🎯 In 30 seconds: Whether a trading method makes money depends on two numbers together: how often it wins and how big the wins are compared with the losses. Expectancy combines them: (win rate x average win) minus (loss rate x average loss). A method that wins only 40% of the time can make money if its wins are three times its losses. A method that wins 60% can lose money if its losses are twice its wins. And you need far more trades than most people think before your measured numbers can be trusted.
The words you need
- Win rate (W): the share of trades that make money. 40 winners out of 100 trades is a 40% win rate.
- Loss rate: 1 minus the win rate. Here, 60%.
- Average win and average loss: the average dollar result of the winning trades and of the losing trades, counted after costs.
- Reward-to-risk ratio: how much you aim to make compared with how much you risk. Buy at $50, stop at $47, target $56: you risk $3 to make $6, a 2:1 ratio. When measured from actual results (average win / average loss) it is often called the payoff ratio. In formulas below it is written R.
- Expectancy: the average amount you expect to make or lose per trade over many trades.
Planned and actual reward-to-risk are often different. You may plan 2:1, but if you take profits early or let stops slip, your real payoff ratio might be 1.2:1. Always compute it from your trading journal, not from your plans.
The expectancy formula
expectancy = (win rate x average win) - (loss rate x average loss)
If you measure results in R, the dollar amount you risk per trade (see Position sizing), and your average loss is 1R, the formula becomes:
expectancy in R = (W x payoff ratio) - (1 - W)
Positive expectancy means the method makes money on average. Zero means it breaks even. Negative means each trade, on average, costs you money, and trading more just loses faster.
Worked example: two hypothetical traders
Trader A wins 40% of the time. Average win $300, average loss $100.
(0.40 x $300) - (0.60 x $100) = $120 - $60 = +$60 per trade
Trader B wins 60% of the time. Average win $100, average loss $200.
(0.60 x $100) - (0.40 x $200) = $60 - $80 = -$20 per trade
Trader B will feel more successful. Most days end green. But a few large losses erase all the small wins. This pattern is common in strategies that take small profits quickly and let losers run, and in some option-selling strategies that collect small premiums but occasionally take a large hit.
Trader A has the opposite feeling. Losing six trades out of ten is uncomfortable, and long losing streaks are normal (see Drawdowns and losing streaks). But the math works. Many trend-following methods look like Trader A.
The breakeven win rate
Set expectancy to zero and solve for the win rate. If your average loss is 1R and your average win is R times that:
breakeven win rate = 1 / (1 + R)
| Average win : average loss | Breakeven win rate (before costs) |
|---|---|
| 0.5 : 1 | 66.67% |
| 1 : 1 | 50% |
| 1.5 : 1 | 40% |
| 2 : 1 | 33.33% |
| 3 : 1 | 25% |
| 4 : 1 | 20% |
| 5 : 1 | 16.67% |
This is why a 40% win rate is not a bad number by itself. At 2:1 you only need 33.33% to break even. At 1:1, 40% is a losing method.
Expectancy grid
Here is expectancy in R per trade for a range of win rates and payoff ratios, before costs:
| Win rate | 1 : 1 | 1.5 : 1 | 2 : 1 | 3 : 1 |
|---|---|---|---|---|
| 30% | -0.40R | -0.25R | -0.10R | +0.20R |
| 35% | -0.30R | -0.125R | +0.05R | +0.40R |
| 40% | -0.20R | 0.00R | +0.20R | +0.60R |
| 45% | -0.10R | +0.125R | +0.35R | +0.80R |
| 50% | 0.00R | +0.25R | +0.50R | +1.00R |
| 55% | +0.10R | +0.375R | +0.65R | +1.20R |
| 60% | +0.20R | +0.50R | +0.80R | +1.40R |
To turn R into dollars, multiply by your risk per trade. At $100 risk, +0.20R is +$20 per trade on average. Over 50 trades that is an expected $1,000, but the actual result will scatter widely around that figure.
Costs move the line
Every trade pays something: the bid-ask spread, any commissions and fees, and slippage on stops. Costs make wins smaller and losses bigger. What trading really costs lists them.
Example: a method wins 50% of the time with a 1.2:1 payoff. Before costs, expectancy is (0.50 x 1.2) - 0.50 = +0.10R. Now add costs of 0.05R per round trip. Wins become 1.15R and losses become 1.05R:
(0.50 x 1.15) - (0.50 x 1.05) = 0.575 - 0.525 = +0.05R
Costs cut the edge in half. The breakeven win rate rises from 45.45% to 1.05 / (1.15 + 1.05) = 47.73%. Methods with small edges and many trades are hit hardest. That is one reason research on very active traders is so discouraging. In a study of 66,465 US households from 1991 to 1996, frequent and infrequent traders earned about the same before costs. After the spread and commissions, the most active group earned 11.4% a year while the market returned 17.9%.
How many trades before you can trust the numbers?
Your measured win rate is an estimate, and small samples are noisy. A rough 95% range for a measured 40% win rate is:
| After 20 trades | about 18.5% to 61.5% |
| After 50 trades | about 26.4% to 53.6% |
| After 100 trades | about 30.4% to 49.6% |
| After 200 trades | about 33.2% to 46.8% |
These use the standard formula for the error of a proportion, 1.96 x square root of (W x (1 - W) / n). After 20 trades, a "40% win rate" is consistent with anything from a clear loser to a strong winner. Even 100 trades leaves a wide range. Payoff ratios are noisy too, because one big winner can change the average a lot.
Practical meaning: do not judge a method after a good or bad week. Keep risk small and keep collecting results. Testing a rule on past data first, with the backtester, can give you a larger sample faster, as long as you avoid the traps in Does technical analysis work?
What the evidence says about expectancy in practice
Positive expectancy is hard to find and harder to keep after costs. The Brazilian day-trading study that followed people who kept day trading for at least 300 days found 97% lost money, and found no evidence that traders improved with practice. That does not prove no one can have an edge. It does mean you should assume you do not have one until your own records, over many trades, say otherwise.
Try it
Take your last 20 trades, real or from the paper portfolio. If you do not have 20, make them in the paper portfolio first. Compute win rate, average win, average loss and expectancy in dollars and in R. Then subtract a realistic cost per trade and compute it again. Finally, look up the 95% range for your win rate in the table above and ask: is my edge still positive at the bottom of that range?
- What is the expectancy formula? Answer: Expectancy = (win rate x average win) - (loss rate x average loss).
- Trader B wins 60% of trades with an average win of $100 and an average loss of $200. What is the expectancy? Answer: -$20 per trade ((0.60 x $100) - (0.40 x $200)), even though most trades win.
- Your average win is twice your average loss (2:1). What win rate do you need to break even before costs? Answer: 33.33% (1 / (1 + 2)).
- After 20 trades your win rate is 40%. How much can you trust that number? Answer: Not much. The rough 95% range after 20 trades is about 18.5% to 61.5%, which fits anything from a clear loser to a strong winner.