Quick definition
The probability-weighted average outcome of a trade — win probability multiplied by average win, minus loss probability multiplied by average loss. Expected value is the honest one-number summary of edge.
The formula, and its trap
EV = (P(win) × avg win) − (P(loss) × avg loss). The trap is that traders reliably overestimate P(win) and underestimate the tail — a credit spread that pays $30 with a $170 max loss needs a very high win rate to be positive EV, and small overestimation of win probability flips the sign.
EV and POP are not the same
A high probability of profit says nothing about the size of the profit or the size of the loss. Iron condors often show attractive POP but modest EV — the loss side is bounded but painful. A directional debit trade can show low POP and still be positive EV if the payoff on the win side is asymmetric.
How Treeova uses it
EV is a first-class input to Conviction Scoring. Agents on Treeova can be constrained to only take positive-EV setups by policy, and the Adaptive Risk Engine tracks realized vs modeled EV per strategy over time — a strategy whose realized EV drifts negative for a rolling window is automatically flagged for review.