What Is the Traders Equation? (How to Become Profitable)

The Trader’s Equation is a simple formula that outlines whether or not you’re profitable overall. It’s the combination of:

• The average size of your losses (Risk)
• The average size of your profits (Reward)
• Your success rate (how many of your trades are profitable).

If the result is positive, you’re a profitable trader. If it’s negative, you’re not. Simple!

How Does It Work?

Let’s say there are two traders and they take both take 500 trades. Trader A has profitable trades 60% of the time and Trader B has profitable trades 40% of the time.

Which one of them is right more often? You'd say it's Trader A.

However, which one is the more successful trader? To answer that we need a bit more information. We need to know how much they gained from the profitable trades and how much they lost from the losing trades.

For example, let’s say Trader A lost an average of $10 on their losing trades, and gained an average of $20 on their profitable trades. Trader B lost an average of $10 on their losing trades, but gained an average of $40 on their profitable trades.

That means from 500 trades, Trader A made an overall profit of $4,000 and Trader B made a profit of $5,000.

This calculation is known as the Trader’s Equation. It’s a combination of the average profits, average losses, and the probability of each occurring (also known as the success rate). What we can see is that you don’t need to profit from most of your trades to be a profitable trader. In fact, if we change the other variables, it’s possible to lose more trades and still be profitable.

By understanding this calculation, we can reverse-engineer what’s needed to succeed as a trader. Rather than looking at trades as being something you’re ‘right or wrong’ with, we can use an equivalent of the Trader’s Equation on each individual trade. This is known as the expectancy of a trade.

We’re looking at the expected profit, the expected loss, and the estimated probability of each of those occurring. We can never predict the future with certainty, we can only estimate the probabilities of things happening. Therefore, when we open a trade we don’t know whether it will be a profit or a loss, but we can estimate the probabilities of each.

If we take trades with a positive expectancy, we’re basically saying that if we took this type of trade over and over again it would lead to a positive Trader’s Equation regardless of the outcome of each individual trade.

In the following example, if I took this trade 500 times over, I’d likely have a positive Trader’s Equation and be making money from my trading. Therefore, when I look at the resulting Trader’s Equation, it doesn’t mean I was wrong 60% of the time. Since I estimated the probabilities as being 60% and 40%, it means I was actually right overall.

This is an important thing to understand for trading, and it’s something most traders miss. They focus on finding profitable trades, but in reality that’s not how things work. Instead, we should be learning how to estimate the probabilities of situations and using that to guide our decisions. Without probabilities, we’ll have no idea whether a trade has the potential to contribute to a positive Trader’s Equation.