What expectancy measures
Expectancy is the average result per trade. If a record of trades made money on average, its expectancy is positive; if it lost, negative. It describes past trades, and it says something about future trades only to the extent that they resemble the past ones.
Win rate cannot do this job alone. A method that wins 70% of the time loses money if its losses are large enough, and a method that wins 30% of the time makes money if its wins are large enough. Expectancy weighs how often you win by how much.
The formula
Expectancy = (win rate × average win)
− (loss rate × average loss)
Win rate and loss rate are fractions of all trades, and the average loss is written as a positive number. Break-even trades count toward the number of trades but add nothing to either side. The result always equals net profit divided by the number of trades, which is a useful check on the arithmetic.
Worked example in dollars
A record of 50 trades has 20 wins totalling $4,800 and 30 losses totalling $3,600.
Win rate 20 ÷ 50 = 0.40
Loss rate 30 ÷ 50 = 0.60
Average win $4,800 ÷ 20 = $240
Average loss $3,600 ÷ 30 = $120
Expectancy = 0.40 × 240 − 0.60 × 120
= 96 − 72
= $24 per trade
The check: net profit is $4,800 − $3,600 = $1,200, and $1,200 ÷ 50 trades = $24.
Expectancy in R
Dollar expectancy depends on position size, and position size changes over time. Expressing each trade in R, its result divided by its planned risk, takes size out, so the figure describes the method rather than the size you happened to trade.
Expectancy (R)
= (win rate × average win in R)
− (loss rate × average loss in R)
A record with a 40% win rate, an average win of 2.0R and an average loss of 1.0R has an expectancy of 0.40 × 2.0 − 0.60 × 1.0 = 0.80 − 0.60 = +0.20R per trade. At a planned risk of $100 a trade that is $20 per trade; at $250 it is $50. The R figure stays the same when the size changes, which is why it is the one to compare across months, accounts and setups.
Win rate and payoff ratio
The payoff ratio is the average win divided by the average loss. Measure expectancy in units of the average loss and the formula shrinks to:
Expectancy = win rate × payoff ratio
− loss rate
That makes the trade-off easy to see:
| Win rate | Payoff ratio | Expectancy |
|---|---|---|
| 30% | 3.0 | +0.20 |
| 40% | 2.0 | +0.20 |
| 50% | 1.0 | 0.00 |
| 60% | 0.5 | −0.10 |
| 70% | 0.5 | +0.05 |
| 80% | 0.2 | −0.04 |
Expectancy here is in units of the average loss. A 30% win rate and a 40% win rate produce the same result, because the lower win rate comes with larger wins. An 80% win rate still loses money when the average win is a fifth of the average loss.
Break-even win rate
Set expectancy to zero and solve for the win rate. The answer is the lowest win rate at which a given payoff ratio stops losing money:
Break-even win rate = 1 ÷ (1 + payoff ratio)
| Payoff ratio | Break-even win rate |
|---|---|
| 0.5 | 66.7% |
| 1.0 | 50.0% |
| 1.5 | 40.0% |
| 2.0 | 33.3% |
| 3.0 | 25.0% |
If your record shows a payoff ratio of 1.5, a win rate above 40% gives positive expectancy and a win rate below it gives negative. The break-even win rate calculator works this out for any ratio.
Why costs matter
Commissions, spreads, swap and slippage come out of every trade, winners and losers alike. They make the average win smaller and the average loss larger, so they cut expectancy and raise the break-even win rate at the same time. Always work out expectancy from net results.
Worked example: a short-term record
A record of 200 trades has a 55% win rate. Before costs, its average win and average loss are both $60. Costs come to $7 per round trip.
Before costs 0.55 × 60 − 0.45 × 60
= 33.00 − 27.00
= +$6.00 per trade
After costs 0.55 × 53 − 0.45 × 67
= 29.15 − 30.15
= −$1.00 per trade
Over 200 trades that is +$1,200 before costs and −$200 after. The break-even win rate moved too. Before costs the payoff ratio was 1.0 and the break-even win rate 50%. After costs the payoff ratio is 53 ÷ 67 ≈ 0.79, and the break-even win rate is 67 ÷ (53 + 67) ≈ 55.8%, just above the record's 55%.
In R, the same $7 is about 0.12R on a trade that risks $60 and about 0.02R on a trade that risks $300. The tighter the stop compared with the costs, the larger the share of every trade that costs consume.
Sample size
An expectancy worked out from 20 trades is a rough estimate. A few large wins or losses move it a long way, and it can easily show a positive figure for a method that loses over a longer run, or the reverse.
The standard error shows how rough. It is the standard deviation of per-trade results divided by the square root of the number of trades. For the record above with a 40% win rate, wins of +2R and losses of −1R:
Variance = 0.40 × (2.0 − 0.20)²
+ 0.60 × (−1.0 − 0.20)²
= 0.40 × 3.24 + 0.60 × 1.44
= 2.16
Std dev = √2.16 ≈ 1.47R
A rough range of two standard errors either side of +0.20R looks like this:
| Trades | Standard error | Rough range |
|---|---|---|
| 20 | 0.33R | −0.46R to +0.86R |
| 100 | 0.15R | −0.09R to +0.49R |
| 400 | 0.07R | +0.05R to +0.35R |
At 20 trades the range covers clearly losing and clearly winning methods. At 100 it still includes zero. Only at several hundred trades does it sit above zero. This is an approximation: it assumes trades are independent and that conditions stayed the same throughout, and neither is guaranteed. The practical point stands anyway: judge a setup on dozens of trades at the very least, and treat anything smaller as a note.
Expectancy and losing runs
Positive expectancy does not prevent losing runs. With a 40% win rate and independent trades, the chance that any given five trades in a row are all losses is 0.605 ≈ 7.8%. Over 300 trades, a record like that contains about nine separate runs of five or more losses on average. The size of each loss decides whether a run like that is survivable, and the risk of ruin calculator puts numbers on that question for your own win rate, payoff and risk per trade.
Working it out from your own record
Import your history into Aurith Journal and the dashboard shows expectancy from your net results on the free plan. Pro adds R-multiple analysis and breakdowns by setup, instrument, weekday and hour. For a quick sum by hand, the trading expectancy calculator takes a win rate and average win and loss.