# Logic behind the TSS formula?

IF is an input to the TSS formula. Specifically, IF is squared in the formula. Why is IF squared, and not raised to a different power e.g. 1.5 or 2.5? Is there some physiological process going on in your body that justifies raising to the power of 2 specifically?

The reason I am asking this question is because of my experience with some recent rides I have done at low intensities - IF of 0.65. These rides I’ve found to be surprisingly tough, but yet they have a very low TSS - e.g. a TSS of 42 for an hour ride.

But if IF was raised to a different power, say, 1.5, the TSS for the ride would be 52 - or about 20% higher.

Feel free to skip onto the next topic if this question is too nerdy/arcane

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Have to ask Dr. Coggan, but I suspect the model is such because he thought that most closely reflects the physiological stress on the body as intensity builds. The lower the impact of IF, the more linear the stress calculation becomes, but I don’t think anyone would tell you they think a one hour ride at .5 IF is half as hard as a one hour ride at FTP. And the opposite applies as you go up above 2 and the effect becomes more drastic the higher you go.

I’d also guess that the square factor is for simplicity of calculation. Since TSS is an estimated (and rather arbitrary) measure of stress which is simply relative to your personal FTP (or HR) and not some absolute measure (where 200 TSS in a day means the same physiological impact to everyone), it is probably impractical and unnecessary to try to drill it down to whether it is more accurate at 1.5 or 2.5 or 4. The square factor seems to be pretty representative and is good enough.

The actual formula for TSS is:

TSS=[(time(s) * NP * IF)/(FTP * 3600)] * 100

So, I’d go with “simplicity” and “good enough”.

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It’s a fair question, but why stop at asking why IF is squared in calculating TSS? Going back to how normalized power is calculated, it uses (1) a rolling 30-second average (why not 1 minute? or 10 seconds?); (2) raises it to the 4th power (why not some other number); (3) sums it up over the whole ride; and (4) takes the fourth root.

I would be curious to see what empirical analysis was used to validate the formula for NP, and subsequently TSS. This is not to throw stones, but just a good reminder to not read too much into these numbers. There’s a whole bunch of ways to get to the exact same number, but each reflecting very different approaches and yielding pretty different adaptations.

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# [DaveWhelan]: Actually, ignoring the time bits and the 100, for any stretch of time, the definitional equation is

TSS = NP * IF / FTP. [eq 1]
It just so happens that IF = NP / FTP,
so, substituting in equation 1, you get the result that you are asking about:
TSS = IF^2.

So, the question is really, not why squared [^2], but what is the physiological reasoning behind the form in which NP, IF, FTP are included in equation 1.

I guess that we need to read through Coggan’s literature to work that out and to see the evidence.

It seems like you’re looking for precision where the general goal of TSS is rough calibration. That is, how do you compare 0.5 IF and 1 IF rides, are they roughly 2x as hard? 4x? 10x? From my experience 4x is reasonably close enough so using the squared term seems fine.

It’s also VERY personal, in that for some people long 0.65s are really hard, but short sprints at 1.25x are manageable, and for other (slower twitch?) athletes they can go to 0.8 IF forever but breaking `FTP causes a material decrease in performance. Use TSS as a guide and then find what works for you in the application.

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Coggan’s TSS, as I understand it’s genesis, is an adaptation of Bannister’s TrImp. TrImp was a heart rate metric & Coggan was looking for something similar but power based.

TrImp is: Time * DeltaHR * IntensityWeighting

Where DeltaHR is heart rate expressed as the increment of heart rate above some reserve heart rate.

So I think what happened when Coggan tried to transfer this from heartrate to power…he used Intensity Factor to replace IntensityWeighting. And he used NP/FTP to replace DeltaHR. And reducing the TSS formula to IF^2 was a quirk of that construction that became obvious later.

Really, Coggan’s attempt to weight TSS by IF probably wasn’t as successful as he would have hoped. TSS inherently OVERestimates lower intensity training stress and UNDERestimates higher intensity training stress. TrImp was designed to do this much less so…that was the specific intent of the TrImp IntensityWeighting term.

Also, Bannister honed his formula with a body of empirical data. I’m not convinced that Coggan did but what TSS is, is what TSS is. Maybe the best thing it has going for it is ubiquity & wide acceptance.

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I submitted a TSS feature request to TR support (prior to the existence of this calendar feature) but I don’t think it has gone anywhere. I thought it would be useful to see the TSS chart, filterable for TSS by Zone. It would be nice to monitor and plan for not just increasing your overall TSS weekly, but monitoring say Zone 2 increase versus Zone 5 increases on a weekly basis at different times of the training cycle.

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My recent rides have been pretty consistent power, where avg power is close to NP, so hadn’t gotten there - yet

I understand the concepts they are trying to capture with the TSS and NP formulas - namely weighting higher intensity rides/efforts more than lower intensity rides/efforts. But it would be interesting to know, like you say, if they used any empirical evidence in coming up with the specific formulas.

