In short. Expectancy is how much one trade brings on average: win rate × average win − (1 − win rate) × average loss. Positive expectancy means the strategy makes money over time; negative means it loses with any money management. It is most convenient in R — units of risk.
The formula in money and in R
Expectancy = win rate × average win − (1 − win rate) × average loss
Example: 45% win rate, average win $150, average loss $100. Expectancy = 0.45 × 150 − 0.55 × 100 = 67.5 − 55 = +$12.5 per trade. Over 100 trades that is about +$1,250 — on average, with a spread.
In units of risk: expectancy in R = win rate × payoff − (1 − win rate), where payoff is the average win divided by the average loss. For the example: 0.45 × 1.5 − 0.55 = +0.125 R. The value in R does not depend on account or position size — it can be compared across strategies and traders. How to work out the R of a single trade is covered in «Risk/reward ratio (RR)».
Break-even win rate
Expectancy is zero when win rate = 1 / (1 + payoff). That is the minimum share of winners at which a strategy does not lose before costs:
| Average win / average loss | Break-even win rate |
|---|---|
| 0.5 | 66.7% |
| 1 | 50% |
| 1.5 | 40% |
| 2 | 33.3% |
| 3 | 25% |
A scalper with small targets and large stops (payoff 0.5) has to win more than two trades out of three just to break even.
Expectancy across trading styles
| Style | Win rate | Payoff | Expectancy |
|---|---|---|---|
| Scalping | 70% | 0.5 | +0.05 R |
| Trading from levels | 45% | 1.5 | +0.125 R |
| Trend following | 35% | 2.5 | +0.225 R |
Costs hurt the scalper most: with a 10-pip stop, 0.5 pip of spread and commission costs 0.05 R per trade — the whole expectancy. Frequency is on the scalper's side, though: 400 trades at +0.05 R make 20 R a month, while 20 trend trades at +0.225 R make 4.5 R. Trend following has a different danger — streaks: at a 35% win rate, a run of 8 losses in a row happens at least once in 100 trades with a probability of about 69%.
For an averaging grid, expectancy on closed trades is misleading: 99 cycles at +$10 and one at −$1,500 mean a 99% win rate and an expectancy of −$5.1 per cycle.
Expectancy and profit factor
Both answer «does the strategy make money», but differently. Profit factor is a ratio: how many times profit exceeds loss. Expectancy is an amount: what one trade brings. A strategy with a 1.1 profit factor on a thousand trades a day and one with a 2.0 profit factor on ten trades a month produce very different results. More in «Profit factor in trading».
Why expectancy alone is not enough
- Sample. Over 20 trades expectancy is almost random; draw conclusions from 50–100 trades or more. What else to check is in «How to evaluate a trading strategy».
- Spread. Positive expectancy does not protect against a losing streak. How deep the drawdown can get is shown by the risk of ruin calculator.
- Costs. Commissions, spread and swaps reduce expectancy; use net results.
How many trades it takes to trust expectancy
With a 45% win rate and payoff 1.5, a trade ends at +1.5 R or −1 R, and the standard deviation of the result is ≈ 1.24 R. The error of the average is deviation / √N: ±0.18 R over 50 trades, ±0.12 R over 100, while the expectancy itself is +0.125 R. For it to sit two errors above zero (about 95% confidence under the normal approximation), you need around 400 trades. So 50–100 trades are the minimum for first conclusions, not proof.
What to do with the number
- Use net results and convert to R.
- Compare periods in R: double the lot and +$12.5 becomes +$25, yet it is still +0.125 R.
- Expectancy below two errors is not proven yet — grow the sample.
- Subtract costs in R: spread and commission divided by the distance to the stop.
- Break it down by setup: setups with a negative average R go first for review.
- Compare on-plan and off-plan trades — the difference is the price of mistakes.
Expectancy in Davinchu
The Davinchu trading journal shows «Expectancy» in money — by the formula above, «Average R» and «Total R». On the «Review» tab the «Discipline and cost of violations» block compares «Expectancy $» and average R of on-plan and off-plan trades — so you see what each mistake costs. The «What to improve» block next to it states that difference per trade and names the best and the weak setup by average R, from 5 trades with R. «Monte Carlo on R» on the «Overview» tab draws 10–200 future trades at random from your R values and shows the spread of the outcome: P10, median, P90 and the share of paths in profit. On the account page «Expectancy» on the «Trades» tab is the sum of net trade results for the period (including commission and swap) divided by the number of trades. On the Free plan two accounts connect at no cost.