TSS-related rambling

Training Stress Score (TSS), is a training load estimator for cycling invented by Dr. Andrew Coggan, and is modeled after Dr. Eric Bannister's heart rate-based training impulse (TRIMPS). It takes into account both the intensity (i.e., IF) and the duration of each training session, and according to the author, it “might be best viewed as a predictor of the amount of glycogen utilized in each workout.”

TSS has the advantage that it is easy to calculate and that it is based on the direct measurement of the applied stimulus (power), unlike TRIMPS that is based on heart rate. However, unlike TRIMPS, TSS has not been validated in any scientific studies, which means that its use by many comes from believing that it is a good tool to estimate training load.

The definition of TSS is

TSS= IF^2 x duration(h) x100

By definition, TSS’ units are time and therefore TSS is a equivalent training time at FTP. If we leave out the constant 100, we will see that in reality TSS is nothing more than equivalent training time in hours at FTP. So a 200 TSS ride is a training load equivalent to 2 hours at FTP (if that was possible in one ride).

So from the definition of TSS we can see that it was created and should only be used as an estimator of training load, and using it as some sort of “effort budget”, besides going beyond the scope of the definition, is fundamentally wrong.

For a given duration/power level, the individual (Power vs Duration) curve gives us the maximum power level possible for a given duration. For durations above one hour, and if we non-dimensionalize power with individual FTP, it is likely that the individual curves (IF vs Duration) for well-trained endurance athletes fall in a very narrow band. For the purpose of this discussion, let’s say that there is an exponential relation between duration and IF. In order to “anchor” this curve, the upper end is obviously FTP (1,1). The other point that defines the curve can be a common intensity estimator for maximum efforts lasting 2 hours – IF=0.95 (2,0.95). Figure 1 shows the non-dimensionalized (Power vs Duration) curve, as well as curves for 95% and 90% intensity, respectively.



Now if we turn our attention to the problem of pacing the bike leg of a triathlon, the issue of running off the bike is going to be dependent on the intensity of the bike effort. It is not a big conceptual stretch to think that there is a threshold of effort above which an athlete won’t be able to run up to his full potential (the answer to what constitutes “running to its potential” is a whole different world). If we express this concept using the (Power vs Duration) curve, for a given duration, there will be an intensity above all running off the bike at a pace according to your running specific level of fitness will be impossible. That intensity threshold should be somewhere between 90 and 95% of the maximum effort for a given duration.

This means that a correctly paced Ironman bike that lasts 4:30h will have an IF between 0.75 and 0.79 and that a correctly paced lasting 6:00h will have an IF between 0.74 and 0.70.

Some approaches to the determination of correctly paced ironman bike rides use TSS as an effort budget. Like it was mentioned above, this does not make much sense, since using TSS as an effort budget goes beyond the scope of the definition, not to mention not being supported by any kind of evidence.

In order to illustrate this, let’s take an example using the above (Power vs Duration) curves. According to some sources, a common range of TSS scores that represent a correctly paced IM ride is between 265 and 290. Figure 2 shows the TSS-constant curves for 265 and 290. So for this range, we can see that for a 4:30h ride we have an IF between 0.77 and 0.80 and for a 6:00h ride an IF between 0.66 and 0.69. As we can see from Figure 2, even if using this approach the values for IF are not far off from those from the approach I delineated above, it is clear that the shape of the constant-TSS curves doesn’t make sense from a pacing point-of-view.




It is clear from the figure that this approach prescribes decreasing IF’s for increasing durations, which makes for extremely conservative estimates for the slower riders. On the other end of the spectrum, for the fastest riders it prescribes high IF’s that are clearly above what is generally accepted as a correctly paced IM bike ride. Above all, the increase in IF with decreasing duration doesn’t make sense from since in the limit we would have IF’s above the maximum (Power vs Duration) curve.

Of course the relative proximity of the TSS-constant curves to the Power/Duration curves is dependent on the “slope” of the (Power vs Duration) curve. If for example, we anchor our maximum curve to a different point, the TSS-constant curves will be closer/further from the (Power vs Duration) curves. Figure 3 shows the comparison for the points (1,1) and (2,0.94), meaning an athlete that for a maximum effort lasting two hours has an IF of 0.94.



For this example we can see that a TSS between 265 and 290 will be in the right range of IF’s for longer durations, but that the IF’s for the shorter durations are grossly overestimated.

In conclusion, through a simple set of examples it was shown how using TSS to choose the intensity to race an IM bike has the potential to either grossly underestimate or overestimate the effort needed. The fact that the 265 to 290 range has come up is likely because it is based on a set of data for durations between 5 and 6 hours. The said range is the product of the correctly paced rides, and does not represent any sort of effort budget. I would suggest that if we’re looking for a realiable effort budget, the actual work being performed for a given duration needs to come into play. But this is hardly a new concept.