Expectancy & Win Rate Are NOT the Same Thing:
Trading expectancy is an equation that tells us how much, on average, we can expect to profit on each trade that we make. In order to make money, we want to find systems that have positive expectancy and avoid systems that have negative expectancy. Along with cultivating the proper mindset, finding a system with a positive expectancy should be one of the first steps in every new trader’s journey. Unfortunately, this is a concept that’s not fully understood by aspiring or even actively operating traders.
Expectancy or Expected Return = (Probability of Winning x Average Win) – (Probability of Losing x Average Loss)
Too many people equate trading success with simply “winning”, or having a high “win rate”, but that alone doesn’t guarantee overall profitability. In fact, win rate/probability of winning is only one part of the expectancy equation. Basically for our entire lives, we’ve been conditioned by our parents, teachers and other authority figures about the importance of being “right” & “winning”, and as a result, we tend to carry those attitudes too heavily into the markets. This mindset, however, clouds our view of what’s really important in trading, and that’s our system’s overall expectancy.
Make Sure You Have a Quantified System With an Edge:
The pursuit of a trading system that produces a positive expectancy is critical to trading success. It’s even considered by some to be trading’s “holy grail”. It’s important to remember that the expectancy equation is only accurate over a large number of trades, which can be time-consuming to validate. It’s possible to see great results on your first handful of trades and be fooled into thinking your system has a positive expectancy when that’s not necessarily the case. Unfortunately, the time and work involved in validating a system’s expectancy discourages most people from even trying. But those who put in the effort to find positive expectancy systems are well on their way to trading success.
Example of How a High Win Rate Doesn’t Necessarily Equate to a Positive Expectancy:
To give an example of why win rate is not nearly as important as expectancy, just imagine a system with a 90% win rate. Sounds great, right? The typical novice trader will get completely consumed by a system with such a high probability of winning, thinking there could be no possible way of losing money. But if the average win is $100 and the average loss is $1,000 then that trader will actually lose money in the long run by following that 90% win rate system. Big losses are usually the primary component of a negative expectancy system. There’s no doubt that being right more often than wrong can be psychologically satisfying, but don’t let high win rates trick you into thinking that you automatically have a positive expectancy system.
Expectancy or Expected Return = (Probability of Winning x Average Win) – (Probability of Losing x Average Loss)
E = (90% x $100) – (10% x $1,000) = ($90) – ($100) = -$10
This number means that for every $100 that is risked with this system you can expect to lose $10, or for every $1,000 risked you can expect to lose $100. So over the course of ten trades with a position size of $1,000 each, 9 out of 10 of those trades can be expected to be winners of $100 for a total of $900, and 1 out of 10 of those trades can be expected to be a loser for the entire $1,000. The end result after 10 trades is a loss of $100 (or a $10 loss for every $100 risked). So even though this system has a 90% win rate, it has a negative expectancy and should be avoided. It’s easy to see that the large average losses are sabotaging the effectiveness of the system.
Bottom Line – Don’t Choose High Win Rates or Being Right Over Making Money:
Bad traders tend to choose high accuracy over making money. They become obsessed with predictions, opinions, newsletters, and most of all, trying to be “right”. The idea of taking a trade with a higher probability of it being a loss than a win seems absolutely crazy to them, but it’s certainly possible to have a positive expectancy system with a win rate below 50%. Most beginners, as the saying goes, “can’t see the forest through the trees”. Regrettably, they’re excessively focused on win rate and the desire to feel “right” when they should simply be focused on having a consistent and repeatable edge in the market.
Overall, we need to make sure we do our homework so that we know with a high degree of certainty that our trading system will create profits over a large series of trades. There will be both wins and losses along the way because there’s no way to avoid losses, but we’re on the right track as long as our trades average out profitable over time. Don’t fall into the trap of giving into short-term emotional satisfaction at the expense of your long-term profits. By understanding this equation and the size of your edge, you can face the market with higher confidence, patience and discipline, knowing exactly what to expect from your system as long as you stay the course.
Is your current trading system one with a positive expectancy? If not, it’s time to do your homework on finding a statistical edge.
While I’m more of a buy-and-hold investor, I found this article very interesting. I have never really considered the importance of mindset in trading. Your description of expectancy vs. win-rate was very good, and I feel like I have a much better idea of these concepts now. I feel that there are lessons that could be carried into other areas. If we don’t focus so much on being right or perfect all of the time then we can accomplish more and make more of a positive impact in the world.
Hi Mike – thanks for your comments. Most traders get so caught up in being “right” in order to support their own ego that it actually has the opposite effect – it makes them wrong even more. By focusing on not being wrong, they avoid taking controlled losses. They’ll remove stop losses and double/triple/quadruple-down on losing positions just to avoid being wrong. They’ll hold out hope for long periods of time hoping for their losing trades to turn around. But this usually ends up in gigantic, painful losses instead of a small, controlled ones. This is just one of many psychological blocks that impact traders.
Overall, it’s not about trading impulsively and “becoming rich” off 1 big trade. Too many traders use the market as a platform for gambling/lottery/entertainment at the expense of legitimate profitability. In order to be consistently successful, however, it’s about developing/following a system with a positive expectancy that you know will produce profits over time as long as that system is executed with discipline. Most traders focus so much on the potential results that it blinds them from the process of actually achieving those results.
Thank you for clarifying the differences between expectancy and winning rate. I have always thought that they are the same, and thanks for the formula. This takes me back to Finance class back in college. Thanks for this lesson. I will keep in mind that the high win doesn’t necessarily mean that I will make money in the long run, it is all about probabilities and expectancy.