Risk-reward ratio, win rate and expectancy: the maths that matters

The risk-reward ratio compares how much you stand to lose on a trade, the distance to your stop loss, with how much you aim to gain, the distance to your target. A 2:1 reward-to-risk trade aims to make two units for every one it risks. On its own the ratio tells you nothing about whether a strategy works; it only matters in combination with how often you win, and the two together give you the number that does matter: expectancy.

The ratio itself

Say you buy EUR/USD at 1.0850 with a stop at 1.0820 and a target at 1.0910. You are risking 30 pips to make 60. The reward-to-risk ratio is 60 ÷ 30 = 2, usually written as 1:2 risk-to-reward or 2:1 reward-to-risk. The industry uses both orders interchangeably, which causes endless confusion, so in this guide we always state it as reward to risk: 2:1 means the target is twice as far as the stop.

It is often more useful to express results in R, where 1R is the amount you risked on the trade. If you risk $100 and make $200, that is +2R. If you lose $100, that is −1R. If you exit early for $50, that is +0.5R. Thinking in R lets you compare trades of different sizes and different pairs on the same scale, and it ties directly into position sizing, where 1R is a fixed percentage of your account.

The break-even win rate

For any reward-to-risk ratio there is a win rate at which you neither make nor lose money, ignoring costs. The formula is:

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

Worked through for common ratios:

• 0.5:1 (target half the stop distance): 1 ÷ 1.5 = 66.7%
• 1:1: 1 ÷ 2 = 50%
• 1.5:1: 1 ÷ 2.5 = 40%
• 2:1: 1 ÷ 3 = 33.3%
• 3:1: 1 ÷ 4 = 25%
• 4:1: 1 ÷ 5 = 20%

This is why the risk-reward ratio gets so much attention. A strategy that targets 3:1 can lose three trades out of every four and still break even. A strategy that targets 0.5:1 has to win two trades out of three just to stand still.

But neither of these is automatically better. Targets further away are reached less often. A 3:1 target on the same entry and stop as a 1:1 target will be hit on fewer trades, sometimes far fewer. The ratio and the win rate are linked by the market, not chosen independently.

Expectancy: the number that matters

Expectancy is the average amount you expect to make or lose per trade over a large number of trades. In R terms:

Expectancy = (win rate × average win in R) − (loss rate × average loss in R)

If losses are always exactly 1R, the formula simplifies to (win rate × average win) − loss rate.

A positive expectancy means the approach has made money on average in the sample you measured. A negative expectancy means it has lost money on average, however good the win rate or the ratio looks.

Three illustrative traders

These are hypothetical figures, chosen to show how the pieces combine.

Trader A: high win rate, small wins. Wins 60% of trades with an average win of 0.8R; losses are 1R.

• Expectancy = (0.60 × 0.8) − (0.40 × 1) = 0.48 − 0.40 = +0.08R per trade.

Positive, but thin. A little extra cost or slippage could wipe it out.

Trader B: low win rate, large wins. Wins 35% of trades with an average win of 2.5R; losses are 1R.

• Expectancy = (0.35 × 2.5) − (0.65 × 1) = 0.875 − 0.65 = +0.225R per trade.

More robust per trade, but Trader B loses nearly two trades in three and has to sit through long losing runs.

Trader C: very high win rate, tiny wins. Wins 70% of trades with an average win of 0.4R; losses are 1R.

• Expectancy = (0.70 × 0.4) − (0.30 × 1) = 0.28 − 0.30 = −0.02R per trade.

Seven winners out of ten, and losing money. This is a very common pattern among newer traders: take profits quickly because winning feels good, let losses run to the stop (or beyond) because taking them feels bad. The win rate looks excellent and the account shrinks anyway. The trading psychology guide explains the loss-aversion behaviour behind this.

Costs change the ratio

The break-even figures above ignore costs. In real trading, every trade pays the spread, any commission, and sometimes slippage. Those costs come off winners and are added to losers, so they push your real ratio down and your break-even win rate up.

The effect depends on how tight your stop is. Costs are roughly fixed in pips, so the smaller the stop, the larger the cost as a share of 1R.

