Expectancy in Trading: The Formula That Predicts Profitability
Expectancy is the closest thing trading has to a crystal ball. It doesn't predict individual trades — nothing can. But it predicts the average outcome over many trades with mathematical precision. A strategy with $85 positive expectancy will, over hundreds of trades, converge toward earning $85 per trade on average. This isn't hope or optimism. It's the law of large numbers applied to trading. Understanding expectancy transforms your relationship with individual trade outcomes: each trade becomes a coin flip in a rigged-in-your-favor game.
The Formula
Expectancy = (Win Rate × Average Win) − (Loss Rate × Average Loss)
Where Loss Rate = 1 − Win Rate
This formula captures everything that matters: how often you win, how much you win, how often you lose, and how much you lose. No other metric integrates all four variables into a single actionable number.
Worked Examples
| Strategy | Win Rate | Avg Win | Avg Loss | Expectancy | Verdict |
|---|---|---|---|---|---|
| Scalper A | 65% | $150 | $200 | +$27.50 | Profitable (barely) |
| Scalper B | 70% | $100 | $300 | −$20.00 | Losing despite 70% wins! |
| Swing Trader | 45% | $800 | $350 | +$167.50 | Profitable |
| Trend Follower | 32% | $2,500 | $500 | +$460.00 | Highly profitable |
Scalper B wins 70% of the time — impressive — but loses money because losses are 3× the size of wins. The trend follower wins only 32% of the time but has the highest expectancy because winners are 5× losers. Expectancy reveals what win rate hides.
Expectancy × Frequency = Income
Expectancy per trade alone doesn't tell you how much money you'll make. Multiply by trade frequency for total expected income:
Expected Monthly Income = Expectancy × Trades per Month
Scalper A: $27.50 × 200 trades/month = $5,500/month
Swing Trader: $167.50 × 15 trades/month = $2,512/month
Trend Follower: $460 × 5 trades/month = $2,300/month
The scalper makes more per month despite the lowest per-trade expectancy because of volume. But higher frequency means higher costs (commissions) and more screen time. The optimal balance depends on your lifestyle and cost structure.
Expectancy Per Dollar Risked
Raw expectancy in dollar terms depends on position size, making cross-strategy comparison difficult. Normalized expectancy solves this by expressing the edge per dollar of risk:
Normalized Expectancy = Expectancy / Average Loss
Using the examples above: Scalper A has $27.50 / $200 = 0.14, meaning every dollar risked returns $0.14 on average. The Trend Follower scores $460 / $500 = 0.92 — each dollar risked returns $0.92. This normalization strips away position size differences and reveals which strategy extracts the most edge per unit of risk. A normalized expectancy above 0.5 is excellent; above 1.0 is exceptional and rare in live trading.
Why Positive Expectancy Isn't Enough
A positive expectancy guarantees long-term profitability — in theory. In practice, three factors can destroy a positive-expectancy strategy:
1. Insufficient capital for drawdowns. A strategy with $85 expectancy will still have losing streaks. If 8 consecutive losses totaling $2,400 wipes out your account before the law of large numbers kicks in, the positive expectancy never materializes.
2. Psychological failure. You stop trading during a losing streak because the pain is too high. The trades you miss during the recovery period are disproportionately profitable (mean reversion from the drawdown).
3. Costs eat the edge. $27.50 expectancy per trade minus $15 in commissions and slippage leaves only $12.50. Costs that seem small as percentages compound into meaningful edge erosion.
Expectancy Decay Over Time
No trading edge lasts forever. Market conditions evolve, volatility regimes shift, and other participants adapt. A strategy with +$85 expectancy in 2022 might show +$40 by 2024 and turn negative by 2026. This gradual erosion — expectancy decay — is the natural lifecycle of every mechanical strategy.
Tracking expectancy on a rolling 3-month or 6-month window reveals degradation before it becomes catastrophic. If your rolling expectancy drops below 50% of its backtest value, the strategy is signaling structural deterioration. At that point, you either re-optimize parameters or retire the strategy entirely.
Connecting Expectancy to the Kelly Criterion
The Kelly Criterion answers a natural follow-up question: given a known expectancy, what fraction of your capital should you risk per trade to maximize long-term growth?
Kelly % = Expectancy / Average Win
For the Swing Trader: $167.50 / $800 = 20.9%. Full Kelly is aggressive, so most practitioners use fractional Kelly — typically 25–50% of the calculated value. The Swing Trader would risk approximately 5–10% per trade. Fractional Kelly sacrifices some growth rate in exchange for dramatically lower drawdowns and a smoother equity curve.
Using Expectancy in Practice
Strategy evaluation: Calculate expectancy from your backtest results. If it's negative, the strategy loses money regardless of any other metric.
Trade journaling: Track your live expectancy monthly. Compare to backtest expectancy. If live is significantly lower, you're either making execution errors or market conditions have changed.
Position sizing: Risk per trade should be calibrated so that the maximum expected losing streak doesn't exceed your psychological or financial tolerance. With $85 expectancy and $300 average loss, the worst 10-trade stretch might lose $2,000–$3,000. Can you handle that?
Journal-based tracking: Record every trade's P&L in a spreadsheet or trading journal. Recalculate expectancy after every 30–50 trades. Plot it on a chart over time. Declining expectancy with a stable win rate means your average win is shrinking relative to your average loss — a sign that market conditions may be changing or that you're cutting winners too early.
Calculate Your Expectancy
StratBase.ai calculates expectancy automatically from your backtest results, showing the average expected profit per trade alongside win rate, average winner/loser sizes, and profit factor. Together, these metrics give you a complete picture of your strategy's mathematical edge.
Further Reading
About the Author
Financial data analyst focused on crypto derivatives and on-chain metrics. Expert in futures market microstructure and funding rate strategies.
FAQ
How do you calculate trading expectancy?▾
Expectancy = (Win Rate × Average Win) - (Loss Rate × Average Loss). Example: 55% win rate, $400 average win, $300 average loss. Expectancy = (0.55 × $400) - (0.45 × $300) = $220 - $135 = $85 per trade. This means each trade earns $85 on average. Over 200 trades: $85 × 200 = $17,000 expected profit.
What is a good expectancy per trade?▾
Any positive number means the strategy is profitable over time. The absolute value depends on trade frequency and size. For percentage-based expectancy (dividing by average trade size), aim for 0.5%+ per trade. Higher is better, but even small positive expectancy compounds significantly over hundreds of trades.
Can expectancy predict future profits?▾
Expectancy predicts long-term average behavior, not individual trades. A strategy with $85 expectancy won't make exactly $85 on every trade — it will have winners and losers. But over 200+ trades, the average will converge toward $85. The more trades, the more reliable the prediction. Think of it like a casino's house edge — each hand is random, but over thousands of hands, the edge plays out predictably.
Comments (0)
Loading comments...