Expectancy and win rate: the formula that ties them together
The Nuqta Markets team · 28 October 2026 · 7 min read · How we write
In short
- Expectancy per trade = win rate × average win − loss rate × average loss.
- Break-even win rate = 1 ÷ (1 + reward-to-risk), before costs.
- Low win rates come with long losing streaks, even when the arithmetic is positive.
"What is the win rate?" is the most common question about any trading rule, and on its own it is the least useful. A win rate only means something next to the size of the wins and the losses. Expectancy is the formula that joins them, and it is short enough to run on a napkin.
The formula
Expectancy per trade = win rate × average win − loss rate × average loss
Measured in R, where 1R is the amount risked to the stop, the average loss is usually close to 1R and the formula becomes:
E(R) = W × average win in R − (1 − W) × 1
Costs (spread, commission, swap) come off every trade, winners and losers alike. The tables below use a cost of 0.1R per trade as an example.
Five hypothetical rule sets
| Win rate | Average win | Expectancy before costs | After 0.1R costs |
|---|---|---|---|
| 70% | 0.3R | −0.09R | −0.19R |
| 60% | 0.5R | −0.10R | −0.20R |
| 50% | 1R | 0 | −0.10R |
| 40% | 2R | +0.20R | +0.10R |
| 30% | 3R | +0.20R | +0.10R |
Illustrative calculation, not an expectation of results. These are hypothetical inputs, not the statistics of any strategy.
The two rule sets with the highest win rates have the worst expectancy. That is the whole point: a high win rate built on small wins and full-size losses can lose money steadily, and a low win rate can be positive on paper if the wins are large enough. The risk-reward calculator shows the reward-to-risk of a single setup.
The break-even win rate
Set expectancy to zero and solve for W:
Break-even W = (1 + c) ÷ (1 + reward-to-risk), where c is the cost per trade in R.
| Reward-to-risk | Break-even before costs | With 0.1R costs |
|---|---|---|
| 0.5 | 66.7% | 73.3% |
| 1 | 50% | 55% |
| 1.5 | 40% | 44% |
| 2 | 33.3% | 36.7% |
| 3 | 25% | 27.5% |
Illustrative calculation, not an expectation of results.
The price of a low win rate: streaks
A positive expectancy at a 30% or 40% win rate comes with long runs of losses. Using basic probability, these are the chances of at least one losing streak of a given length somewhere in 100 independent trades:
| Win rate | 5+ losses in a row | 8+ in a row | 10+ in a row |
|---|---|---|---|
| 40% | about 98% | about 49% | about 20% |
| 50% | about 81% | about 17% | about 4% |
Illustrative calculation, not an expectation of results.
A trader who does not expect eight losses in a row tends to abandon the rules exactly when the arithmetic says it is normal. What those streaks do to an account at different risk levels is the subject of risk of ruin.
Where the inputs come from
Expectancy is only as good as its sample. Twenty or thirty trades are easily dominated by luck; many traders want 100 or more backtest trades before treating the figure as more than a rough estimate, and live results can still differ. The playbook in this course publishes each backtest as it is completed, losing streaks included, rather than a single win rate.
Turning R into money
1R is a sum of money only once the size is set. With $10 at risk per trade, +0.10R is an average of $1 per trade before variance, which is why expectancy says little about any single month. The lot size calculator converts 1R into a lot.
In short
A win rate is half a number. Multiply it by the average win, subtract the losses and the costs, and check the streaks that come with it. Then see what expectancy and fixed-percentage risk do over many trades in compounding a small account.
Questions people also ask
What does R mean in expectancy?
R is the amount risked on a trade, the distance to the stop in money. A 2R win gains twice what was risked. Measuring in R lets trades of different sizes be compared.
How many trades are needed to estimate expectancy?
There is no exact number, but 20 or 30 trades are easily dominated by luck. Many traders use 100 or more backtest trades as a minimum before treating the figure as more than a rough guess, and even then it can change.
Is a 70% win rate good?
It depends on the size of wins and losses. At 70% with wins of 0.3R and full 1R losses, expectancy is 0.21 − 0.30 = −0.09R per trade before costs. The win rate alone cannot answer the question.
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