Tuesday, July 8, 2008

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.


Kevin said...

I am sharing similar views with athletes who are tempted to try monitoring TSS during IM over other (in my view) more accurate available markers & data (including PE); albeit with less detailed maths. Thanks, you have nailed it.


cramer said...

Interesting, but I'm curious. It is your contention that an IM bike effort that falls within 90-95% can always be considered a well-paced effort, regardless of whether the athlete was on the bike for 4.5 hours or 7? You don't think that 90-95% range should scale with duration?


The Grand Master Crackhead said...

I'm a 6:30-6:50 IM bike split (slow, I know, but hey, I'm an old lady), and I can just never hit that magical TSS 300 number--I always go over, except may if I did IMFL I might be right on the nose.

I've had good results at IF=.76-.78, depending on the course, which if you go by the TSS table, should make me totally blow up on the run, but it doesn't, but maybe that's because I'm not a great runner, either. But I have been happy with my IM performances anyway. I just can't see riding at IF of .70 (which is what has been recommended to me).

This time, I'm going with the IF that I think I can manage, which will be about .76 at IMLP.

Thanks for this analysis.

manny82 said...

Would it be best to do a tt at the desierd distance and use a percent of that?


Lakerfan said...

I constantly see this and don't understand. Why do people focus ONLY on a single global descriptive metric -- meaning that it's used for post-hoc analysis ONLY -- and find ways to determine why, how or when it doesn't work? Or confuse it as a prescriptive means for determining proper pacing?

I would think this is obvious but maybe it's not: It's not about any one single metric. Never has been and never will be.

People also need to understand the fundamental differences between descriptive metrics (used for post-race analysis) and prescriptive advice/guidance for determining proper pacing. I know you do but it appears many others are often confused.

Those of us who use TSS are well aware that it's far from perfect. Again, no ONE single metric should ever be used to determine success or failure. We highly suggest to use TSS in conjunction with other global descriptive metrics during post-race analysis. Success or failure isn't determined solely on whether an athlete's TSS sits between 265 and 290. It's based on a complete analysis of several metrics. At times one or more of those metrics might or will fall outside of the recommended range.

Btw, you give high-level examples on a chart. Can you provide some examples of real-life performances with reasonable proof that the athlete has done their due diligence in determining their FTP for racing IM?

I know for a fact that those of us who use TSS have collected hundreds of IM power files from pros, top AGers and MOPers. There's common "theme" among the successful ones.

wilf said...


I fail to see how you can claim that TSS is only to be used for post race analysis, when you've produced a paper which consistently talks about TSS TARGETs.

You've been very prescriptive about it.

Matt Calarco said...

Agreed. But it would be even more fun if you wrote about the other topic you mentioned in passing: an athlete running to his or her potential. If you could debunk some of the VDOT-based pacing strategies in the process, that would be an added bonus. ;-)

Kevin said...

To be clear, I think Chris, Rick, Jason, Rich, Patrick, et al have done a great job sharing ideas on power and race execution. I can think of very little we don’t agree on when it comes to using power as a means of improving execution for some athletes over long course. My main point is that I advise athletes not to consult TSS during IM as a guide. There are too many other more accurate metrics to consult. I see some value in TSS as a signal of trends over time but not as a race tool. I should also have mentioned that I know first hand that Chris agrees with this.


Paulo Sousa said...


Thanks for the questions, I will try to address them and ramble a bit more about TSS next week.


Thanks for the entertainment, as usual, priceless stuff. Thanks to 'wilf' for reading my mind.

cramer said...


Since it looks like you'll be addressing comments, I thought I'd offer one thought I had about your curve comparison: Given that you're comparing the TSS-derived curve of a specific distance (IM) to the overall power-duration curve, I'd expect there to be some differences. After all, as we approach the limit of what is actually possible for a ride of that distance, we'd expect the curve to spike upwards. The junction of the curve with the 100% power-duration curve would mark, for all intents and purposes, the best possible bike split for the distance.

What would be interesting to consider (though it has almost zero practical use) is whether similar TSS ranges result from different distances, from sprint to Oly to HIM, etc. Ignoring for the moment the question of whether such a range will be as easily identifiable for shorter distances, the result could allow you to produce a "distance-graded" TSS curve, and I think it would be interesting to see how THAT curve would compare with the power-duration curve.

Just a thought. I obviously believe there's merit in acknowledging the tendency for well-paced IM bike rides to fall within a fairly narrow TSS range (at least, for a certain window of splits). In the end, though, we're all just trying to maintain our best possible effort while leaving enough in the tank for the run, so any predetermined "targets" must be tempered with what's actually happening around you on race day.

Thanks for the thoughts!


Paulo Sousa said...


I didn't publish your last comment because my blog is not a Forum. There was a good thread on Slowtwitch about it (!) and I didn't see you post there. If you want to debate, Slowtwitch or your own private Forum is really the place to go.

Also I think that your routine of saying you were misunderstood everytime you are challenged is getting a little old. But maybe that's just me.

Thanks for reading,


Blake Becker said...

Good stuff Paulo...I have many power files of my own that demonstrate that TSS is not always a good predictor of a good IM performance ;) KP can vouch for that one!

Lakerfan said...

No problem, Paulo. Sorry I couldn't be more helpful.

Thanks, Chris

jonnyo said...

wow...that blog was one of the most boring i have ever read from you. do me a favor and dont write back about this. I think it s time for athlete to be athlete and use there mind to figure out a few things....

scott said...

Using TSS and/or IF to create a pacing plan for athletes is not a bad concept in my opinion. However, it seems that there is an assumption that there is a universal "magic" number, or range of numbers for an athlete to shoot for.
Consider that all athletes are unique and may not fit in this "box."
Muscle fiber type and training age are just 2 factors that affect an athlete's respective rate of fatigue. This can be measured with a short and long TT to create calculate the athlete's "Rate of Fatigue."
If you are able to determine an athlete's Rate of Fatigue, you can create a Fatigue Curve that will predict the pacing strategy you seek. Then it might be wise to introduce TSS and IF to refine a pacing strategy.

Paulo Sousa said...


Hopefully by now you've read the rest of the posts on this series and realize that TSS REALLY doesn't have a place in defining a pacing strategy for racing.

Cara said...

Excellent post. This blog was one of the most favotite I have ever read from you. I think it s time for athlete to be athlete and use there mind to figure out a few things.This is my first time i visit here. Keep up this triathlon blog.