Positive EV Calculator

Understanding the EV Formula

Expected value (EV) is the average outcome of a bet if you could repeat it infinitely. The formula weights each possible outcome by its probability:

EV = (Probability of Win × Profit if Win) − (Probability of Loss × Loss if Loss)

Example:

• Stake: $100
• Odds: +150 (decimal 2.50)
• True win probability: 45%

Calculation:

• Profit if win: $100 × (2.50 − 1) = $150
• Loss if loss: $100
• EV = (0.45 × $150) − (0.55 × $100) = $67.50 − $55 = $12.50

This bet has +$12.50 EV, meaning you'd profit an average of $12.50 per $100 wagered over many trials. Your EV per dollar is $12.50 / $100 = $0.125 (12.5% edge).

Positive vs. Negative EV

+EV bets: Expected value is positive. Over many trials, you profit. This is the goal of all sharp bettors.

−EV bets: Expected value is negative. Over many trials, you lose. All standard sportsbook bets are −EV due to vig unless you find mispriced lines.

Neutral EV: Expected value is exactly zero (breakeven). Rare in practice, but useful for hedging or arbitrage.

The key insight: Even a small +EV edge (2-5%) is highly profitable when bet consistently with proper bankroll management. Conversely, even a small −EV disadvantage (the typical 4-5% vig) guarantees long-term losses.

The Role of Variance

EV tells you the average outcome, but variance describes the spread of actual results around that average. High variance means you'll experience larger swings—both winning and losing streaks—even with positive EV.

Example of variance:

• You make 100 bets with +5% EV ($100 stake each)
• Expected profit: 100 × $5 = $500
• Possible outcomes due to variance: −$200 to +$1,200

Even with an edge, you can lose over small samples. This is why bankroll management and bet sizing are critical—variance can wipe out your bankroll before EV has time to materialize if you're betting too aggressively.

Standard deviation measures variance. For a single bet with probability p and stake S, the standard deviation is approximately:

σ ≈ S × √(p × (1 − p))

For a 50% probability bet with $100 stake: σ ≈ $100 × √(0.5 × 0.5) ≈ $50. This means your actual result will often fall within ±$50 of the expected value.

How to Find +EV Opportunities

To calculate EV, you need two inputs: the sportsbook's offered odds and the true win probability. Finding +EV bets means identifying situations where the sportsbook's implied probability is lower than the true probability.

Common methods:

• No-vig comparison: Remove vig from sportsbook odds to find fair odds, then compare to other books or your own models
• Line shopping: Compare odds across multiple sportsbooks—if Book A has Team X at +120 and Book B has them at +140, Book B offers more value
• Statistical models: Build predictive models (Elo ratings, Pythagorean expectation, advanced metrics) to estimate true win probability
• Market inefficiencies: Exploit public bias (overvalued favorites), stale lines (slow to react to news), or mispriced props (books less sharp on player props)

The most reliable +EV strategy combines multiple approaches: use no-vig odds as a baseline, refine with your own models, and line-shop to maximize value.

Bankroll Management & Bet Sizing

Finding +EV bets is only half the battle—you also need to size your bets correctly to survive variance and maximize long-term growth. The Kelly Criterion is the mathematically optimal bet sizing formula:

f* = (b × p − q) / b

Where:

• f* = fraction of bankroll to bet
• b = decimal odds − 1 (net payout per dollar)
• p = true win probability
• q = 1 − p (loss probability)

Example:

• True win probability: 55%
• Odds: +110 (decimal 2.10, so b = 1.10)
• f* = (1.10 × 0.55 − 0.45) / 1.10 = 0.145 / 1.10 ≈ 0.132 (13.2% of bankroll)

Most professional bettors use fractional Kelly (25-50% of full Kelly) to reduce variance and account for estimation errors in win probability. For the above example, half-Kelly would suggest betting 6.6% of your bankroll.

Never bet more than Kelly recommends—overbetting dramatically increases risk of ruin even with +EV bets.

Common Mistakes When Evaluating EV

1. Using implied probability instead of true probability

If you input the sportsbook's implied probability (from their odds) as your "win probability," the EV will always be negative due to vig. You must use a true probability estimate from no-vig odds, models, or sharp books.

2. Ignoring variance and bankroll constraints

A bet with +5% EV is great, but if you bet 50% of your bankroll on it, you risk going broke during a losing streak. Always size bets according to bankroll and edge size.

3. Chasing +EV without proper data

If your win probability estimate is wrong by even 2-3%, a perceived +EV bet can actually be −EV. Always validate probability estimates with multiple sources (models, sharp book consensus, historical data).

4. Mistaking short-term results for EV validation

Winning 3 out of 5 bets doesn't prove you have an edge—that's well within normal variance. You need hundreds of bets to validate a +EV strategy. Track your bets with Closing Line Value (CLV) to assess long-term edge.