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# Win Rate: The Most Important Performance Measure

– Michael Harris, Price Action Lab Blog

Shortly after my post on Kelly maximization I received a number of emails from traders who are developing systems but are, understandably so in my opinion, a bit confused about which performance criterion or criteria to use when evaluating them. I understand why those traders are confused, or to be more exact, what or who has confused them and why.

The most important criterion to use when measuring the performance of a trading strategy is its success rate, a.k.a. win rate. A year ago, in the post “What Every Trader Should Know About the Win Rate, Profit Factor and Payoff Ratio“, I mentioned a formula I derived 20 years ago that first appeared in a book of mine published in 2000 and in a few papers in popular magazines. The formula describes the relationship between the win rate, payoff ratio and profit factor:

w = pf/(pf+r)   (1)

where w is the win ratio, expressed as the ratio of the number of winning trades to the total number of trades, pf is the profit factor calculated as the sum of winning trades divided by the sum of losing trades and r is the ratio of average winning trade to average losing trade, also known as the payoff ratio.

Now, a frequent argument is that the win rate can be low, such as, for example, 30%, but the ratio r can be high enough so that the resulting profit factor is greater than 1, i.e., a profitable strategy. The formula for the profit factor can be derived from equation (1):

pf = w x r /(1-w)   (2)

We can see from equation (2) that if w =0.4 and r = 1.5, then pf = 1.0. Thus, if r is kept above 1.5, then the strategy will be profitable. Then the argument is that r is maybe more important than w, and strategies should be developed for maximum r. For example, trend-following strategies have usually low w but high r.

I will try to shed some light on these issues; Trend-following strategies need to have high r but there is no guarantee for it. It is not up to strategy to decide what value of r it will have as that depends on market conditions. If the market moves sideways, then trend-following generates a profit factor less than 1. This was the case during 2011 with most trend-following funds. The ratio r is not something that can be controlled by the trader. If you rely on hopes then you can measure performance based on the ratio r. But if you rely on skill, then you measure performance based on win rate and for maximum achievable ratio r.

### The Source(s) of the Confusion

Why do most traders and system developers prefer to use metrics such as net profit, Sharpe ratio, payoff ratio, profit factor, max drawdown, etc., when developing systems instead of the straightforward win rate?

The answer in my opinion is that finding strategies with high win rate for maximum achievable payoff ratio r is extremely difficult where use of the other ratios often facilitates curve-fitting but the strategies usually have low win rate, in the range of 40% to 60%, but high payoff ratio r, as a result of the optimization. As a matter of fact, this is what most strategy development tools based on neural networks, genetic optimization and programming usually accomplish because of their nature. These algorithmic approaches have been successfully applied to many fields but are misapplied in the case of trading system development. One reason is that they generate TYPE-I optimized systems and the data-mining bias is too high.

Even more important is the fact that the risk of ruin of a trading strategy depends primarily on its win rate. The lower the win rate, the highest the risk of ruin. In the special case of ruin due to consecutive losers, this can be seen from this simple equation:

RoR = (1-w)^R

where ROR is the risk of ruin, w is the win rate and R is the inverse of risk percent. It may be seen that for fixed risk percent, for example 2% of capital, the risk of ruin decreases as w increases. However, consecutive losers are a special case of ruin and in general the probability is higher. This special case was used to show the importance of win rate.

### Summary

If you cannot develop a strategy with a sufficiently high win rate, higher than 70% in my opinion, regardless of the value of a sufficiently high payoff ratio, the risk of ruin is high. Strategies with low win rate that appear good during backtesting or even perform well during the first couple of years of actual trading may rely on luck and specifically on the payoff ratio remaining high. Software vendors who implement various types of metrics to assist traders in developing trading systems often do so because that offers many more choices of curve-fitting strategies that appear to have a high profit factor and payoff ratio at the expense of win rate. Such strategies carry high risk of ruin because they make unrealistic assumptions about the future behavior of the markets, such as, for example, that the market will keep on rewarding a trader with a low win rate for an extended period of time.

– Michael Harris, Price Action Lab Blog

Update:  Jeff here…I’ve coded the Win Rate into a function which you can use in your own strategies. Download it here.

