The Central Idea

Every bet you place should have positive expected value. This sounds obvious — who would intentionally make a negative expectation bet? — but most recreational bettors do exactly that, repeatedly, without realizing it. Understanding expected value (EV) changes how you see every market.

Expected value is the average outcome if you could repeat a bet thousands of times. A +EV bet wins money over time. A -EV bet loses money over time. It is that simple, and that ruthless.

How to Calculate EV

The basic formula for expected value in betting:

EV = (Probability of Win × Profit if Win) - (Probability of Loss × Stake)

Example: You estimate a team has a 55% chance to cover the spread at -110 odds. You bet $110 to win $100.

EV = (0.55 × $100) - (0.45 × $110)
EV = $55 - $49.50 = $5.50

Your expected value is $5.50 on a $110 stake, or +5.0% expected return. Over many similar bets, you expect to earn 5% of your stake on average.

The same calculation can be expressed as a percentage:

EV% = (Your Estimated Probability × Decimal Odds) - 1

For the same example: (0.55 × 1.909) - 1 = 1.050 - 1 = 0.050 = 5.0%

The EV Calculator does this on every bet you log — plug your estimated probability and the offered price in, it returns EV in both dollar and percentage form.

Where Does Your Probability Estimate Come From?

The entire EV framework depends on one critical input: your estimated probability. If your probability is wrong, your EV calculation is meaningless. Garbage in, garbage out. This is why betting is hard.

Sources of probability estimates:

  • Statistical models: Build or use existing models that output probability forecasts. These might incorporate team ratings, player statistics, pace metrics, and historical data.
  • Market reading: Compare lines across multiple books. If Pinnacle has a team at -130 and a recreational book has them at -110, the market is telling you something about the true probability.
  • Domain expertise: Deep knowledge of a sport or league can identify factors models miss — injuries the market hasn't fully priced, motivational edges, schedule spots.
  • Derivative markets: First half lines, team totals, and alternative spreads contain information about the full game that might not be fully incorporated.

The Vig Is Part of the Calculation

When calculating EV, you must account for the vig. If you naively use the book's raw implied probability as "the market's estimate," you'll systematically underestimate your edge. The book's line already includes margin against you.

Proper EV calculation uses devigged probabilities as your baseline. Remove the book's margin first using the No-Vig Calculator, then compare your estimate to the true market probability. The difference — your edge minus the vig — is what you're actually capturing.

Example: A moneyline at -140 / +120.
Raw implied: 58.3% and 45.5% (sum = 103.8%)
After proportional devigging: 56.2% and 43.8%

If your model estimates 60% for the favorite, your edge is 60% - 56.2% = 3.8 percentage points. That's smaller than the naive comparison of 60% - 58.3% = 1.7%, but it's the correct number.

"You're not just competing against the game. You're competing against the bookmaker's margin. Your edge must exceed both."

Minimum Edge Thresholds

Not every positive EV bet is worth making. A +0.5% EV bet is technically positive, but the variance and execution costs may swamp the tiny edge. Most professionals apply a minimum edge threshold — typically 2-5% — before placing a bet.

This threshold should depend on:

  • Your confidence in your estimate: Model outputs with high uncertainty need larger edges to compensate.
  • Market liquidity: Can you get the full amount down at the quoted price?
  • Bet sizing constraints: Very small edges require large sample sizes to realize. Do you have the bankroll and patience?
  • Execution costs: If you're paying -115 instead of -110 at your available book, that may eliminate a marginal edge.

Edge + Time = Profit

Expected value compounds. A bettor placing 1,000 bets per year at +3% EV will, over time, earn approximately 3% return on turnover. With $1 million in annual turnover, that's $30,000 in expected profit. With $10 million, it's $300,000.

The math is unforgiving but also generous. If you genuinely have an edge and you size correctly, the market will pay you over time. The challenge is maintaining that edge as the market evolves, as books limit you, and as variance tests your psychological resolve.

Testing Your EV

The hardest part of EV betting is knowing whether your probability estimates are actually accurate. You cannot observe the "true" probability of a sporting event. You can only observe outcomes.

Track your predictions against market prices in the Bet Tracker — every bet you log captures the closing line and surfaces in the CLV Tracker. If you consistently identify +EV bets and your actual results converge toward your expected returns over a large sample (500+ bets), you likely have a genuine edge. If your results systematically underperform your EV estimates, your probability model is overconfident.

Calibration is everything. A well-calibrated model that slightly underestimates its edge will still profit. An overconfident model that overestimates its edge will eventually fail, no matter how good the underlying analysis.