Expectancy

Expectancy is the average amount a trading strategy wins or loses per trade over a large number of trades. It combines your win rate with the size of your average win and average loss into one number. If expectancy is positive, the strategy makes money over time, before considering how variable the results are. If it is negative, no amount of discipline or position sizing can make it profitable in the long run.

The formula#

Expectancy = (Win rate × Average win) − (Loss rate × Average loss)

Expressed in R multiples, where 1R is the amount risked per trade:

Expectancy (R) = (Win rate × Average win in R) − (Loss rate × 1)

when losses are typically about 1R.

Turning expectancy into results#

Expectancy times the number of trades estimates total results over time:

• +0.40R per trade over 100 trades is about +40R. If 1R is 1% of the account, that is roughly 40% before compounding and costs.
• +0.05R per trade over 100 trades is about +5R, and small enough that costs or a slight drop in win rate could erase it.

Costs belong in the calculation: subtract average commissions, spreads and slippage per trade in R. See All-In Trading Cost.

Expectancy vs win rate#

Win rate alone tells you almost nothing. A 90% win rate can lose money if the 10% of losses are huge, which is typical of strategies that sell options or never use stops. A 30% win rate can be very profitable with large average wins, typical of trend following. See Win Rate and Payoff Ratio.

How reliable is your expectancy number?#

Expectancy calculated from a small sample is unreliable. Twenty trades can show strongly positive expectancy by luck alone. As a rough guide, you need dozens of trades for a first impression and hundreds for confidence, especially for strategies with low win rates and occasional large wins. See Statistical Significance in Trading and Law of Large Numbers.

Ways to improve expectancy#

1. Cut losers at the planned stop, keeping average loss near 1R.
2. Let winners run with targets that reflect real market structure, or trailing stops. See Trailing Stop Orders.
3. Filter out low quality setups that drag the average down; your journal shows which ones. See Post-Trade Analysis.
4. Reduce costs: better execution and fewer marginal trades.
5. Avoid trading in conditions where your strategy has negative expectancy, such as ranges for a trend strategy.

Expectancy and prediction markets#

In prediction markets, expectancy per share is simply the probability you assign times $1, minus the price you pay. Buying Yes at 60¢ when you believe the true chance is 65% has expectancy of +5¢ per share. If your probability estimates are not better than the market's, expectancy after fees is negative. See Expected Value and What Are Prediction Markets?.

Common mistakes#

• Judging a strategy by win rate alone.
• Calculating expectancy on too few trades.
• Leaving out costs.
• Ignoring variance: two strategies with the same expectancy can have very different drawdowns. See Risk of Ruin.

Frequently asked questions#

What is expectancy in trading?#

The average profit or loss per trade over many trades, combining win rate, average win and average loss.

What is a good expectancy?#

Any positive expectancy after costs can be profitable, but higher values give more room for error. Many traders consider +0.2R to +0.5R per trade solid.

Can a strategy with a low win rate have positive expectancy?#

Yes. If average wins are much larger than average losses, a strategy can win less than half the time and still be profitable.

Next, learn how to estimate the chance of a disastrous drawdown with Risk of Ruin.