Relationship between Reward to Risk Ratio(RRR) and Win Rate in trading

Win rate and Reward to Risk Ratio is among the most commonly used term in defining the characteristics of a trading strategy. Let's start from the beginning and define these terms.

Win Rate (W): This is the percentage of trades that hits the target without hitting the stop loss. The win rate has to be calculated with a large sample (large number of trades). Small sample will lead to incorrect win rate calculations.

Reward to Risk Ratio (RRR): This is the ratio of target points and the stop loss points within a trade. In defining the RRR of a strategy, we intend to refer RRR with the win rate. For example, If we say that the RRR is 2 with win rate of 40%, then we mean that 40% of the time the trade goes twice the stop loss decided under the strategy.

Win rate and RRR are always used with each other as none of them alone can't help us understand the overall effectiveness of a strategy. For instance, a strategy with low win rate with very high RRR might be more profitable than a high win rate strategy with low RRR. To draw a line between profitable strategy and a non profitable strategy we need to find the breakeven win rate for a given RRR. Let's try to derive the same.

For a strategy with win rate (W) and Reward to risk ratio (R), the expected value of each trade will be defined as:

EV=(W×R)−((1−W)×1)

For a breakeven condition , EV=0.

0=(W×R)−((1−W)×1)

Rearranging this will give us

W=1/(1+R)

So any strategy that has win ratio of less than 1/(1+R) will not be profitable in the long term.

Let's try to plot the RRR and win rate in a table.

Win rate Vs RRR in trading curve

Break even win rate	Reward to risk ratio	10%	20%	30%	40%	50%	60%
50%	1	loss	loss	loss	loss	profit	profit
40%	1.5	loss	loss	loss	profit	profit	profit
33%	2	loss	loss	loss	profit	profit	profit
29%	2.5	loss	loss	profit	profit	profit	profit
25%	3	loss	loss	profit	profit	profit	profit
22%	3.5	loss	loss	profit	profit	profit	profit
20%	4	loss	profit	profit	profit	profit	profit
18%	4.5	loss	profit	profit	profit	profit	profit
17%	5	loss	profit	profit	profit	profit	profit
15%	5.5	loss	profit	profit	profit	profit	profit
14%	6	loss	profit	profit	profit	profit	profit
13%	6.5	loss	profit	profit	profit	profit	profit
13%	7	loss	profit	profit	profit	profit	profit
12%	7.5	loss	profit	profit	profit	profit	profit
11%	8	loss	profit	profit	profit	profit	profit
11%	8.5	loss	profit	profit	profit	profit	profit
10%	9	profit	profit	profit	profit	profit	profit

In the curve above we can see that, any strategy above the curve will be profitable and any strategy below the curve will be in loss. As a trader, we need to select a strategy that is above the curve. This curve actually defines the trading style of all the traders. Some are comfortable with strategies with high win rate and relatively low RRR (scalpers) and some are more comfortable in high RRR with relatively low win rate( trend following traders) .

Before entering any trade in the market, the trader has to select the area on the curve where they feel comfortable. There is no right or wrong answer in this. Traders have to see which style is suiting their mindset and stick to it. Ideally, one would want a very high RRR and a very high win rate. However, when we wait for a confirmation in a trade, we let go the high RRR as the chance to enter at the bottom gets missed. But this in turns increase our win rate as we waited for a confirmation. This mechanism works in reverse when we choose a low win rate strategy with high RRR.

The process should be to find strategies and then back test them for a good sample size and then try to see if the strategy is better then their present strategy. See what is the expected value of a strategy and compare it with other strategies. With time and experience you will be able to filter out strategies that are highly probable and highly profitable.