How can a system that wins 40% of the time make money?
Because how often you're right and how much you're right by are two different numbers, and only their combination determines the outcome. That combination has a name.
The formula
Expectancy per trade = (Win rate × Average win) − (Loss rate × Average loss)
It is the average dollar result of one trade, computed over a record. Positive means the process makes money as trades accumulate; negative means it loses; zero means it's a very elaborate way of paying commissions.
Worked: the 40% system
A hypothetical record of 200 trades: 80 wins averaging $600, 120 losses averaging $250.
- Expectancy = 0.40 × $600 − 0.60 × $250 = $240 − $150 = +$90 per trade.
- Cross-check the long way: (80 × $600) − (120 × $250) = $48,000 − $30,000 = +$18,000 over 200 trades. And $18,000 ÷ 200 = $90. The two routes must agree; if they don't, a number is wrong.
Now in R, with the average loss defining 1R = $250. The average win is $600 ÷ $250 = 2.4R:
- Expectancy = 0.40 × 2.4 − 0.60 × 1 = 0.96 − 0.60 = +0.36R per trade.
And the bar it had to clear: breakeven win rate = 1 ÷ (1 + 2.4) = 29.4%. The system wins 40% — comfortably above. The 40% is not a flaw to be fixed. It's an input.
Why R is the better unit
The dollar expectancy of +$90 is true only at that account size and that position size. The +0.36R survives everything: double the account, double the sizing, trade a different instrument — as long as the process is unchanged, the R expectancy is unchanged. Records kept in R stay comparable for years. Records kept in dollars don't.
Costs are not a footnote
Everything above is a gross number. Subtract commissions, the spread you cross, financing and slippage. At an average round-trip cost of $8 per trade the +$90 becomes +$82 — a 9% haircut here, and a fatal one for a system whose gross edge was $10. This is the arithmetic reason turnover matters: the same cost per trade is charged more times to a high-frequency process.
Sample size is not a footnote either
Expectancy computed on 12 trades is an anecdote with a decimal point. Individual trade results vary by roughly 1R while the edge being measured might be 0.2R, so the average takes a long time to separate from zero — the standard error of a mean shrinks only as 1 ÷ √n. Four times the trades, half the uncertainty. There is no shortcut and no substitute.
Try it now
- Compute expectancy for this hypothetical record: 50 trades, 18 winners averaging $420, 32 losers averaging $180. Do it both ways (per-trade formula and the long total) and confirm they agree.
- Restate it in R, taking 1R = $180. What is the average win in R, and what is the breakeven win rate for that payoff?
- Subtract a $6 average round-trip cost per trade and recompute. What percentage of the gross edge did the costs consume? Then look at why that cost line is not one number: the two volume panes below are a broad, heavily traded fund and a much thinner one, drawn the same way.
Read a typical session off each, then say which of the two your $6 assumption belongs to. The thin one is where an edge quietly disappears.