Trading Expectancy: Three Ways to Measure the Same Edge

Two traders compare strategies. One reports an edge of thirty-four dollars a trade, the other an edge of zero point four one. Both numbers are called expectancy, both are correct, and they cannot be placed side by side. The unit was never stated, and the unit is what decides which strategy is in front.

What follows works through the formula, the three units it can be expressed in, the costs that belong inside the result, and the number of trades needed before the figure separates from zero.

What Expectancy Measures, and the Formula Behind It

Expectancy is the average result of a single trade taken across a completed sample. Multiply the proportion of winners by the average size of a winner, multiply the proportion of losers by the average size of a loser, and subtract the second product from the first.

Two properties follow from that definition and both are frequently mislaid. The figure is backward-looking: it summarises trades that have already closed and carries no claim about the next one. And it is an average, so a single unusually large result moves it, while the order in which the results arrived leaves no trace in it at all.

Take a strategy that wins 38 percent of the time, with an average winner of 310 and an average loser of 135 in account currency. The winning side contributes 0.38 times 310, or 117.80. The losing side subtracts 0.62 times 135, or 83.70. Expectancy is 34.10 per trade.

A second strategy wins 71 percent of the time with an average winner of 88 and an average loser of 145: 0.71 times 88 is 62.48, 0.29 times 145 is 42.05, and expectancy is 20.43 per trade.

On those two numbers alone the first strategy is ahead by two thirds. That conclusion survives exactly as long as nobody asks what was risked to earn it, or how often either strategy trades.

Three Expectancies, Three Different Answers

The same closed trades can be averaged in three units, and each answers a different question.

In account currency the question is how much one trade returns on average. That is the calculation above, and it is the version most often quoted. Its weakness is that it inherits whatever position size was used, so it rewards size rather than skill.

In R the question is how much is returned per unit of money risked, where one R is the amount the stop was set to lose. Suppose the first strategy risks 200 per trade and the second risks 50. Dividing each expectancy by its own risk gives 0.17R for the first and 0.41R for the second. The ranking has reversed. The second strategy is producing more than twice as much per unit of exposure, which was invisible while both were measured in currency.

Because R is measured against the stop distance, this is the unit that couples expectancy to sizing decisions, and the arithmetic behind that stop distance is worked through in the position size calculator.

Per unit of time the question is what the method returns over a month or a year, and it needs one more input that neither of the first two carries: how often the strategy trades. If the first strategy produces four trades a month and the second produces thirty, the monthly figures are 136.40 and 612.90. The second is now ahead by a factor of four and a half.

Three units, one trade history, and the first strategy leads on one of the three. None of the three is wrong. They answer how much per trade, how much per unit of risk, and how much per month, and a trader who has not said which one is being optimised has not yet stated the objective.

Why a Benchmark Without Units Says Nothing

Target figures for a healthy expectancy circulate widely. Some are amounts per trade, some are multiples of risk, some are percentages of an account. They are quoted together, as though a trader could check a strategy against whichever one is nearest to hand.

The table above is the reason that fails. An amount per trade and a multiple of risk are not the same kind of quantity, and converting between them requires the risk per trade, which the benchmark never states. A strategy at 0.17R clears a benchmark written in currency and misses one written in R, on identical trades.

A benchmark is usable when three things travel with it: the unit, the risk per trade the unit was measured against, and whether costs were inside the results. Without all three it is a number without a measurement behind it, and comparing a strategy to it produces a verdict about nothing.

Expectancy After Costs, Not Before Them

Every average above is only as good as the per-trade results fed into it, and a retail forex result is not the difference between entry and exit. Commission is charged on the position, and a position held past the daily rollover is credited or debited financing on the currency pair.

Both belong inside each trade result before the averaging starts. Their effect falls hardest on exactly the profile that looks strongest in the monthly column: a high-frequency method with small average winners pays commission on every one of them, and 30 trades a month carry 30 charges against 30 modest gains.

How each platform reports those costs is the trap. The Profit column of one MetaTrader report is gross and keeps commission and swap in separate columns beside it, while the other nets them into each deal before deciding whether it counted as a winner. Which fields to sum on which platform is worked through in the guide to the MetaTrader account statement, and the answer differs by platform.

