Expectancy

Expectancy answers the question "on average, what does one more trade of this method make or lose?" It is the reason a low win rate can still be workable and a high win rate can still lose money.

• Expectancy = (win rate × average win) − (loss rate × average loss)

It can be expressed in money or in "R", where 1R is the amount risked on a trade.

Example

Illustrative figures from a journal of 100 trades:

• 40 winners averaging $300; 60 losers averaging $150.
• Expectancy: (0.40 × 300) − (0.60 × 150) = 120 − 90 = $30 a trade.

In R terms, if each trade risks $150, the average win is 2R and the average loss is 1R: (0.40 × 2) − (0.60 × 1) = 0.2R per trade.

Now a high win rate example: 70% winners averaging $100 and 30% losers averaging $300. Expectancy: (0.70 × 100) − (0.30 × 300) = 70 − 90 = −$20 a trade. Seven trades in ten win, and the method still loses money over time.

Practical notes

• Include costs. Spread, commission and swap reduce every winner and increase every loser. A small positive expectancy before costs can become negative after them.
• It is an average. Positive expectancy does not prevent long losing streaks; that is what risk of ruin and drawdown describe.
• Past figures, uncertain future. Expectancy calculated from a backtest or a short live record is an estimate with wide error bars, and market conditions change.

Expectancy ties together the risk-reward ratio and win rate; our guide to the risk-reward ratio explains the link. A trading journal is where the inputs come from.