### About the Author Michael Harris

Michael Harris is a trading expert and a developer of advanced pattern recognition software for the benefit of position and swing traders. Michael developed APS Automatic Pattern Search software which has received great acclaim and recently Price Action Lab, a program that includes an advanced technical analysis indicator based on price patterns, called the p-Indicator. He also provides consulting services about trading system development and market analysis to institutional investors and hedge funds.

In years past, Michael has also done work for a number of different financial firms, where he developed a bond portfolio optimization program and trading systems for commodities and stocks. Since 1989, he has been as an active trader.

Michael is also a best selling author. His first book “Short-Term Trading with Price Patterns” was published in 1999. His other two books “Stock Trading Techniques with Price Patterns” and “Profitability and Systematic Trading” were published in 2000 and 2008, respectively.

• WQ says:

Hi Michael,

Thanks for the post and it made me know about win rate. What metrics do you recommend to be used in optimizing to choose the best result?
I don’t think win rate is the proper one because I believe max draw down should be considered while win rate not.

• Hello WQ,

I only optimize exits because optimizing entries increases data-mining bias considerably. See a previous article Jeff has posted “Optimization and Curve-Fitting…”

Having said that I understand your question. It is a good one. But consider that fact that in the case that win rate is 100% the closed trade drawdown is exactly 0. By that I do not imply that one should try to find the Holy Grail but this means that increasing the win rate naturally decreases the drawdown and especially the risk of ruin. However, I understand that a high win rate is not always possible as you probably imply. In that case you could consider maximizing a linear function of the form:

F = aW-bD+cX…

where a,b,c are weights, w is the win rate, D is the drawdown and X is some other parameter, such as for example, the profit factor or net profit, etc.

However, that still does not take away from the fact that the win rate is the most important performance measure. In addition, optimization always increases data-mining bias and you risk of generating a trade sample that is not representative of the population. Well, I never said trading system development is easy..

All the best.

• Rick says:

I have to disagree that win rate is the most important performance measure. And, in fact, a very high win rate can be misleading.

For example, let’s take 2 systems. They each have made 5 trades. The first system had 4 losses of \$100 and 1 win of \$500 giving a win rate of 20%. The second system had 1 loss of \$500 and 4 wins of \$100 giving a win rate of 80%. Looking at win rate, the second system is superior, even though it lost money. I would prefer the first system.

A system could have a 100% win rate and still be inferior if the total of its wins is less than a system having a a lesser win rate but a higher profit.

Because we are all in this to make money, I think that we should be measuring the quality of the system (ie profits vs losses) as opposed to the fact that the system has more winning trades vs losing trades even tough the size of the losing trades is larger than the sizeof the winning ones.

In my opinion, expectancy, MAR, or the Sortino ratio would be far better measures.

Rick

• “The first system had 4 losses of \$100 and 1 win of \$500 giving a win rate of 20%. The second system had 1 loss of \$500 and 4 wins of \$100 giving a win rate of 80%. ”

You compare a winner to a loser. The point is given two equivalent winning systems in terms of profit, do you prefer low or high win rate?

” The first system had 4 losses of \$100 and 1 win of \$500 giving a win rate of 20%.”

Do you expect to get uniformly 4 losses and 1 win for every 5 trades? You can get 8 losers in a row and then 2 winners and still your win rate will be 20%. In the meantime the system will be broken. This is the point and this is the reason risk of ruin calculationa demand that win rate > 50%, otherwise it does not even make sense to speak of reaching a certain equity level before getting ruined. Many trend-following funds were ruined in 2011 – 2012 because they were based exactly on the idea you described, i.e., a low win rate and a high payoff ratio. During the whipsaw they generated enough losses to cause substantial drawdown. You want to avoid that. One way to do it math says is by increasing win rate. This is why it is the most important performance measure. I never said it is the only important measure. Obviously, Sharpe ratio or Sorting ratio are also important. High Sharpe ratio contributes towards significance of the results, for example, because the t-statistic is a liner function of it (t-statistics = Sharpe ratio times square root of number of years)

High expectancy is good but this metric is a linear function of win rate. The highest expectancy (expectation divided by average loss)for given payoff R is obtained for win rate of 100% Just look at the formula:

Expectancy = w(R + 1) – 1 where R = payoff ratio

Thus, if w = 0.5 and R = 2, you expect to win \$0.5 for every \$1 risked. This is still not good. For w=0.5 and R = 3, you win \$1 for every \$1 risked, i.e., marginal. You must increase win rate because it is difficult to get R > 3.

