One of the real secrets of trading success is to think in terms of risk-to-reward ratios every time you take a trade.


Ask yourself, before you take a trade, “what’s the risk on this trade, and is the potential reward worth the potential risk?


What can I expect my trading system to do for me in the long term?




What is Expectancy?


A trading system can be characterized as a distribution of the R-multiples it generates. Expectancy is simply the mean, or average, R-multiple generated.


But what does that mean, exactly?


A Brief Overview of Risk and R-Multiples


If you've read any of Dr. Tharp's books, you know by now that it is much more efficient to think of the profits and losses of your trades as a ratio of the initial risk taken (R).


Let’s just go over it again briefly, though:


One of the real secrets of trading success is to think in terms of risk-to-reward ratios every time you take a trade. Ask yourself, before you take a trade, “what’s the risk on this trade? Is the potential reward worth the potential risk?”


So how do you determine the potential risk on a trade? Well, at the time you enter any trade, you should pre-determine some point at which you’ll get out of the trade to preserve your capital. That exit point is the risk you have in the trade, or your expected loss. For example, if you buy a $40 stock and decide to get out if it falls to $30, then your risk is $10.


The risk you have in a trade is called R. That should be easy to remember because R is short for risk. R can represent either your risk per unit, which, in the example, is $10 per share, or it can represent your total risk. If you bought 100 shares of stock with a risk of $10 per share, you would have a total risk of $1,000.


Remember to think in terms of risk-to-reward ratios. If you know that your total initial risk on a position is $1,000, you can express all of your profits and losses as a ratio of your initial risk. For example, if you make a profit of $2,000 (2 x $1000 or $20/share), your profit is 2R. If you make a profit of $10,000 (10 x $1000), your profit is 10R.


The same thing works for losses. If you lose $500, your loss is 0.5R. If you lose $2000, your loss is 2R.


"But wait," you may say. "How could I have a 2R loss if my total risk was $1000?"


Well, perhaps you didn’t keep your word about taking a $1000 loss and failed to exit when you should have. Perhaps the market gapped down against you. Losses bigger than 1R happen all the time. Your goal as a trader (or as an investor) is to keep your losses at 1R or less. Warren Buffet, known to many as the world’s most successful investor, says the number one rule of investing is to not lose money. But that's not particularly helpful advice for those who are trying to create a meaningful risk framework for their trading. After all, even Warren Buffet experiences losses. A much better version of his rule would be, "keep your losses to 1R or less."


When you have a series of profits and losses expressed as risk-reward ratios, what you really have is what Van calls an R-multiple distribution. Consequently, any trading system can be characterized as an R-multiple distribution. In fact, you’ll find that thinking about trading system as R-multiple distributions really helps you understand your system and learn what you can expect from them in the future.


Tying it All Together


So what does all of this have to do with expectancy? Simple: the mean (the average value of a set of numbers) of a system's R-multiple distribution equals the system’s expectancy.


Expectancy gives you the average R-value that you can expect from a system over many trades. Put another way, expectancy tells you how much you can expect to make on the average, per dollar risked, over a number of trades.

"At the heart of all trading is the simplest of all concepts—that the bottom-line results must show a positive mathematical expectation in order for the trading method to be profitable."—Chuck Branscomb

So when you have a distribution of trades to analyze, you can look at the profit or loss generated by each trade in terms of R (how much was profit and loss based on your initial risk) and determine whether the system is a profitable system.


Let’s look at an example:



Entry Price



Actual Exit Price



Trade One





2R gain

Trade Two





3R loss

Trade Three





10R gain

Trade Four





1R loss






        Total R 8R
Expectancy (Mean - 8R / 4)


This “system” has an expectancy of 2R, which means that, over the long term, you can “expect” it to make two times what you risk, based on the available data.


Please note that you can only get a good idea of your system’s expectancy when you have a minimum of thirty trades to analyze. In order to really get a clear picture of the system’s expectancy, you should actually have somewhere between 100 and 200.


