# Thinking in Probabilities

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Did you know that you do not have to be right each time you interact with the market? Heck, you don't even need to be correct 50% of the time to bank a profit in this business! Once one has mastered a setup with an edge, trading should, to a point, be no more than a repetitive chore. However, because of our natural tendency to always want to be correct, we make trading difficult.

This is where thinking in probabilities comes into the picture. By switching one's mindset to this way of thinking, it will not only help your trading psychologically, but also your bottom line. We understand that this may seem somewhat of a paradox, but by detaching yourself and letting go of whether or not the next trade will be a winner or a loser, is exactly what's required to achieve consistent profits you can rely on. Hopefully, the following article will provide a clearer vision on how to begin accomplishing this…

Trading expectancy or, if you prefer, statistical expectancy, essentially provides one an effective and objective way of evaluating a trading method's performance. In simple terms, your trading expectancy is the average amount you can expect to win/lose using a particular method. While the probability of each individual trade cannot be calculated, the statistical measure can be applied to a large sample size of trades. We recommend at least fifty trading examples to be statistically significant.

The following components are needed to calculate this:

• Firstly, you'll need to estimate the win/loss ratio i.e. how many trades produced a winning reaction. Then, from your trade samples, divide the value of winning setups by the total number of trades taken. This will give the win/loss ratio. By way of example, let's say that you have recorded 100 trades, and out of those 100, 40 came in as winners. The win/loss ratio for this segment would therefore be 40/60, or 40%. However, although the method produced 60 losing trades, it does not invalidate the approach. As a matter of fact, some of the most profitable systems have win/loss ratios that are less than 50%.
• Secondly, the risk/reward ratio needs to be considered. This is the average size of a profitable trade divided by a typical losing trade. As an example, say that on average your winning trades register \$200 and the losers come in at \$100. With that in mind, we can see that we have a risk/reward ratio of 2:1, meaning that on every winning trade, the method yields two times its risk.
• Finally, we have to merge the two aforementioned ratios to reach an expectancy ratio i.e. the trading expectancy. We know that the method has a 40% chance of producing a winning trade. We also know that on average the winners achieve two times the risk. So, let's calculate this.

With the above calculation, we can see that we have a method with a positive expectancy, even though it lost 60% of the time. In addition to the above, you can, if you prefer, also calculate It as such (reward/risk ratio * wins) – losses = trading expectancy ratio. In this case the ratio would come in at .20 (2*40 – 60). Anything above 0 is positive. So, on average, this method will return .20 times the size of the losing trades.

While the above illustrates a profitable method, one must also take into account that there will be trading fees and commissions which, of course, will reduce profits. Furthermore, historical calculations are not a guarantee that the method will produce the same results in future trades. Nevertheless, this is the best alternative we have when formulating a trading method.

What is crystal clear from the above calculations, however, is that it is not necessary to win every trade. In fact, if a method is able to generate 3 times its risk on winning trades, meaning you'll have a risk/reward ratio of 3:1, one can afford to lose 70% of the trades and still come out on top: 10 trades risking \$100 on each: (\$300 win * 3) = \$900 – \$100 * 7 = \$700 = \$200 profit.

Unfortunately, trading expectancy is not a widely discussed concept. It SHOULD be though! Not only is calculating expectancy a fantastic way to analyse and compare trading methods, it also does wonders for one's psychology.

Thinking in probabilities rather than focusing on each individual trade

Probability is the measure of how likely an event is to occur out of the number of possible outcomes. Therefore, if we know that the method we're trading has a positive expectancy i.e. it has a high probability of making money over the long term, is there really any need to place emphasis on whether or not the next trade will be a winner? Absolutely not!

We all know of traders who get furious at the sight of a losing trade. Unfortunately, these are the same traders who usually sit glued to their screen talking, sometimes even shouting, at their monitors urging the market to move in their desired direction! We are fairly confident that the majority of experienced traders have also faced this same dilemma in the early days of their trading journeys. As you become more experienced, you'll understand that there is really very little point in getting excited over your next trade. Shouting at the screen, trying to jeer the market on, will have absolutely no effect whatsoever!

We understand that to think in probabilities is easy in theory, but a rather difficult approach to implement, especially when your hard-earned money is on the line. What we have found that helps is using analogies:

• A good visual for this is to imagine that your holding a small bag of rice. In this bag of rice there's around 1000 grains of rice, and let's say that each grain represents an individual trade. Assuming that one knows how to size positions correctly and is thinking in probabilities, how significant is that one trade in the grand scheme of things? Negligible is a word that springs to mind!
• Let's look at another simple analogy: a train ride. This may be considered a little cheesy, but it is certainly a valid example, in our view. The train journey has two central destinations, three if the tracks change due to adverse weather conditions (you move your stop to breakeven). However, let's just focus on the main two destinations for now. Destination A is named 'target hit' and a destination B is called 'stop-loss hit'. The train has no driver. It's also automated and random. Using our trading expectancy calculations from above, we know that every time one boards the train they have a 40% chance of reaching destination A. Now, let's imagine that before the crowds boarded the train, the platform conductor (we can think of him as a typical market guru who proclaims to know where the market is headed at each swing) announces that there's a very good chance that the train will reach destination A today because on the past two journeys, the train managed to clock in at this platform. When you think about it though, does that really matter? Considering that the passengers know over the course of 100 journeys (trades), they'll reach that destination at least 40 times? Of course not!

With two analogies under our belt, let's check out the equity curve below:

Over the course of 220 trades, the account grew massively. Now, this could have been over a year, five years or even the span of a trader's career. This does not matter. What does matter though is understanding that each individual trade should, as long as you keep to your trading rules and money management strategy, have little effect on the collective outcome. Do we panic if we have a loss, do we panic if we have two, or even three consecutive losses? Absolutely not. Remember, there is no way of knowing the outcome of each trade you take! Do you think the trader who managed the account pictured above panicked when the equity curve started to turn south (see black arrows)? Highly unlikely given the results.

In our humble opinion, trading a method that has a clear edge and following it religiously, while thinking in probabilities, is key to a successful trading career. This type of thinking will not happen overnight. It takes time to develop, but we're sure you'll agree with us that it is certainly worth pursuing!