**One plus one are three**

When the reward-to-risk ratio and winning percentage are evaluated together, it becomes easy to determine if a trading strategy has promise — or if it’s doomed to financial failure. The equation for combining these numbers is:

**(Win % / 100) * (Reward:Risk) - [(100 – Win%) / 100]**

As long as this equation is greater than zero, the strategy will be profitable. Additionally, the higher the resulting number, the better the system. Many good, tradable systems can be found with values between 0.10 and 0.50.

The number is commonly referred to as “expectancy,” and it is an excellent statistic. In plain English, it tells you the amount of money you would win per dollar risked. For example, a value of 0.20 indicates that in the long run you will make 20¢ for every dollar you risk trading this system. In other words, it is a really good system.

One word of warning, however. Another incorrect formula for expectancy, at least in the context we’re interested in, is prevalent, particularly if you simply search this topic on the internet. The following is the incorrect formula: (probability of win * average win) – (probability of loss * average loss). Often, this will be described as expectancy; it is not. This is the average trade value. In our correct formula, we divide the average trade value by the negative of the average loss. This is the extra step that gives us the amount of money we would win per dollar risked.

Let’s evaluate our initial simple example using the correct formula for expectancy. In “Questionable curves,” the blue curve shows a system that has a reward-to-risk ratio of three-to-one, but the winning percentage (not initially disclosed) was only 20%. Plugging these numbers in, we get:

**(20 / 100) * (3) - [(100 – 20) / 100] = -0.2 **

Because this is less than zero, the strategy is a losing one, which is obvious from the chart. Any trader using such a strategy eventually will, and inevitably, go broke trading it.

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