Why Large Winning percentages are a bad measure for trading systems
by: Jeff Malec

[Editors’ note: Our author outlines a very important point for traders to understand when considering various trading systems. Does a large winning percentage actually mean a more profitable system? Take a look at the numbers and see how other variables play into overall profit results. For example, how much the system wins on average versus how much it loses on average is a key component for traders to consider.]

Something deep inside our human nature makes most people love to bet on a winner. We go to the movie with the best reviews, read the books on the bestseller list, frequent the popular restaurants and generally go with a winner. Who wants to sit through a bad movie or read a boring book anyway?

Nowhere is this bit of human nature more evident than with investing. It is nearly second nature to yearn for an investment that has been doing well. “How has it done this month, this quarter...” and so on are frequent questions fielded by investment professionals. These types of questions emerge often around the supposedly safe world of mutual funds, where 75 percent (by my estimation) of investors pick funds through simply sorting funds by five-year performance, then by three-year performance, then by one-year performance and finally pick one of the top three on the list.

Glory Days
This is called momentum investing – and boy, was it great for stock and fund traders in the glory days of 1999 and 2000. The basis behind momentum investing is to “jump on, go with the winner and ride it higher.” It seemed all you had to do was get on the hot stock, fund or IPO, and everything fell into place. As we now know, about the only thing that fell were account values.

Many trading system investors rival these stock and fund investors as momentum players, constantly searching for the next hot system. But too often, investors look to a trading system or strategy’s winning percentage to gauge its worth. A concerned customer called me towards the end of last month asking why her system doesn’t take winning trades a higher percentage of the time. She equated a winning percentage of less than 50 percent as random action and equated random action to unprofitable.

“The system is just guessing which way the market will go,” she surmised. “That’s why its winning percentage is no better than that of a coin flip.”

Are we looking at the same system?” I asked. Past performance is no guarantee of future results – I reminded her – but who cares how often it makes money? The important part is that it makes money.

The customer was not wrong when she said that the system was guessing which way the market would go. That is all it can do. It is an educated guess based on years of data and statistical probabilities, but in the end it is a simple guess of which way prices will go. Anyone can look at a chart of stock or futures prices and point out which way prices did go. But looking at the far right edge of a chart (where prices can either go up or go down) and knowing with absolute certainty which direction they will go next – and, thus, knowing with that same certainty when to buy and when to sell – is impossible. There is always a level of uncertainty, and therefore, there is always the risk of being wrong or losing money. Unfortunately, many investors have a deep-seeded need to be right and are more interested in feeding that desire than actually making money in their investment. These are the people with bumper stickers reading: “Success is in the journey - not the destination.”

It’s the Results That Count
But in investing, the bottom line or destination is more important. Whether you make $100 by being right nine out of ten times or make $100 being wrong nine out of ten times, does it really matter? Both investments made $100. Someone who has to be right a high percentage of the time is someone who needs constant reinforcement that he or she is an intelligent person. Quite frankly, a good investment for this type of person has more to do with psychology than profits.

Option Selling
Perhaps this is why many novice investors are drawn to option selling. They get to be right a high percentage of the time because the majority of options expire worthless. Why do most options expire worthless? Simply, the probability of many of these positions moving in the money is extremely remote. But, as some Florida insurance companies that went bankrupt after three different major hurricanes hit the same areas last year can attest to, the flip side of a remote possibility is near infinite risk. For this reason, the option seller often makes money on nine out of ten trades, and then loses everything he made on the tenth trade. So while the winning percentage for an option seller is very high, the average loser is much larger than the average winner for an option seller, usually resulting in catastrophic losses.

A Look at the Numbers
Many of the more successful trading systems operate on completely different logic and take on more of an option buyer profile. This profile sees higher average winners than average losers, but may only win 40 percent or 50 percent of the time. An option buyer will make relatively small bets, knowing full well that he will lose more often than he will win in exchange for the chance of inordinately large gains on the winners. The day trading systems in the table in this article, including RC Success, Compass, DayBreaker and BWT Zones, all are good examples of how winning percentage isn’t everything. In fact, the first two systems in the table make money less than half of the time! How can something, which loses money more often than it makes money be profitable over the long term? The answer lies in how much the system wins on average versus how much it loses on average.

If you make the same amount of money when you’re right that you lose when you’re wrong, all you need to be profitable at the end of the day is to win more than 50 percent of the time. This is more easily said than done, but the mathematical concept is pretty straightforward. However, few trading systems or strategies lose the exact same amount they expect to win. Most work off the “cut-your-losses-and-let-your-winners-run” philosophy.

Both RC Success and Compass average a good deal more on their winners than losers, as shown in the “difference” column in the above table, and for that reason they can afford to be right less than half of the time. In contrast, BWT Zones actually loses more when it loses than it makes when it wins, so it must have a winning percentage greater than 50 percent to remain profitable overall. BWT Zones does just that, achieving a winning percentage of 56.40 percent by taking quick, smaller profits when available.


click image for larger view

A Pattern Emerges
So we start to see a pattern develop where the lower the difference between a system’s average winning trade and average losing trade, the greater its winning percentage must be to compensate for the bigger losses. This pattern is merely a result of one of trading’s few axioms: you must have a positive expectancy to make money. What is expectancy? In simple terms, it is the average amount of profit or loss you expect on each trade. In more complex terms, it is the product of the average winning trade, the average losing trade, and the winning percentage. If you want to be profitable, you need a positive expectancy.

