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Statistical Formulae

By Edited Jan 24, 2016 0 0

Statistical formulae can be used by traders to ascertain if they will be profitable in the long run or not. I will explain the most important formula that I have used and it’s called the Expectancy Ratio.

The expectancy ratio essentially gives you a good estimate of what your trading system will yield. I used this formula religiously when testing new systems as it allows you to compare systems fairly.

The formula is very simple

Expectancy Ratio = [(Average Win × Win Rate) ÷ (Average Loss ×Loss Rate)]

So let’s say my...

Average Winner = 100

Average Loser = 50

Win Rate = 40% therefore (40÷100)

Loss Rate = 60% therefore (60÷100) both would then make up 100%


Expectancy Ratio = [(100 × 0.4) ÷ (50 × 0.6)]

                                   = 1.33 which is profitable

Any Expectancy over 1 will yield a profit theoretically but remember that trading fees or commissions are not included in this calculation.

Thus it’s safer to aim for an expectancy of 1.5 or better as a rule of thumb.


Important Points to remember

  1. This formula is very simple but it needs accurate input data. This requires you to have a trader’s journal where every cent of your trading is accounted for.
  2. Do not even consider a trading system that has an expectancy below 1 over a decent sample size. You will simply lose money, confidence and time.


How I have used Expectancy Ratio

  1. Back testing systems. The expectancy ratio provides a quick answer to back testing results and it can easily be used to compare different systems. This will allow you to get rid of systems that simply don’t perform, leaving you with more time to thoroughly back test the promising systems.
  2. Continual Monitoring of my Trading. I update my expectancy ratio every day; this allows me to see if I am still on track.
  3. Benchmarking. Simply knowing what my standard monthly expectancy should be gives me confidence to trade without emotion. Confidence allows you to trade with more discipline because you know more or less what your system will achieve if you trade it perfectly every time.


Make sure not to get rid of a trading system to early. Expectancy ratio requires a decent sample size especially if you are back testing (1 year minimum but more is ultimately better).

Trading is a numbers game and your single trades cannot be used to make decisions, you need to look at all your trades collectively to ascertain if you are on the right track.



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