Becoming a successful trader is a challenging journey. The odds of success are stacked against each individual from the beginning. Not only do you have to learn how the markets work, but you also have to determine which markets to trade and how to trade them. Everyone starts out with the same goal in mind: to make money. The challenging question is how?

Unfortunately, most traders start off focusing on the wrong pieces of the puzzle. They work diligently trying to identify the perfect setup and entry point with little or no regard for what it really takes to succeed. If folks are fortunate enough to survive the first year or two, they ultimately learn that trading is simply a numbers game. Stated differently, it is all about the math. Each individual must clearly understand which formulas are most important in trading and then determine how to apply those formulas to their individual trading approach.

Once you understand the role math plays in trading, you need to determine which formulas are important. With so many terms loosely used in the industry, it is difficult to know which ones matter and which do not. Let’s start with the basics (see “The core variables,” below).

**The full picture**

One of the most important concepts for new traders to understand is that to properly analyze a potential trading methodology, all of the core variables are required. Analyzing a trading methodology based on individual components alone is not enough. Just because a system has a high win rate doesn’t mean it makes money. And a methodology with a high win rate and high win/loss ratio can produce far less in total profits than another if it trades too infrequently. A successful trader must know each of these three mathematical data points to properly analyze a trading approach.

The first variable, win rate, simply identifies your system’s probability of a winning trade. Win rate also is used in two of the most important mathematical terms related to trading: profit factor and expectancy. Both formulas define whether a system is profitable or not (see “Profit factor” and “Expectancy,” below).

So what is the difference between profit factor and expectancy? The answer: nothing. They are two different ways of expressing the same result. It is critical to know either the profit factor or the expectancy of your trading system. If you don’t, then you are destined to contribute your money to another trader’s account.

Win/loss ratio and reward/risk ratio also are two different terms for the same result. One is expressed as a value and another as a ratio. These terms are widely discussed in the industry and everyone seems to have an opinion on what are the optimal values. How often have you heard or read, “Never take a setup that doesn’t have a minimum reward to risk ratio of 2 to 1?” Is that really enough information? Is it even a true statement?

Which of these systems would you rather trade (assuming S&P 500 futures contract, ES = $50 per point):

A)Two-point target ($100) and four-point stop ($200) = (1:2 reward/risk ratio).

B)Four-point target ($200) and two-point stop ($100) = (2:1 reward/risk ratio).

That’s a no brainer, right? Answer “B” clearly meets the guidelines that most of the “experts” discuss. But, what if you had more information? Say:

A)Two-point target ($100), four-point stop ($200) and 80% win rate.

B)Four-point target ($200), two-point stop ($100) and 40% win rate.

Now, the answer is not as clear and it looks like it is time to break out the calculator. Let’s use the expectancy formula to conduct our analysis of both examples:

A)($100 x 0.80) Ð ($200 x 0.20) = $40 expectancy per trade

B)($200 x 0.40) Ð ($100 x 0.60) = $20 expectancy per trade

The picture is now much clearer and the answer for most folks would likely change now that they have adequate information to compare the two setups correctly. But even these data are not enough to determine the superiority of one system over another.