Illustrative example on EUR/USD with an all-in round-trip cost of 1 pip (spread plus commission equivalent; see spreads and commissions):

• 30-pip stop, 60-pip target. Cost is 1 ÷ 30 = about 0.03R per trade. A winner is worth about 1.97R and a loser about 1.03R. Break-even win rate rises from 33.3% to roughly 34.4%.
• 10-pip stop, 20-pip target. Cost is 1 ÷ 10 = 0.1R per trade. A winner is worth 1.9R and a loser 1.1R. Break-even rises to 1.1 ÷ 3.0 = about 36.7%.
• 5-pip stop, 10-pip target. Cost is 0.2R per trade. A winner is worth 1.8R and a loser 1.2R. Break-even rises to 1.2 ÷ 3.0 = 40%.

Same nominal 2:1 ratio in all three, very different real economics. Short-term strategies with tight stops are extremely sensitive to costs and to slippage. If your stops are under 15 pips, include costs in every calculation or your results will look better on paper than they are.

To recompute the break-even with costs: break-even win rate = (loss in R including costs) ÷ (win in R after costs + loss in R including costs).

Losing streaks are part of the maths

Low win-rate strategies are not just psychologically harder; they mathematically produce longer losing streaks. If each trade is independent, here is the chance of seeing at least one run of consecutive losses over 100 trades:

• 50% win rate: about 55% chance of a run of 6 or more losses; about 17% chance of 8 or more.
• 40% win rate: about 87% chance of a run of 6 or more; about 49% chance of 8 or more; about 20% chance of 10 or more.
• 33% win rate: about 97% chance of a run of 6 or more; about 76% chance of 8 or more; about 45% chance of 10 or more.

So a trader using a 2:1 approach with a one-in-three win rate should expect to sit through a run of eight losses at some point in a hundred trades, and has close to even odds of seeing ten. At 1% risk per trade, ten consecutive losses costs just under 10% of the account. At 5% risk, it costs about 40%. This is the strongest argument for keeping risk per trade small, and the position sizing guide shows how.

It is also why traders abandon perfectly reasonable approaches at exactly the wrong moment. A losing streak that the maths says is normal feels like proof the strategy is broken.

Planned ratio vs realised ratio

The ratio you plan when you enter is not the ratio you achieve. Several things pull the two apart:

• Early exits. Closing winners before the target because the trade "looks tired" reduces your average win.
• Moved stops. Widening a stop during a losing trade makes the average loss bigger than 1R.
• Partial closes. Taking half off at 1R and running the rest changes the shape of your results, sometimes for the better, sometimes not.
• Slippage and gaps. Stops that fill late make some losses larger than 1R.
• Trailing stops. Turn some potential 3R winners into 1R or 1.5R winners, and some losers into small winners.

The only way to know your real figures is to measure them. Record the planned entry, stop and target, and the actual exit, for every trade, and calculate the result in R. Our guide to keeping a trading journal sets out what to record. After enough trades you will know your actual win rate, average win, average loss and expectancy, which is worth far more than any target ratio.

How many trades do you need?

Win rates measured over a small number of trades are very noisy. A rough guide uses the standard error of a proportion:

• After 50 trades with a measured 40% win rate, the true win rate could plausibly be anywhere from about 26% to 54%.
• After 100 trades, about 30% to 50%.
• After 400 trades, about 35% to 45%.

Those ranges are wide enough to cover both a working strategy and a losing one. That is why a good month proves very little, a bad month proves very little, and why testing an approach on historical data before trading it live is so valuable. The guide on how to backtest a strategy covers how to do that without fooling yourself through overfitting.

Setting targets that make sense

A ratio is only meaningful if the target is somewhere price can realistically go. Picking 3:1 because it sounds good, then placing the target past three resistance levels, produces a nice-looking plan and a low hit rate.

