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Backtesting

Expectancy and Profit Factor

Pomegra Learn

What Is Expectancy and How Do You Calculate It?

Expectancy is the average amount you expect to win (or lose) per trade, calculated from your historical win rate, average win size, and average loss size. Profit factor is the total gross profit divided by total gross loss—a simpler ratio that also measures edge but lacks the predictive power of expectancy. Together, these two metrics cut through the clutter of backtest results and reveal whether your strategy actually makes money on average.

Many traders obsess over win rates, imagining that a 60% win rate guarantees success. But a strategy with a 60% win rate and tiny average wins versus large average losses is doomed. Expectancy forces you to account for both the frequency of wins and their size, giving you a single number that predicts your long-term outcome. A positive expectancy means the strategy makes money on average; a negative expectancy means it loses money, no matter how many trades you place.

Quick definition: Expectancy is the average profit or loss per trade, calculated as (Win Rate × Average Win) − (Loss Rate × Average Loss). Profit factor is total gross profit divided by total gross loss; a ratio above 1.5 generally indicates profitable edge.

Key takeaways​

  • Expectancy is the single best predictor of whether a strategy will be profitable long-term
  • A positive expectancy (greater than zero) means the strategy wins money on average; negative expectancy means it loses
  • Profit factor supplements expectancy by showing the ratio of dollars won to dollars lost
  • A healthy strategy has an expectancy of at least $0.10–$0.50 per share (or per contract) and a profit factor above 1.5
  • Expectancy assumes consistent trade sizing and doesn't account for market regime changes, slippage, or commissions

Understanding the math of expectancy​

Expectancy is calculated using this formula:

Expectancy = (Win Rate × Average Win) − (Loss Rate × Average Loss)

Let's say your backtested strategy shows:

  • Win rate: 45% (0.45)
  • Average winning trade: $200
  • Loss rate: 55% (0.55)
  • Average losing trade: $100

Expectancy = (0.45 × $200) − (0.55 × $100) = $90 − $55 = $35 per trade

This means that over a large sample of trades, you expect to profit $35 on average. If you place 100 trades, the expected total profit is roughly $3,500, though individual trades will vary.

The beauty of expectancy is its simplicity and predictive power. One number—$35 per trade—encapsulates whether your strategy is viable. You don't need to memorize your win rate, average win, and average loss separately. The expectancy tells you immediately: this strategy makes money.

Positive vs. negative expectancy​

A positive expectancy means the strategy is profitable over a long run. A negative expectancy means it's losing, and you should stop trading it (or redesign it). An expectancy of zero means the strategy breaks even on average, ignoring commissions and slippage.

Consider two strategies:

Strategy A: 40% win rate, $500 average win, 60% loss rate, $250 average loss. Expectancy = (0.40 × $500) − (0.60 × $250) = $200 − $150 = $50 per trade. This is profitable.

Strategy B: 55% win rate, $150 average win, 45% loss rate, $200 average loss. Expectancy = (0.55 × $150) − (0.45 × $200) = $82.50 − $90 = −$7.50 per trade. This loses money on average.

Despite a higher win rate (55% vs. 40%), Strategy B has negative expectancy because the average loss exceeds the average win. Strategy A is clearly superior, even though most traders would be seduced by Strategy B's "better" win rate.

This is why win rate alone is dangerous. A 70% win rate with tiny wins and huge losses can easily produce negative expectancy. Conversely, a 30% win rate with large wins and small losses can generate strong positive expectancy.

Profit factor as a companion metric​

Profit factor simplifies the picture by comparing total dollars won to total dollars lost, without regard to trade frequency:

Profit Factor = Total Gross Profit / Total Gross Loss

If your strategy generated 100 trades with $50,000 in total wins and $20,000 in total losses: Profit Factor = $50,000 / $20,000 = 2.5

A profit factor above 2.0 is generally considered excellent. Above 1.5 is healthy. Below 1.0 means the strategy is unprofitable (gross losses exceed gross wins). Between 1.0 and 1.5 is borderline and usually not robust enough for live trading.