This function is maximum when w is maximum or R is maximum. You can choose between the two but for reasons previously mentioned I prefer maximum possible w and R > 1.

All the best.

• Mark Brockway says:

If win rate was the most important parameter then Victor Niederhoffer and Long Term Capital Management would still be relevant today. Rather, risk control and MAR is most important as evidenced by the myriad of successful trend based systems. Black Swans can wipe out a high win rate system quite easily if risk control is poor. Take an option selling strategy for example. Very high win rates, but all it takes is one disaster to cause a catastrophe. I wouldn’t have wanted to be short CHF call options 2 weeks ago when the Swiss Government removed the peg to the Euro!

• “If win rate was the most important parameter then Victor Niederhoffer and Long Term Capital Management would still be relevant today. ”

Niederhoffer was a naked options seller. No relation to a system trader the way it is discussed here. Long Term Capital Management was an over-leveraged fund and also not related to our discussion.

“Rather, risk control and MAR is most important as evidenced by the myriad of successful trend based systems”

I don’t know about “myriads”. Risk control and MAR are important in all cases. MAR is CAR/DD and a high MAR does not preclude a high drawdown if CAR is high. A system with 20% CAR and 20% drawdown has the same MAR as a system with 60% CAR and 60% drawdown. Which one do you prefer based on MAR alone?

“Black Swans can wipe out a high win rate system quite easily if risk control is poor.”

Black swans will wipe out all systems if risk control is poor.This has little to do with win rate. A drawdown from black swan does not care what your win rate was before it occurred.

• Ryan says:

I will go against the crowd and agree with your assessment on WR%. A high WR% also allows for the use of various statistical tools to assess system break down and can be psychologically easier to trade as you’re winning more than losing.
I have found that short term mean reverting strategies can be a great place to start developing a system if a high WR% is what you’re after.

-thanks,
Ryan

• Jim says:

I agree with the author and Ryan. I can’t think of any sound reason why anyone would prefer winning less often than losing. Mean reverting and also swing trading are good places for high win rate trading. Trend followers are forced to go longer time frames and the low win rate is outcome of their systems failing when there is no trend. No trend follower wants to lose money even when there is no trend. The truth is that trend following systems are not robust in design. Very good article and the author offered some useful formulas above.

• James says:

The evidence is all around:
Mean-reversion (MR) systems work – High WR% is optimised for. They generally need more parameters and optimization to be profitable over the long-term;
Trend-following (TF) systems work – High R is optimised for. They generally need fewer parameters and optimisation to be profitable over the long term.

The WR% is irrelevant to Risk of Ruin if you can’t quantify the risk in the first place. It’s been highlighted on this blog before, stops hurt MR systems and the best performance comes from having no stop at all. Clearly a compromise away from infinite risk has to be made by giving a very loose stop so that only a small fraction of trades exit on a stop loss – so they’re always running with high open-risk. TF systems on the other hand generally always exit on stops. I would contend that tail-risk (risk of ruin) is more quantifiable in a TF system and therefore safer than a MR system. The greater parameter count and optimisation necessary in a MR system just makes the problem worse unless you’re very careful to avoid curve-fitting.

Nevertheless, MR systems are much easier to trade and more profitable in the short term despite being riskier. Even if a TF system works just as well, who wants to sit through a multi-year drawdown? The author clearly prefers this. Nothing wrong with that.
Either you’re a mean-reversion trader or a trend-following trader. The debate will never end!

• I agree with some of the points you made but I disagree with the following statement:

“The WR% is irrelevant to Risk of Ruin if you can’t quantify the risk in the first place. ”

Inability to quantify the risk due to the fact that it is a path dependent function does not imply that WR% is irrelevant. It only implies that the risk is not known but what is known is that it depends on win rate.

“Even if a TF system works just as well, who wants to sit through a multi-year drawdown? The author clearly prefers this.”

