The break-even win rate for any risk-reward ratio is 1 / (1 + R): a 2:1 setup needs to win more than 33.3% of the time, and a 3:1 setup needs more than 25%. The catch is that bigger targets get hit less often. Over 2,479 daily setups on $QQQ from November 2016 to October 2026, a +2R target (with R set at 2× ATR) was reached before the −1R stop only 23.7% of the time within 20 sessions. The stop came first 43.4% of the time, and neither level was touched in 33.0% of cases.
The ratio on its own tells a trader nothing. It only means something next to the win rate it actually produces, and the math below shows how the two fit together.
The break-even win rate formula
Risk one unit (1R) to make R units. At the break-even win rate W, the wins exactly pay for the losses:
W × R = (1 − W) × 1, so W = 1 / (1 + R)
The table works through the common ratios. The last column shows how the same 30% win rate plays out at each ratio, using the expectancy formula from the next section.
| Reward:risk (R) | Break-even win rate = 1 / (1 + R) | Expectancy at a 30% win rate |
|---|---|---|
| 0.5:1 | 1 / 1.5 = 66.7% | −0.55R |
| 1:1 | 1 / 2 = 50.0% | −0.40R |
| 1.5:1 | 1 / 2.5 = 40.0% | −0.25R |
| 2:1 | 1 / 3 = 33.3% | −0.10R |
| 3:1 | 1 / 4 = 25.0% | +0.20R |
| 4:1 | 1 / 5 = 20.0% | +0.50R |
| 5:1 | 1 / 6 = 16.7% | +0.80R |
The expectancy formula
Expectancy is the average result per trade:
Expectancy = (win rate × average win) − (loss rate × average loss)
When every loss is a full 1R and every win is R, that becomes W × R − (1 − W), measured in R. A positive number means the system earns something per unit risked. A negative number means it bleeds, however good any single trade looks.
Here is a hypothetical. A trader who wins 45% of trades at 1.5:1 earns 0.45 × 1.5 − 0.55 = +0.125R per trade. A trader who wins 20% of trades at 3:1 earns 0.20 × 3 − 0.80 = −0.20R per trade. Risking $500 a trade, that second trader is down $10,000 after 100 trades (−0.20 × $500 × 100), even though every winner tripled the risk.
Why a high risk-reward ratio can still lose
The ratio and the win rate are not independent. Moving the target further away gives price more room to hit the stop first. A win rate measured on 1:1 trades does not carry over to a 3:1 target.
The $QQQ data shows the trade-off clearly. Among the setups that hit either level within 20 sessions, a 1R target won 60.4% of the time. A 2R target won 35.3% and a 3R target won just 14.4%. The 3R case falls far below its 25.0% break-even: 0.144 × 3 − 0.856 = −0.42R per decided trade. Pushing the target further out made the ratio better and the expectancy worse.
Worked example: $QQQ at the November 4, 2026 close
$QQQ closed at $691.95 on November 4, 2026. Its 14-day Average True Range was $13.01 (Wilder smoothing, the method described by StockCharts ChartSchool), or 1.88% of price. That is above the 10-year median ATR of 1.49%. The ETF closed above its 200-day simple average of $680.56.
The setup puts the stop 2× ATR below the close, so 1R = 2 × $13.0148 (the unrounded ATR) = $26.03 per share.
| Level | Arithmetic | Price |
|---|---|---|
| Stop (−1R) | $691.95 − $26.03 | $665.92 |
| Target 1R | $691.95 + $26.03 | $717.98 |
| Target 2R | $691.95 + $52.06 | $744.01 |
| Target 3R | $691.95 + $78.09 | $770.04 |
The stop sits 3.76% below the close. Take a hypothetical $50,000 account risking 1% ($500). That buys $500 / $26.03 = 19.2 shares, rounded down to 19. Those 19 shares cost $13,147.05 and risk $494.57. Reaching 2R would make $989.14, and reaching 3R would make $1,483.71. The sizing math is covered in the position sizing formula guide.