Profit factor has a weakness: it doesn't account for the number of trades. A strategy that generated one $50,000 win and one $20,000 loss has a 2.5 profit factor, but that's based on a single trade in each direction. Over 100 trades, the ratio might collapse. Expectancy handles this better because it averages across the full sample.

Still, profit factor is useful for quick mental math. If you see a profit factor of 1.8, you can reasonably estimate the strategy is viable. Combined with expectancy, it paints a full picture.

Decision tree​

How sample size affects expectancy reliability​

A single profitable trade doesn't prove your strategy works. You need a large sample—at least 30 trades, ideally 100+—before expectancy becomes statistically meaningful. With only 10 trades, luck dominates over edge.

The standard error of your expectancy estimate improves as you accumulate more trades. With 20 trades, your expectancy might be ±$50 in noise. With 200 trades, the margin of error shrinks to ±$15. This is why backtests spanning multiple years (generating hundreds of trades) carry more weight than backtests on a single market or instrument.

When evaluating a strategy, ask: How many trades generated this expectancy? If the answer is fewer than 30, treat the result as preliminary. Treat 30–100 trades as reasonably robust. Treat 100+ trades as solid evidence of edge (assuming the data is clean and representative).

Expectancy in real trading with commissions and slippage​

Your backtest expectancy is a theoretical number based on clean fills at exact closing prices. In real trading, you pay commissions, face slippage (getting worse prices than expected), and encounter market impact on larger trades.

If your backtest expectancy is $35 per trade and commissions are $10 per trade, your real expectancy drops to $25 per trade. If slippage averages another $5, you're down to $20 per trade. These frictions can easily halve or eliminate your expectancy, which is why many profitable-looking backtests fail live.

A good rule: assume 20–40% of your backtest expectancy will evaporate due to real-world frictions. If your expectancy is $100 per trade, expect $60–$80 net in live trading. If your backtest expectancy is only $20 per trade, frictions might reduce it to zero or negative.

This is why strategies with larger average trades (in dollar terms) are often more realistic. A scalping strategy with a $5 expectancy per 1-minute trade will struggle with commissions. A swing strategy with a $200 expectancy per multi-day trade is more robust to frictions.

Real-world examples​

Consider a breakout strategy on crude oil futures. Over two years of daily data, you record 150 trades:

  • Wins: 65 trades, total $45,000 (average $692 per win)
  • Losses: 85 trades, total $30,000 (average $353 per loss)
  • Win rate: 43%, Loss rate: 57%

Expectancy = (0.43 × $692) − (0.57 × $353) = $297 − $201 = $96 per trade. Profit factor = $45,000 / $30,000 = 1.5.

With a crude oil futures contract representing $100 per tick (each trade typically covers many ticks), an expectancy of $96 per trade translates to real dollars. Even after accounting for commissions of ~$20 per round-trip and occasional slippage, you retain $60–$70 in edge per trade. Over a typical month of 10–15 trades, this translates to $600–$1,050 in expected profit.

By contrast, a day-trading strategy on a micro E-mini S&P contract shows:

  • 200 trades over six months
  • Wins: 110 trades, $8,000 total ($73 per win)
  • Losses: 90 trades, $7,200 total ($80 per loss)
  • Win rate: 55%, Loss rate: 45%

Expectancy = (0.55 × $73) − (0.45 × $80) = $40.15 − $36 = $4.15 per trade. Profit factor = $8,000 / $7,200 = 1.11.

With commissions at $2 per round-trip and slippage averaging $1, the net expectancy becomes $1.15 per trade. Over 200 trades annually, that's $230 in expected profit—insufficient to cover the emotional and mental cost of active trading.

Common mistakes​

Conflating win rate with edge. A 70% win rate feels safe but is meaningless without average win and loss sizes. Always calculate expectancy. A 50% win rate with twice the average win as average loss beats a 70% win rate with half the average win.

