Risk-to-Reward

Core concepts

Use these concepts as explicit rules rather than changing them after seeing the outcome.

R

R as a unit

One R is the initial planned loss from entry to stop. Outcomes can then be compared across trades.

B

Break-even rate

The average win-to-loss ratio determines the theoretical win rate required before costs.

E

Expectancy

Combine win rate, average win, average loss, and costs to estimate the average result per trade.

Interactive lesson

Change entry, stop, target, win rate, average loss and costs; every figure on the right is recomputed from the formulas further down the page.

The balanced preset, worked

Every figure on the calculator comes from these five lines. Follow them once by hand, then change one input and predict the new figures before reading them.

ENTRY 100.00 · STOP 98.00 · TARGET 104.00 · long WIN RATE 45% · AVG LOSS 1.00R · COSTS 0.05R RISK = |100.00 − 98.00| = 2.00 REWARD = |104.00 − 100.00| = 4.00 R MULTIPLE = 4.00 ÷ 2.00 = 2.00R BREAK-EVEN = 1.00 ÷ (2.00 + 1.00) = 33.3% EXPECTANCY = 0.45 × 2.00 − 0.55 × 1.00 − 0.05 = 0.90 − 0.55 − 0.05 = +0.30R

Now change one input. Set the average loss to 0.50R and the break-even rate becomes 0.50 ÷ (2.00 + 0.50) = 20.0% — a system that loses less than 1R on average needs fewer wins, which the old shorthand 1 ÷ (1 + 2) could not show. Set the win rate to 30% instead and expectancy becomes 0.30 × 2.00 − 0.70 × 1.00 − 0.05 = −0.15R: the same 2R plan loses money. The ratio did not change; the estimate behind it did, and the estimate is the part that has to come from Backtesting.

Risk-to-reward evaluation process

Use the ratio to measure a structurally valid plan—not to invent one.

1

Validate entry and stop

Confirm price risk is structurally justified and on the correct side of entry.

2

Identify realistic targets

Use visible structure before calculating the reward multiple.

3

Calculate break-even rate

Understand the minimum hit rate implied by average win and loss size.

4

Estimate expectancy

Use backtested outcomes and include transaction costs and slippage.

Risk-to-reward drill

Score 0 / 0

Use expectancy, not reward-to-risk alone.

Key formulas

RISK = |ENTRY − STOP| REWARD = |TARGET − ENTRY| REWARD-TO-RISK = REWARD ÷ RISK BREAK-EVEN WIN RATE = AVG LOSS R ÷ (AVG WIN R + AVG LOSS R) (= 1 ÷ (1 + AVG WIN R) only when the average loss is 1R) EXPECTANCY = (WIN RATE × AVG WIN R) − (LOSS RATE × AVG LOSS R) − COSTS IN R

Important: A positive calculation is only as reliable as the win-rate and average-outcome estimates. Those estimates should come from a sufficiently large, relevant backtest.

Common mistakes

1

Treating 2R as a universal minimumDifferent systems can be viable with different combinations of win rate and payoff.

2

Assuming planned R equals realized average winPartial exits, slippage, gaps, and management rules change actual outcomes.

3

Ignoring costsSmall theoretical edges can disappear after spread, commissions, and slippage.

4

Using guessed win rates as factsExpectancy is meaningful only when estimates come from relevant, sufficient data.

Completion standard

✓

Finish when you can compute all five figures by hand for any entry, stop, target and cost.

Risk, reward, the R multiple, the break-even win rate and expectancy — and say why a positive result is only as good as the win-rate estimate behind it.

Scope: This lesson teaches process and measurement. It does not provide live market data, personalized recommendations, or trade signals.