I accept that "arbitrary" was not quite the right word, because you did have a rationale for the choice of those constants (30 s for the moving average, then raised to the 4th power before averaging).  I should have said that you had a rationale that it is not directly related to performance. 

It would be good to derive values for the constants that optimize prediction of time-trial power.  This approach would amount to the calibration phase of development of an instrument.  It would also give you a typical (standard) error of the estimate of endurance performance, which would be more meaningful for interpretation of the validity of normalized power.  (Note that you don't need a subsequent validity study to confirm the value of the standard error of the estimate.  The calibration study provides an unbiased estimate of the standard error of the estimate, when you use the instrument on cyclists similar to those in the calibration study.) 

It's hard to know how to interpret the change of ~5% in normalized power that you get when you change the values of 30 s and 4th power.  It sounds like a lot, but maybe it's not, because it applies to every athlete, so it might not have much of an effect on the rank order of the athletes.  On the other hand, the bottom line may be that normalized power derived from a competitive road race (where there are team strategies based on drafting) has a standard error that is simply too large for the measure to be useful.  The measure derived from training rides would probably have an even larger standard error.  Whether the measure derived from training rides would be useful to quantify training loads is also unclear.  Any overall average of power loses the information about time spent in the various power bands.

Will

Will G Hopkins, PhD FACSM
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