Trade Expectancy Explained:
Combining Win Rate and Ratio
Learn the trade expectancy formula, which combines win rate and average win/loss size into a single measure of expected trading outcomes.
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This final lesson introduces trade expectancy, a formula that brings together win rate and risk-to-reward ratio (expressed through average win and average loss) into a single, more complete measure, directly addressing the gap identified in the previous lesson.
All figures in this lesson are hypothetical and illustrative, used purely to demonstrate a mathematical concept, not a performance claim or prediction.
The Trade Expectancy Formula
Trade expectancy is generally calculated as: Expectancy = (Win Rate × Average Win) − (Loss Rate × Average Loss). This formula produces a figure representing the average expected outcome per trade, based on a given win rate and average win/loss size.
Worked Example: A Lower Win Rate with a Wide Ratio
Consider a hypothetical strategy with a 40% win rate, an average win of $300, and an average loss of $100 (a 1:3 ratio). Applying the formula: Expectancy = (0.40 × $300) − (0.60 × $100) = $120 − $60 = +$60 per trade.
This illustrates a positive expectancy despite the trader being wrong 60% of the time, since each win is worth three times each loss.
Worked Example: A Ratio Below Its Breakeven Win Rate
Now consider the scenario from the previous lesson: a 1:2 ratio (average win $200, average loss $100) with a win rate of only 30%, below the approximate 33.3% breakeven threshold. Applying the formula: Expectancy = (0.30 × $200) − (0.70 × $100) = $60 − $70 = −$10 per trade.
This confirms mathematically what the previous lesson demonstrated conceptually: a seemingly favourable 1:2 ratio still produces a negative expectancy when the win rate falls short of what that ratio requires.
Interpreting Expectancy — and Its Limitations
A positive expectancy suggests a strategy has, on average and based on the specific win rate and average win/loss figures used, a mathematical edge over the figures used in the calculation. A negative expectancy suggests the opposite. However, expectancy is calculated from historical or assumed win rate and average win/loss figures — it does not guarantee that future results will match these inputs, since actual trading involves changing market conditions and inherent uncertainty. Expectancy is a tool for evaluating a strategy's historical or hypothetical mathematics, not a guarantee of future performance.
🔖 Summary
Trade expectancy — calculated as (Win Rate × Average Win) minus (Loss Rate × Average Loss) — combines win rate and reward ratio into a single measure, showing how a 40% win rate with a 1:3 ratio can produce a positive $60-per-trade expectancy, while a 30% win rate with a 1:2 ratio produces a negative $10-per-trade expectancy. This closes out the unit by demonstrating mathematically why ratio and win rate must be assessed together, though expectancy itself reflects historical or assumed inputs and does not guarantee future results.
Frequently Asked Questions
What is the trade expectancy formula?
Expectancy = (Win Rate × Average Win) − (Loss Rate × Average Loss), producing a figure representing the average expected outcome per trade.
Can a strategy be profitable with a win rate below 50%?
Yes, as shown in the worked example, a 40% win rate with a 1:3 ratio produces a positive expectancy of $60 per trade in that hypothetical scenario.
Can a strategy with a 1:2 ratio still have negative expectancy?
Yes, if the win rate falls below the approximate 33.3% breakeven threshold for that ratio, as shown in the second worked example.
Does a positive expectancy guarantee future profitability?
No, expectancy is calculated from historical or assumed figures; it does not guarantee that future win rates and average win/loss sizes will match those inputs.
Risk Warning
Trading forex and CFDs involves significant risk and may not be suitable for all investors. You may lose all of your invested capital. Please ensure you fully understand the risks before trading.
GTCFX operates as a multi-regulated group of companies, clients are kindly advised to confirm the specific legal entity, regulation, and jurisdiction under which they are being onboarded.
