## Do you need a high winning rate?

It's certainly good to have a trading system for your favorite e-mini futures or stock market which boast a high winning rate. Say, over 60% or even over 70%. The higher the better, although realistically anything over 70% is already very good and rarely ever gets better over a longer period of time unless it was curve fitted and we are talking about the backtested results and not the results achieved in actual trading.

I mean mechanical trading systems as in the case of discretionary ones (which I usually call methods rather than systems) this rate can be easily higher, even 90% over a longer period of time.

It is good to have a winning rate for two major reasons, the first of which is that this gives us a smoothly growing equity curve with relatively small drawdowns. The second reason is somewhat related. Namely, small drawdowns are easier to handle both mentally and financially than bigger ones. And who wouldn't like to feel comfortable rather than uncomfortable in their trading? It's a rhetorical question, of course.

It is so good to have a high winning rate that virtually every peddler of e-mini trading systems of suspect quality stresses how great their systems are in this respect. Sometimes they even tie their money back guarantee to their system performance formulated in terms of its high winning rate. For instance, if over three months since its purchase the system does not maintain a winning rate of at least 70%, you get your money back.

And therein lies the problem. Whenever you see a guarantee phrased like that you are almost always better off to take your business somewhere else. For it is not the system winning rate (WR), no matter how impressive, that determines the system profitability, but the expected value (EV) which is a function not only of the system winning rate, but also of its average win per trade (W) and of its average loss per trade (L). The formula that defines this quantity, also frequently referred to as the system edge, is:

EV= WR*W-(1-WR)*L.

What this means in practice will be best seen from two examples that follow. Let us note that to calculate W, you sum up profits accumulated in, say 10 trades, and divide this sum by the number of trades, being 10 in our example. To calculate L, one needs to sum up all losses and divide them by the total of trades.

It is possible to have a system that wins 80% of the time and yet it loses money over time. This happens when its average loss per trade is significantly larger than its average win per trade. Imagine a system with such a winning rate that makes 1 pt of profit per trade on average, but when it loses, it loses 4.5 pts per trade on average. Its EV is thus EV=0.80*1-0.20*4.5=-0.10 (pt) and since this number is negative, the system will lose money in the long run.

And vice versa: even a system with a 30% winning rate can be highly profitable if its profits tend to be much larger than its losses. This is not uncommon for good swing systems. Imagine that your system loses 3 out of 4 trades on average (WR=0.25), but its profits are on average 6 times greater than its average loss that is 2 pts only. Using our formula for EV we obtain that the profit per trade is EV=0.25*12-0.75*2=1.5 (pt). Such a system will thus still make money and that's what ultimately matters.

It is a mistake to consider only systems with a high winning ratio for your trading. Just as it is a mistake to consider systems based on their "psychological attractiveness." While it's good to have systems with a high winning rate, it's even better and more important to make sure that such systems are highly profitable and robust as well.