Originally Posted by RChung

Your understanding isn't quite correct.

First, NP isn't terribly reliable for shorter intervals. Coggan recommends that you don't use NP for intervals shorter than 20 minutes (though that may be a bit conservative). TSS depends on NP, so TSS for short intervals probably isn't reliable, either.

Second, NP was originally envisioned as a way to approximate "equivalent" demands of a steady state power output with a highly variable output -- like the efforts for a crit race. The proof of a pudding is in how it tastes, and the NP for an hour-long crit race where riders say they've been going *hard* is very close to the steady state FTP -- much closer than the average power for that race is. So the empirical evidence is that in this kind of situation, NP is closer to FTP than average power is.

Are you familiar with how to calculate a standard deviation of a random variable? It can be described as the square root of the mean of the squares of the values. In statistical parlance, there is something called the Lp-normalization where you take the pth root of the mean of values x^p. So the standard deviation is the L2-normalization. Coggan's algorithm is the L4-norm of the power (actually, it's the L4-norm of the rolling 30 second mean of the power), which is where the name "normalized power" comes from.

Lots of people have tried different p's in for the Lp-normalization. Lots of people have tried different smoothing intervals than the 30 second rolling "box" smooth Coggan originally came up with. (For example, Phil Skiba uses a fixed decay smoother in xPower). There's nothing sacred about using a different p or a different smoothing window, but p=4 and 30 seconds puts you in the right ballpark.

So, when your FTP is well-measured, and if you don't try to infer too much from very short intervals NP, IF, and TSS are pretty useful summaries, imperfect though they may be. Try not to let the perfect be the enemy of the good.