A more grounded process:

1. Set the stop where the trade is invalidated, as described in where to put a stop loss.
2. Look for the nearest level where the move is likely to meet opposition: the next support or resistance zone, a previous swing high or low, a round number.
3. Measure the distance from entry to that level and compare it with the stop distance.
4. If the ratio is too low for your strategy's win rate, skip the trade or wait for a better entry. Do not move the target further away or the stop closer to manufacture a better ratio.

Market volatility also matters. If the daily range on a pair is 60 pips, a 150-pip target on an intraday trade is unlikely to be reached the same day.

A worked example from start to finish

Illustrative numbers throughout.

You have a $10,000 account and risk 1% per trade, so 1R = $100. On GBP/USD you see a long setup at 1.2650. The invalidation level puts your stop at 1.2615, 35 pips away. The nearest resistance is at 1.2740, 90 pips away. Reward-to-risk is 90 ÷ 35 = 2.57:1.

Costs on this account are about 1.2 pips round trip, which is 1.2 ÷ 35 = about 0.03R. So a winner is worth about 2.54R net and a loser about 1.03R. The break-even win rate is 1.03 ÷ (2.54 + 1.03) = 28.9%.

Your journal says that over your last 120 trades of this type you won 37%, with an average realised winner of 2.1R (not every trade reached the full target) and an average loser of 1.05R. Your expectancy on that sample:

• (0.37 × 2.1) − (0.63 × 1.05) = 0.777 − 0.6615 = +0.12R per trade.

That is a modest positive figure on a sample that is still small enough to be uncertain, as the previous section showed. A sensible conclusion is to keep risk at 1% and keep collecting data, not to double your size.

Position size for this trade, in a dollar account where GBP/USD is worth $10 per pip per lot: $100 ÷ (35 × $10) = 0.285, rounded down to 0.28 lots.

Common mistakes

• Chasing a high win rate. It feels good and often hides negative expectancy, as Trader C shows.
• Chasing a high ratio. A 5:1 target that is almost never reached is worse than a 2:1 target that often is.
• Ignoring costs on short-term trades. On tight stops, costs can move the break-even win rate by several percentage points.
• Judging an approach on 20 trades. The numbers are too noisy to tell you anything.
• Changing the plan mid-trade. Moving the stop or the target after entry destroys the link between your plan and your statistics.
• Forgetting that expectancy is an average. A positive expectancy says nothing about the next trade, or the next ten.

And the wider context: most retail CFD accounts lose money, and leverage magnifies losses. Our guide on why most retail CFD traders lose looks at the reasons, and the risk warning sets out the disclosures. The maths in this guide does not change those odds. It helps you see clearly whether what you are doing is helping or hurting.

Frequently asked questions

What is a good risk-reward ratio?

There is no universally good ratio. A ratio only means something alongside the win rate it produces. Many traders look for at least 1.5:1 or 2:1 because it leaves room for a win rate below 50% and for costs, but a 1:1 approach with a high enough win rate can work, and a 3:1 approach with a very low win rate can lose.

How do I calculate the risk-reward ratio?

Divide the distance from entry to target by the distance from entry to stop. If you buy at 1.0850, with a stop at 1.0820 and a target at 1.0910, the reward is 60 pips and the risk is 30 pips, so the ratio is 2:1.

What win rate do I need with a 1:2 risk-reward?

Before costs, just over 33.3%, because 1 ÷ (1 + 2) = 0.333. Once you include the spread, commission and slippage, the break-even rate is higher, and the tighter your stop, the more costs push it up.

What is expectancy in trading?

Expectancy is the average result per trade over many trades: win rate times average win, minus loss rate times average loss. Expressed in R, a figure of +0.1R means you have made, on average, a tenth of your risk per trade in the sample measured. It is an average, so individual trades and short runs will vary widely.

Why do I lose money with a high win rate?

Usually because your average loss is much larger than your average win. Closing winners early and letting losers run, or widening stops during losing trades, can produce a win rate above 60% or 70% with a negative expectancy. Measure your average win and loss in R to check.

How many trades do I need to know if my strategy works?

More than most people think. After 50 trades, a measured 40% win rate is consistent with a true win rate anywhere from the mid-20s to the mid-50s. A few hundred trades, from live trading or careful backtesting, give a much clearer picture.