February 20, 2017 Greedy Ram 4Comment

This is an incredibly basic and simple concept that is often overlooked because of how simple it really is, however it is absolutely essential to being profitable as a trader.  It is the interaction of your win to loss ratio and your winning percentage. It is basic math and whether you are aware of it or not these two factors MUST be in balance to be profitable there is no arguing that or way around it, it is math and as indisputable as 1 + 1 =2.  There are a few ways to look like this, I’ll do my best to go over them all. If you are more interested in the psychological side of this math, click here to read a post on Outcome bias.

First lets define the two numbers that we’ll be looking at:

Winning Percentage (W%) :  Pretty self explanatory but for the sake of being thorough this is the percentage of your trades that are profitable.  Calculated by dividing your winning trade by your total number of trades.


W% =        # of Winning Trades

                     Total Number of Trades

Win to Loss Ratio(W:L):  Your average winning trade divided by your average losing trade. This can be in either dollar or ROI terms, I’d recommend you do look at both.

W:L = Avg Winning Trade

             Avg Losing Trade


These two key statistics need to be in balance in order to be profitable, what exactly do I mean by balance though?

If your W% is low your W:L ratio needs to be high, if your W:L ratio is low then your W% needs to be high.  I’ve seen strategies on both extreme ends of this spectrum, and they both can work and be profitable. I’ve known traders who were making $2000 to $5000 per day around 85%  to 90% of the time but when they lost it was for $20 000+.  I’ve seen other traders lose 70% or more of the time but when they have a trade hit it hits hard and they make back all of their losing days and then some. I personally tend to end up somewhere in the middle having winning trades roughly 60% of the time with a W:L around 1.5 to 2.  The point is any style and strategy can work as long as these factors are in balance. The market usually has its own way of forcing these into balance for you, its pretty tough to come across a strategy that has both a high W:L and W%, but if you find one please let me know ;).

Here are the actual numbers to show what I mean by balance:

This chart shows what combinations of W:L and W% you need in order to break even, increase either side and in becomes profitable, decrease either side and it is a losing strategy.

For example, if your W:L is 3:1 you only need to have 25% winning trades in order to break even. If you increase the w% to 30% it is a profitable strategy, if the w% stays at 25% but your W:L increase it is a profitable strategy. If your W:L is 3:1 and your w% drops to 20%, guess what? now its a losing strategy.

It’s interesting looking at the extremes on this, if your W:L is 5:1 then you only need to have winning trades 17% of the time to break even, if your W:L is .1 (1:10), meaning your losers are 10x bigger than your winners you need to have profitable trades 91% of the time to break even!

There is no way around this, its simply math.

I’ll show you how this looks using my actual results from one of my strategies during both a good and bad month (you should always keep accurate records of your trades on excel so you can do the same).

Comparing this to the chart above you can see that during the good month my w% was only 50% but my W:L was 4.45:1, well above the threshold to break even. Compare that to the bad month where both my w% and W:L dropped below the break even levels resulting in a losing month.  When I combined the two months you can see I was still profitable only having a winning trade 37.8% of the time!

Another way to look at this is an expected value or EV calculation.  This can show you what your expected value or average per trade will be. The formula for this is

EV = (W% * Avg Winner) + ((1-W%)*Avg Loser)

Using the numbers from my good month above this would be

EV = (.5 * 2504.04) + (.5 * -562.57)

EV = $970.74

In other words a strategy with a win rate of 50%, an average win of $2504.04, and an average loss of $562.57 will have an expected value (or average) per trade of $970.74.

How do you implement this into your trading?

This isn’t a trading strategy in itself but it is the backbone behind EVERY strategy.  It can help losing traders see where they are going wrong, and winning traders how to be more profitable.  After trading for a while and tracking your trades in excel you will probably have a pretty good idea of what your w% is and w:l is.  If you are losing money look at these 2 statistics and figure out how you can tinker your strategy to bring them into a profitable balance. For example assuming you are taking the same set up with a set stop loss, it may become apparent to you that you need to hold your winners longer and resist the urge to cover a position quickly (just having knowledge and remembering math like this can help you to resist emotionally based urges like this) . Of course changing your profit targets and stops will also cause your w% to change but using these statistics is the kind of basic thought process you need in order to develop a profitable strategy.

There is a mistake in the way most people think about trading and gambling called the outcome bias. It ties into this math concept well. Read more about it and the errors you may have here.

4 thoughts on “Basic Trading Math

  1. No need of this complicated formula to calculate the EV = (W% * Avg Winner) + ((1-W%)*Avg Loser)

    Just take the net P/L divided by the number of trades. You get the same expectancy value.

    1. Ya, I mentioned that you can get the same value by calculating your average trade.

      I wrote it out in the more complicated way to show how your winning % / avg win and avg loss play a role in arriving at your expected value.

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