Maybe it’s as simple as “it seems to make sense, and it seems to work”. But given how much time we all spend looking at these numbers, it would be helpful to know any assumptions, limitations, possible flaws, etc.

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Yep - that’s another way to ask the question. As per above, did they have any empirical evidence they were relying on in setting the formula, or was it just “it seems to make sense and it seems to work”?

Great points: it’s an approximation and it varies by individual.

A few questions prompted by this:

1. Is there another/better way to measure training stress other than TSS? I.e. in showing TSS did not accurately measure stress, how was the training stress measured to know TSS was not accurate?

2. Is there any reading on this topic? Would be interested to see any empirical evidence that sheds more light on this.

It would be nice if there was a physiological measure of training stress, instead of relying on training load (TSS, CTL, etc).

I’ve been looking at my HRV over the past number of weeks. It seems to work OK, but not great, but I need to get more experience with it through full training cycles.

I’d imagine there may be now, or under development, a blood test to do this - but this is obviously norlt practical for everyday athletes. Maybe a saliva test similar to what is under development for lactate testing? We’ll just have to wait I guess…

Is there another/better way to measure training stress other than TSS? I.e. in showing TSS did not accurately measure stress, how was the training stress measured to know TSS was not accurate?

DaveWhelan, there are a lot of interesting answers to THAT question, for sure! I am not qualified to comment on most of them probably.

But do consider the approach that TR has taken to this problem (probably without knowing it), which is to apply a notch filter to TSS. In other words, the bulk of training stimulus TR guides it’s user base to is in a pretty narrow range of intensity factor. If we all focus most of our training on a sweet spot intensity we can be more confident that Rider A’s 350TSS week is a pretty similar training stress to Rider B’s 350TSS week.

On the other hand, if Rider A does 90% of his riding in Zone 2 while Rider B focuses on a sweet spot intensity…Rider A’s 350TSS week is going to be a very different training stress to Rider B’s 350TSS week.

In reality, it seems to me that 70% of all debate about training regiment stems from the fact that TSS UNDERreports training load at higher intensities and OVERreports training load at lower intensity. And most folks who use TSS for any period of time implicitly understand this is true. If I told you I regularly do back-to-back-to-back 600+ TSS weeks the first thing you might suspect is that I’m just spinning around in Z2/recovery for a lot of hours…because you understand that 600+ TSS at a sweet spot intensity is a LOT of training load but 600+ TSS at a Z2 intensity, while still a lot of training load, is easier to achieve.

I know for sure that Bannister published but I only have his work on an ancient medium called a ‘photocopy’.

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Maybe I’ll go to a library and see if they have it on microfiche

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That would be extremely useful for a coach or self-coached athlete building their own plans. That said, I asked in another thread if they were planning to incorporate ATL and TSB here to allow tracking, and Nate basically said he didn’t see the utility in those numbers for most people and that their training plans peaked very well, so they wouldn’t be useful. If I extrapolate that, it seems the CEO is telling us that they don’t intend TR to become a full-service platform for coaches to customize training (like WKO4 or TP), but instead TR will always be mostly based on the (very good) training plans Chad comes up with.

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I’d say two things to this:

1. I don’t think there was much empirical evidence used to come up with it given that Dr. Coggan was really forging into the dark. Look no further than the already cited fact that he based his model off of TRIMPS. The empirical data for power-based training stress simply didn’t exist when Coggan was approached to develop TSS.

2. After years of spending a lot of time looking at these numbers, and as the coaches on the podcast have said a few times, the numbers themselves are all relative and must be compared with how you feel and how you’re performing in training and racing. A few years ago, a CTL of 55 meant I was pretty fit, and a 200 TSS day put me away for a while. This past season, I crested over 100 CTL and 200 TSS was a twice a week thing. Simply basing your training and racing off of TSS/CTL misses the mark. I think it’s a pretty good indicator of vast over- or under-training, but ultimately its all about your body’s ability to absorb actual training stress, not what your TSS (or CTL) number is. Coach Chad has bristled a couple of times when people ask questions talking interchanging TSS and “training stress”, and rightly so. We shouldn’t focus so much on these numbers because it’s not an exact empircal science and so many outside factors matter.

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I’m very happy with TR, and do not expect them to change anything on how they calculate training stress, or come up with other proprietary calculations for things like training stress.

I’m just interested in educating myself so I know best how to interpret things to guide my training.

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I think TSS is relatively useful, but only when tied with results and a good sense of how those numbers are meaningful for you. That’s only really built through experience looking at numbers and comparing how you feel over time. I think basically any such metric will always be somewhat subjective rather than empirical because its meaning is different for everyone.

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There is also TRIMP, which is a heart rate equivalent training stress measurement. There are other tools out there on the Interwebs that can show you the TRIMP measurement for a workout, if you are wearing an HRM.

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I’d expect that the factoring would also vary by how an individual is currently trained, the ratios of different muscle fibers and mitocondria etc. The perfect factor for the athleet coming off base would not likely work when they’re done with build.