**Kirk wrote:**
... measures whose identities are known.

It's just math...as is a measure of "average" over a 1 or 5 or 20 minute duration. Why is one form of mathmatical equation better than another? I think our DNA is silent on the matter.

One of the first things one learns in advanced statistics is the limitations of the arithmetic mean as a source for plugging in a summary value or expected value. There are dozens of ways to compute a summary or expected value. Perhaps we should try Bayesian, or maybe a Markov Chain, or perhaps we should raise short-term arithmetic mean values to the fourth power, do the arithmetic mean again, then take the fourth root. That one seems pretty well "known" within cycling circles. A popular software program will even do it for us.

Another thing about using any form of mean -- it is meaningless without its being paired with a dispersion or variance measure. Where is your variance measure when you look at your averages? Do you compute it at all? There are ways of embedding the dispersion of a set of observations within the expected value estimator. Arithmetic mean doesn't do

*at all,* but a

*ratio *of an exponential method to the arithmetic method does it very nicely (well-known as "IF" in some circles).

A neat thing I've learned about fooling around with all those bins mentioned in my earlier post -- it never tells me anything more than merely looking at an exponentially-derived estimator, an arithmetic estimator and the ratio of the two. It's a lot easier to just look at a couple of numbers and gauge the load that way.

I look for a nice high exponentially-derived estimator, a nice high arithmetic estimator, and a ratio of the former to the latter of at least 1.12. That tells me that I worked hard overall, and that I worked

*very hard* for at least an extended portion of the ride. What else is there to know?