Like I mentioned in this post, although TSS is inspired on Dr. Eric Bannister's heart rate-based training impulse (TRIMP), it has the downside that, unlike TRIMP, it has not been validated in any scientific studies.
The biggest downside of TRIMP is that it is heart rate based, which means that in the context of quantifying training load in the impulse-response model of training adaptation, the input is itself a response and not a direct measure of the stimulus.
TRIMP is calculated as
TRIMP= Duration (min) x fraction of heart rate reserve x exp(1.92 x fraction of heart rate reserve)
Now if we equate the fraction of heart rate reserve, an indirect measure of intensity, with IF, a direct measure of intensity, we will have as input on TRIMP a direct measure of the stimulus in the impulse-response model.
Given that under controlled conditions heart rate will vary linearly with power, we can assume that IF=1 will correspond to a percentage of heart rate reserve. In the following discussion, it was assumed that IF=1 corresponds to 90% of heart rate reserve. This was a number thrown around frequently back in the days when the “Karvonen formula” was used for the heart rate corresponding to what we call now Functional Threshold (IF=1). Also some of the assumptions made are only valid for durations over one hour.
By equating heart rate reserve to IF, we can define a power-based training impulse as
TRIMP_IF= Duration (min) x 0.9 x IF x exp(1.92 x 0.9 x IF)
In order to compare it to TSS, we can use the value of TRIMP_IF that corresponds to FTP, i.e.,
TRIMP_IF(FTP) = 60 x 0.9 x 1 x exp(1.92 x 0.9 x 1) ~ 303.99
in order to scale what we called TRIMP_IF. So we can define a new training load stress score, that we are calling P_TRIMP, for Power_TRIMP:
P_TRIMP = TRIMP_IF/ TRIMP_IF(FTP)
P_TRIMP has the advantage that is directly based on TRIMP, which means it is strongly correlated to the considerable amount of scientific evidence that supports TRIMP. Furthermore, it uses a direct measure of intensity as the input on the impulse-response model of training adaptation.
Figure 1 shows the curves for P_TRIMP =1, 2 and 3 respectively. For comparison, curves for TSS/100=1, 2 and 3 are plotted, as well as a universal Power vs Duration curve.
As we can see, the P_TRIMP-constant curves differ considerably from the TSS-constant curves, with the difference being greater for longer durations.
Figure 2 shows a comparison between P_TRIMP and TSS, using as input the above mentioned approximation for the Power vs Duration curve. Therefore, what is shown are the curves for the maximum TRUMP and TSS possible for a given duration.
It is clear from the comparison that TSS overestimates the training load for increasing durations. This somewhat agrees with the sentiment by those that use TSS to quantify training load that it puts an excessive weight in duration vs intensity.
Conclusion: A new training load estimator directly based on TRIMP was presented. Further validation through scientific studies is needed in order to warrant its use. However, the fact that it is directly based on TRIMP means it is already a considerable improvement over TSS.