However, when taking a closer look at the formula, I realized how awfully random TSS really is:

When I ride at FTP for an hour, then at 50% for another hour, that gives me a TSS of 145.8.

Now when I ride at FTP for an hour that gives me a TSS of 100. Riding for an hour at 50% gives me 25.

That means, the overall TSS (145.8 vs 125) is quite significantly different for the same session, depending on whether or not I stop and start my bike computer mid-ride. What am I missing?

My calculation:

The formula for TSS is TSS = [(s x NP x IF) / (FTP x 3,600)] x 100, where s is the time in seconds, NP is the normalized power, FTP is the functional threshold power and IF=NP/FTP.

(Side note: I don't know why they over-complicate it like that. The above formula is equivalent to

TSS = IFÂ˛ x t/h x 100, with t/h the time in hours. Seems easier to me.)

NP is basically the 4-norm (p-norm for p=4) (the 30 s average is negligible here) and therefore the overall NP of the session is NP=((a^4+b^4)/2)^(1/4), where a = 100% x FTP is the power for the first hour and b = 50% x FTP the power in the second hour.

--> NP=(1+0.5^4)^(1/4) x FTP=0.8537 x FTP

--> IF = NP/FTP = 0.8537

--> TSS = 0.8537Â˛ x 2 x 100 = 145.8

The second case (two seperate files) is easy to calculate: An hour at FTP gives TSS=1 x 1 x 100=100 by definition and for 50%, IF=0.5 and therefore TSS=0.5Â˛ x 1 x 100=25.