How to use probability analysis in your FOREX trading can appear daunting if you don't have a mathematics background. I'll have to mention some math in this post, but I'll be careful not to make that the thrust of understanding.

When I do use some math, I'll explain it so you get the concepts of the use. All mathematics is based on explaining something that happens in the real world.

Welllll... for the most part, that is. There's a lot of theoretical mathematics that have little to do with specific application in our lives. What happens is that someone doing research on a topic finds that the previously theoretical aspect actually can be applied to real world situations.

Of note is that to this post, I have a companion video of the same title: Simple Probability Analysis In FOREX Trading that puts all of this together from a different view point.

If you've come from watching that video, then press on here. However, if this is your starting point, I might suggest that you read through this before watching the video. Or, if you want, you can skip to the bottom of this post to watch that video now.

Definition of Probability

Probability is a field closely related to statistics that deals with the likelihood of an event or phenomena occurring.

It is quantified as a number between 0 and 1 inclusive, where 0 indicates an impossible chance of occurrence and 1 denotes the certain outcome of an event.

— Investopedia: What Is a Joint Probability?

There are some simple examples in that article of how you calculate probability, so you might want to take a brief look at that reference.

Along side of probability is the use of what's called a probability distribution, and its use in giving us the very meaningful standard deviation of that distribution.

One piece at a time here....

Definition of Probability Distribution

A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.

— Investopedia: What Is a Probability Distribution?

Let's say you were measuring the height of 100 horses, and you found the following:

That's pretty interesting information. In this very simple distribution example, it's easy to see that most of the horses in the 100 horse sample size are 5 feet tall, i.e. 71, or 71% of them. And that's actually a real value: the average height of an adult horse is about 5 feet, i.e. with a distinct range between 4.7 feet and 6 feet.

Wow! What's up with that 1 horse at 2 feet? He's way 'off the scale' of that 'expected average value'.

To understand the significance of that, we need to take a look at what's called the standard deviation of that 'sample size probability distribution of the height of adult horses'. Whew....

Definition of the Standard Deviation of a Probability Distribution

The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

— Investopedia: What Is Standard Deviation?

Yeah... if you're not familiar with standard deviation, then that article is going to be pretty difficult to get through. Skip down to the section titled: A Big Drawback. Read that, and then the following section: Example of Standard Deviation.

Still not really helpful is it? Well, the key to standard deviation is what's called the variance of that distribution.

If you follow the link on the page to normal distribution, you'll find a discussion of what that all looks like in the 'bell curve' model that's shown in the video there. Watch that video....

That 2 foot horse data point would be way down on the narrow part of the left 'tail' of the bell curve.

The implication of that is: it's highly unusual to find an adult horse with a height of only 2 feet, whereas you would most expect to find horses with a height of 5 feet, and the tallest at 6 feet.

You don't need any math or understanding of probability distribution, variance, standard deviation, or how horses grow. All you have to do is look at a chart of the standard deviation of something, and it becomes pretty clear what the 'likelihood' of an event occurring. The closer to that mean, or central point on the chart the event is, the more 'likely' it is to happen.

And for our purposes as traders, that 'likelyness' is kinda-sortta an indication of the probability of that event happening. While a mathematician may just puke all over their desk at that, I'm just trying to get you to a point where all that complicated math can be more easily expressed in terms more palatable to traders.

As traders, we don't really need to know what a standard deviation is, but we do need to understand it's significance in determining the probability that some price action event will or will not occur.

*** IMPORTANT: When I mention the word 'probability' to someone, many times they tend to interpose the terms 'probability' with that of the 'odds' of something happening. Not so. The 'odds' of something happening is a much more complex issue that I'll define, but not discuss because it only clouds the issue of the use of probability analysis in trading.

"The probability that an event will occur is the fraction of times you expect to see that event in many trials. Probabilities always range between 0 and 1. The odds are defined as the probability that the event will occur divided by the probability that the event will not occur."

Let's just not worry about the 'odds' of something happening. Besides, you take odds on horses, not currency trades....

So, as traders, we'd like to be able to get an answer to something similar to the following: "What's the probability that price will be able to continue upward toward my final profit target 20 pips away?"

The simple answer is that you can't.

Why not? Well, there's a huge difference in being able to say there's a 71% probability that my new baby horse, Fred, will grow up to be around 5 feet tall as opposed to being able to say there's a 71% probability that price will be able to push 20 pips higher.

The reason for this is that horses are quantifiable whereas currency price action is not. Horse growth is governed by the laws of... well, let's just call it 'horse growth biology'. Currency prices have no such 'price action biology'.

Price action is random and fractal, and is not governed by any physical law, either through mathematics or physics. Price action comes about through the economic needs of two countries exchanging goods and services via the translation of their currencies into the currency of the other.

And that's a good thing!

Why is that a good thing? In fact, doesn't that just invalidate the premise of this entire article?

Okay: what was the premise of the post?

This post concerns using a branch of mathematics called probability in the analysis of trading in the FOREX market.

But if you can't use probability to do this, then what can you do?

Remember that bell curve diagram showing the standard deviation? That bell curve represents a mathematical model of some probability distribution.

So, where you may not be able to determine the probability of what currency price may do in the next 5 minutes, you can develop a price action model based on different possible price movements which can then become a probability distribution. And from that probability distribution, you can determine standard deviation and variance.

Sounds like I just went into a gibberish gerbil circle....

And it also seems to have introduced even more complexity into the mix.

Let me simplify it by pointing out from all of that 'gibberish' the following phrase: "...you can develop a price action model...."

