An interesting question. What lies behind it? A belief held by many traders that they must have a win rate where they win 70% or more of their trades and also be able to place their targets using some magic ratio (usually 3:1), the distance from their stop. Of course, the stop must also be really tight. Indeed, here a picture that I made from a trading forum where I am active. See, he wants a 99% accurate trading system, and he wants it to be given to him for free!

In the United States, traders have typically gone through a school system where a 67% or so score is considered a failing grade! Is it any wonder that so many US traders think that even a 70% win rate is barely acceptable? Contrast this to a school system where a 40% score is the minimum passing score, and a 70% score is an A. People who grew up in such a system would have no issue thinking that a 50% or even a 45% win rate is a viable method to trade. So what is your minimum acceptable win rate?

Regardless, let us now look objectively, using statistics, probability and Expected Value, at how to determine if you need to have a high (like 80%) winning rate in order to be successful. We shall use the same criteria that we have used so far in our look at how to validate a trading method. See Parts 1 and 2 of the *Trading with Expectation/Expected Value* series of posts. The only difference is that we shall now postulate a 70% probability of loss and a 30% probability of gain, rather than 80% and 20% respectively. We shall still use the putative 3:1 Reward/Risk ratio. So here are the numbers:

- Target ticks = 30
- Stop ticks = 10
- Target hit first 30 times out of 100
- Stop hit first 70 times out of 100

From this, and what we discussed in Trading with Expectation/Expected Value – Part 2c, we can make the following calculations:

*Expected Value*of loss,**EV**= probability of loss x size of potential loss = 0.7 x 10 ticks = 7 ticks._{loss}*Expected Value*of gain,**EV**= probability of gain x size of potential gain = 0.3 x 30 ticks = 9 ticks._{profit}

Giving us a EVRatio of 9/7 = 1.28, or 128% approximately. We round down, because we want to be conservative when we calculate gains.

This means that we can expect a 28% net gain from trading such a method. Notice however, that we only have a **30% win rate**!! Also notice, that contrary to naïve expectations, **we are not making the 200%** that is expected by those who just look at the so-called Reward/Risk ratio of 3:1, without adjusting for probability.

What the heck?! It is possible to be profitable while winning only 30% of our trades? The problem though is that very few traders would actually be psychologically able to trade a system that loses 70% of the time, no matter what the statistics say.

Of course, most traders would want to be able to use a 3:1 (unadjusted) Reward/Risk ratio and have an 85%+ win rate. Sorry folks, that is the typical get-rich-quick mentality, and it will not fly. To get a higher win rate, one must use smaller targets and/or larger Stop Losses. Something has to give. Just as with almost everything in life, we cannot get something for nothing. TANSTAAFL.

So what is our lesson here?

Set realistic targets, for the trading method that you are using, and be aware of how probability can impact your results.

After all, a 3:1 Reward/Risk ratio means nothing if your targets are almost never hit.

We, of course, would love to read your comments, even if you disagree with what we say.