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- The Cold Hard Statistics
  - Part 1

- The Cold Hard Statistics
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How to Pick an Expert Advisor

Learn How to Find the Best MetaTrader Trading Robot

A Continuation of Drawdown Analysis
To continue from where we last left, we will further investigate the measures and characteristics of drawdowns, as well as focus on a very important factor when considering trading performance. As stated in our previous article there are three key parts to the drawdown; max drawdown, average drawdown, and drawdown recovery. We've already covered max drawdown and will now focus on the second measure, average drawdown.

Average drawdown is the mean drawdown percentage of all drawdowns incurred by the EA over its historical performance. To calculate this statistic you need to take each and every drawdown, sum their individual percentage losses up, and then divide by the total number of drawdowns that have occurred. Although this is an important statistic, it can be very tedious and time consuming to manually calculate. In many cases if this figure is not provided, it is can found by directly contacting the EA vendor and requesting this information. If the provider is unwilling, or unable to provide this information to you, then you should most likely eliminate the EA, and any EA produced by that vendor. The inability to produce simple statistical information is a giant red flag you need to be aware of. However, in most cases you will be able to obtain the information on average drawdown with minimal effort. Once you have the information, you will gain a better perspective of the average movement in a typical peak-to-trough cycle, and estimate whether or not you could handle that type of fluctuation.

Another piece of information that is useful to add along with average drawdown is the range of drawdowns; which can be found by taking the largest and smallest drawdowns that have historically occurred. When combined with your average drawdown, you will get a detailed idea of how the fluctuation and range of your account can vary. Once you discern the final part of drawdown analysis, drawdown recovery, you will have a decisive picture of how long the variations occur and the amount of fluctuation your account is likely to endure.

The drawdown recovery measure shows the time frame it has taken, on average, for the EA to recover from the bottom of the drawdown and return back to a positive level. The main point to take away from this statistic is how long, or how many trades you should expect in a typical recovery period. Although it would be best to have a quick drawdown recovery, a less volatile EA will often take a longer period of time to recover. Additionally it will recover in a slow and steady manner. Ideally an EA like this would be preferable for a steady consistent growth of capital, whereas a faster recovery time could be due to large swings in both directions and would require a higher level of maintenance and risk management.

Although the three parts of drawdown analysis are important on their own, when combined they provide an invaluable picture of the overall risk and volatility of the EA. Once you have thoroughly analyzed and considered each factor, you should have a good idea of the type of volatility you can expect in your account, how long it will typically take to recover from losses, and ultimately if the overall potential risk of the EA is acceptable or entirely too risky for your preference. Now that we understand the importance of risk through the drawdown analysis, we can delve into performance measures and gain a perspective of how to rate and compare different EAs by these measures.

Accuracy and the Win/Loss Ratio
Once you have assessed the profitability and risk components of an EA, and have screened out any that do not meet your criteria, it is time to make an assessment about the trading performance of the EA. There are two key statistics used to measure this, which are accuracy and expectancy.

Accuracy is the percentage of winning trades vs. losing trades that are placed. There are two important things to consider when viewing the accuracy. First, the scope of the accuracy, and second the average win/loss ratio. The scope is the amount of trades used to calculate the accuracy, and in almost every case should encompass the entire history of the EA. The most important part of the scope is ensuring that there is a statistical data set large enough to ensure a sound statistical base of measure. Mathematically speaking, a statistic is not reliable unless there are at least 32 data points included. However this is the bare minimum to consider reliable, and in most cases you would fair better to shoot for a minimum of 50-100 trades to ensure the data is truly reliable. It is absolutely imperative that there are a sound amount of trades in the computation of accuracy; otherwise you can receive greatly distorted numbers.

For instance, take an example of an EA that has done 15 trades and 10 of these were profitable, this would produce an accuracy of 66.6%. However over the next 30 trades the EA only produced 12 additional winning trades, bringing the total accuracy of the EA to 22/45 or 48.8%. This drastic change in accuracy could completely change the analysis of the EA and may potentially cause the EA to become unprofitable. Remember, the less trades there are, the bigger the change in accuracy per each trade. Very few EAs will consistently perform perfectly in line with their accuracy measure. It is important to understand that accuracy is the measure of the complete performance. It is not unusual for an EA to go on winning or losing streaks, however in the long term an EA should ultimately revert to its mean accuracy in the long run. This is why it is critical to always ensure that enough trades have been encompassed in the computation of accuracy. If too little trades are captured then you cannot be sure whether you have calculated the true accuracy of the system, or inadvertently calculated the accuracy of the system during an abnormal period of performance. Once you have assessed that the accuracy is reliable, you must consider the average win/loss ratio, because without this the accuracy statistic is essentially useless.

Expectancy of Performance
Contrary to what may seem obvious, a high accuracy is not always an indicator of profitability. Only when you combine both accuracy and average win/loss can you truly gain a sense of the potential profitability of the EA. With these two measures you can calculate the expectancy of an EA, which will give you an in depth perspective of the actual performance of the EA. Expectancy is calculated with the following equation: (Accuracy * Average win) / ((1- Accuracy) * Average loss). This calculation will show what you should expect to return, on average, for each trade over the life of the EA. Below is an example of a hypothetical EA and the calculated expectancy:

Winning Trades Losing Trades Accuracy Average Win Average Loss Expectancy
EA 1 230 195 54.12% 3.1 2.9 1.26
EA 2 172 280 38.05% 4.4 2.4 1.13
EA 3 395 120 76.70% 1.5 5.3 0.93

It is important to realize that any expectancy above 1 indicates a net positive return on the account over the measured period; while an expectancy that is less than 1 represents a negative return. Although theoretically you can think of expectancy as the average amount gained per trade, practically there will be a much greater variance on a trade by trade basis.

Expectancy is a key factor to gauge and rate an EA, but it is important to remember that it shows an overall view of the per trade perspective. It does not necessarily indicate the actual performance of each trade. It is important when comparing expectancy to keep the average amount of trades placed in a period in mind. For example a scalping EA will most likely have a rather low expectancy, for this example let's consider an expectancy of 1.15. Despite the low number it may produce a large amount of trades in a particular period thus creating a sizable gain. If you were to compare this to a breakout EA with an expectancy of 5.75, which may only make a few trades in the same period, you would most likely immediately discount the scalping EA. By ignoring the nature of the EA and its total profit, you ultimately miss out on a potentially better EA. This is why it is wise to not only try to compare similar EAs to one another; i.e. scalping EA with another scalping EA, but also to consider the full range of quantifiable statistics that we have covered in this two part report.

To reiterate, these statistics include overall profitability, and justifying profitability based upon the risk associated through your drawdown analysis. With these measures you should be able to grade and objectively look at each EA and get a sense of what statistically makes the best sense for you. Although quantified measures are of the highest importance; relatively important and vastly underestimated factors are the qualitative stats that should be considered when choosing an EA. We will cover this in our next report and focus on what important factors you need to look for when assessing the psychological and mental effects that an EA may cause.

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