How to calculate risk reward ratio and why win rate decides it

Contents

1. How do you calculate a risk reward ratio?
2. What win rate do you need to break even at each ratio?
3. How do you calculate expectancy from win rate and the ratio?
4. Why does your backtest ratio differ from the ratio you planned?
5. Does a higher risk reward ratio mean a better strategy?
6. What can the risk reward ratio not tell you?
7. Frequently asked questions
8. References

How do you calculate a risk reward ratio?

To calculate a risk reward ratio, divide the distance from entry to target (the reward) by the distance from entry to stop (the risk). A ratio of 2 means you aim to make twice what you risk, which needs one win in three to break even before costs. Expectancy after costs decides whether the strategy has an edge.

A risk reward ratio is the planned profit of a trade divided by its planned loss. The calculation takes four steps:

1. Risk. Measure the distance between the entry price and the stop price.
2. Reward. Measure the distance between the entry price and the target price.
3. Ratio. Divide the reward by the risk.
4. Money. Multiply both distances by the contract's point value and by the number of contracts. This gives the planned profit and loss in your account currency.

The same idea goes by two names. "Risk:reward 1:2" and "reward-to-risk ratio 2" describe the same trade. This article uses reward ÷ risk, so a bigger number means a bigger target compared with the stop. Many traders also call the risk on one trade "1R". A 10-point target with a 5-point stop is then a "2R target".

For futures, the stop and target are usually set in ticks. The futures contract calculator converts ticks and points into money for a given contract. Exchanges can change contract values, so check the exchange's contract page for the current tick size and tick value.

What win rate do you need to break even at each ratio?

The breakeven win rate is risk divided by the sum of risk and reward, so a higher ratio needs fewer winners. The breakeven win rate is the share of winning trades at which total wins exactly pay for total losses. With a ratio of 2, one win of 2R pays for two losses of 1R each. That is one win in three trades, or 33.3%.

Reward-to-risk ratio	Risk:reward written as	Breakeven win rate (before costs)
0.5	1:0.5	66.7%
1	1:1	50.0%
1.5	1:1.5	40.0%
2	1:2	33.3%
3	1:3	25.0%
4	1:4	20.0%

The table has a catch. A target twice as far away is not hit as often as a near one. When you widen the target, the win rate usually falls. The ratio and the win rate are two sides of the same stop-and-target choice, so you cannot judge one without the other.

How do you calculate expectancy from win rate and the ratio?

Expectancy combines win rate and the size of wins and losses into one number: the average result per trade. Expectancy is the amount a strategy makes or loses per trade on average, over many trades. This is the one formula worth remembering:

Expectancy = W × average win − (1 − W) × average loss

• W is the win rate as a decimal. For example, 40% is 0.40.
• 1 − W is the share of losing trades.
• Average win is the average profit of winning trades, after costs.
• Average loss is the average loss of losing trades, after costs, written as a positive number.

If you measure wins and losses in R, the average loss is 1 and the average win is the ratio. Two very different strategies can then have the same expectancy:

	Strategy A	Strategy B
Reward-to-risk ratio	3	1
Win rate	30%	60%
Calculation	0.30 × 3 − 0.70 × 1	0.60 × 1 − 0.40 × 1
Expectancy per trade	+0.2R	+0.2R

Both strategies make the same amount per trade on average. Strategy A has three times the ratio but no extra edge. The win rate and expectancy calculator runs this calculation for your own numbers. The guide to expected value and expectancy in trading covers how to judge whether an expectancy figure is large enough to trust.

Why does your backtest ratio differ from the ratio you planned?

The ratio you plan on the chart is almost never the ratio you get, because costs and real exits change both the wins and the losses. To see what actually happened, use the payoff ratio. The payoff ratio is the average winning trade divided by the average losing trade, both after costs, taken from the backtest's trade list. Six things push it away from the plan:

1. Commission and fees. They reduce every win and enlarge every loss.
2. Slippage on stops. A stop usually becomes a market order, so it often fills worse than the stop price. Fast markets and gaps can make the loss much larger than 1R.
3. Target fills. A limit target fills at your price or better, but only if the market trades there. A backtest that counts a fill whenever price only touches the target is too optimistic.
4. Other exits. Time exits, session-close exits and opposite signals close trades before the stop or target. These trades are often small wins or small losses.
5. Trailing stops and partial exits. They change the size of wins from trade to trade, so there is no single planned reward.
6. Execution timing. A strategy that decides at the bar close and fills on the next bar enters at a different price than the signal price.

