Risk-reward ratio and R multiples: the math of a trade

Every trade has two distances: how far price can move against you before you admit the idea is wrong, and how far it might move in your favor. The risk-reward ratio compares them. On its own it says little. Combined with how often trades actually win, it tells you whether a set of rules can make money at all, and that combination is the most important arithmetic in trading.

This guide explains the ratio, the cleaner way to express it as R multiples, the break-even win rate for any ratio, and expectancy, the average result per trade. Every example uses illustrative numbers. Nothing here suggests that any ratio, target or method is profitable; the point is to understand how the pieces fit.

Defining the ratio

For a long trade, the risk is the distance from the entry down to the stop, and the reward is the distance from the entry up to the target.

People write it both ways. "Risk-reward of 1:3" and "reward-to-risk of 3" mean the same thing: the target is three times as far away as the stop. This page uses the reward-to-risk form, so a bigger number means a bigger potential win per unit risked.

R multiples: measuring results in units of risk

Dollar results are hard to compare. A $600 gain is a triumph on a trade that risked $100 and a disappointment on one that risked $2,000. The trader and author Van Tharp popularized the fix: define 1R as the amount you planned to lose on a trade, then express every outcome as a multiple of it.

R multiples make a trade log readable at a glance. A run of results such as +2.0, −1.0, −1.0, +3.0, −0.5 tells you more than the dollar figures, because it strips out how big each position happened to be. If a −1R loss is regularly turning into −1.6R, the stops or the order types need attention.

The break-even win rate

How often must trades win for a given ratio to break even? Suppose every win is +R and every loss is −1. Over many trades the total is zero when W × R = (1 − W) × 1, where W is the win rate. Solving for W:

The curve flattens quickly. Going from 1R to 2R cuts the required win rate by 16.7 points; going from 3R to 4R cuts it by only 5. That is the arithmetic behind the popular advice to look for high ratios, and also the reason the advice can mislead, as the next sections show.

Expectancy: the average result per trade

The ratio and the win rate combine into expectancy, the average gain or loss per trade over a long series. In dollars:

The table below shows expectancy in R for a grid of win rates and ratios, assuming every win is exactly R and every loss exactly 1R. A positive number means the rules make money on average before costs; a negative one means they lose.

Multiplying expectancy by the dollar value of 1R gives the average dollar result. At 0.32R with a $300 risk unit, that is $96 per trade on average, with individual trades ranging from −$300 to +$900 in this log.

Costs move the break-even point

Commissions, spreads and slippage come out of every trade, winner or loser. Expressed in R, a cost of c per trade changes the break-even condition to W × R − (1 − W) − c = 0, so the break-even win rate rises to (1 + c) ÷ (1 + R).

In the US, short-term gains on positions held one year or less are also taxed at ordinary income rates, according to the IRS (Topic 409, as of 2026). Taxes are not a per-trade cost in the same way, but they reduce what a positive expectancy is worth.

Why a higher ratio is not automatically better

It is tempting to read the table and conclude that everyone should aim for 3R or more. The catch is that the target and the win rate are linked. A target three times farther away than the stop is, by simple geometry, reached less often than one the same distance away. Push the target out and the win rate falls; pull it in and the win rate rises. The question is never "what ratio?" in isolation but "what ratio and what resulting win rate?"

Other traps:

• Arbitrary targets. Setting a target at exactly 3R because a rule says so, rather than at a level the chart or the business case supports, produces a nice planned ratio and a poor realized one.
• Moving the stop. Widening a stop after entry quietly changes 1R. The planned ratio no longer describes the trade.
• Planned versus realized. Gaps, partial exits and early exits mean the realized R of closed trades usually differs from the planned R at entry. Measure what happened.
• Small samples. A win rate measured over 20 trades has a wide margin of error. Twelve wins out of 20 (60%) is quite compatible with a true rate of 45%.
• Fat tails. A single −4R gap loss wipes out two +2R wins. Averages computed without the occasional disaster overstate expectancy.

Ratio, win rate and expectancy compared

How Finabase helps

Finabase does not execute trades, but it can help you study the numbers:

• The backtester runs an indicator or candlestick strategy over real prices and lists the trades, wins and losses and the account value. Each signal trades a fixed $10,000, so convert its results to R yourself if you want to compare them with a risk-based plan.
• Portfolios track positions, cost basis and gains at live prices, a starting point for computing each closed trade's realized R.
• The Position sizing: how many shares to buy for a set risk guide shows how 1R becomes a share count.

Frequently asked questions

What is a good risk-reward ratio?

There is no universally good ratio; it only makes sense alongside the win rate it produces. A 1:1 ratio with a 60% win rate has a higher expectancy (+0.20R) than a 1:3 ratio with a 25% win rate (0.00R), before costs.

How do you calculate the break-even win rate?

Divide 1 by (1 + R), where R is the average win divided by the average loss. At 2R the break-even win rate is 1 ÷ 3 ≈ 33.3%. With costs of c (in R) per trade, use (1 + c) ÷ (1 + R).

What does 1R mean?

1R is the amount you planned to lose on a trade: the distance from entry to stop times the number of shares. A result of +2R means you made twice that amount; −1R means the stop was hit as planned.

Is expectancy the same as profit?

No. Expectancy is the average result per trade over many trades. Any short stretch can lose money even when expectancy is positive, and expectancy estimated from a small sample can simply be wrong.

Summary

The risk-reward ratio compares the distance to a target with the distance to a stop. Expressed as R multiples, it makes every trade comparable, and the break-even win rate of 1 ÷ (1 + R) shows how often a given ratio has to win. Expectancy combines the two into an average result per trade, which must survive costs to mean anything. Because distant targets are reached less often, ratio and win rate cannot be chosen independently, and only realized results over many trades reveal what a set of rules actually does.