ARMFThe win rate and expectancy in trading
The win rate is the share of profitable trades, and expectancy in trading turns it into the average outcome of a trade. A win rate taken on its own says nothing about profitability: a system with 70 % winners can be a losing one, while one with 35 % can be steadily profitable. Meaning appears only together with the size of the win, and one formula joins the two values — expectancy.
How to count the win rate
win rate = profitable trades ÷ the total number of trades × 100 %
It is counted from closed trades over a period. Three frequent errors in the counting show up in almost everyone who keeps statistics by hand.
- Break-even trades are counted as profitable
- A close at break-even is not a win. It is more correct to count such trades as a separate category and to state its share next to the win rate.
- Only manually closed trades are counted
- If part of the positions closed on the stop while you count «the ones where I decided to exit», the sample is skewed towards successful outcomes.
- Different instruments and periods are mixed together
- The win rate on EUR/USD in a trending quarter and on a cross in a sideways market are different values. A common average hides both of them.
The expectancy formula
expectancy (in R) = the win rate × the average R − (1 − the win rate)
The value shows how much one trade brings in on average if the result is measured in units of the initial risk. A positive value is a necessary condition for a system to be profitable; a negative one means the account will shrink over the distance regardless of the position size.
An example. A win rate of 45 %, an average ratio of 1 : 2. Expectancy = 0.45 × 2 − 0.55 = +0.35 R. At a risk of 1 % of equity per trade that is on average +0.35 % per trade — a hundred trades give about +42 %, provided the parameters hold and the distribution turns out close to the average.
The point where each line crosses zero is the break-even win rate for the corresponding ratio: 50 %, 33.3 % and 25 %.
Why a high win rate can be dangerous
Strategies with a win rate of 80–90 % do exist, and they are all built the same way: a close target and a distant stop. Almost every single trade is profitable, but a rare loss covers many wins.
| System | Win rate | Average R | Expectancy | What happens in practice |
|---|---|---|---|---|
| A close target, a distant stop | 85 % | 0.15 | −0.02 R | A smooth curve and a collapse on a streak of three losses |
| Balanced | 45 % | 2.0 | +0.35 R | Noticeable drawdowns, a positive expectancy |
| Rare large moves | 28 % | 4.0 | +0.40 R | Long losing streaks, the result is made by single trades |
The trap of the first row. Such a system looks better than any other for the first few months: eight or nine trades out of ten in the plus, an equity curve that is almost a straight line. The negative expectancy shows up only on a losing streak — and it comes the later, the higher the win rate. That is exactly why a sample of a hundred trades is not enough for such strategies.
How many forex trades it takes to believe a win rate
A win rate is an estimate of a probability from a sample, and it has an error. At a true win rate of 45 % the result on a sample fluctuates roughly like this:
| Number of trades | Typical spread of the win rate | What can be said |
|---|---|---|
| 20 | from 34 % to 56 % | Practically nothing |
| 50 | from 38 % to 52 % | Only a rough reference point |
| 100 | from 40 % to 50 % | The first cautious conclusions |
| 500 | from 43 % to 47 % | An estimate you can rely on |
The spread is given as an interval of one standard deviation of the binomial estimate: about two thirds of samples fall into it at a true win rate of 45 %. The rest deviate further.
The practical conclusion: changing the system after ten losing trades means reacting to noise. Changing it after two hundred trades with a negative expectancy is a justified decision.
What changes the win rate on currency pairs and what only seems to
The win rate is not a property of a trader and not a measure of skill. It is a consequence of how the exits from trades are arranged. Below is what actually affects it.
From this follows something important for comparing systems: a win rate named without the ratio and without the exit rules is comparable to nothing. The statement «I have 70 % profitable trades» says as much about the result as «I walk seven kilometres a day» says about speed.
Frequently asked questions
How do you count the win rate in trading?
Divide the number of profitable trades by the total number of trades closed over the period. Trades closed at break-even are separated out: counting them as profitable means inflating the figure.
What win rate is considered good?
The one that is above the break-even level for your ratio of risk to reward. At 1 : 2, 34 % is enough, at 1 : 1 you need more than 50 %. Comparing the win rates of different systems without their ratios is meaningless.
What is the expectancy of a trade in simple words?
The average result of one trade if it is repeated many times. It is counted as the win rate multiplied by the average win, minus the share of losses multiplied by the average loss. In units of risk the formula simplifies to p × R − (1 − p).
Can a system with an expectancy below zero be profitable for a while?
Yes — that is exactly why losing approaches survive for years. Over short stretches the result is determined by chance; a negative expectancy shows up only over a stretch of hundreds of trades.
How do you convert an expectancy in R into a percentage of the account?
Multiply it by the risk per trade. An expectancy of +0.35 R at a risk of 1 % gives on average +0.35 % of equity per trade. That value is then used in calculating how long it takes to come out of a drawdown.
Should expectancy be counted separately by pair?
Yes, if you trade several instruments. An overall expectancy averages sets of trades of different quality, and a losing pair can hide behind a profitable one.
What do I do if the expectancy is around zero?
Look at the costs: the spread and the commission are often exactly the difference that takes a system out of the plus. Reducing the number of trades with short stops or moving to an account with lower costs changes the picture without changing the strategy.
Does partial closing affect the expectancy calculation?
It does: the result of a trade becomes a weighted average of its parts. That is what has to be written into the journal — otherwise the average R comes out inflated and the expectancy more optimistic than the real one.
What win rate is normal in forex?
Any, as long as it is above the break-even level for your ratio. Trend systems on currency pairs often give 35–45 % at an R/R from 1 : 2, intraday ones with close targets give 55–65 % at an R/R of about 1 : 1.
How quickly does the win rate change when the market regime changes?
Noticeably over a few dozen trades. A trend system loses part of its winners in a sideways market, but the ratio usually does not grow with it — which is why the expectancy falls faster than the win rate.
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