fitting power-duration data, mean versus envelope fit example

Andrew Coggan published the following data on Twitter, showing a cyclist's power-duration data from two separate years:

image

In the above, FTP is power which can be sustained for 1 hour. FRC is "functional reserve capacity" which represents how much work over FTP can be done. I've never myself tried to extract that, but it's a nice concept: similar to anaerobic work capacity in the critical power model.

I extracted the data as best I could from the plot using PlotDigitzer, then fit my 4-parameter model using an envelope fit:

image

The philosophy on the envelope fit is that only a limited number of durations represent a rider's best effort; most durations are part of longer efforts and so are sub-optimal for that particularly time duration. The fit only has validity if there are actually as many quality efforts as there are parameters in the model. So a 4-parameter model requires at least 4 quality efforts.

The philosophy on the mean fit is to treat all durations essentially of equal importance.

Anyway, the result is that with my envelope fit, it's clear that year 2 has more short-duration "anaerobic" power, but the modeled FTP (1 hour power) is much closer for the two years than it is with the original fit.

I tried two alternate ways to determine FTP. First, I eliminated the iterative weighting from my fit to make it a mean fit, rather than an envelope fit. This yielded values of 2.91 W/kg for year 1, and 2.85 W/kg for year 2, a difference of 0.06 W/kg. This is larger than the difference of 0.02 from the envelope fit. Another approach is to interpolate the 1-hour data directly from the curves. This yields 3.09 W/kg for year 1, and 2.93 W/kg for year 2, a difference of 0.16 W/kg. So the 3 approaches yield substantially different conclusions about the magnitude of the change in 1-hour power: 0.02 W/kg, 0.06 W/kg, or 0.16 W/kg. Coggan's fit yielded a fourth difference, 0.13 W/kg, since he uses a different model and different fitting algorithm. Personally I like the envelope fit, as I think it's more predictive. The best case, though, is to use the same standard intervals for fitness testing in both years, thus avoiding comparing interpolated to direct estimates.

Comments

You've got a misstatement in this post: you need 5-50x as many sample points as parameters to obtain a valid fit; not the just 1x as you claimed.

Popular posts from this blog

Proposed update to the 1-second gap rule: 3-second gap

Post-Election Day

Marin Avenue (Berkeley)