You Win 40% of Your Trades and Still Make Money. The Math Behind Win Rate and Payoff Ratio
6 min read
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6 min read
Two traders each make 100 trades. Trader A wins 70 of them. Trader B wins only 40. Which one finished the year with more money?
Most people guess Trader A. In the example below, Trader A loses money and Trader B makes money. The reason is not luck. It is the link between win rate and payoff ratio, and one simple number called expectancy ties them together.
All the figures in this post are made-up examples chosen to show the math. They are not a claim about how real traders perform.
Win rate is the share of your trades that make money. Win 4 trades out of 10 and your win rate is 40%.
It feels like the score of a game. A high number feels good. A low number feels like failure.
But win rate only counts how often you win. It says nothing about how much you win, or how much you lose when you are wrong. That missing half is the payoff ratio.
Payoff ratio compares your average win to your average loss.
Payoff ratio = Average win ÷ Average loss
If you win Rp2.000.000 on a typical winning trade and lose Rp1.000.000 on a typical losing trade, your payoff ratio is 2. Your wins are twice the size of your losses.
If you win Rp500.000 and lose Rp1.500.000, your payoff ratio is 0.33. Your losses are three times the size of your wins.
Expectancy is the average amount you make or lose per trade, if you repeat the same pattern many times.
Expectancy = (Win rate × Average win) − (Loss rate × Average loss)
Loss rate is simply 100% minus your win rate. If your win rate is 40%, your loss rate is 60%.
A positive expectancy means the pattern makes money on average. A negative one means it loses money on average. Zero means you are only paying fees to stand still.
Here are our two made-up traders, side by side.
| Trader A | Trader B | |
|---|---|---|
| Win rate | 70% | 40% |
| Average win | Rp500.000 | Rp2.000.000 |
| Average loss | Rp1.500.000 | Rp1.000.000 |
| Payoff ratio | 0.33 | 2.0 |
Now apply the formula to each.
Trader A: (0.70 × Rp500.000) − (0.30 × Rp1.500.000) = Rp350.000 − Rp450.000 = −Rp100.000 per trade.
Trader B: (0.40 × Rp2.000.000) − (0.60 × Rp1.000.000) = Rp800.000 − Rp600.000 = +Rp200.000 per trade.
Over 100 trades, Trader A is down about Rp10.000.000. Trader B is up about Rp20.000.000.
Trader A wins seven times out of ten and still loses. Each loss wipes out three wins. Trader B loses six times out of ten and still comes out ahead. Each win pays for two losses.
You can flip the formula around. For a given payoff ratio, what win rate do you need just to break even?
Break-even win rate = 1 ÷ (1 + Payoff ratio)
| Payoff ratio | Break-even win rate |
|---|---|
| 0.33 | 75% |
| 0.5 | 66.7% |
| 1 | 50% |
| 2 | 33.3% |
| 3 | 25% |
Read the table like this. If your average win is the same size as your average loss (a ratio of 1), you must win more than half the time. If your wins are three times your losses, you can be wrong three times out of four and still break even.
That is why the two numbers cannot be judged apart. A strategy that wins 80% of the time with a ratio of 0.2 needs a break-even win rate of 83%. It sounds safe, and it loses money.
Fees and taxes are a flat cost on every trade, win or lose. They come straight off your expectancy.
Say each round trip costs Rp50.000 in broker fees. Trader B's Rp200.000 per trade becomes Rp150.000. Trader A's loss grows from Rp100.000 to Rp150.000.
A thin edge can vanish after costs. So if you want to test your own numbers, use results after fees, not before.
Say you have made 20 trades and won 8. Your win rate is 40%. Can you trust it?
Not much. With only 20 trades, the plain statistical margin of error is large. A true win rate anywhere from about 18% to 62% could easily produce a result like yours. (That range is two standard errors either side of 40%, worked out as 2 × √(0.4 × 0.6 ÷ 20).)
Streaks also look scarier than they are. If your win rate is 40%, the chance that any given 5 trades in a row are all losses is 0.6 to the power of 5, or about 7.8%. Over a hundred trades, a run like that is normal. A losing streak is not proof that your approach is broken. Equally, a winning streak is not proof that it works.
So the honest read is this: expectancy is only as good as the sample behind it. Fifty or more trades tell you much more than ten.
Expectancy is a tidy idea, but real trading is messier.
None of this predicts what any asset will do next.
You do not have to be a trader for this to matter. The idea behind expectancy is that one number should describe both how often and how much.
Open the Portfolio Health card on your NetWort dashboard. It shows your portfolio's IRR (your return, adjusted for when you invested), volatility, Sharpe ratio and Max Drawdown. Look at Max Drawdown first. It is the real size of your worst fall so far, and it tells you how much loss you have actually had to sit through.