Well, okay then: what's a price action model, and how does that reduce complexity caused by all the mathematics?

Let's work backwards here: what does a model represent?

A model is a simple representation of a complex thing.

Maybe you built a model ship when you were a kid, or you're an architect and build model representations of drawings. Whatever. But more importantly, the football coach jumping up and down on the sidelines is calling in plays to the quarterback based on his (the coach's) overall view of the field and the interaction of the two teams on the field.

Here's the point I'm trying to make: That coach is not building mathematical probability distributions of player movement and then making decisions based on looking at a standard deviation chart to determine what the probability of success could be if he called in Play A as opposed to Play B.

He's making his decisions based on his cumulative experience at participating in hundreds, if not thousands, of football games. This cumulative experience can loosely be called intuition, or 'gut feel', but it's correctly based on the conversion of that experience into decision making.

And it doesn't require any f'n complex math....

Our experience would interpret how 'autumn-y' it was, i.e. early autumn with rich oranges and yellows, or late autumn with its muted browns and deep reds. Thus, a trader's experience interprets current price action with respect to past price action over many years of experience such that he can state that price currently has a high probability of moving up 20 pips.

That all sounds like a lot of arm waving. And it is. And not very mathematical either.

But it is mathematically based. It's just that you don't need the math to trade. That's because, if you understand how the math explains what you see intuitively based on your experience, then you don't need the math. But price action can be completely mathematically expressed.

That's the good news: Though you don't need the math to make a trading decision, it's nice to know that price action follows mathematical laws.

As an aside to price action following mathematical laws, if you're interested in exploring all of that in more detail, I discuss that in my blog post The Myth of Using FOREX Currency Trading Indicators where I mention the following:

From a scientific standpoint — from someone who has a B.S. in Physics and a lot of mathematics — the reality is that you can not predict through probabilistic calculations what a specific element will or could do, but rather only the probability of what the entire system of those elements might do.

In addition: probabilistic calculations against market data are not the same as making those same types of calculations, for example, against the movement of particulate in a fluid, called Brownian Motion.

It's that discussion of Brownian Motion which shows the complexity of doing this sort of mathematical probability analysis. You're just not going to be able to do this type of analysis in real time, even if you could do the equations. And that's why experience enables the trader to build a sort of intuitive 'price action probability distribution behavior model' in real time.

So, why talk about probability at all then?

Even though the probability of price action doing something is based on experience, that experience is the result of seeing the outcomes of many, many trades such that the trader has this theoretical price action probability distribution behavior model ingrained in them without even knowing it.

As traders, regardless of our 'intuition', we need a basis for that intuition that is derived from the probability distributions we've experienced trading. The more experienced we are at being able to identify this correlation, the more valid our intuitive probability analysis in real time will be.

That analogy is totally map-able into trading. First, you have to have a sense of what the market does under various conditions, and then you have to understand how you, and your particular trading style or character, respond to those market conditions.

And, actually: all of that should form the basis of your individual trading plan.

So, let's build an example probability model, and see how you'd use that. For simplicity sake, I'll just use one that I developed for exiting a profitable position. There are actually several parts of this model. For example, exiting when price hits the profit target, or exiting based on some external condition — like an NFP event.

Now, you might ask why I'd develop an exit model for when price hits the profit target. The answer to that is simply because that condition exists in my problem domain of position exit options, and thus must be accounted for. Because of this, a scenario must be developed for that regardless of how stupid it might at first appear.

But, you groan.... It's just soooo stupidly obvious that when the profit target is hit that you get out.

No, it is not. What if price action is strong, and the analysis indicates further movement beyond the profit target is highly likely; wouldn't you want a rule to discuss what to do? Sure. And what about the trader that ignores that profit target, price turns around and starts to go against them, and they freeze? You need a rule to prevent that from happening.

Look, you just can't miss the stupid stuff because that could potentially be a decision you incorrectly make that costs you 40% of your account.

The scenario I'll share with you is the one for exiting a position that has made progress toward the profit target, but is not continuing in the manner expected in which the original trade entry probabilistic analysis indicated it should.

That stalling in the price action can be of several forms. For example, price was going up fine, but all of a sudden it drops and leaves the current candle in a pin bar form. That's not the 'stalling' I'm talking about. Rather what I look for, and what my analysis model is developed around, is when price begins to 'chatter'.

How do I define 'chatter'?

By defining 'chatter', I'm not only identifying a market condition (like the hot stove), but that I'm also actually constructing a probability model that will provide me the rules to deal with that market condition.

Here's how I framed my probability model for this chatter event:

Based on my experience with the pair being traded, on the time frame I evaluate such movement on, and its ATR, then, when price on a very, very low time frame that's in relationship to the overall trading time frame begins to oscillate more or less horizontally in a channel over just a few pips amplitude (and again, this is in relationship to the overall ATR) I define this as 'chatter'.

And the rule that I use when I notice this probability model evolving is pretty simple:

When I see this chatter over an ATR number of candles (i.e. ATR of 10 would thus indicate about 10 candles) I exit the trade.

Where's the math in that?

There is none. And that's the point.

However, my description of that event is the result of my experience which enables me to determine sort of 'intuitively' in real time the probability of price reversing against me under those conditions.

This is based on me seeing this configuration enough times in the past that I don't even need to calculate the probability distribution, or how many standard deviations I'm off from my originally projected probability of success to make the decision to exit the position.

Regardless of all of that: my decision still has a foundation in mathematical probabilistic analysis, whether I know it or like it, or not.

Video: Simple Probability Analysis In FOREX Trading