Expectancy and profit factor calculator
Expectancy is the expected return per trade given your win rate and average win or loss size. Profit factor is the ratio of gross winnings to gross losses. Both are foundational institutional metrics for evaluating whether a trading edge is worth scaling. Calculator below returns expectancy in R-multiples and AUD, profit factor, the breakeven win rate at your reward-to-risk ratio, and the sample size needed for statistical confidence.
Calculator
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What is trading expectancy?
Expectancy is the single most important number in evaluating any trading strategy. It answers: across many trades, what is the average return per trade in R-multiples (multiples of the risk per trade)?
The metric is foundational because it directly answers whether the strategy is profitable in the long run. Positive expectancy means the strategy makes money on average, even though individual trades will lose. Negative expectancy means the strategy loses money on average, even if individual trades win. No amount of position sizing, money management, or psychological discipline can rescue a negative-expectancy strategy. The math compounds against the trader.
Institutional traders evaluate strategies by expectancy first. Only after expectancy is confirmed positive do they assess Sharpe ratio, drawdown, profit factor, and other risk-adjusted metrics. Retail trading literature often inverts this order, focusing on win rate or recent equity curve appearance, which obscures whether the underlying expectancy is actually positive.
The formulas
Where p is win rate (decimal), q = 1 - p is loss rate, and avgWin / avgLoss are in R-multiples.
Profit factor:
Equivalently: total gross winnings ÷ total gross losses across the sample.
Breakeven win rate at reward-to-risk ratio b:
For symmetric R:R = 1 the breakeven is 50%. For R:R = 2 the breakeven is 33.3%. Higher R:R lowers the breakeven.
Sample size for 95% statistical confidence:
Where σ is the standard deviation of trade outcomes. Larger expectancy or smaller variance reduces the required sample.
Worked example
An Australian retail trader has tracked 150 trades over the past year. The trade journal shows:
- Win rate: 48 percent (72 wins, 78 losses)
- Average winning trade: 1.8R
- Average losing trade: 1.0R
- Risk per trade: AUD 200
Expectancy calculation:
E = (0.48 × 1.8) - (0.52 × 1.0) = 0.864 - 0.52 = 0.344R per trade.
In dollar terms: 0.344R × AUD 200 = AUD 68.80 expected per trade. Over 150 trades, total expected profit: AUD 10,320.
Profit factor calculation:
Profit factor = (0.48 × 1.8) / (0.52 × 1.0) = 0.864 / 0.52 = 1.66.
Above the 1.5 institutional minimum, below the 2.0 strong threshold. Decent edge.
Breakeven win rate at 1.8:1 R:R:
Breakeven = 1.0 / (1.8 + 1.0) = 35.7 percent.
The trader is operating well above breakeven (48 percent vs 35.7 percent), giving a 12.3 percentage point buffer if win rate degrades.
Sample size for statistical confidence:
Variance per trade: σ² = 0.48 × 1.8² + 0.52 × 1.0² - 0.344² = 1.555 + 0.52 - 0.118 = 1.957. Standard deviation: σ = 1.40.
Required sample: N* = (1.96 × 1.40 / 0.344)² = (7.98)² = 64 trades.
The trader's 150-trade sample exceeds the 64-trade threshold, giving 95 percent statistical confidence that the measured expectancy is genuinely positive and not a small-sample artefact.
Statistical significance of edge
Most retail trading content treats win rate and expectancy as observed facts. They are estimates from a finite sample, and like all estimates they carry standard error. The key question is whether the measured edge is statistically distinguishable from zero (no edge) given the sample size.
The relationship between expectancy, variance, and required sample size is:
- Higher expectancy → fewer trades needed to confirm
- Lower variance → fewer trades needed to confirm
- Mean-reversion strategies (low variance) need fewer trades than trend-following strategies (high variance) for the same expectancy
Practical implication: a 50-trade sample showing 0.5R expectancy is statistically meaningful (very high expectancy easily clears the confidence threshold). A 50-trade sample showing 0.15R expectancy may be statistical noise. The calculator above tells you which side of the threshold you are on.