Could you point where in my article I said that I prefer to sit through a multi-year drawdown? I am curious how you concluded that. I believe that a trader should use both TF and MR systems because they are complimentary. My point was that in both cases WR% must be high and it is a misconception that TF systems can have low win rate, much below 50%, and still be profitable in the longer-term. As you correctly pointed out, that depends on optimizing R.

Trend-following systems rarely generate representative samples during backtesting and even when tested on multiple markets and it is rather impossible to assess their significance. Most trendfollowers rely on luck and the reason that most funds use TF systems is because they cannot move size with MR systems. There are examples of funds that tried MR and they went bust. In my opinion, TF with low win rate is an excuse to say “I have a system” when in fact there is no system but a random process. MR is a different story. Samples can be representative but as you correctly pointed out, stops hurt. However, I am convinced that TF systems with low win rate can never be robust. Thanks.

• James says:

“Even if a TF system works just as well, who wants to sit through a multi-year drawdown? The author clearly prefers this.”
Thanks for picking me up on this – poor writing on my part, I was trying to say that you appear to prefer MR rather than TF.

It’s not clear to me how you arrive at the logic in your assumptions about trendfollowing being “lucky” and “can never be robust” – I find the exact opposite! Trends have existed in markets for centuries, and it would be safe to assume that trends will exist in the future as long as herding behavior and psychology play a part in free markets. That’s robust.
Despite the counter-intuitive nature of low WR% trendfollowing strategies there’s an ever-growing body of academic literature showing that it really does work. And there’s a lot of representative samples of backtesting going back decades to support it.

If a trader has a system that trades long and short in enough non-correlated markets, limits losses in noisy trendless periods and gets on a trend that last for months or years, that system can be consistently profitable despite the low WR%.

A polarizing topic! Thanks for raising some valuable points.

• Bo says:

As Ed Seykota says, “All system trades are ultimately discretionary.”. It’s better the evalute the system qualitatively. If you remove some rules from the system, will it perform much poorly? Can you plug the system in to trade new markets without changing the parameters? The ratios are important but the system has to make sense to you and fit your style.

• Hi BO,

” If you remove some rules from the system, will it perform much poorly?”

This is an important test.

“Can you plug the system in to trade new markets without changing the parameters?”

Extremely important test.

“the system has to make sense to you and fit your style.”

That is important too.

All good points. Thanks.

• Mark Brockway says:

Ed Seykota is a source of inspiration. Does anyone know what his win/loss percentage was on his systems? I have a feeling his win percentage was under 50% and yet he was tremendously successful over a long period of time.

• In 1988 when I started developing trading system with System Writer Plus (an ancestor of Tradestation)I used a triple ma crossover for TF and my partner and I made 120K in a few months trading currency futures. The system worked fine for one more year. Then it stopped working suddenly in 1991 and we lost some of the profits before we abandoned it. It has never worked since. I say this because what worked in the past rarely worked nowadays. Possibly his win rate that time was about 30%. Nowadays, my point is, a low win rate can lead to ruin.

• Ola says:

Hi Mike,

Interesting discussion indeed! This may be off on a slight tangent from the original topic but I thought I’d put my 2c worth in anyway and the following might offer a compromise of the views expressed.

Different strategies like MR and TF would complement each other in that they are likely to perform well under different market conditions and my view is that a set of complimentary strategies are easier to trade than each one in isolation. You can justify different win rates due to the nature of each strategy. A way to ‘ease the pain’ of trading may be to adjust your position size depending on how well each system is performing.

Dr Howard Bandy suggests using his Safe-f position sizing for this purpose and also describes how you would go about measuring a system’s performance while it is being traded.

• Hi Ola,

“Different strategies like MR and TF would complement each other in that they are likely to perform well under different market conditions ”

Actually they do complement each other. I think I mentioned that in one of my replies. Good point.

Michael, thanks for the very interesting article and for all your responses to commenters.

I appreciate you mentioning the risk of over-optimization and selection bias. I’m sorry, I’m not understanding though: is it not possible to over-optimize just as easily via win rate?

The sample size can still drop below statistical significance. And/or the optimization process may generate a random winning parameter combination, as you described. In either of these cases, one could conceivably be misled by a very high nominal win rate, no?

