Expectancy vs profit factor: when to use which

The two definitions side by side

Expectancy per trade is the average result of a trade: `E = (W × avgWin) − ((1 − W) × avgLoss)`. It comes out in currency, or in units of risk if you divide through by avgLoss, in which case it is the average R multiple per trade.

Profit factor is the ratio of totals: gross profit divided by gross loss. Both are computed from the same W, avgWin and avgLoss, so they are related — but the relationship is not a one-to-one mapping, because profit factor does not contain the trade count.

That single omission is the source of every practical difference between them.

What each one is actually good for

**Expectancy is the number you size on.** Position sizing needs to know what a trade is worth relative to what it risks, which is exactly what expectancy in R units provides. If your expectancy is 0.2 R per trade and you risk 1% per trade, your expected gain per trade is 0.2% of the account, and that figure feeds directly into how the account compounds.

**Profit factor is the number you screen on.** It is fast to read, normalised by the losses rather than by capital, and comparable across strategies on the same instrument and window. It is a reasonable first filter and a poor basis for a decision on its own.

A useful division of labour: use profit factor to decide which strategies deserve a closer look, and expectancy to decide how much to risk on the ones that survive.

The case that shows why they diverge

Consider two strategies, both with a 50% win rate. Strategy A wins 1.2 units and loses 1 unit. Strategy B wins 12 units and loses 10 units.

Expectancy: A is `0.5 × 1.2 − 0.5 × 1 = 0.1` units per trade. B is `0.5 × 12 − 0.5 × 10 = 1` unit per trade. B is worth ten times as much per trade.

Profit factor: both are `(0.5 × 1.2) / (0.5 × 1) = 1.2` for A, and `(0.5 × 12) / (0.5 × 10) = 1.2` for B. Identical.

The profit factor says the two strategies are equivalent. The expectancy says one is ten times more valuable per trade. Both statements are true, and they are about different things: profit factor is scale-free by construction, and expectancy is not.

Now add costs. If a round trip costs 0.05 units, Strategy A's expectancy falls to 0.05 — halved. Strategy B's falls to 0.95 — barely changed. The same cost destroys half the edge of one and none of the other, and the profit factor, computed on gross results, shows nothing at all.

How a good profit factor can hide a thin expectancy

This is the failure mode worth internalising. Profit factor is normalised by losses, so it is silent about absolute magnitude. A strategy with many small trades can post a profit factor of 2.0 while its expectancy per trade is smaller than the cost of executing it.

The arithmetic: if the average win is 1.0 and the average loss is 0.5, with a 50% win rate, expectancy is `0.5 × 1.0 − 0.5 × 0.5 = 0.25` and profit factor is `0.5 / 0.25 = 2.0`. Healthy. Now suppose each round trip costs 0.3 — large relative to the 1.0 average win because the strategy trades a short horizon on a wide-spread instrument. Expectancy falls to −0.05. The strategy loses money on every trade while its gross profit factor still reads 2.0.

This is not a contrived example. It is precisely what happens to short-horizon strategies on instruments where the spread is a meaningful fraction of the average move, and it is why the same rules can be profitable for one participant and unprofitable for another.

How they behave differently as the sample changes

Expectancy is an average, so it is sensitive to outliers. One trade that made ten times the average win moves the mean noticeably. That is why the median win and median loss are worth computing alongside the means: if the means and medians tell different stories, the edge depends on rare large winners and the expectancy estimate is unstable.

Profit factor is a ratio of sums, so it is also outlier-sensitive, and in a way that is harder to see — a single enormous winner can lift it substantially without changing the typical trade at all. The standard check applies to both: remove the best few trades and recompute.

Where they differ most is in how they respond to frequency. Doubling the number of identical trades leaves profit factor unchanged and leaves expectancy unchanged, but it doubles the total profit and doubles the total cost. Neither ratio tells you that the strategy's viability depends on whether the edge per trade exceeds the cost per trade — that comparison has to be made explicitly.

A short procedure that uses both

1. Compute the profit factor with realistic costs included. If it is below about 1.2, stop and treat the strategy as unproven rather than marginal.

2. Compute expectancy in R units, from out-of-sample trades only. This is the number that feeds your sizing.

3. Compare expectancy to your cost per trade in the same units. If costs are a large fraction of expectancy, the strategy is a bet on execution quality rather than on its signal.

4. Check the trade count and remove the best few trades before recomputing both. Two numbers that survive the same robustness checks are worth more than two that do not.

5. Use the expectancy to size and the profit factor to rank. Do not use either as a verdict.

What neither number tells you

Neither tells you the risk of ruin. That depends on position sizing and the loss distribution, and a strategy can have a good expectancy and blow up at a size that is too large for its variance.

Neither tells you about correlation with what you already hold. Two strategies with identical expectancies can be one bet or two, and the portfolio consequence is completely different.

Neither tells you whether the edge persists. Both are averages over a past window, and the next window is not obliged to resemble it.

And neither tells you whether you would have kept trading. A strategy with a positive expectancy and a 50% drawdown is a good strategy that most people abandon at the worst possible moment.