# Limitations of TSS

Discussion in 'Power Training' started by bmoberg337, Nov 29, 2012.

1. ### daveryanwyoming Well-Known Member

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I can't get your link to work, but is this the same article you've looked at: http://www.twowheelblogs.com/intensity-factor-and-training-stress-score

I think part of the confusion is that yes, blood lactate levels roughly match a power^4 (closer to p^3.9 as RDO mentioned) curve but 'Stress' is not being strictly defined as blood lactate level.

In terms of NP calculations the p^4 averaging is actually closer to a RMS style A^2 averaging commonly used to analyze the average amplitude of a sinusoid but the resultant NP is not a p^4th term, the averaging is performed at the 4th power then the 4th root is used to take it back to a linear effective power term. I'm sure you know this, but the blood lactate vs. power exponent is related to this pseudo-RMS averaging and not to the definition of 'Stress'.

TSS as defined in the article above is:

TSS = exercise duration x average power x an intensity-dependent weighting factor
But yes, once you normalize it to a rider's FTP (not necessary as mentioned in the linked article but helps generalize the metric) you end up with: duration*IF^2 represented as a percentage of FTP for an hour. Some of that is just mathamatic gymnastics but the key is that TSS is not defined as a literal mapping of blood lactate level but as duration*power*intensity_weighting and it turns out that the intensity weighting is basically IF and 'power' when normalized to a rider's FTP is also IF.

From a practical standpoint a lot of folks already feel TSS overvalues short bursty efforts in that it's possible to 'inflate' TSS values by doing some very hard bursty work then padding the workout with a lot of easy time on the bike. If TSS was proportional to IF^4 that would be much more pronounced and I doubt many folks would consider that a more accurate estimate of overall stress.

I think the bigger mathematical problem with TSS is that TSS is not piecewise linear in summation as you've pointed out. Break a ride in half and in general the sum of the TSS for each half does not equal the TSS for the entire ride. That may be valid in the sense that the sustained ride offers less recovery time then two separated rides so it's possible the sustained ride actually has more stress but it's a very hard thing to prove. But the bigger problem is that CTL and ATL as long and short term daily average TSS rely on linear summations or actually averaging which implies piecewise linear summation of the individual ride TSS values. That's a bit of a head scratcher as it's hard to take a linear (or exponential as is used in WKO+) average of data values that can not be summed in a piecewise fashion and at one point Andy was talking about a TSS v2 but I haven't seen anything about that in a long time.

FWIW, you're not alone in your NP/TSS skepticism and there are plenty of outspoken coaches who dismiss the concept and prefer to track things like kj of work performed which is completely linear with average power and duration. I guess the question is whether you find NP, TSS, and from it CTL valuable in terms of guiding your training and predicting fatigue and or freshness. If so, use it, if not then there are plenty of other methods.

I do think it would be interesting to choose alternative input channels for the PMC in WKO+. IOW if you could select kj of work or say TRIMPS for folks tracking HR data or even miles or hours as the input to the PMC you'd still get a visualization of Bannister's impulse response model but could see which workload tracking metric better tracked your fatigue and freshness. IMO, the real beauty of the PMC is seeing how long term and short term average workloads trend and how they relate to each other and not strongly tied to what workload metric you prefer.

-Dave

2. ### gudujarlson New Member

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Hmm, you're right, that link does not work anymore. The article you linked, Dave, is not the same one. I've attached the article I referred to.

However, I don't think you need to read it because everything you said leads me to believe you completely understand what I'm saying.

I agree that calculating TSS so it is proportional to P^4 leads to nonsensical results. I tried it. See below.

I'm still curious why/how Andy Coggan made the leap from the lactate data fit to a generalized mean with a power of 4. That's not an obvious leap of logic to me.

Ya, I also found it curious that TSS from different rides are simply summed but stress during a ride is not. I've assumed it is just a matter of approximation. Once the events are X hours part they are considered to not be coupled but below that threshold the coupling is considered to be constant. There's no middle ground where things are lightly coupled. But it seems like that approximation might not be valid for some types of rides.

I did some playing around with a different way to calculate TSS that worked more like ATL/CTL, but I didn't get satisfactory results. I calculated TSS as the integral of a stress function. The stress function was an exponentially weighted average of all preceding power values to the power of 2. It didn't feel right because the power of 2 didn't have any basis on any physiology I am aware of, but it did agree with normal TSS for steady state efforts. Using a power of 4 gave completely unbelievable results. The calculation did give more believable values for rides like my example above, but I was not satisfied that it worked well for interval and race type efforts.

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3. ### bmoberg337 Member

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I think felt rider put it best by saying people take the terms way to literally. This was a motivating factor for me to start the thread because despite my skepticism, a lot of literature and blogs I came across seem to strictly support the accuracy of TSS and the PMC and how these tools can be used to produce freshness and fitness. IMO, TSS is no more valuable than looking at Kj expended each week. It's a number that quanitfies workload, the number itself is not important but it does provide a basis for comparison.

