Positive Expectancy

My sincere advice to people who are contemplating trading, or who are even trading at the moment, and who are not familiar with the concept of positive expectancy, is to make it their priority to fully understand its meaning and importance to successfully trading.

From my experience positive expectancy is an idea that is least understood by the majority of people who are planning to, and who are actually, trading. When I have been invited to present I always ensure that at some point during my presentation that I ask the audience whether they understand the term “positive expectancy”? Rarely would anyone volunteer even a mild grunt of understanding. And yet these audiences are people who have an interest in trading, and yet are not aware of what I believe is trading’s “Holy Grail”. and that is the pursuit of a trading methodology that produces a positive expectancy.

And why do you think this is the case?

I suppose its because they equate success in the market, that is making money, with the accuracy of their trading. They believe if they win more often then they lose then they’ll be ahead. That’s it, “winning” is the secret to making money. Although your accuracy rate is important its only one half of the puzzle as you’ll learn later on, however for the majority of people they don’t proceed further. Their focus on what is necessary to succeed stops at “winning”. I suppose this begs the question, why is it so?

Well in my mind I think it’s because the majority of people bring to “trading” the same attributes that have made them successful in their lives, and that is their competitive “winning” nature.

  • We just love to compete and we love to “win”.
  • We love to “win” at sport.
  • We love to “win” in business.
  • We love to “win” in all aspects of our lives.

Pure and simple.

However to “win”, also means to be “right“.

We have been taught from an early age that a good mark at school is far better than a low mark. We know that a higher exam mark at University is far preferable than a lower exam mark. And the only way we’re able to achieve higher marks is to be “right” more often than not!

So we have been conditioned about the importance of being “right” throughout our lives.

Instinctively we want to;

  • .. know the “right” answer
  • .. buy the “right” car
  • .. purchase the “right” house
  • .. purchase the “right” insurance cover
  • .. select the “right” school for our kids
  • .. pick the “right” share investment
  • .. pick the “right” horse that will win the Melbourne Cup, and
  • .. let’s not forget to mention picking the “right” lotto numbers!

Unfortunately, it’s this one powerful attribute of ours that works against our objective in making money trading.

This is because the consequences of loving to “win” and being “right” propels us instinctively to pursue/develop/find or purchase a high winning, or high accuracy, trading methodology. We would just love to have an 80% to 95% accuracy rate!

Hey, it’s not fun being wrong and losing is it?

Yet for trading, wishing to “win” and being “right” isn’t that important, and if anything, will work against our objective in making money. However, as we begin our trading journey it takes many “blind alleys” and nasty “speed bumps” before we come to realise this. And unfortunately some of these “blind alleys” sometimes feel like they’re “endless highways” while some of the nasty speed bumps could easily be mistaken for “crash barriers”! Well don’t despair as I believe, if you aren’t already aware of positive expectancy, that you are about to discover what is in my mind trading’s “Holy Grail”.

So I can hear you ask ….

“… what’s so important about this positive expectancy? ..”

Well in my mind, I would say positive expectancy is the most important element in trading. And this goes for all traders, regardless of whether they’re discretionary or mechanical. Unless we as traders know that our methodology produces a positive expectancy, then we’re doomed to failure from the very start and we can forget all about money management and psychology.

So what is positive expectancy?

Positive expectancy is defined as how much money, on average, we can expect to make for every dollar we risk .

Positive expectancy requires us to have done enough research and validation to prove to ourselves beyond doubt that our trading methodology (Gann, Elliot Wave, Cycles, Geometry, Murray Maths, Candle Sticks, Mechanical Trading Systems, Astrology etc, etc) will produce profits over the long run. It’s probably all the work involved in validating a methodology’s expectancy that discourages most people from even pursuing it! Now positive expectancy and the likelihood of winning (i.e. a system’s accuracy) are not the same thing. Most people confuse the two and as I’ve mentioned above we instinctively move towards methodologies that have, or promise to have, a high level of accuracy, or “wins”. The problem with our need to find “winning” methodologies is that “winning” systems usually have large losses that leads to marginal or negative expectancies. You’ll win often until you experience a less frequent BUT damaging trade.

So how can we calculate a methodology’s positive expectancy?

Well it’s quite simple. The formula is;

E(R) = (PW x AW) – (PL x AL)


E(R): Expectancy/ or Expected Return
PW: Probability of winning
AW: Average win
PL: Probability of losing
AL: Average loss

Positive Expectancy: is a positive “E(R)”

To help explain this I’ll use a couple of simple examples.

Let’s look at a system that has the following performance profile. After reviewing 30 trades we can determined that the system;

  1. Has an accuracy (or win rate) of 50%.
  2. Has an average losing trade of $10.
  3. Has an average winning trade of $15.

Our expectancy, if we were to trade this system, would be calculated as follows;

E(R) = (50% x $15) – (50% x $10)
E(R) = (0.5 x $15) – (0.5 x $10)
E(R) = $7.50 – $5.00
E(R) = $2.50

So if we have to trade a minimum of $10 (our average losing trade) we can expect on average to earn $2.50 … our “positive” expectancy.

Our $2.50 expectancy per trade, assuming an average trade of $10, can also be represented as a percentage. That is;

E(R) = $2.50/$10.00
E(R) = 0.25
E(R) = 25%

So in other words, we can expect to win 25 cents for every $1 we risk!

So this system has a “positive” expectancy.

Now lets have a look at a poor system, one that we would usually lose on. Lets look at the “roulette” system where we trade/bet just $1.

We know the “roulette” system has the following performance profile. It;

  1. Has an accuracy (or win rate) of 2.6% (or 1 in 38 chances).
  2. Has a percentage losing rate of 97.4% (or 37 in 38 chances).
  3. Has an average losing trade of $1.
  4. Has an average winning trade of $35.

Our expectancy if we were to trade this “roulette” system would be calculated as follows;

E(R) = (2.6% x $35) – (97.4% x $1)
E(R) = (0.026 x $35) – (0.974 x $1)
E(R) = $0.92 – $0.974
E(R) = -$0.054

So if we have to trade a minimum of a $1(our average losing trade/bet) we can expect on average to lose -$0.054.. our “negative” expectancy!

Our -$0.054 expectancy per trade, assuming an average trade/bet size of $1, can also be represented as a percentage. That is;

E(R) = -$0.054/$1
E(R) = -0.054
E(R) = -5.4%

So in other words, we can expect to lose -5.4 cents for every $1 we risk!

As you can see this system has a “negative” expectancy.

So we as traders need to determine, from a representative sample size of trades, a system’s percentage accuracy, average win and average loss. If the system doesn’t produce a positive expectancy then it should be left alone. To trade it would only lead to ruin!


Reprinted with permission by Brent Penfold at