Expectancy trading formula: how to calculate it and what is good

The formula

E = (W × avgWin) − ((1 − W) × avgLoss)

W is the win rate as a fraction, avgWin is the average profit on a winning trade, and avgLoss is the average loss on a losing trade expressed as a positive number. The result is the expected profit per trade in the same units as avgWin and avgLoss.

An equivalent and often more useful form divides through by avgLoss to get expectancy as a multiple of your risk: E / avgLoss = W × (avgWin / avgLoss) − (1 − W). The term avgWin / avgLoss is the payoff ratio, usually written R. So expectancy in units of risk is W × R − (1 − W), and that version is independent of your position size, which makes it comparable between strategies and instruments.

Both forms are the same statement. Which one you use depends on whether you want the answer in money or in risk units.

Worked example

Take a strategy that wins 45% of the time, with an average win of 220 and an average loss of 120.

Expectancy = 0.45 × 220 − 0.55 × 120 = 99 − 66 = 33 per trade. Over 200 trades that is 6,600 of expected profit before costs.

In risk units: R = 220 / 120 = 1.833. Expectancy = 0.45 × 1.833 − 0.55 = 0.825 − 0.55 = 0.275 R per trade. So each trade is worth about 0.28 times what you risk on it.

Now change one number. Drop the win rate to 35% and keep everything else: 0.35 × 220 − 0.65 × 120 = 77 − 78 = −1 per trade. The strategy has crossed from profitable to losing on a ten-point change in a statistic that sounds small. This is why expectancy has to be recomputed out of sample: the win rate is the input most easily flattered by a backtest.

Notice also that the average magnitudes matter more than the win rate at the extremes. A strategy winning only 30% of the time with an average win four times the average loss has expectancy 0.30 × 4 − 0.70 = 0.50 R, which is better than the 45% example above.

How to calculate it from your own trade history

Export your closed trades with the profit or loss on each. Split them into winners and losers.

Count the winners, divide by the total, and you have W. Take the mean of the winning profits for avgWin and the mean of the absolute losing amounts for avgLoss. Put them into the formula.

Then do it a second time with costs included. If your export shows gross profit, subtract the spread and commission on every trade, including winners. High-frequency strategies often find that expectancy is positive gross and negative net, which is a fact about the strategy rather than a reason to distrust the arithmetic.

Then do it a third time on an out-of-sample period only. Expectancy computed on the data you used to tune the strategy is an in-sample statistic, and it is biased upward in the direction that makes the strategy look fundable.

One practical warning: the mean is sensitive to outliers. A single trade that made ten times the average will lift avgWin noticeably. Compute the median win and median loss alongside the means. If the means and the medians tell different stories, the strategy's edge depends on rare large winners, and your expectancy estimate is much less stable than it looks.

What counts as a good expectancy?

There is no universal threshold, because expectancy in risk units has to be compared against how often you get to use it and what it costs you to wait.

A reasonable way to think about it: expectancy in R tells you what each trade is worth, and your trade frequency tells you how many of those you get per year. A strategy with 0.1 R per trade and 500 trades a year compounds very differently from one with 0.5 R per trade and 20 trades a year, and the first is not obviously worse — but a 0.1 R edge is much easier to erase with costs and estimation error than a 0.5 R edge.

The more useful practical screen is not the level of expectancy but its relationship to uncertainty. Compute the standard deviation of your per-trade results, divide expectancy by it, and multiply by the square root of your trade count. If that figure is small, your expectancy estimate is not distinguishable from zero, whatever its sign — which is a statement about how many trades you have, not about the strategy.

And compare expectancy to the cost per trade. If your average cost is 0.05 R and your expectancy is 0.1 R, half of your edge is going to the broker, and a small deterioration in either number turns the strategy negative. That ratio is worth knowing before you scale up.

Common ways expectancy is computed wrongly

**Using the win rate from a different sample than the average win and loss.** The three inputs must come from the same set of trades. Mixing an out-of-sample win rate with in-sample average magnitudes produces a number that describes no period at all.

**Treating losses as negative in both terms.** The formula subtracts (1 − W) × avgLoss, so avgLoss should be entered as a positive magnitude. Entering it as a negative number flips the sign of the whole result — an easy slip and a total inversion of the conclusion.

**Ignoring position-size variation.** If your trade sizes differ, a simple average of profit and loss weights each trade equally, which is wrong in money terms. A strategy that won big on its largest position and lost small on its smallest can show a flattering expectancy per trade while being flat in money terms. Use the actual currency results, and if the sizes vary a lot, normalise to R multiples per trade instead.

**Averaging expectancy across strategies.** Expectancy is not additive in a useful way across strategies with different trade counts. The portfolio's expectancy per trade is a trade-weighted average, which can look fine while the capital-weighted result is poor.

What expectancy does not tell you

It does not tell you the risk. A positive expectancy with enormous variance will produce long losing stretches, and the probability of surviving them is a separate calculation about position sizing and ruin.

It does not tell you how long the edge lasts. It is an average over a past window, and a market that changes regime will not honour it.

It does not tell you whether it is statistically distinguishable from zero. That requires the trade count and the dispersion of results, which is why the ratio of expectancy to its standard error is more informative than the raw figure.

And it does not tell you what to trade. Two strategies with the same expectancy can have completely different correlation with each other, and therefore very different value in a portfolio. Expectancy ranks individual candidates; it does not decide what to combine.