However, this assumes you are doing similar types of workouts each week. If I go from a low intenity base period into a high intensity build period then I'm comparing apples to oranges. The TSS equation doesn't care what kind of strain I'm causing, but my legs and body do.

4. ### An old Guy Member

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TSS is garbage. I can do 3 1 hour rides a day (1 hour ride; stop for a a drink; 1 hour ride; stop for a drink; 1 hour ride; shower; eat) at 90-95% IF. About 250TSS a day. No need for a day off.

But I have job obligations so I have been doing 2 1 hour rides a day at 95-100% IF. About 170-200 TSS.

Your math is wrong. If your 16 and 13 are close to correct, you should be getting something around 30 TSS not 147.

5. ### RChung New Member

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Hmmm. I'm getting TSS = 74.

6. ### wysinwyg New Member

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Here you go. A workout with 30-45 seconds big ring hill attacks follow by ~2 minutes recovery.

NP of 336 for the full 2 hour workout including a highest 60 minute NP of 373. If I were to just do 60 minutes I could undoubtably get higher.

My FTP is about 330. It could be 340, but there's no way it's 373.

7. ### frost New Member

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Just a side note/question, without taking strong opinion one way or another, did you do the attacks seated or standing? I think that has been discussed somewhere in the past that the additional power gained from upper body during standing effort would indeed skew/aid in creating a "NP-buster".

8. ### wysinwyg New Member

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Yeah standing. That could make sense. I come from a full-body sport background, and although I've lost ~4 kilos of upper body muscle I'm still carrying more than most cyclists.

I read somewhere that Andy Coggan's highest ever observed IF for an hour was 1.08.

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It also sounds as though your high-intensity efforts were close to 30s, which is the rolling average duration in the NP formula. This is one of the reasons that I suggested doing 1min efforts to attempt to get a 1hr NP that is signifantly in excess of your FTP (i.e., "NP-buster").

10. ### frost New Member

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I think it would be very difficult to produce a NP-buster with 1min 1:1 work/recovery ratio. If there were a formula for one it would be such that work segment is indeed quite close to 30s and recovery period is long enough to adequatly replenish the CP-stores. Then add a fast-twitcher who can put out 1kW for 30secs for starters.

Still, even if one could produce a NP-buster it by no means invalidates normalized power as a really useful tool but it would go to the same basket of PMC limitations and exceptions as if FTP should be adjusted to match environment (TT-bike, extreme heat/cold, trainer, altitude,etc) where you always should use a common sense and think what is the effect on big picture, how many TSS-points is this going to affect one way or another?

11. ### Freddy Merxury New Member

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I did a hilly group ride last year where my NP was 320+ I'll try to find the file tonight. All the hill efforts were over a minute.

12. ### gudujarlson New Member

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I think you guys are splitting hairs or, as Dave likes to blame me for, taking things too literally. TSS and NP are a gross simplification of what is really going on. Experimental results that match the model within 5-10% are better than can be expected. I think what is more important is recognizing scenarios where error might be 10x or 100x that much.

13. ### acoggan Member

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Looking through my collection of "NP busters", 1.18 is actually the highest, although the vast majority are closer to 1.10.

14. ### acoggan Member

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373/330 = 1.13, so if your FTP is indeed 330, you've clearly generated an NP buster. Indeed, even if your FTP is 340, the IF is still >1.05.

On the flip side, though: you don't mention the AP for that hour, but I'm 99.99% certain that it was less 287 W. IOW, even if the NP is an overestimate, it is still closer to the truth than the AP.

15. ### acoggan Member

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Try telling that to Shane Sutton, Tim Gerrison, and/or Bradley Wiggins. /img/vbsmilies/smilies/wink.gif

16. ### alienator Well-Known Member

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And just as before, you offer zero proof and instead just throw out personal smears. Andy Coggan has at least as much credibility as you and then some. Without proof, you've got absolutely nothing.

17. ### acoggan Member

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1. You've got that backwards: Team Sky pays to use TSS, not the other way around.

2. Once again, you're making things up.

18. ### quenya New Member

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Oh Lord, I don't know how Andy has the patience to deal with AOG. Old Guy, you've more than adequately demonstrated your total lack of; understanding of NP and the metrics derived from it, reading comprehension, and honesty. TSS is certainly garbage to you but "one man's trash is another man's treasure."

19. ### wysinwyg New Member

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Oh definitely, it was about 230.

Still it's good to realize the limitations of a tool when using it. Short, standing attacks followed by sufficient recovery seem to stress the model a bit. It would probably work better if the true power^3.9 relationship was used instead of the power^4 approximation wouldn't it?

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