systematically wrong.
- Correlated bets can distort results. If you bet both the over and the over/under in the same game, the outcomes aren't independent — your EV calculations assume they are.
- Market efficiency matters. In highly liquid markets (Premier League, NFL, NBA), bookmaker odds are very efficient. Finding +EV requires genuine information advantage, not just different assumptions. In less-efficient markets (lower leagues, niche props), EV opportunities are more common.
Use the EV calculator consistently as part of a disciplined, systematic approach. Track every bet, compare your pre-bet probability estimates to actual results over time, and let the data reveal whether your process has a genuine edge.