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Positive expectancy

The condition in which expected net outcome per trade is above zero for stated rules, costs and population.

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Who this is for — Readers checking whether the estimated net average of a process is above zero while keeping the calculation separate from estimation uncertainty and other dimensions of risk.

Positive expectancy is the condition in which expected net outcome per trade is above zero for a stated strategy and population. The general Expectancy entry explains the calculation; this page explains what E_net > 0 means and what it cannot establish.

In plain terms — Estimated average outcome can be positive even when many individual trades lose. It is not a forecast of the next outcome and does not, by itself, describe drawdown, tails, capacity or risk of ruin.

Expectancy: from gross to net estimate Breakdown of gross expectancy, costs and net estimate with an example in R multiples and a reminder about sampling uncertainty. Expectancy: from gross to net estimate Probabilities and average outcomes produce an estimate; costs and uncertainty change how it should be read. 1 · Gross estimate E_gross = p(win) × average win− p(loss) × average loss magnitude Illustrative estimate: 0.20R per trade beforecosts. 2 · Costs − 0.05R Commissions, spread,slippage and otherrelevant costs. 3 · Net estimate = 0.15R Estimated mean after costs, notguaranteed profit. ± 4 · Uncertainty Confidence interval · trade dependence · regime shifts · selection error 0.20R gross − 0.05R costs = 0.15R net Cyclepedia diagram · Emiciclo
The formula yields an estimate from the observed sample. Costs and slippage separate gross from net value; uncertainty separates the estimate from the unknown population parameter.

Formula and measurement unit

In the simplified case with winning and losing trades only:

E_net = p(win) × average(win) − p(loss) × |average(loss)| − average cost

Here |average(loss)| is the positive magnitude of the average loss. The absolute value prevents a double negative when losing outcomes are stored as negative numbers.

If breakeven trades or more outcome categories exist, the correct calculation adds every outcome multiplied by its probability, then subtracts costs. Currency amounts, percentages and risk multiples R must not be mixed in the same series.

Arithmetic example — With 40% of trades at +2R and 60% at −1R, gross expectancy is 0.40 × 2R − 0.60 × 1R = +0.20R. If spread, commissions and slippage average 0.05R per trade, estimated net expectancy becomes +0.15R. The result describes those data and assumptions, not a future guarantee.

A positive estimate and the true value

The probabilities and averages in the formula are usually estimated from a sample. A positive number may therefore reflect chance, data selection, many tested variants or a regime that will not recur. No universal trade-count threshold works for every strategy: uncertainty, out-of-sample stability and process consistency matter.

Check Question
Costs Are spread, commissions, slippage and impact consistent with size?
Sample Are observations sufficiently representative and non-duplicated?
Out of sample Does the result hold on data not used to select the rules?
Regime Does the average depend on one market context only?
Distribution Is the result broad or concentrated in a few outliers?

Limit — `E_net > 0` is an average condition, not an automatic capital-allocation decision. Two strategies with the same expectancy can have very different drawdowns, serial dependence, tails and capital requirements.

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