I want to begin a series of blog posts on the mathematics of evaluating your trading results. Rather than trying to write one or two mega-posts, I’m going to split it into smaller pieces.

Imagine trader A and B, both trading the same stock (for the sake of argument, let’s assume it is LVS). Trader A really wants to “limit her risk”, so she takes a lot of trades against support and resistance levels, and usually uses stops in the .05 range. Trader B trades patterns that he thinks need bigger stops—his stops are usually .20, and sometimes even bigger. The question is, all other things being equal (and they never are), which trader is trading with lower risk?

Consider the question from Trader A’s perspective. She realizes that she can literally take four losses on her average .05 stop before she loses as much money as Trader B does on a single one of his trades. Of course, she’s trading with less risk, right? Maybe not.

Here is an important piece of math. We do not care about the outcome of any one event (or any one trade), but the question we need to ask is “what happens, on average, if I do the same trade over and over.” Be aware that this is not a natural way for most people to think, and, for instance, classic logic does not even have the tools for dealing with randomness and probability. If you aren’t used to this kind of thinking, it will take some time before it becomes a natural part of your thought process, but it is time well spent.

The expected value or expectancy of an event can best be thought of as what the average result would be over a large number of trials. Mathematically:

 Expected value = payoff if the event happens * probability of the event happening

Most of us intuitively use this concept for day to day risk management. For instance, the payoff from getting hit by an asteroid is very bad (certain annihilation), but the probability of that event happening is vanishingly small, so most of us don’t spend a lot of time thinking about this scenario. What about not picking up the bread your spouse asked you to get on your way home? Very high probability of a bad outcome, but that outcome probably does not carry dire consequences, so in many cases the overall “expected value” of that scenario isn’t that bad. Or, imagine a raffle where 1,000 tickets are sold for a $10,000 pot. What would you pay for a ticket? Your chances of winning are 1/1000 times the $10,000 payout, meaning that each ticket has a fair value of $10.  If you are able to buy a ticket for less than that, you are playing a positive expectancy game.

Consider the question with the two traders’ stops again. You now know that the “real risk” (expected value) of their stops is determined by this formula:  real risk = loss if stop is hit * probability of stop being hit. Could Trader A be using a tight stop that is hit so often that the actual risk in her small stop is much larger than Trader B’s bigger stop? Can a small stop actually carry more risk than a large stop? Yes to both questions.

For some of you, you have seen this kind of math before, but take a moment to consider its significance anew. For others of you, this will be new, so commit it to memory. If you are going to trade well, you need to internalize this kind of thinking. Good gamblers do it. Good traders do it, and you must too if you’re going to make it in this business.

I’ll dig a little deeper into this concept in a future blog post.

(Follow me on Twitter AdamG_SMB)