Costs hurt small stops the most. A $10 cost is 20% of a $50 risk but only 5% of a $200 risk. This is why tight-stop, high-ratio plans often look strong on paper and weak after costs. The guide to trading costs in backtests explains how to estimate commission and slippage.

Does a higher risk reward ratio mean a better strategy?

No. A higher ratio trades a lower win rate for bigger wins, and that changes how the account feels long before it changes the average result. Think of two drivers who arrive at the same time on average. One drives steadily. The other waits at long red lights and then speeds. The average is the same, but the second trip is much harder to sit through.

A low win rate means long losing streaks. If trades are independent, the chance that a given run of 10 trades are all losers is about 5.6% at a 25% win rate (0.75 multiplied by itself 10 times). At a 50% win rate it is about 0.1%. Over a few hundred trades, a 25% win-rate strategy will very likely show streaks of 10 losses or more. Each streak is a drawdown of at least 10R. To see how a 25% win rate and 10 losses in a row play out on the account, the free risk of ruin calculator simulates sequences from your win rate, win/loss ratio and risk per trade.

To compare strategies with different ratios, use these numbers instead of the ratio:

• Expectancy after costs, in money and in R.
• Average trade compared with the round-trip cost. The gross average trade should be several times the cost.
• Maximum drawdown and longest losing streak, measured in R, so you can size the position for them.
• Number of trades. More trades with the same expectancy give a larger total result and a more reliable estimate.

What can the risk reward ratio not tell you?

The ratio cannot tell you whether the win rate behind it is real. A win rate measured on few trades has a wide margin of error. A win rate found by trying many stop and target combinations is likely to be inflated.

Each trade in a 40-trade sample moves the win rate by 2.5 percentage points. That is the problem with small samples. The selection problem adds to it. If you test fifty stop and target pairs and keep the best one, the best result is partly the luck of that period. Research on backtest overfitting shows that the more variants you try, the more the best one's backtest overstates its later performance (Bailey et al., 2014; Harvey and Liu, 2015).

These checks tell you more than the ratio does:

1. Count the trades. Ask how many trades would have to flip before the win rate falls to breakeven.
2. Test neighbouring settings. A stop of 9 or 11 ticks should give a similar result to a stop of 10 ticks. If only the 10-tick stop does well and its neighbours do not, the result probably fits noise in that period.
3. Test out of sample. Choose the stop and target on one period. Then test them unchanged on a later period, for example with walk-forward analysis.
4. Stress the costs. Repeat the run at twice the slippage. If the payoff ratio collapses, the plan depended on cheap fills.

In AlphaPrime (Valynox), the trade list and drawdown in the Performance Report give you the average win, average loss and losing streaks after fees and slippage. Strategy validation runs walk-forward analysis and other checks at Basic, Standard or Extensive depth. This tests whether a stop and target choice holds up beyond the period it was picked on.

What this means if you use AlphaPrime: judge a strategy by its payoff ratio and expectancy after costs, as shown in its trades, not by the stop and target in its rules. Then let validation show whether that result survives out of sample.

Frequently asked questions

What is a good risk reward ratio?

There is no single good ratio, because the ratio only matters together with the win rate. A ratio of 1 with a 60% win rate and a ratio of 3 with a 30% win rate both give an expectancy of +0.2R per trade. Check whether your win rate is clearly above the breakeven win rate for your ratio after costs.

Is risk reward ratio the same as reward to risk ratio?

They describe the same trade, written in opposite order. "Risk:reward 1:2" means you risk 1 to make 2, which is a reward-to-risk ratio of 2. Check which order a tool or article uses before you compare numbers.

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

Before costs, you need a win rate above 33.3%, because one win of 2R pays for two losses of 1R. Costs raise this level. In a hypothetical case where costs turn a $100 win into $90 and a $50 loss into $60, the breakeven win rate rises to 40%.

How do I calculate risk reward for a futures trade in ticks?

Count the ticks from entry to stop and from entry to target, and divide the target ticks by the stop ticks. Multiply each by the contract's tick value and your number of contracts to get the money at risk and the planned profit. Subtract the round-trip cost from the win and add it to the loss to get the ratio after costs.

References

• Bailey, D. H., Borwein, J., López de Prado, M., & Zhu, Q. J. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance. Notices of the American Mathematical Society, 61(5), 458–471.
• Harvey, C. R., & Liu, Y. (2015). Backtesting. The Journal of Portfolio Management, 42(1), 13–28.