I’m presuming that you must be advocating win rate in a context of high statistical significance and proven out-of-sample replication. In addition, as you point out, there has to be a minimum net “effect size” hurdle that any system must clear in order to be worth trading.

“is it not possible to over-optimize just as easily via win rate?”

Absolutely. It’s done all the time. All performance metrics can be optimized and even liner or non-linear functions of them (see earlier comment).

“I’m presuming that you must be advocating win rate in a context of high statistical significance and proven out-of-sample replication”

Exactly, this is the point. I’m not against the other performance metrics. I only say that win rate in the most important even in the case of trend-following. Of course, I do not imply that the payoff ratio can be anything and not to pay attention to it. It boils down to this: If there is a sufficient representative sample, then the win rate is approximately equal to the probability of success of the next trade. I want this to be high. If it is low, then a streak of losers can ruin my system before the next trend arrives. It’s that simple of an argument but it is also justified mathematically. Thus, I argue that trend-followers with low win rate are knowingly gambling and they just hope that a trend will arrive before a streak of losers or a streak of losers followed by a mediocre trend that will not suffice to cover part of losses. Thanks.

• “Michael, thanks for the very interesting article and for all your responses to commenters.”

Thanks, let us also thank our host Jeff, who is doing an excellent job here.

• Tom says:

Great article. While win rate is very important I use other methods for judging system performance. Nothing by itself is representative in my opinion, it has to be used alongside other metrics to arrive at a conclusion.

I was going over your Price Action Lab product and found that your approach is very similar to mine. A lot of what I do is automatic system generation as I feel thats the most hassle-free way of playing the markets. Like you, I didn’t go the GA/GP/NN search approach as it introduced so much randomness that seemingly welcomes curve fit.

As with any automatic search, the results must be verified. In your blog you give a lot of information about this which is awesome. One approach that I am hypothesizing doing is instead of separating in-sample verses out of sample, I will take the entire dataset and mine for trading systems. Each individual system performance from this search is used as an benchmark. I then do the search N times again; each time I will randomly select an interval of data to search. Each of these N search will come up with models that may or may not be in the initial full sample search. Tally up the instances whereby the interval search came up with the same trading system (or similar). The more times a system is repeatedly discovered again, the more robust the system is. A step further would be to do a out of sample test. Since you randomly selected an interval, there is the other half of the data. Test the models against that other half and compare performance to the full sample search…idea is the closer the performance the better.

Love your thoughts on this thanks.

• Hello Tom,

I agree that one must use other metrics in addition to win rate. One that I use is the profit factor. I will not consider any system with PF 1 is preferable but given that DD is small, usually < 15%.

The data-mining procedure you described is interesting provided that the sampling is done with no replacement. If replacement occurs, then data-mining bias increases due to data reuse. Eventually, after about N = 7 data-mining bias is already too large. If in addition the out-of-sample for some N = k becomes in-sample for some N = M, there is data snooping involved and the significance of the results is about 0. This is of course if I understood correctly what you are doing.

A method I prefer involves cross-validating first the data-mining method using random data. If the method is sound, then just ignore out-of-sample testing and use the benchmark models. Perform portfolio backtests to increase samples. Here is an example: http://www.priceactionlab.com/Blog/2013/05/fooled-by-out-of-sample-testing/

Thanks. Interesting comment.

• Tom says:

The method I proposed is essentially a way to judge the consistency of the trading system. If every trade made throughout the entire testing period had the same performance, then it should end up being discovered every time if searched for it in smaller intervals.

Astute observation on sampling without replacement. The maximum N should equate to the size of the interval and the size of the OOS.

One question I had is given your metric based system search, wouldn’t you always have to use all the searched systems to minimize selection bias? Are there any procedures you take to filter out some potential candidates? For example, I understand that you suggested portfolio backtesting. Let say you discovered 500 models. All match your desired performance. You then do a portfolio backtest. Half of that sample become inferior when you test it on a correlated instrument. What then? I feel there is subjectivity involved passed this point.

Can you further elaborate on your method of cross validating on random data? I am not following.

