Risk-reward ratio (R:R)
Combine payoff and probability
For a two-outcome model, break-even win probability is loss / (gain + loss). Before costs, a $100 loss and $200 gain require 33.33%; with the stated $10 costs, the figure is 110 / 300 = 36.67%. These are model calculations, not estimates of the probability that a target will actually be reached.
Do not count costs twice
If P&L already uses executable entry and exit quotes, the spread may already be reflected. Apply commissions, financing, conversion and slippage assumptions consistently. Price-distance ratios need not equal cash payoff ratios for nonlinear products or different currency conversions.
Record plan and outcome separately
Keep the initial planned risk for R-multiple calculations. Partial exits and moved stops can change realised payoffs. A larger target changes the trading problem; it does not create a structural edge by itself. There is no universal minimum ratio that makes every strategy suitable.
Definition, formula and notation
Risk:reward compares the planned cash loss with the planned cash gain under the stated exit assumptions. Keep that proportion distinct from a reward-to-risk multiplier. If the stop is 30 pips from entry and the target is 60 pips away, the multiplier is q = 60 / 30 = 2; the proportion is risk:reward = 30:60 = 1:2. Writing “60/30 = 1:2” mixes a quotient with a proportion.
The price-distance shortcut assumes a linear payoff, the same position size and compatible currency conversion on each outcome. Actual cash amounts can differ when costs, partial exits, financing or nonlinear payoffs enter the calculation. A planned stop is not a guarantee that realised loss stays within the budget.
Worked EUR/USD example
Suppose an illustrative long EUR/USD trade has an executed entry of 1.0850, an assumed stop fill of 1.0820 and an assumed target fill of 1.0910:
- Planned price-loss distance: 1.0850 − 1.0820 = 0.0030, or 30 pips.
- Planned price-gain distance: 1.0910 − 1.0850 = 0.0060, or 60 pips.
- Reward/risk multiplier: 60 / 30 = 2; risk:reward proportion: 1:2.
With an assumed USD 10 pip value per standard lot, a 0.50-lot position has USD 5 per pip: the planned gross loss is USD 150 and the gross gain USD 300. Across ten trades with exactly five of each outcome, gross gains are 5 × USD 300 = USD 1,500 and gross losses 5 × USD 150 = USD 750. Their difference is USD 750 before any costs not already included. This is an arithmetic sample, not a forecast of a 50% win rate or a promise that either exit fills at its level.
The break-even relationship
For a simplified model with only a fixed gain G and fixed loss magnitude L, the mean is pG − (1 − p)L, where p is the probability of the winning outcome. Setting this to zero gives pBE = L / (G + L) = 1 / (1 + q), with q = G/L and L positive. The probabilities and payoffs must refer to the same model and cost convention.
| Risk:reward | Reward/risk q | Break-even win rate | Interpretation |
|---|---|---|---|
| 1:1 | 1 | 50.0% | Exactly 50% breaks even before costs. |
| 1:1.5 | 1.5 | 40.0% | Four wins out of ten offset six equal-model losses. |
| 1:2 | 2 | 33⅓% | One win out of three breaks even before costs. |
| 1:3 | 3 | 25.0% | One win out of four breaks even before costs. |
The rounded displayed rates are not estimates of a strategy's success probability. A more distant target can change how often it is reached. Neither a 1:2 nor a 1:3 label demonstrates profitability.
How costs change the comparison
At gross risk:reward of 1:1, exactly 50% wins break even in the stated two-outcome model. If additional costs reduce the gain and increase the loss, the required win rate rises above 50%. That does not make every 1:1 strategy unprofitable; the actual net payoffs and probabilities determine the expectation.
For example, a USD 150 gross gain or gross loss with an additional USD 10 cost on either outcome becomes a USD 140 net gain and USD 160 net loss. The break-even rate is 160 / (140 + 160) = 53.33%. Include slippage, commissions, financing and conversion consistently, and do not charge a spread again if it is already reflected in executed prices. There is no universal minimum ratio of 1:1.5 or 1:2 that makes an untested strategy suitable.
Using the plan without assuming the outcome
Before a trade is considered, specify the intended entry, invalidation or stop instruction, target or other exit rule, contract size and costs. A personal payoff filter is useful only as part of rules whose complete behaviour has been evaluated; a visually attractive ratio does not replace evidence or justify moving a target solely to manufacture a preferred number.
Combine the plan with structured risk management, and record the original planned cash risk separately from the eventual result. For illustration, five losses each equal to 1% of a fixed initial account value total 5% of that initial value before costs; three gains each equal to 2% total 6%. If instead risk is recalculated from current equity, the percentages compound and the five-loss decline is 1 − 0.995 ≈ 4.90%, not exactly 5%. Neither version guarantees that losses are capped or that recovery follows.
The link with process versus outcome is to assess whether a trade followed a tested plan and to distinguish a planned ratio from a statistical edge. A well-executed trade can lose, while a profitable trade can have violated the rules. Review the complete sample rather than treat a few target hits as proof.