Using expectancy from a small sample (fewer than 30 trades). Luck heavily influences small samples. If your last 10 trades generated an expectancy of $50, don't assume that rate continues. The confidence interval is huge. Require at least 30 trades, preferably 100+, before trusting the expectancy number.

Ignoring commissions and slippage in expectancy calculations. A backtest showing $40 expectancy per trade might drop to $20 or less in live trading once costs are applied. Always deduct realistic commissions, slippage, and market impact from your backtest expectancy before committing capital.

Assuming constant expectancy across different market regimes. A mean-reversion strategy might have positive expectancy in range-bound markets but negative expectancy in strong trends. A trend-following strategy shows the opposite. Expectancy is regime-dependent. Track whether your expectancy holds during bull markets, bear markets, high volatility, and low volatility.

Overstating profit factor on low trade counts. A profit factor of 3.0 based on five winning trades and five losing trades is less reliable than a 1.8 profit factor based on 100 trades. Profit factor can be misleading on small samples. Always cross-check with expectancy and sample size.

FAQ​

What is a "good" expectancy?​

It depends on trade frequency and average trade size. For a daily chart swing trader, an expectancy of $100–$500 per trade (depending on contract size) is healthy. For a day trader scalping with many trades, an expectancy of $5–$20 per trade might be sufficient if you execute 50+ trades per day. A strategy with an expectancy below $5 per trade and fewer than 20 daily trades is unlikely to overcome commissions and risk capital in meaningful ways.

How does expectancy relate to Sharpe ratio?​

Sharpe ratio measures risk-adjusted returns, factoring in volatility. Expectancy measures average profit per trade. A strategy can have high expectancy but poor Sharpe ratio if it has high drawdowns or volatile returns. Conversely, a low-volatility strategy might have modest expectancy but an excellent Sharpe ratio. Use both metrics: expectancy for pure edge, Sharpe ratio for risk adjustment.

Should I maximize expectancy or profit factor?​

Maximize expectancy because it accounts for trade frequency and sizes. However, use profit factor as a secondary filter: profit factor above 1.5 paired with positive expectancy is a healthy combination. A high profit factor with low expectancy often means few trades, which might hide regime dependence. A high expectancy with low profit factor often means many small losses outweighing fewer big wins—potentially risky if market structure shifts.

Does expectancy predict actual live trading returns?​

Expectancy predicts long-run statistical returns, assuming consistent market conditions, trade sizing, and risk management. In reality, live trading will show variance around the expectancy due to luck, changing market regimes, and emotional discipline. If backtest expectancy is $50 per trade, real live trading might average $40–$60 per trade over many months, not exactly $50. The larger your sample of live trades, the closer actual returns approach expectancy.

How do I improve expectancy if it's low?​

Increase either win rate or average win size relative to loss size. Widening stops (increasing average loss) to catch more wins (higher win rate) is sometimes a trade-off, but if the average win grows faster than the average loss, expectancy improves. Alternatively, tighten exits to reduce average losses without sacrificing win rate. Or shift to higher-probability setups that increase both win rate and average win. Use backtesting to explore these improvements.

Can expectancy be negative and still be worth trading?​

No, not for live trading. A negative expectancy strategy loses money on average, and no matter how many trades you place, the losses will compound. You might win individual trades (and certainly will, given randomness), but over a sample of 100+ trades, you're statistically destined to lose money. Walk away and redesign.

Summary​

Expectancy is the average profit per trade, calculated as (Win Rate × Average Win) − (Loss Rate × Average Loss). It's the single best number for predicting whether your strategy will be profitable. A positive expectancy combined with a profit factor above 1.5 and a sample of at least 100 trades indicates genuine edge. Profit factor (total gross profit divided by total gross loss) serves as a companion metric, providing a quick ratio of wins to losses. Remember that backtest expectancy is theoretical and will shrink in live trading due to commissions and slippage. Always apply realistic cost estimates to your backtest expectancy before committing capital. A strategy with positive expectancy, healthy profit factor, reasonable sample size, and consistent performance across market regimes is ready for further validation through forward testing.

Next​

Drawdown Analysis in a Backtest