Risk-Reward Ratio Explained: R-Multiples and Expected Value

The risk-reward ratio is the ratio of what you stand to lose on a trade to what you stand to gain if your target is hit. If you buy EURUSD at 1.0800 with a stop at 1.0780 (20 pips of risk) and a target at 1.0860 (60 pips of reward), your risk-reward ratio is 1:3 – one unit of risk for three units of potential reward.

The number itself is useless in isolation. A 1:10 ratio sounds brilliant until you notice the setup only hits the target once in twenty tries. A 1:1 ratio sounds mediocre until you notice the strategy wins 70% of the time. The ratio only becomes meaningful when you multiply it by the probability of winning and subtract the probability of losing – that is expected value, and it is the only number that decides whether you have an edge or not.

Most retail traders fixate on the ratio because it is visible on the chart – stop here, target there, done. The probability of reaching the target is invisible and requires data to estimate. This asymmetry of effort is why the ratio gets worshipped and the probability gets ignored.

For any risk-reward ratio, there is a single win rate at which you break even before costs. Below it you lose, above it you win. The formula is simple:

Break-even win rate = 1 ÷ (1 + risk-reward ratio)

A 1:2 system needs 1 ÷ (1 + 2) = 33.3% winners to break even. A 1:3 system only needs 25%. A 1:0.5 system needs 67%. Memorise this formula and you will stop being impressed by screenshots of "80% win rate strategies" – if the reward is smaller than the risk, 80% is the minimum to survive.

The third column is illustrative – it assumes 200 trades per year at 1R risk each, with winners at the advertised ratio and losers at exactly 1R. In reality slippage, partial exits, and variable stop distances will erode these numbers.

Van Tharp, in Trade Your Way to Financial Freedom (1998), proposed that every trade should be described as a multiple of initial risk – an R-multiple. Your initial risk is 1R. A trade that hits a target twice the risk is +2R. A trade that gets stopped out at your planned stop is −1R. A trade that gets stopped early by a trailing stop at half the risk is −0.5R. A trade that blows through your stop due to a gap and loses 1.7× the planned risk is −1.7R.

This framework strips the dollars out of the analysis. Whether you are trading a $10,000 personal account or a $200,000 funded account, a +3R winner is a +3R winner. Your job as a trader is to produce a distribution of R-multiples with a positive mean – the arithmetic average of all R-multiples you generate is your expectancy.

Expectancy of +0.3R means for every 1R you risk, you earn 0.3R on average. Risk 100 times per year at 1R each, and you should end the year up about 30R – translate that into dollars using your position-sizing rule. A prop trader running a $100k account with 0.5% risk per trade (0.5R = $500) would expect $15,000/year at that expectancy, before costs and variance.

Expected Value (EV) is the weighted average outcome of a trade, given its probability of winning and losing:

EV = (Win% × Avg Win) − (Loss% × Avg Loss)

Example: a breakout strategy wins 45% of the time, winners average +2.2R, losers average −1.05R (slippage bleeds the stop slightly). EV = (0.45 × 2.2) − (0.55 × 1.05) = 0.99 − 0.5775 = +0.41R per trade. Positive expectancy. Trade 300 times a year at 0.5% risk per trade and you expect roughly 61.5% account growth – before commissions, spreads, and borrowing costs. Model the reward side of a setup before entry with our CFD calculator.

The same strategy with a 35% win rate: EV = (0.35 × 2.2) − (0.65 × 1.05) = 0.77 − 0.6825 = +0.09R per trade. Barely positive. Any cost drag pushes it into negative territory. This is why small win-rate changes matter enormously – a strategy at +0.4R can absorb a rough patch, a strategy at +0.05R dies to a bad week of slippage.

The chart below shows expected value in R-multiples across win rates from 20% to 80%, for three risk-reward ratios. The flat line at 0 is break-even. Anything above it is profitable; anything below bleeds money.

The practical lesson: systems with a higher reward-per-unit-risk tolerate variance better. A trend-following system that wins 30% of the time at 1:4 is almost bulletproof to a bad month. A mean-reversion system that wins 65% of the time at 1:0.7 is fragile – a single 10-percentage-point dip in win rate turns it unprofitable.

