Positive Expectancy Model: It Will Make You Or Break You As A Trader

Source Article: Expectancy

Positive Expectancy: A system (or game) that will make money over the long term if played at a risk level that is sufficiently low. It also means that the mean R-value of a distribution of R multiples is a positive number.

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




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.