Hello All,

I’ve been looking at the concept of Positive Expectancy, its calculation, and what is/isn’t a robust benchmark for positive expectancy.

A hypothetical day trading system produces the following results:

81% are winners

19% are losers

av. win is $492

av. loss is $416

I’ve come across two formulas to calculate expectancy. Both generate the same end result. But the proponents of each formula conflict in terms of what is/isn’t a desirable expectancy benchmark.

Formula one:

[probability of win x av. win] – [prob. of loss x av. loss] = expectancy

using the above hypothetical:

[0.81 x 492] – [0.19 x 416] = 319 rounded

319/416 = 77

So our hypothetical trader with the above stats expects to make 77 cents for every dollar $1 risked.

My research shows that proponents of this formula argue that an expectancy of 60 cents or greater represents a “good” system.

ie., an expectancy of 60 cents is the benchmark.

Formula two:

[reward to risk ratio x win ratio] – loss ratio = expectancy ratio

[492/416 x 0.81] – 0.19 = 0.77 expectancy ratio

Each formula obviously gives the same answer. But the proponents of this second formula state that an expectancy ratio >1.0 is the benchmark.

So formula one advocates would be happy with their 77 cents, but formula two advocates would not.

My question,

Have I missed something in my attempt to understand expectancy and formulate a benchmark? Is it 60 cents or $1.00??

Thanks for feedback.

James.

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