Your Platform Already Computes It, With a Caveat

The figure does not have to be calculated by hand. MetaTrader reports it under the name Expected Payoff, defined in the documentation of MetaQuotes as a statistically derived average return for one deal, and offered as an estimate of what the next trade returns.

The same documentation carries a qualification that no strategy blog repeats. Alongside Expected Payoff the report prints the geometric mean of the equity curve, the average factor by which capital changed per trade, and MetaQuotes states that this relative change is often the more objective of the two.

The reason is compounding. An arithmetic average of currency amounts treats a gain of 500 on a 1,000 account and the same gain on a 50,000 account as one event. The geometric reading does not: it measures proportional change, which is what an account experiences as it grows and shrinks.

Where a strategy is judged from a tester run rather than from live results, the further caution in the guide to backtesting a trading strategy applies to the whole report, not only to this line.

How Many Trades Before the Estimate Means Anything

Round minimum trade counts are quoted as though the number were a property of trading. It is a property of the individual strategy, and it can be worked out.

An expectancy taken from a sample is an estimate of a mean, and the uncertainty in a sample mean is the standard deviation of the results divided by the square root of the number of trades. For the estimate to sit clearly away from zero at the conventional level, the expectancy has to exceed roughly 1.96 of those units of uncertainty.

Rearranged, the required sample is 1.96 times the standard deviation, divided by the expectancy, and the result squared.

Strategy A returns either 310 or minus 135, at 38 percent and 62 percent. The standard deviation of that pair is 216 in account currency. Dividing 1.96 times 216 by an expectancy of 34.10 gives 12.41, and squaring that gives 154.0, so the sample has to reach 155 closed trades. Strategy B, whose results scatter far less at 88 against minus 145, has a standard deviation of 106, and the same arithmetic returns 103 trades.

Two conclusions follow. The strategy with the larger currency expectancy needs the longer sample, because its results are more spread out, so the strategy that looks stronger is the one whose evidence takes longer to accumulate. And both figures are floors: real results scatter more widely than a two-outcome model, and every trade added after a rule change starts a fresh sample rather than extending the old one.

Expectancy and Risk of Ruin Answer Different Questions

A positive expectancy describes where a sample of trades ended up on average. It says nothing about the path, and the path is what closes accounts. A method with a genuine edge can still string together enough consecutive losses to breach a stop-out level, after which the remaining edge has nothing left to work with.

That is a separate calculation with separate inputs, driven by risk per trade rather than by average result, and it is set out in full in the risk of ruin guide. Expectancy answers whether the method is worth trading. Ruin probability and maximum drawdown answer whether the account survives long enough to find out.

When Expectancy Is the Wrong Thing to Optimise

Pushed on its own, expectancy per trade has an obvious maximum: widen the target until only the largest moves qualify. Average win rises, the figure rises with it, and the number of trades collapses until a year produces no usable sample. The monthly column falls while the headline number improves.

Two other cases sit outside what the metric can see. A strategy whose results are not independent, such as one that adds to a position in the same direction, breaks the assumption that each trade is a fresh draw. And a discretionary method with changing rules never accumulates a stable sample, because every adjustment resets the count that the previous section priced.

Frequently Asked Questions

What counts as a good trading expectancy?

No number answers that on its own. A figure in account currency depends on position size, a figure in R depends on where the stop was placed, and a monthly figure depends on how often the method trades. Any benchmark worth checking against states its unit, the risk per trade behind it, and whether costs were already deducted.

How is trading expectancy calculated?

Multiply the share of winning trades by the average winner, multiply the share of losing trades by the average loser, and subtract the second from the first. Every trade result entering the average must already include commission and any financing charged for holding overnight.

Does expectancy predict what a strategy will earn per day?

No. It is an average taken over trades that have already closed, and it carries no information about the next trade or the order in which future results arrive. Multiplying it by a trade frequency produces a projection, and a projection inherits every limitation of the sample it came from.

How many trades are needed before an expectancy figure is reliable?

That depends on how widely the results scatter, and it can be calculated rather than guessed. Divide 1.96 times the standard deviation of the trade results by the expectancy and square the result. Strategies with large winners and large losers need longer samples than steadier ones.

Is expectancy the same as profit factor?

No. Profit factor divides gross profit by gross loss and returns a ratio with no size attached, so it cannot say what one trade is worth. Expectancy returns an average amount per trade, in a stated unit, and the two can disagree about which of two strategies is preferable.