Thanks,

• Hello Tom,

“Let say you discovered 500 models. All match your desired performance. You then do a portfolio backtest. Half of that sample become inferior when you test it on a correlated instrument. What then? I feel there is subjectivity involved passed this point.”

You are correct and this is the reason. The final system includes all 500 systems and no selection is made based on any test. The portfolio backtest is applied to a a system that consists of all 500 systems and if it fails then all 500 systems are rejected.

In reality, the number of systems is much less than 500.

“Can you further elaborate on your method of cross validating on random data? I am not following.”

This is an involved process and maybe the subject of another article. If you apply a data-mining algo to random series and you get many systems that satisfy the metrics, then this could mean that the algo is curve-fitting to noise. The number of systems should be less than 10% of what you get when using the actual data. In my experience NN/GP/GA all fail this test as they fit to noise.

• Emanuel says:

Great article. What do you think about trailing stops and chandelier exit stop trading systems? Do you think that exits are more important than entries? Someone I know is managing a fund out of Cyprus and he uses your Price Action Lab software. I noticed that trailing stops are not one of the exit choices. He told me that he has been successful with it and I am thinking of buying it. I have not had any success with NNs in the past and I have also used genetic programming but results suffer from curve-fitting. Also, what do you think about maximizing the Sharpe ratio. Thank you in advance.

• Hello Emanuel,

Trailing stops may allow “letting profits run and cutting losses short” and are especially useful to trend followers but during backtesting can lead to curve-fitted results. See this article for more details: http://www.priceactionlab.com/Blog/2012/06/trailing-stops-and-curve-fitting-in-trading-system-development/

I also believe that entries and exits are equally important and my experience says that systems with random entries are artifacts of curve-fitting. However, opinions may vary on this issue.

The Sharpe ratio is an important parameter because it is directly related to the statistical significance of the results (see formula in earlier comment) but focusing on it may cause you to reject some good ideas that you could latter improve. In my opinion this parameter should not be optimized but only be used to evaluate the results. Otherwise optimization may be to circularity, i.e., the results are good because they were forced to be good. Thank you.

• If win rate were the most important factor to maximize, then all of the billion dollar CTA’s wouldn’t exist. Successful trend-following strategies often have 30%-40% win rates (not 70% or higher). How are they profitable? Because the average win is twice as much as the average loss.

Profit expectancy is the most important factor to maximize, which takes into account probabilities of win and loss, AND the accompanying profits per trade.

The goal of trading is not to be right (win-rate) it’s about being profitable.

• Thank you for your comment.

Profit expectation (long-term) = w x avgwin +(1-w)x avgloss

Since this is a linear function in win rate w, it is maximum when w is maximum.

The fact that CTAs have low win rates does not imply that win rate is not the most important parameter. It implies that there are limitation in the way they trade. Ask any CTA and he will tell you that he would love to have a higher win rate.

(1) Trend following is only one specific trading style. Other popular styles requite high win rates because the payoff ratio is low.

(2) Survivorship bias: when considering only the successful CTAs, this ignores many unsuccessful ones that went bust.

“The goal of trading is not to be right (win-rate) it’s about being profitable.”

As you can see from the equation I wrote, the goal of trading is indeed to be right as often as you can because that increases profitability. If you would like to be just profitable, you could manage that with lower win rates. But a higher win rate will increase profitability and this was the main point here. The fact that some people cannot do it it does not mean that others should not try. Theoretically one can be profitable with a 10% win rate but a long whipsaw period will take its toll on equity.

• Jim says:

The point that almost everyone here (including the author) is missing is that win rate and payoff ratio are inherently linked. Raising the win rate lowers the payoff… raising the payoff lowers the win rate. This is a mathematical fact. Being able to raise one without lowering the other is the “holy grail” of trading and is not, and never will be, attainable. If the author would like to show his math to prove me wrong then go ahead and try… you can’t do it, it’s IMPOSSIBLE.

You can skirt the issue by comparing apples to oranges all you like (as done in the comments above), but unless you can “unlink” win rate from payoff ratio then win rate is no more important a factor than anything else when it comes to risk of ruin (or risk of drawdown).

Unless the author can do this then I think the next comment should be a post by him saying “I’m sorry, I’m wrong. Win rate is no more important than win SIZE when it comes to risk of ruin.”