The billions of dollars in the casino industry are based entirely on expectancy. The casinos have a positive expectancy on every game they offer you. This often is referred to as the “odds in their favor” or the “house edge.” A gambler may win on one roll of the dice, but over the course of a few hours or if the gambler stays at it long enough, the casino will always win because it relies on positive expectancy.

The formula for expectancy is:
Expectancy = (Probability of Win * Average Win) -
(Probability of Loss * Average Loss)

Formula for Profitability
Common sense tells us that a trading system’s average trade needs to be positive in order for an investor using it to make money. All expectancy is telling us is the probable average trade, based on the past winning percentage and average amount of the winning and losing trades. If that number is greater than zero, then you can expect to be profitable.

In the table, see each system’s expectancy in the far right column. Readers can see that a higher winning percentage does not equate to a higher expectancy. There is one missing factor in this table, and that is the number of trades. A sophisticated investor obviously would seek out the system with the highest expectancy – but remember that expectancy is only the value per trade. A truer apples-to-apples comparison would see the single trade expectancy multiplied by the number of trades per year to get an annual expectancy. Consequently, a day trading system like DayBreaker has a much lower expectancy than a trend-following system like Andromeda, but it trades ten to 20 times more often per year.

Long-term trend-following systems such as Aberration, Andromeda and Brix offer another example. Trend followers are designed to “survive” periods when the markets are not trending by stopping out numerous trades for small losses. These not only limit losses, but also ensure that you catch the next trend (by getting you into all of the breakouts – both the real and the fake ones).

It is interesting to note the large difference between Brix’s 36.03-percent winning percentage and BWT Zones’ 56.40-percent winning percentage. This would be disconcerting but for the fact that Brix has a much larger spread between its average winning trade and average losing trade, giving it the long option profile of having few but large winning trades.

The Lottery Gamble
The lottery is a great (although extreme) example of an option buyer’s risk profile. You risk an insignificant amount ($1) on a ticket for the chance at $100 million. Of course, most lottery players know the winning percentage is so far below one percent as the odds of winning are one in a billion or so. Note in the table that the expectancy of the lottery is $1 per “trade.” Those unfortunate souls who play the lottery every day have an annual expectancy of -$365. State governments are not providing lotteries for fun; they have a positive expectancy and make a great deal of money – just like the casinos – selling negative expectancy packaged as a chance for riches.

Consider the lottery in “reverse” as an example of an option seller’s risk profile, where there is a very high wining percentage, like 99.9999999 percent. You would win $1 virtually every time you bought a ticket, but at any time chance losing $100 million. Would you play? The winning percentage sure looks nice, and the expectancy is positive, but the maximum loss sure is scary.

The novice investor has a hard time comprehending that a system that loses on more than half of its trades makes money. Well, take a closer look. How does a system that wins on a large percentage of trades accomplish it? The system does so by risking a great deal more per trade. Just like the lottery in “reverse” outlined above. This keeps the system in more trades, allowing it to profit on more trades.

Imagine looking back over the past three trades on your system, and seeing that a $1,500 loss a week ago would have turned out to be a winner if the stop level had been just a half a point further away. Adjusting the stop price that half point would have resulted in an extra trade in the win column versus in the losing column, in turn causing the win percentage to tick up. The developer may then find another trade where the stop only needed to be moved another half point, then another only a quarter point, and so on, creating a curve-fit nightmare.

The risk-averse system, on the other hand, will look at how much needed to be risked on the handful of runaway trades and go from there. These systems will risk a lot less per trade, getting the system out of more trades while waiting for that one “runaway” trade. It is mathematically difficult to develop a system that can have both a low risk per trade and a high winning percentage – thus the reason you rarely will see a good trading system that has greater than a 60-percent win percentage. It’s simply not worth the additional risk that must be taken on to increase the winning percentage.

Winning Rules
It is quite simple to create a trading system with a high winning percentage. The rules to a system which wins on 100 percent of its trades are:

• Rule 1: Buy right now.
• Rule 2: Sell when profitable.

This system, by definition, will have a 100-percent winning percentage, as it only exits when profitable. This system probably makes a very, very attractive rate of return also. You better bring your checkbook for this one, however, as it has unlimited risk. Imagine taking the signal in March 2000 on Nasdaq futures. You still would be watching your screen for that sell signal, your account would have lost approximately $400,000 (although not closed out the trade yet), and your glorious win percentage would still be intact.

People who have trouble with this concept often are victims of a societal system, which teaches us that success and being right are one in the same thing. One can see from the above example how wrong that can be. The true lesson should be that it’s OK to be wrong; just don’t be wrong for long. In other words, cut those losses short.

In summary, each investor must look at himself in the mirror and ask what is more important – being right or making money? If profit is the ultimate goal and not pumping the ego, then understand that a smaller winning percentage is not only OK, it often is necessary for success.