What Is a Worked Example of Expectancy?

Direct answer

A worked example of Expectancy shows how to compute the average result per trade (or decision) from a small set of inputs: the probability of winning, the probability of losing, and the payoff amounts for wins and losses. The worked part means you actually plug numbers into the formula and keep every assumption visible.

Mechanics: definition and how the calculation works

Expectancy (often written as E) is a way to estimate the long-run average outcome of a repeatable decision process. A common setup for a trade-like decision is:

Let p(win) be the probability of a win.
Let p(loss) be the probability of a loss.
Let W be the net profit of a winning trade (after costs).
Let L be the net loss magnitude of a losing trade (as a positive number).

Then expectancy can be expressed as:

E = p(win) × W − p(loss) × L

If you are using the simplest two-outcome model, you also assume:

p(win) + p(loss) = 1

Units matter. If W and L are measured in “account currency per trade,” then E is also in “account currency per trade.” If you use “pips” or “percent,” then E will be in those same units.

Evidence or example: a transparent numerical worked scenario

Assume a decision rule that results in only two outcomes: win or loss, with the following clearly stated assumptions:

p(win) = 0.40 (40% of decisions end in a win)
p(loss) = 0.60 (60% end in a loss)
W = +2.0 units (a win is +2.0 after costs)
L = 1.5 units (a loss is −1.5; we treat L as the magnitude 1.5)

Now compute:

E = 0.40 × 2.0 − 0.60 × 1.5 E = 0.80 − 0.90 E = −0.10 units per decision

Interpretation (careful wording): under these assumptions, the average net outcome per decision is negative. Importantly, this does not predict future results for any specific sequence; it summarizes what your model implies when those inputs are correct and stable.

To sanity-check the arithmetic, compare weights:

The win contribution is 40% of +2.0 → +0.8
The loss contribution is 60% of −1.5 → −0.9
Net average → −0.1

Limitations and risks: what can make Expectancy misleading

At least one material failure mode is that expectancy depends entirely on the correctness and stability of inputs:

Costs and netting mistakes: If you use gross profit/loss instead of net amounts (including spreads, commissions, slippage), the computed expectancy can look better than it really is.
Changing market/provider conditions: Probabilities and payoffs can shift. Even if expectancy is positive in one sample, it may not hold when conditions change.
Outcome selection and non-representative data: If the sample used to estimate p(win) or payoffs is biased, the worked calculation will be mathematically correct but empirically unreliable.
Two-outcome simplification: Real outcomes can include breakeven, partial fills, or varying win sizes. A “win/loss only” model may hide important distribution details.

Verification or next question

Because the calculation is simple, you can independently verify it:

Recompute E using your own stated p(win), W, and L.
Confirm that probabilities sum to 1 (in the two-outcome model).
Check that payoffs are measured consistently (same units, and net of costs).

A practical next question is: Does your definition of “win” and “loss” match the net results you can actually measure (including costs) and is the probability estimate based on a representative sample?