And by the way, saying that Victor Neiderhoffer was a naked option seller doesn’t dispute the point of one of the previous commenters… it PROVES IT. Naked option sellers are the ultimate example of why a “high win rate” doesn’t necessarily work over the long run. Their win rate is 100% with a very small payoff ratio on each transaction until that big market move comes along… then suddenly that win rate doesn’t mean a darn thing anymore.

Jim

Those leaving comments who refer to expectancy as the most important attribute to system design are correct. There is no arguing this fact… and if you continue to do so you show your absolute ignorance of one of the basic precepts of actually understanding trading.

• Jim, I think you should read the article carefully before commenting. You wrote:

“This is a mathematical fact.”

Which the author has detailed in his books and papers 15 years ago, as stated in the article:

The article states:

“If you rely on hopes then you can measure performance based on the ratio r. But if you rely on skill, then you measure performance based on win rate and for maximum achievable ratio r.”

This means that you try to achieve maximum win rate for maximum achievable or desirable payoff ration.

and Jim writes:

“and if you continue to do so you show your absolute ignorance of one of the basic precepts of actually understanding trading.”

On the contrary, most of those that talk about expectancy are probability fools. Expectancy is nothing more than the average trade. It is not expected value. Only for sufficient samples it become expected value. That means many many trades.

http://www.priceactionlab.com/Literature/secret/secret.html

BTW, expectancy is a linear function of win rate. The higher the win rate, the higher the expectancy for given payoff ratio.

Look at the equation:

E = avgwin x w – avgloss x (1-w)
= (avgwin+avgloss)x w – avgloss

Therefore, E is maximum when w, the win rate, is maximum. Since one cannot control avgloss in general, maximizing w maximizes expectancy in general.

I recommend that you get up to speed with these simple equations. They say the whole story and debunk your claims that are based on wishful thinking and not on mathematical facts.

• Jim says:

Again you are INCORRECT.

I recommend that YOU “get up to speed” by using the correct methodology for the situation at hand (trading). Unless you plan on placing only ONE trade in your trading career your 8th grade algebra is useless.

In your example the win rate is the determining factor solely because the “simple equation” is bound by the win rate being positive (above 50%) and is therefore INVALID for a proper calculation in any situation that does not have a static binary input/outcome. For anything else (including trading MORE THAN ONCE) it is INVALID as a measure of risk, especially risk of ruin. It works fine for some of the situations but not all. In case you missed it somewhere along the way, that’s not how math is supposed to work.

You are providing a disservice here for anyone who is actually considering putting their money at risk in the market by using simple “coin flip” formulas to explain risk of ruin in a situation where they are not necessarily applicable.

Again… a higher win rate DOES NOT GUARANTEE MAXIMIZING EXPECTANCY. I (and many other profitable traders) found the flaws in your examples/arguments many years ago… thankfully before it cost me all of my trading capital.

Here’s some parting advice for you (and anyone reading these comments); put down the high school algebra book and actually design some trading systems and you’ll find the answer isn’t as simple as presented by the author of this post.

• Emanuel says:

I think what Michael Harris is saying is simple as this:

System 1: R:R 3:1, win rate 60%

System 2: R:R 3:1, win rate 70%

Which system do you prefer? In both cases the R:R is the maximum one can get from price series. But let’s say you can increase R:R to 4:1

System 3: R:R 4:1, win rate 60%

System 4: R:R 4:1,win rate 70%

Now,which system do you prefer from 3 and 4?

Toss a coin with prob of heads 50%. What is the prob of 4 losses in a row? Ans.(0.5)^4

Now toss acoin with prob of heads 70%. The prob of 4 consecutive losers is (0.6)^4

Which coin do you prefer? Obviously, the highest prob of heads the better for given R:R. This is common sense. I thought this article was not really necessary but after I see that some do not understand the importance of a high win rate I think it was a good one.

• Jim says:

If that is what he is saying then he should say that a higher win rate is PSYCHOLOGICALLY superior, not mathematically superior… end of story.

• Alessandro says:

Jim – Emanuel and the author are correct. If you do not understand that wining bias is necessary in trading but you rely on expected high payoffs that may never come then you are probably ruined by this time I post my reply.