The expectancy formula
Expectancy combines how often you win with how much you win and lose:
expectancy = WR × avg win + (1 − WR) × avg loss
- WR is your win rate as a decimal (45% = 0.45).
- avg win is the average profit of your winning trades.
- avg loss is the average loss of your losing trades, written as a negative number.
Because the loss is negative, the second half of the formula pulls the result down. If the result is positive, your trades made money on average over the sample. If it is negative, they lost money on average.
Expectancy is the single number that answers "is this working?" more directly than win rate or profit factor, because it is measured in money (or R) per trade.
Worked example in dollars
Say your journal shows 100 closed trades with a 45% win rate, an average win of $300 and an average loss of −$150.
expectancy = 0.45 × 300 + 0.55 × (−150) = 135 + (−82.50) = +$52.50 per trade
Over those 100 trades that is 100 × $52.50 = $5,250 in total. Note this describes what happened, not what will happen next.
Now subtract costs. If commissions and fees average $6 per round trip, net expectancy is 52.50 − 6 = +$46.50. If you trade frequently with a small edge, costs can take a large share of it, so compute expectancy on net results.
Here is the reverse case. A 70% win rate, $100 average win and −$250 average loss:
expectancy = 0.70 × 100 + 0.30 × (−250) = 70 − 75 = −$5 per trade.
Seven wins out of ten, and still losing money on average. That is why win rate alone is not enough, as the win rate guide explains.
Expectancy in R
If you record every trade as an R-multiple, you can compute expectancy in R. Set the average loss to −1R (your planned risk) and the average win to your typical winner in R:
expectancy = 0.45 × 2 + 0.55 × (−1) = 0.90 − 0.55 = +0.35R per trade
Expectancy in R is independent of position size, so it lets you compare strategies or periods even if you changed your sizing. The table below shows expectancy in R for different win rates and average wins, with the average loss fixed at −1R:
| Win rate | Avg win 1R | Avg win 1.5R | Avg win 2R | Avg win 3R |
|---|---|---|---|---|
| 30% | −0.4R | −0.25R | −0.1R | +0.2R |
| 40% | −0.2R | +0R | +0.2R | +0.6R |
| 50% | 0R | +0.25R | +0.5R | +1R |
| 60% | +0.2R | +0.5R | +0.8R | +1.4R |
The zero cells are break-even. Reading across the 30% row, a strategy that wins only three times in ten still has a positive expectancy if winners average more than about 2.3R. Check your own figures with the R-multiple calculator.
Which lever moves expectancy most?
Start from the dollar example: 45% win rate, $300 average win, $150 average loss, expectancy +$52.50. Now improve one input at a time by a modest amount:
| Change | Calculation | Expectancy |
|---|---|---|
| Baseline | 0.45 × 300 + 0.55 × (−150) | $52.50 |
| Cut avg loss by 20% to −$120 | 0.45 × 300 + 0.55 × (−120) | $69 |
| Raise win rate 5 points to 50% | 0.50 × 300 + 0.50 × (−150) | $75 |
| Raise avg win by 10% to $330 | 0.45 × 330 + 0.55 × (−150) | $66 |
Each change helps. Which one is realistic for you depends on your trading. Losses are often the easiest to work on, because they are driven by decisions you control: stop placement, honouring the stop, and avoiding trades you never planned. Your journal tells you where the gap actually is.
How many trades do you need?
Expectancy from a small sample is noisy. With 20 trades, one large winner or loser can flip the sign. There is no magic number, but a few habits keep you honest:
- Always report the trade count next to expectancy.
- Recompute after every 25 or 50 trades and see whether the figure is stable or jumping around.
- Compute expectancy with and without your single largest win. If removing one trade turns the result negative, the edge rests on that trade.
- Split by setup. A combined positive expectancy can hide one setup that loses money on average.
Expectancy also tells you nothing about the path. Two strategies with the same expectancy can have very different losing streaks and drawdowns. Pair it with your maximum drawdown and your profit factor.
Expectancy versus profit factor
Expectancy and profit factor use the same raw material but answer different questions. Profit factor is a ratio: gross wins ÷ |gross losses|. Expectancy is an amount: how much the average trade made or lost.
Both cross their break-even line at the same moment. When expectancy is exactly zero, gross wins equal gross losses and profit factor is exactly 1.0. Above that, both say the sample was profitable.
Where they differ is scale. A profit factor of 1.5 could come from trades averaging $5 or $500. Expectancy tells you which, and that matters when you compare the edge with your costs. If expectancy is $5 per trade before costs and your round trip costs $4, most of the edge goes to fees, which a ratio computed before costs would not show.
Use expectancy to judge whether the edge is large enough to be worth trading, and profit factor to compare periods or setups on a size-free scale.
Tracking expectancy in your journal
You need four numbers, and a journal gives you all of them: number of wins, number of losses, total of winning trades and total of losing trades. From those:
- WR = wins ÷ (wins + losses).
- avg win = total of winners ÷ wins.
- avg loss = total of losers ÷ losses (a negative number).
- expectancy = WR × avg win + (1 − WR) × avg loss.
Decide how to treat break-even trades and stick to it. Counting them as neither wins nor losses is common, but then mention how many there were.
The trading journal spreadsheet sets up these formulas. A journal app that imports closed trades from your broker can calculate expectancy per setup automatically.