Expectancy
Definition
Expectancy is the average profit (or loss) per trade, computed as (win rate × average win) − (loss rate × average loss). Positive expectancy is mandatory for any viable trading system. A strategy with positive expectancy will make money over many trades regardless of short-term variance; a strategy with negative expectancy cannot be saved by money management.
Formula
E = (P_{win} \cdot \overline{W}) - (P_{loss} \cdot \overline{L})E = (probability of win × average win) − (probability of loss × average loss)
In-depth: Expectancy
Expectancy is the bedrock metric of any trading system evaluation. Without positive expectancy, no money management technique can produce sustainable profits — variance averages out over time, and a negative-expectancy strategy approaches ruin asymptotically.
Formal definition (dollar terms): E = (P_win × avgWin$) − (P_loss × avgLoss$)
Formal definition (R-multiple terms): E_R = (P_win × avgWinR) − (P_loss × 1R), where 1R is the initial risk per trade and avgWinR is the average win expressed as multiples of initial risk.
The R-multiple version is preferred for strategy comparison because it normalises for position sizing. Two strategies with E = $50 per trade may differ in capital efficiency: one risks $100 per trade (E_R = 0.5), the other risks $1000 per trade (E_R = 0.05). The first is fundamentally more efficient.
Practical bands for forex EAs: - E_R < 0: losing strategy; no edge - 0 ≤ E_R < 0.1: break-even after costs; difficult to scale - 0.1 ≤ E_R < 0.3: marginal edge; typical of mediocre retail EAs - 0.3 ≤ E_R < 0.5: good edge; sustainable for retail operation - 0.5 ≤ E_R < 1.0: strong edge; uncommon over multi-year live tracks - E_R > 1.0: exceptional; almost always evidence of short tracks, regime favourability, or hidden risk
Example: a scalping strategy with 65% win rate, average win 0.8R, average loss 1.0R. E_R = (0.65 × 0.8) − (0.35 × 1.0) = 0.52 − 0.35 = 0.17. Marginal edge per trade; profitability depends on trade frequency and execution costs.
Key insight: expectancy is preserved across position-sizing choices (dollar amounts scale linearly), but the variance around expectancy depends on position sizing. A Kelly-optimal position size maximises geometric growth rate; aggressive sizing increases variance and can ruin a positive-expectancy strategy through bad luck.