Win rate is lying: expectancy, profit factor, AHPR and GHPR

Why win rate is the most quoted and least useful number

Win rate is the share of trades that closed in profit. It is quoted on every forex robot sales page because it is easy to understand and easy to make look good. It is almost useless on its own because it says nothing about the size of wins and losses.

A strategy that takes $10 winners 90% of the time and a $200 loser 10% of the time wins nine trades in ten and loses money: nine times $10 is $90 against one loss of $200. A trend follower that wins 35% of the time with winners three times the size of losers makes money steadily. You cannot tell these apart from win rate. You can tell them apart from the three numbers below.

Expectancy: the average trade

Expectancy is net profit divided by number of trades: what the average trade made or lost. It can also be written as (win rate × average win) − (loss rate × average loss), which makes the point explicit: win rate is only one of four inputs.

ConfirmedTrades shows expectancy in account currency. Positive expectancy is the minimum requirement for a strategy to be worth anything; the Score's profitability component is zero unless expectancy is positive. Compare expectancy with the typical cost per trade from the Execution panel. If the average trade makes $4 and costs $3 in spread and slippage, the edge is paper thin.

Profit factor: gross wins over gross losses

Profit factor is total gross profit divided by total gross loss. A profit factor of 1.5 means the strategy made $1.50 for every $1 it lost. Below 1 it loses money; exactly 1 is break-even.

The Score uses profit factor as its profitability input, scaling from 1.0 (no points) to 2.5 (full 25 points). Most honest, durable strategies on real money sit between about 1.3 and 2.0 over long records. Very high profit factors on short records usually mean the losing trades have not happened yet, which is the martingale pattern described in spotting fake EA results. If there are no losing trades at all, profit factor is undefined and the page shows that rather than a number.

Average win vs average loss

The payoff ratio (average win divided by average loss) is the other half of win rate. With these two numbers you can calculate the break-even win rate: 1 / (1 + payoff ratio). A strategy with winners twice the size of its losers only needs to win more than a third of the time.

The AI review flags a record where the average loss is far larger than the average win, because that shape is the one that ends badly. It is not automatically disqualifying; a high-probability mean-reversion strategy can legitimately have small winners and larger losers. But the win rate then has to be high enough, and the tail loss has to be bounded by a stop.

AHPR and GHPR: what compounding actually does

Holding-period return is the profit of a trade divided by the equity before it, in other words the return as a percentage of the account at the time. The average of those across all trades is the arithmetic mean holding-period return, AHPR. The geometric mean, GHPR, is the rate that, compounded once per trade, would produce the same final result.

GHPR is always less than or equal to AHPR, and the gap between them is the cost of volatility. Two Expert Advisors with the same AHPR can have very different GHPR if one of them has wilder swings; the wild one compounds worse. When an account page shows a healthy AHPR but a GHPR near zero, the account is being whipsawed and the per-trade risk is too high for its edge.

Both are shown in percent on the account page, computed from the per-trade returns. Because they are percentages of equity rather than currency, they compare across account sizes, like the time-weighted return described in time-weighted return explained.

Streakiness: the Z-score

One more number that rewards a look: the runs-test Z-score. It asks whether wins and losses cluster more or less than random. A strongly negative Z means wins follow wins and losses follow losses more than chance, which is typical of trend systems and, less happily, of martingale systems about to hit a long losing run. A strongly positive Z means wins and losses alternate. Near zero means the sequence looks random. The page shows a confidence alongside it so small samples do not over-claim.

A four-number habit

When you look at any record, read these before the win rate:

• Expectancy: positive, and bigger than costs?
• Profit factor: above 1.3 on a long record?
• Average win vs average loss: is the payoff ratio consistent with the win rate?
• GHPR vs AHPR: is compounding being wasted on volatility?