Risk Management & StatisticsBeginner

Expectancy

How to calculate trading expectancy in R (win rate × average win − loss rate × average loss), a worked example, and why a low win rate can still be positive.

Library categories

What it means

Expectancy is the average result per trade. In R (multiples of the amount risked): E = (win rate × average win) − (loss rate × average loss).

A positive expectancy means the method made money on average over the sample; it does not mean the next trade will.

Why traders use it

Win rate alone is misleading. A method that wins 37% of the time at +2R and loses 1R otherwise has a positive expectancy; a method that wins 80% at +0.2R and loses 1R otherwise does not.

Chart examples

Expectancy from 30 example trades

E = 0.37 × 2 − 0.63 × 1 ≈ +0.10REquity (R)Each trade (R)
11 wins of +2R and 19 losses of −1R: net +3R, or +0.10R per trade. Note the long flat and losing stretches even with a positive expectancy.Schematic diagrams drawn to explain the idea; they are not market data.

How to identify it objectively

  • 1Record every trade in R (profit ÷ initial risk).
  • 2Win rate = wins ÷ trades.
  • 3E = win rate × average win R − loss rate × average loss R.
  • 4Report it with the sample size.

Bullish use

  • 1Expectancy applies to longs and shorts alike.
  • 2Calculate it separately for long and short trades to see if one side carries the method.

Bearish use

  • 1A negative expectancy means the rule loses on average over the sample.
  • 2More trades only grow the loss.

What confirms it

  • A large sample (100+ trades) with costs included.
  • Similar expectancy out of sample.

What invalidates it

  • Positive in-sample, negative out-of-sample.
  • Costs not included.

How a hypothetical setup is built

Entry

Not an entry rule: a measurement of one.

Stop

Always record the planned stop so R can be calculated.

Target

Compare expectancy across target choices (for example 1.5R vs 2R).

A hypothetical illustration of how the concept is turned into a plan, not a recommendation. Practise it on a paper account first.

Historical testing

The diagram uses a made-up sequence of 30 trades (11 wins of +2R, 19 losses of −1R) to show the arithmetic; it is not a backtest of any method.

Limitations: when it fails

  • 30 trades is far too few to trust; the example only shows the formula.
  • Expectancy can change as markets change.
  • Ignoring costs overstates it.

Knowledge check

Pick an answer to see the explanation. Nothing is saved.

Win rate 40%, average win 2R, average loss 1R. Expectancy?

1. Win rate 40%, average win 2R, average loss 1R. Expectancy?

Can a 30% win rate be profitable?

2. Can a 30% win rate be profitable?

Why measure in R?

3. Why measure in R?

Practise it risk-free

Open the free chart, use replay to go back in time and look for this concept candle by candle with $20,000 in virtual money.