The formula
EV = p × profit − (1 − p) × stake ROI = EV / stake = p × decimal − 1
- Profit if it wins: $280. Loss if it loses: $100.
- EV = 0.30 × 280 − 0.70 × 100 = $14.00.
- Break-even at +280 is 26.3%, so the edge is 3.7% points.
EV is only as good as p
Change the probability by five points and the same price flips sign:
| Your p | EV per $100 at +280 | ROI |
|---|---|---|
| 22.0% | −$16.40 | -16.4% |
| 25.0% | −$5.00 | -5.0% |
| 26.3% | −$0.06 | -0.1% |
| 28.0% | $6.40 | 6.4% |
| 30.0% | $14.00 | 14.0% |
| 33.0% | $25.40 | 25.4% |
This is why every calculator in the Model Lab asks for — or encourages — an uncertainty on your probability. An edge that disappears inside your uncertainty is not an edge you can rely on.
EV across multiple legs
For independent legs, probabilities multiply and so do decimal prices. The book's margin compounds with every leg, which is why most parlays carry far more margin than a single bet. When legs are correlated — a quarterback's yards and his top receiver's yards — the product rule no longer holds. See the parlay calculator.
EV is a long-run average. It says nothing about the path, the drawdowns, or how many bets it takes before the average shows up — that is what Bankroll & sizing and Simulation are for.