AverageReturnPerBarCriterion: formula about ta4j HOT 4 CLOSED

I think, it uses pow because it calculates the geometric average return per bar, because of the compounding nature of returns over multiple bars. But I am not sure..

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Despite the fact that AverageReturnPerBarCriterion includes the ReturnCriterion (with base) which seems to be a bug (because the AverageReturnPerBar implicitly inlcudes 100% and assumes that it's a profit, which is not)

We must include the base here if we use this formula with pow, because if we do not, then if we have a negative number (e.g. return = -0.3) with a fractional exponent, it returns NaN as the result (e.g. Math.pow(-0.3, 0.2) = NaN).

Using simply Return(without base) / NumberOfBars, then it would work. Actually, I don't fully understand why we need to add the compounding effect (with pow) for this use case as we already have the full value of Return which we can simply divide by the number of bars. I think this is more accurate than having pow and "including the base", or am I missing something?

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No, we can't simply divide the percent profit by the number of bars, as this does not take into the affect of compounding.
The fractional use of power was used to effectively "undo" the power of compounding in order to correctly calculate the return (on the assumption that ReturnCriterion is implemented correctly).

It is worthwhile to use to spreadsheet to see the effects of the formula to verify one's understanding.

The Return used includes the base as with everything in ta4j.

I think this is what the intended criterion was supposed to calculate:

AvgExcessReturnPerBar = Math.pow(FinalReturnWithBase, 1/NumOfBars) - Base
where NumOfBars is the number of bars after the initial bar.

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To clarify further, the value returned by the current AverageReturnPerBarCriterion is actually the Return Multiple.
By that, I mean, if it returns a value of 2, this means the account is doubled every bar on average.

This is not to be confused with the absolute or dollar value.

Two sides of the same coin:

1x return = 100% return = 0% profit after subtracting base
2x return = 200% return = 100% profit after subtracting base
...
10x return = 1000% return = 900% profit after subtracting base

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