No, you misunderstood that bit, I was referring to justifying the validity of CP models: the larger the number of athletes size, the clearer the evidence that the power-duration curve follows one of the CP models — or not. So in this sense, study size does matter and a huge data pool like the one TR is sitting on has any sports science study beat.
These models are validated with studies. If N is small, then you cannot necessarily expect to be able to predict the values of all parameters with sufficient accuracy.
That issue also arises if you apply a particular model to a single athlete: if they don’t have enough all-out efforts in the relevant range of the power-duration curve, you cannot reliably predict the parameter values as the statistics are too bad.
Both issues can make a model with more parameters less useful.
That’s problem for WKO, if it is based on a simple physiological model. Speaking for the semiconductor industry, also here some of the models are published as it is necessary for them to be known so that different tools (= machines) from very different manufacturers can work well together.
The only reason why I hesitate is that any discussion of what FTP really is can lead to a death spiral of circular posts.
I agree that CP and FTP have the same basic aim and therefore must arrive at very similar numbers. Differences can easily be due to the different test protocols.
I agree with the first sentence, but not with the second. To me FTP is defined as MLSS measured in a field test, and strictly speaking, numbers are only comparable if you keep the test protocol the same.
CP arises out of a 2±parameter model for the power-duration curve, assuming it is given by a particular equation (with 2+ parameters).