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Expectancy

Expectancy is presented everywhere as a single number. It is an estimate from a sample, which means it has an error bar, and on most real samples that bar crosses zero.

2 min read

The formula

expectancy = (win rate × average win) − (loss rate × average loss)

The output is what one average trade is worth. Positive means the method pays; negative means it costs, regardless of how the winners feel.

Both averages must be net of costs — see net P&L. Expectancy computed on gross results describes a market you cannot trade in.

The number it implies: break-even win rate

For any pair of average win and average loss sizes, there is a win rate below which the method loses money:

break-even win rate = average loss ÷ (average win + average loss) × 100

With a $320 average win and a $200 average loss, that is 38.5%. Below it the arithmetic loses no matter how disciplined you are; above it, a "low" win rate is perfectly healthy. This is why win rate quoted alone is close to meaningless — the same 45% is excellent at 2:1 and fatal at 1:2.

The edge case: it is an estimate

Expectancy is computed from a sample, so it carries a standard error. Nearly every tool reports it as though it were measured.

The uncertainty in the win rate follows the standard error of a proportion, and it propagates into the expectancy figure. On a thirty-trade sample the resulting range routinely covers both a healthy positive number and a clearly negative one — which means the point estimate on its own supports no decision at all.

Our expectancy calculator asks for the sample size for exactly this reason and returns the range rather than only the average. If the interval crosses zero, the honest statement is that you do not yet know.

In R instead of money

Expectancy is often quoted in R — multiples of the amount risked — rather than currency:

expectancy in R = (win rate × average win in R) − (loss rate × average loss in R)

An expectancy of 0.25R means the average trade returns a quarter of what you risk on it. The advantage is that the figure survives a change in account size, so it can be compared across time and between traders. See R-multiple.

What it hides

Order. Expectancy is an average, and averages have no memory. A method with +0.3R expectancy that delivers its losses in a run of fourteen can still end an account before the average asserts itself. That risk is a question about sequence, which is what a Monte Carlo simulation answers and an average never will.

More in Trading terms, defined by how they are computed

  • Net P&LThe result of a trade after commission and swap, and why the sign convention in broker exports makes double-counting so easy.
  • Profit factorGross profit divided by gross loss, the edge case that breaks it, and why a high profit factor on few trades means almost nothing.
  • R-multipleExpressing results as multiples of the amount risked, why it survives account growth, and the case where R stops being comparable.
  • Win rateWhat share of trades finished positive, how break-even trades are counted, and why the figure is uninterpretable without the win-to-loss ratio.
  • Maximum drawdownThe largest peak-to-trough fall in your account, and the measurement choice that decides whether a prop account survives.
  • Trailing drawdownA loss limit that rises with your account and usually never falls back, plus the two sentences in a rulebook that decide when it can end your account.
  • Consistency ruleA cap on how much of your profit may come from a single day or trade, why it exists, and how it turns a winning account into an unpayable one.