Statistics
What profit factor leaves out
Profit factor is the first number most traders quote and the least useful one on its own. Two systems can share a profit factor of 1.5 and produce completely different amounts of money.
Profit factor is gross profit divided by gross loss. Above 1 the system made money, below 1 it lost money, and that is very nearly everything the number tells you.
a ratio, so the units cancel and the dollars disappear
Because the units cancel, profit factor cannot distinguish between a system that grinds out small consistent gains and one that makes a few large ones. Expectancy can. It is the average amount a single trade is worth:
W and L are the win and loss rates, A the average sizes
Two systems, one profit factor
Take a system that trades 40 times, wins half of them, makes $300 on a winner and loses $200 on a loser. Gross profit is $6,000, gross loss is $4,000, so the profit factor is 1.5. Expectancy is $50 a trade and the account ends up $2,000 ahead.
Now take a system that trades 400 times, wins 40 percent, makes $60 on a winner and loses $26.67 on a loser. Gross profit is $9,600, gross loss is $6,400. Same 1.5. But expectancy is $8 a trade across ten times as many trades, which is $3,200.
| System A | System B | |
|---|---|---|
| Trades | 40 | 400 |
| Win rate | 50% | 40% |
| Average win | $300 | $60 |
| Average loss | $200 | $26.67 |
| Profit factor | 1.50 | 1.50 |
| Expectancy per trade | $50.00 | $8.00 |
| Net profit | $2,000 | $3,200 |
System B earns more with a lower win rate and a sixth of the expectancy, because it does the thing more often. Profit factor sees none of that.
Where each number is useful
Profit factor is a quick sanity check on whether an edge exists at all, and it is comparable across instruments and account sizes, which is why services publish it. Expectancy tells you what a trade is worth. Multiply it by how many trades you get and you have the only figure that pays for anything.
The pairing to watch is expectancy and frequency together. A tiny edge repeated often beats a large edge you rarely get to use, until execution costs eat the small one. That is a separate problem, and it has its own arithmetic.