For traders building a track record from scratch, the recommended approach is: trade at minimum size (well below Kelly, well below institutional caps) for the first 100-200 trades. Compute expectancy and profit factor after each batch of 50 trades. Only scale position sizes once expectancy is confirmed positive AND sample size exceeds the statistical threshold returned by the calculator.
Related tools
- Risk of Ruin Calculator - probability of blowing up the account at a given bet size. Pairs with expectancy: confirm positive expectancy first, then check ruin probability.
- Kelly Criterion Position Sizer - the optimal bet size given the expectancy you just calculated.
- Drawdown Recovery Calculator - the non-linear math of recovering from drawdowns, which is more important when expectancy is low.
- Position Size Calculator - translates risk percentage into broker lot size.
Frequently asked questions
Trading expectancy is the expected return per trade calculated as: expectancy = (win rate x average win) - (loss rate x average loss). Expressed in R-multiples (multiples of the risk per trade), expectancy is the foundational measure of edge quality. Positive expectancy means the strategy is profitable in the long run; negative expectancy means it is unprofitable regardless of position sizing. Most institutional traders evaluate strategies by expectancy first and only assess Sharpe ratio, drawdown, and other metrics once expectancy is confirmed positive.
Institutional convention targets expectancy of at least 0.2R per trade for retail-grade strategies (where R is the risk per trade). For example, a strategy risking 1 percent of capital per trade should produce at least 0.2 percent expected return per trade after costs. Above 0.5R is strong. Above 1R is exceptional and usually requires re-verification because edges that large are rare in efficient markets. Below 0.1R is fragile: small execution variance or slippage flips it to break-even or negative.
Profit factor is the ratio of total gross winnings to total gross losses across a sample of trades. Profit factor = sum of winning trades / sum of losing trades (absolute value). A profit factor of 1.0 is breakeven, 1.5 is the institutional minimum target, 2.0 is strong, and above 3.0 is exceptional. Profit factor is more sample-efficient than win rate alone for evaluating strategies because it captures both the win rate and the average win size relative to average loss size in one number.
Statistical confidence in an edge estimate scales with the inverse square root of sample size. For 95 percent confidence that a measured expectancy is distinguishable from zero, the standard rule of thumb is: required sample = (1.96 x standard deviation / expectancy)^2. The calculator above computes this for your specific inputs. For typical retail edges with expectancy of 0.2 to 0.4 R per trade and standard deviation around 1.2 R, the required sample is usually 200 to 800 trades. Estimates from fewer than 100 trades carry high standard error.
The breakeven win rate is the win rate at which expectancy equals zero. For reward-to-risk ratio b: breakeven win rate = 1 / (1 + b). For 1:1 R:R the breakeven is 50 percent. For 1:2 R:R the breakeven is 33.3 percent. For 1:3 R:R the breakeven is 25 percent. Higher reward-to-risk lowers the breakeven win rate. The calculator above outputs your breakeven for any R:R you input. Any win rate above the breakeven produces positive expectancy at that R:R.
Yes for evaluating strategy quality. A high win rate with low profit factor (a strategy that wins often but loses big when it loses) is fragile. A moderate win rate with high profit factor (a strategy that wins less often but bigger when it does) is more robust. Trend-following strategies typically have 30-45 percent win rates with profit factors of 1.8-2.5. Mean-reversion strategies typically have 60-75 percent win rates with profit factors of 1.3-1.7. Profit factor unifies the two evaluations.
Positive expectancy is the necessary condition for a positive Kelly fraction. The Kelly criterion uses the same win rate and R:R inputs as expectancy but produces an optimal bet-size fraction instead of an expected per-trade return. Both are downstream of the same edge math. Workflow: confirm expectancy is positive first using this calculator, then use the Kelly Criterion Position Sizer on SatoshiMacro to determine the optimal bet size.
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