Hi all,
I hope this post doesn’t make any duplicate. I read a lot of other ones related to TSS calculation too, but no one seems to describe the same “pathology”.
A few weeks ago I ran the same track twice in the week, beeing proud the 2nd time because I ran significantly faster. But I noticed that the TSS of this fast run was lower than the one of the slow run :
date km D+ duration km/h tss
2025-12-15 04:49:02 22.08 166 02:15:27 9.8 121.0
2025-12-23 04:59:50 22.04 157 02:03:45 10.7 115.5
Note: except from the speed, all data come from my Suunto Ambit 3 Peak, used without heart rate tracking. Thus I “tss” should mean tss[r] (aka rTSS).
According to me the 2nd run should give a higher TSS. I see that the measured distances and denivelation are both slightly lower for the 2nd run, but I don’t think this should counter the big difference (almost 10%) in the duration and thus the speed.
To complete deeper this analysis, I gathered all the fit files of the activities made on the same track and with the same watch. Then I plot the calculated TSS as a function of the duration, which gives me this figure :
[image: 1770658549807-strange_tss.png]
I don’t mind the few strange values which are out of the “main line” (they represent around 10% of the 32 selected points), but once again I don’t understand its shape.
The definition of TSS should produce a descending line (see my demonstration at the end of the message), not an ascending one.
So what does happen here ?
Bonus : I suspect that this behaviour can be generalized over other workouts even if the analysis is more difficult when comparing different tracks.
I found two other interesting recordings from my last summer holidays :
date km D+ duration km/h tss
2025-07-13 06:30:25 22.6 1487.0 03:46:42 6.0 185.2
2025-07-15 08:28:33 12.0 806.0 04:57:16 2.4 201.0
The first run is a competition ran fast though, not at my maximum.
The second one is a very gentle walk with my wife and my kids. Both recorded with the same watch using the same sport mode.
So do I need to stop running fast if I want to progress more ?
PS : my “proof” of why the plotted curve should decrease (let’s do some maths as we were still at school) :
Neglecting the constants used for normalisation, raw definition of TSS[r] can be expressed as formula (1) source: trainingpeaks
(1) TSS = duration . NGP . IF / FTP
but because IF = NGP/FTP we can simplify it as :
(2) TSS = duration . NGP² / FTP²
Now let’s define ND as the “Normalized Distance” to match with NGP as NGP = ND / duration. Then we get :
(3) TSS = ND² / FTP² / duration
Because all the selected workouts are recorded on the very same track, ND is a constant through the plotted data.
And I assume that FTP doesn’t change over the time because I use neither pace nor heart levels (I can’t remember when I modify them for the last time, considering that I really did it once). And according to me this is confirmed by the chosen colorscale on the plotted data.
So for this example we end with :
(4) TSS = Const / duration
which tells us that : lower the duration, higher the TSS.
All but suprising !
