Risk-reward ratio is the concept that every trading course mentions but few explain with the mathematical precision it deserves. Most traders understand that a 1:2 R:R means risking 1 to make 2 — and they have been told to aim for at least 1:2 on their trades. But the deeper question — why that specific ratio, and what is the relationship between R:R and win rate — is the question this lesson answers. Understanding the mathematics of R:R transforms it from a vague guideline into a precise planning tool that tells you exactly what win rate your system needs to be profitable at any given R:R.
What Is Risk-Reward Ratio?
The risk-reward ratio compares the potential loss of a trade (from entry to stop loss) to the potential gain (from entry to take profit). A 1:2 R:R means that if the stop loss is hit, you lose 1 unit of risk. If the target is hit, you gain 2 units of risk. The ratio is calculated simply: divide the potential gain by the potential loss.
Entry: 1.0850 (long EUR/USD). Stop: 1.0800 (50 pips away). Target: 1.0950 (100 pips away). Risk: 50 pips. Reward: 100 pips. R:R = 100 ÷ 50 = 2. This is a 1:2 R:R (risk 1 to make 2). At 1% risk ($100) on $10,000 account: Potential loss: $100 (1R). Potential gain: $200 (2R).
The Mathematics of R:R
The power of R:R becomes clear when you calculate expectancy — the average expected outcome per trade across a large number of trades.
System: 1:2 R:R. 45% win rate. Risk per trade: $100. Average win: $200 (2R). Average loss: $100 (1R). Per 100 trades: 45 winners × $200 = $9,000 profit. 55 losers × $100 = $5,500 loss. Net: +$3,500. Expectancy: +$35 per trade. This system loses more than half of its trades but is solidly profitable. The R:R ratio compensates for the sub-50% win rate. Now same win rate with 1:1 R:R: 45 winners × $100 = $4,500 profit. 55 losers × $100 = $5,500 loss. Net: -$1,000. Expectancy: -$10 per trade. The same win rate is unprofitable at 1:1 R:R.
Win Rate and R:R Together
The relationship between win rate and R:R determines whether any system is profitable over time. Every combination of win rate and R:R either produces positive expectancy (profitable) or negative expectancy (unprofitable).
At 1:1 R:R: need win rate > 50%. At 1:1.5 R:R: need win rate > 40%. At 1:2 R:R: need win rate > 33%. At 1:3 R:R: need win rate > 25%. At 1:5 R:R: need win rate > 17%. Higher R:R allows profitability at lower win rates — because each win compensates for multiple losses. A system that wins 30% of trades at 1:2.5 R:R is profitable. A system that wins 60% of trades at 1:0.8 R:R is not.
Minimum Viable R:R
The minimum viable R:R for most trading systems is 1:1.5 — meaning for every pip risked, you target at least 1.5 pips of potential gain. This provides enough buffer that even a modest win rate above 40% produces positive expectancy. Most professional traders target a minimum of 1:2 on all trades.
In practice, this means you should only take trades where the distance from entry to target is at least twice the distance from entry to stop. If your stop is 50 pips away and the nearest significant target is only 60 pips away — a 1:1.2 R:R — the trade does not meet the minimum. Wait for a higher-quality setup where the target is genuinely 100 pips away or more.
Common R:R Mistakes
The most common R:R mistake is placing the take profit at an arbitrary distance — a clean round number or a psychological target — rather than at the next significant structural level. If the next meaningful resistance is 80 pips away but you set your target at 100 pips for a clean 1:2 R:R, you are forcing a ratio that ignores what the chart is actually saying. Targets must be placed at logical structural levels — the R:R that results from that placement is the genuine R:R of the setup.
The R:R of a trade is not something you choose — it is something you observe. You place the stop at the logical structure level. You place the target at the logical resistance or liquidity target. The ratio between those two distances is your R:R. If it is below 1:1.5, the setup does not qualify — pass it and wait for the next one.