When traders post screenshots of "1:5 setups" they are showing the planned ratio – entry, stop, and target that they hope will play out. The realised ratio is different and usually worse for three reasons:

1. Partial exits drag the ratio down. A trader who scales out half at 1R and lets the rest run to 3R realises an average of 2R per winner, not 3R. The math still works, but it is not 1:3.

2. Trailing stops truncate the tail. A 1:5 target is rarely reached in a straight line. Most trend-followers trail their stop and exit earlier. The distribution becomes a pile of +1R to +3R winners with rare +5R outliers, mean around 1.8R.

3. Slippage erodes the stop side. News events, thin liquidity, and gaps mean the realised average loss is often −1.1R or −1.2R, not exactly −1R. Over a year this alone can halve a marginal edge.

The honest number is the one in your trade journal, calculated across hundreds of closed trades. See the trading journal template for the fields that make this calculation possible.

Prop firms do not read your risk-reward ratio off the marketing material – they read your realised R-distribution off the trade history. The metrics they actually care about:

Average R per trade (expectancy). Positive is mandatory. Above +0.2R is good, above +0.4R is excellent, above +0.8R is suspicious and they will check for over-fitting or short-sample luck.

Standard deviation of R. Consistency matters. Two traders with identical +0.3R expectancy but one with std dev of 0.8R and the other with 2.5R are treated very differently – the tighter distribution is easier to scale capital against.

Largest loss / 95th percentile loss. One −5R disaster undoes ten +1R winners. Firms flag traders whose worst loss exceeds 2× their stated stop, because it suggests overriding the plan or trading through news.

Ratio of winners ≥2R to total winners. A high share of small +0.3R to +0.8R winners suggests cutting profits early – a classic disposition-effect tell. Firms prefer fewer, larger winners.

Trap 1 – Moving the stop. When price approaches your stop, widening it turns a −1R into a −2R or worse. The R-distribution is invalidated; your expectancy calculation is useless.

Trap 2 – Moving the target closer. Taking a +0.5R winner because "it might reverse" destroys the positive skew of a trend strategy. After 100 such decisions your 1:3 system is actually a 1:0.8 system.

Trap 3 – Skipping losers. "I had a bad feeling so I didn't take it." Cherry-picked sample, invalidated backtest. The system you are trading is no longer the system you measured.

Trap 4 – Oversizing winners, undersizing losers. Trading bigger when you feel good means your expectancy calculation (which assumes equal sizing) overstates the realised return.

Trap 5 – Counting fees out of the ratio. A 1:2 setup on a 0.5-pip spread product pays differently than on a 3-pip spread product. Bake costs into the stop side.

Trap 6 – Ignoring correlation. Five "independent" 1:3 trades that are all long the DXY basket are really one trade. Sum their R and compare to your portfolio stop, not each slot separately.

Trap 7 – Short sample triumphalism. Twenty trades do not establish an edge. Academic studies of strategy robustness typically want 100+ trades per regime before drawing conclusions.

Step 1: define 1R before entry. Your stop distance times your position size, in dollars. Every position sizing tool – including the one in our calculators guide – should output this number.

Step 2: log every closed trade as an R-multiple. Divide P&L by the 1R from entry. A $350 gain on a $200 risk is +1.75R. A $215 loss on a $200 risk is −1.08R (slippage).

Step 3: compute running expectancy weekly. Arithmetic mean of the R column across your last 30–50 trades. If it turns negative for three consecutive weeks, stop and audit the strategy.

Step 4: aim for a 2-number dashboard. Expectancy (in R) and std dev of R. That is your edge and its stability. Everything else – win rate, profit factor, Sharpe – derives from these two.

Step 5: stress-test. Monte-Carlo your R-distribution – shuffle the last 100 trades 10,000 times and look at the worst drawdown across runs. If your worst modelled drawdown exceeds your prop firm's daily or max loss rule, you are under-capitalised for this strategy regardless of the headline expectancy.