Expectancy
Expectancy
Estimate expectancy from win rate and win/loss ratio.
Per trade
+12.50 $
In R
+0.13 R
The balance of an average trade
Expectancy answers one simple question: on average, how much does each trade of your strategy make or cost? The calculation combines three numbers you already know if you keep a journal: your win rate, your average win on winning trades and your average loss on losing trades. The result is expressed per trade, in your account currency.
A positive expectancy means that over the period you measured, your method made more than it cost on average. A negative expectancy means the opposite, and it can happen even with a high win rate: winning small amounts often does not make up for rare but heavy losses. The calculator also shows the result in R multiples, using your average loss as the unit of measure, which makes it possible to compare strategies that do not risk the same amounts.
The formula explained
Expectancy = (win rate × average win) - (loss rate × average loss). The loss rate is simply 100% minus the win rate. Example with a 45% win rate, 150 average win and 100 average loss: 0.45 × 150 - 0.55 × 100 = +12.50 per trade. For the R version, the calculator first divides the average win by the average loss to get the reward-to-risk ratio, then applies: win rate × ratio - loss rate.
The calculator's example, step by step
Take the prefilled values above: 45% win rate, 150 $ average win, 100 $ average loss. First the winners' share: 45 trades out of 100 won 150 $ on average, so 0.45 × 150 = 67.50 $ per trade. Then the losers' share: 55 out of 100 lost 100 $ on average, so 0.55 × 100 = 55.00 $ per trade. The balance is 67.50 - 55.00 = +12.50 $: that is the expectancy, and exactly what the calculator shows. In R units, the average win is 150 ÷ 100 = 1.5 times the average loss, so 0.45 × 1.5 - 0.55 = 0.125, rounded to +0.13 R on screen. Note the proportion: two flows of 67.50 and 55.00 leave only 12.50 behind · expectancy is almost always a small remainder between two large numbers, which is why it flips sign so easily.
Expectancy in R, by win rate and ratio
The zeros mark break-even: at a 1:1 ratio it takes a 50% win rate, and at a 30% win rate only 3:1 comes back above.
| Win rate | 1:1 ratio | 1.5:1 ratio | 2:1 ratio | 3:1 ratio |
|---|---|---|---|---|
| 30% | -0.40 R | -0.25 R | -0.10 R | +0.20 R |
| 40% | -0.20 R | 0.00 R | +0.20 R | +0.60 R |
| 50% | 0.00 R | +0.25 R | +0.50 R | +1.00 R |
| 60% | +0.20 R | +0.50 R | +0.80 R | +1.40 R |
What the number does not say
Expectancy is an average over your past trades, nothing more. It says nothing about the order results came in: a method with positive expectancy still goes through losing streaks, sometimes long ones · the Monte Carlo simulation is what shows that spread. It is only as good as its three inputs: over twenty trades, a single large position moves the whole average, and the number changes with every new trade. It includes fees, financing and slippage only if your averages already include them. Above all, it describes a past · nothing forces the next trades to look like the previous ones.
The classic mistake
Judging a method by its win rate. It is the most visible number, and it is never enough on its own. Put the arithmetic on a concrete case: 70% winning trades, but a 50 $ average win against a 150 $ average loss. Winners' share: 0.70 × 50 = 35.00 $. Losers' share: 0.30 × 150 = 45.00 $. Balance: -10.00 $ per trade, with seven winners out of ten. The reverse exists too: a 30% win rate with a 3:1 ratio gives 0.30 × 3 - 0.70 = +0.20 R. A win rate only takes on meaning next to the win/loss ratio · expectancy is precisely the number that holds them together.
Frequently asked questions
What does a negative expectancy mean?
On the numbers you entered, each trade cost that amount on average. It can happen even with more than 50% winning trades, as soon as the average loss clearly exceeds the average win. The figure describes your past history; it does not predict your next trades.
What is the R shown next to the result?
R uses your average loss as the unit of measure. An expectancy of +0.20 R means a trade returned on average 20% of what a typical loss costs. This view is useful for comparing two strategies that do not stake the same amounts, whereas the currency value depends directly on your position sizes.
How many trades do I need before the number means something?
The calculation works with any values, but averages drawn from a dozen trades swing wildly with every new trade. The larger your sample, the more your win rate and averages settle down. Many traders wait until they have several dozen trades in their journal before reading expectancy as a characteristic of their method.
Are fees and slippage included in the expectancy?
The calculation only knows the three numbers you feed it. If your average win and average loss come from your journal, net of fees and execution slippage, then the expectancy reflects them. If you start from theoretical values · the planned target and stop · it ignores them, and around zero, a few dollars of fees per trade are enough to push an expectancy from positive to negative.
Why does my expectancy change so much from month to month?
Because it is an average, and an average over few trades is fragile: one unusual result · an exceptional win, a loss widened by a gap · shifts all three inputs at once. Over a small sample these swings are normal and say little about the method. What can be read is the trend of the number as the sample grows, not its day-to-day value.
See also
Monte Carlo
Replay your trading system across hundreds of randomly drawn trade sequences. See the median, best and worst outcomes and how wide the range of paths really is.
Required win rate
Work out the minimum win rate you need to break even from your average win and average loss. Free, with no sign-up, everything runs inside your browser.
Kelly
Compute the Kelly criterion from your win rate and win/loss ratio, and see the half and quarter Kelly figures traders actually watch. Free, no sign-up.