So in the real world of investing or trading, expectancy tells you the net profit or loss you can expect over a large number of single-unit trades. If the total amount of money lost is greater than the total amount of money gained, you are a net loser and have a negative expectancy. If the total amount of money gained is greater than the total amount of money lost, you are a net winner and have a positive expectancy.


For example, you could have 99 losing trades, each costing you a dollar, for a total loss of $99. However, if you had one winning trade of $500, you would have a net payoff of $401 ($500 less $99), despite the fact that only one of your trades was a winner and 99% of your trades were losers.


We’ll end our definition of expectancy here because it's a subject that can become much more complex.


Van Tharp has written extensively on this topic; it's one of the core concepts that he teaches. As you become more and more familiar with R-Multiples, position sizing and system development, expectancy will become much easier to understand.


To safely master the art of trading or investing, it's best to learn and understand all of this material. It may seem complex at times, but we encourage you to persevere. When you truly grasp it and work toward mastering it, you will catapult your chances of real success in the markets.

The best place to learn more about this topic:


Introduction to Position Sizing™ E-learning Course


How do you decide how much you should risk on your next trade?


Risk too much and you could blow up your account. Risk too little and a big win won’t even pay for your dinner.

Dr. Tharp’s Introduction to Position Sizing™ Strategies Course includes audio-visual and interactive learning activities that explain this complicated subject in clear, easy-to-understand terms. You will learn the basics of position sizing strategies and the dramatic difference they can make in your results.


Because the course is an introduction to position sizing strategies, it covers basic material and offers a great start to the process of understanding and utilizing the concepts and includes material on understanding expectancy, including examples.


The book The Definite Guide to Positing Sizing covers very extensive material and goes into technical depth in many areas. As its name implies, it is indeed quite definitive. However, some people find position sizing strategies to be a complicated topic and have a hard time grasping and applying the ideas from the book, so we developed this e-course for two primary groups of people: auditory/visual learners who learn more effectively from an instructional format full of interactive features, and those who aren't really interested in the deeper technical aspects of position sizing strategies but realize that an introduction to the topic would still help their trading.


This course is perfect for busy professionals who need a practical way to understand risk and how to keep losses to a minimum.


Learn More.

Buy Now. ($149)

We see a natural course of study starting with the e-course and then moving up to the Definitive Guide.


You will also learn a lot about positing sizing when you play the Positing Sizing Trading Simulation Game. The first three levels are free!

The Rest of The Tharp Think Concepts:


Psychology of Trading

Perfectionism, gambling, unnecessary losses, not being able to pull the trigger….

These are just some of the issues that traders contend with in the markets every day. What causes us to think this way and how can we learn to become better and more profitable traders? ….read more

System Development

Everyone is looking for the Holy Grail in the markets. How do you find the ideal trading system, the stock that is going to take off or that one big winner with your name on it?

There are hundreds, if not thousands, of trading systems that work. But most people, after purchasing such a system, will not follow the system or trade it exactly as it was intended. Why not? …read more

Risk and R-Multiples

Risk to most people seems to be an indefinable fear-based term – it is often equated with the probability of losing, or others might think being involved in futures or options is “risky.” Van’s definition is quite different to what many people think …read more

Position Sizing™

Position sizing is the part of your trading system that tells you “how much.” How many shares or contracts should you take per trade? Poor position sizing is the reason behind almost every instance of account blowouts…read more

System Quality Number® (SQN®)

After a number of years researching position sizing™ strategies, Dr. Van Tharp developed a proprietary measure of the quality of a trading system that he calls the System Quality Number or SQN. ….read more

Planning Business

The market does not owe you or anyone great riches. The market does, however, occasionally tease a large number of people with seemingly easy gains (during bubbles and other manias) only to take them away again. If you are serious about being a good trader, then you need to approach the practice of trading with the same level of rigor with which you would approach any high level endeavor …read more

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