I'm a recreational cyclist who likes numbers and data-analysis. Having a powermeter and analysing rides is fun for me, and the 'performance manager' in WKO works nicely as a motivational tool - trying to work up the TSS.
But, I just wanted to point out a detail:
TSS (training stress score) is based on IF (intensity factor), which is based on NP (normalized power). Normalised power is the 4th root of the average of power to the 4th power (squared squared, or matematically put P^4). The reason for this is very smart - it takes into account that training feedback is more than linear in training load - NP rewards you e.g. for interval training.
However, there is a mathematical problem here. If we defined TSS as the sum over P^4, then all is fine - only draw back that the unit for TSS is not watts but watts^4.
The wish to keep simple units (more understandable for lay people and those cyclists who don't have a PhD in physics) lead to using the 4th root. However, in doing so TSS is no longer additive.
A simple example:
Suppose we have FTP of 200W and ride 1 hour at 200W, download to WKO, which rewards us 100TSS. We then take another 1 hour ride at 100W, which WKO rewards us with 50TSS. That would give total 150TSS.
Now, lets instead take one 2 hour ride, riding 200W first hour and 100W second hour. NP will be ((200^4+100^4)/2)^1/4=171W. This corresponds to an IF=0.854 for 2 hours and is rewarded by 171TSS.
We did exactly the same training, but in second example we were rewarded 21TSS more. In other words, I think the concept of TSS is mathematically ill founded.
But, there may not be reason to despair. I think what saves the concept is that the P^4 is anyway just a crude approximation (and generalisation across all athletes) to the physiological fact that intense training pays off. In other words, the mathematical error built into the TSS concept is probably inferior to the approximation in applying the simple expression P^4 to a physiological effect, and using this same formula for all different athletes.
In other words, TSS is an approximation - and as such it works.
But, I just wanted to point out a detail:
TSS (training stress score) is based on IF (intensity factor), which is based on NP (normalized power). Normalised power is the 4th root of the average of power to the 4th power (squared squared, or matematically put P^4). The reason for this is very smart - it takes into account that training feedback is more than linear in training load - NP rewards you e.g. for interval training.
However, there is a mathematical problem here. If we defined TSS as the sum over P^4, then all is fine - only draw back that the unit for TSS is not watts but watts^4.
The wish to keep simple units (more understandable for lay people and those cyclists who don't have a PhD in physics) lead to using the 4th root. However, in doing so TSS is no longer additive.
A simple example:
Suppose we have FTP of 200W and ride 1 hour at 200W, download to WKO, which rewards us 100TSS. We then take another 1 hour ride at 100W, which WKO rewards us with 50TSS. That would give total 150TSS.
Now, lets instead take one 2 hour ride, riding 200W first hour and 100W second hour. NP will be ((200^4+100^4)/2)^1/4=171W. This corresponds to an IF=0.854 for 2 hours and is rewarded by 171TSS.
We did exactly the same training, but in second example we were rewarded 21TSS more. In other words, I think the concept of TSS is mathematically ill founded.
But, there may not be reason to despair. I think what saves the concept is that the P^4 is anyway just a crude approximation (and generalisation across all athletes) to the physiological fact that intense training pays off. In other words, the mathematical error built into the TSS concept is probably inferior to the approximation in applying the simple expression P^4 to a physiological effect, and using this same formula for all different athletes.
In other words, TSS is an approximation - and as such it works.