In Part 2a, we showed how despite using the much vaunted 3:1 reward/risk ratio of 3:1, a trader could still end up with a losing trading system. We asserted that the profitability of a trading system depends not only on the relative sizes of the distance to target and stop, but also on the probability of reaching those marks. In this post, we shall formalize a method to evaluate a trading method for **potential **profitability.

We return to the arithmetic in Part 2a. As a reminder, these were the statistics that we had got from our counts.

- Target ticks = 30
- Stop ticks = 10
- Target hit first 20 times out of 100
- Stop hit first 80 times out of 100

Again we see the vaunted 3:1 reward/risk ratio.

From which again we can say:

## First we look at the losing side

Total ticks lost = (number of losing trades) x (Number of ticks lost per losing trade) = 80 x 10 = 800 ticks.

But someone might point out that that is all well and good for 100 trades; what about if I evaluated a different number of trades. That question points to the weakness of looking only at total returns. What we want to do is to look at the *average return per trade*. To do this, we just have to divide out total return by the total number of instances that we examined. Hence, we can say:

Average loss per trade = (number of losing trades) ÷ (number of instances examined) x (Number of ticks lost per losing trade)

Remember how in Part 1c, we said that ProbabilityStopHitFirst = (number of instances) ÷ (sample size) ? As the sample size is simply the number of instances examined, we can now say that:

Average loss per trade = ProbabilityStopHitFirst x (Number of ticks lost per losing trade)

This *Average Loss per trade* is called the **Expected Value** or Expectation or Expectancy (by some traders), in this case, of a losing trade. The equation used to calculate the *Expected Value* is sometimes called “The Trader’s Equation” by some traders. We shall denote this by our symbol **EV _{loss}.**

**EV _{loss} **=

**P**x

_{loss}**StopTicks**, where

**P**is the “probability of a losing trade” and “StopTicks” is the number of ticks lost in a single trade.

_{loss}So, **P _{loss}** is simply the ProbabilityStopHitFirst value; and StopTicks is “10” from the values shown at the top of the post. So, to recap, from Part 1c, for our statistics, ProbabilityStopHitFirst = 80 ÷ 100 = 0.8

Therefore, **EV _{loss} **= 0.8 x 10 = 8 ticks.

By the same token, we can also say:

## Now, looking at the profitable side

Using a parallel argument from our examination of the losing side:

Average profit per trade = (number of profitable trades) ÷ (number of instances examined) x (Number of ticks profit per profitable trade)

Again, remember how in Part 1c, we said that ProbabilityTargetHitFirst = (number of instances) ÷ (sample size) ? As the sample size is simply the number of instances examined, we can now say that:

Average profit per trade = (Number of ticks profit per profitable trade) x ProbabilityTargetHitFirst

We shall denote this by our symbol **EV _{profit}. **It is the Expected Value of a profitable trade.

So, **EV _{profit} **=

**P**x

_{profit}**TargetTicks**, where

**P**is the “probability of a profitable trade” and “TargetTicks” is the number of tick profit in a single trade. We simply changed our reference to “profit”, where before we referenced “loss”, and changed from references the “stop” to referencing the “target”.

_{profit}So, **P _{profit}** is simply the ProbabilityTargetHitFirst value; and TargetTicks is “30” from the values shown at the top of the post. So, to recap, from Part 1c, for our statistics, ProbabilityTargetHitFirst = 20 ÷ 100 = 0.2

Therefore, **EV _{profit} **= 0.2 x 30 = 6 ticks.

## Summary

In this post, we showed how to calculate the Expected Values for losses and profits in a trading method. We used the same sample statistics that we have used so far for this series of posts. If these calculations show you why this particular trading method, with these particular statistics, would be a losing one in the long run, then you have began to understand why it is important that all factors are taken into account when evaluating a trading method, not just the initial static reward/risk ratio.

To recap, in order to evaluate a trading method, a trader must take into account **both the size of the targets/stops and the probability of reaching them.**

In the next write-up in this series, we shall examine how to use the information about *Expected Value*, to qualify a trading method.

In the meantime, if you found this useful, please leave a comment. On the other hand, if this post was obtuse, please tell us why.