How often $QQQ hit +2R before −1R
Method: the test enters a hypothetical long at every close from November 25, 2016 to October 7, 2026, which gives 2,479 setups. At each entry, R = 2 × ATR(14). It then scans the next 20 sessions' highs and lows to see whether the target or the stop was touched first. If both were touched on the same day, the test counts a loss, which happened only once, in the 1R test. Any setup that touched neither level is marked at its session-20 close, in R.
| Target | Target first | Stop first | Neither in 20 | Win rate, decided trades | Break-even | Expectancy, decided only | Expectancy, all setups |
|---|---|---|---|---|---|---|---|
| +1R | 57.2% | 37.5% | 5.2% | 60.4% | 50.0% | +0.21R | +0.21R |
| +2R | 23.7% | 43.4% | 33.0% | 35.3% | 33.3% | +0.06R | +0.33R |
| +3R | 7.4% | 43.9% | 48.7% | 14.4% | 25.0% | −0.42R | +0.37R |
The 2R bracket barely clears its hurdle, at 35.3% against 33.3%. Most of its +0.33R comes from the 817 setups that touched neither level. Those finished at +0.88R on average, which reflects $QQQ's uptrend over the decade. For comparison, simply holding every entry for 20 sessions averaged +0.52R (+1.62%). That beat all three brackets (+0.21R, +0.33R and +0.37R). A fixed target cuts off the best runs in a rising market.
What the 10 years actually show
- Trend helped. From August 2017 onward, when the 200-day average first exists in the data, 1,881 setups taken above it reached 2R first 24.2% of the time, for +0.35R. The 413 setups taken below it reached 2R first 16.0% of the time, hit the stop first 51.6% of the time, and averaged +0.10R. The ATR trailing stop is the trend-following alternative to a fixed target.
- Bad years were very bad. In 2022, 2R came first only 10.0% of the time and the stop came first 65.7% of the time, for −0.32R. In 2018 the figures were 10.4% and 55.8%, for −0.07R. In 2017, 2R came first 39.4% of the time.
- Stops are not exact. Of the 1,075 stop-outs in the 2R test, 177 (16.5%) opened beyond the stop. Those trades averaged −1.24R, and the worst lost −2.35R. Booking the actual open lowers expectancy from +0.33R to +0.31R.
- Losses come fast. The median stop-out took 6 sessions. The median 2R win took 13.
Limits: the prices are not dividend-adjusted, so all returns are price-only. The test ignores costs, taxes and slippage, and fills entries at the close. The 2,479 setups overlap, so they are not independent trades. $QQQ is one surviving ETF, and this is a single 10-year window, drawn from Nasdaq.com historical data. More analysis lives on the Traders On Trend homepage and in the Analysis section.
Bull/Bear Verdict
Bull Case: Where it helps: the 1 / (1 + R) formula gives every setup a hard hurdle to clear. On 10 years of $QQQ, a 2× ATR stop with a 1R or 2R target cleared that hurdle on decided trades, and the 2R version did better above the 200-day average than below it.
Bear Case: Where it misleads: a bigger ratio quietly lowers the win rate. The 3R bracket won 14.4% of decided trades against a 25.0% break-even. Even the brackets that cleared the hurdle averaged less than holding for 20 sessions, and 2022 broke the 2R version outright.
FAQ
What win rate does a 2:1 risk-reward ratio need?
More than 1 / (1 + 2) = 33.3%, before costs. On $QQQ from 2016 to 2026, a 2R target with a 2× ATR stop won 35.3% of the setups that hit either level within 20 sessions.
Is a 3:1 risk-reward ratio better than 2:1?
Not automatically. It lowers the break-even to 25.0%, but in the $QQQ test the 3R target came first in only 14.4% of decided setups. That works out to −0.42R per decided trade.
How is expectancy calculated in R?
Expectancy = W × R − (1 − W), where W is the win rate and R is the average win divided by the average loss. For example, 0.45 × 1.5 − 0.55 = +0.125R.
Why use ATR to set R?
ATR scales the stop to recent volatility. A 2× ATR stop on $QQQ was $26.03 at the November 4, 2026 close, but the same rule gives a tighter stop in calm markets. Traders use it so that 1R means roughly the same amount of noise across different periods.