Expected value per trade: why three calculators give three different answers

Expected value tells you what one trade brings on average. The formula is short and looks beyond dispute. Yet take one trade history, run it through three tools, and you get three different numbers. Nothing mystical is going on: the arithmetic agrees, the definitions do not.

Three methods that are supposed to agree

One. Add up every trade result and divide by the number of trades. The average trade.

Two. Through the win rate: win rate × average win − (1 − win rate) × average loss.

Three. In R multiples, where risk is the unit: win rate × average win in R − (1 − win rate) × 1R.

The first two are algebraically identical — provided the sample is the same and everyone agrees on what counts as a winning trade. The third answers a different question: not how much money, but how many risks. Mixing them is a mistake, and mixing them is exactly what usually happens.

Where the numbers part company

Break-even trades. A trade closes at zero — is it a win, a loss, or neither? Drop those from both sides and your win rate climbs while the money stays the same. There is no universal rule here, but there must be one rule, written down.

Commission. Before or after? For a scalper with hundreds of trades, commission alone flips the sign. Gross expected value is not a lie — it simply answers a question nobody needs answered.

Partial exits. A position closed in three pieces: one trade or three? The answer sets your denominator. Both readings are defensible — one by intent, the other by execution.

Mixed currencies. Trades in different currencies get added at which rate — the rate on the trade date, or today's? The second is easier to compute and further from reality.

Period boundaries. Opened in March, closed in April — which month owns it? Select by open date in one report and by close date in another, and two tables built from the same data will disagree while both are "correct".

Our own case

We caught this in our own product. For a while MaxProfit displayed three different expected values for the same sample — in the summary, in the report and in a dashboard tile — because three places handled break-even trades and commission differently. Fixed in 6.12, along with moving trade calculation to a strict FIFO that applies commission across every allocation row.

The same release fixed period selection: trades are now picked by close date, so a trade crossing a month boundary stopped falling out of both neighbouring reports at once.

We mention it not out of penitence but because the lesson generalises: a disagreement between metrics is almost never in the formula. It is in definitions nobody agreed on.

What to do about it

• Fix four rules: what counts as a trade, what happens to a zero result, where commission enters, and which date selects the period.
• Compute expected value after commission. Anything else is an exercise.
• Do not compare your expected value with someone else's until you know their definitions. Usually you are comparing different things.
• Compare yourself with yourself over time. With rules held constant, that is the only honest comparison available.

And remember the number means little on a short history: thirty trades produce an expected value that one lucky outlier can overturn. How many trades you need before the figure deserves trust is the subject of a separate post on profit factor.