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Is TSS a useful parameter? (Warning: Includes Maths)
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We recently had a discussion about TSS (Training Stress Score). My criticism was that it seemed a random parameter to me. Why should half an hour at FTP equal two hours at 50%, stress-wise? In my opinion the half hour at 100% FTP is way more taxing, however one could argue that the higher volume induces some stress on other levels.

However, when taking a closer look at the formula, I realized how awfully random TSS really is:

When I ride at FTP for an hour, then at 50% for another hour, that gives me a TSS of 145.8.
Now when I ride at FTP for an hour that gives me a TSS of 100. Riding for an hour at 50% gives me 25.
That means, the overall TSS (145.8 vs 125) is quite significantly different for the same session, depending on whether or not I stop and start my bike computer mid-ride. What am I missing?

My calculation:

The formula for TSS is TSS = [(s x NP x IF) / (FTP x 3,600)] x 100, where s is the time in seconds, NP is the normalized power, FTP is the functional threshold power and IF=NP/FTP.
(Side note: I don't know why they over-complicate it like that. The above formula is equivalent to
TSS = IF² x t/h x 100, with t/h the time in hours. Seems easier to me.)

NP is basically the 4-norm (p-norm for p=4) (the 30 s average is negligible here) and therefore the overall NP of the session is NP=((a^4+b^4)/2)^(1/4), where a = 100% x FTP is the power for the first hour and b = 50% x FTP the power in the second hour.
--> NP=(1+0.5^4)^(1/4) x FTP=0.8537 x FTP
--> IF = NP/FTP = 0.8537
--> TSS = 0.8537² x 2 x 100 = 145.8

The second case (two seperate files) is easy to calculate: An hour at FTP gives TSS=1 x 1 x 100=100 by definition and for 50%, IF=0.5 and therefore TSS=0.5² x 1 x 100=25.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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Why do you think that 2 one hour sessions should be given the same score as a single 2 hour session?

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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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vps wrote:
((a^4+b^4)/2)^(1/4), where a = 100% x FTP is the power for the first hour and b = 50% x FTP the power in the second hour.
--> NP=(1+0.5^4)^(1/4) x FTP=0.8537 x FTP
--> IF = NP/FTP = 0.8537
--> TSS = 0.8537² x 2 x 100 = 145.8


Can't be arsed to do the maths properly, but is it valid for you to take FTP outside the brackets in your first line, and where are you dividing by total duration for your NP calculator? I'm guessing you just forgot to type the /2 ?

I don't know how you are taking the 4th root of a number >1 and coming away with <1.

Shouldn't it read NP = ( ( (1xFTP)^4 + (0.5xFTP)^4 )/2 )^(1/4)

Can you still simply take FTP outside the brackets when you do this? For the same reason why RMS /= average in electronics.

But it's half past midnight so I could be off.

Rich.
Last edited by: knighty76: Mar 3, 19 16:52
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [JasoninHalifax] [ In reply to ]
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JasoninHalifax wrote:
Why do you think that 2 one hour sessions should be given the same score as a single 2 hour session?

They do count that way.

There isn’t a duration multiplier at a nonlinear rate.

So 2x = x + x

I feel also that having both power as a ratio against ftp AND having IF in it double counts against you. Really killing TSS for “tempo” rides.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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vps wrote:
We recently had a discussion about TSS (Training Stress Score). My criticism was that it seemed a random parameter to me. Why should half an hour at FTP equal two hours at 50%, stress-wise? In my opinion the half hour at 100% FTP is way more taxing, however one could argue that the higher volume induces some stress on other levels.

However, when taking a closer look at the formula, I realized how awfully random TSS really is:

When I ride at FTP for an hour, then at 50% for another hour, that gives me a TSS of 145.8.
Now when I ride at FTP for an hour that gives me a TSS of 100. Riding for an hour at 50% gives me 25.
That means, the overall TSS (145.8 vs 125) is quite significantly different for the same session, depending on whether or not I stop and start my bike computer mid-ride. What am I missing?

My calculation:

The formula for TSS is TSS = [(s x NP x IF) / (FTP x 3,600)] x 100, where s is the time in seconds, NP is the normalized power, FTP is the functional threshold power and IF=NP/FTP.
(Side note: I don't know why they over-complicate it like that. The above formula is equivalent to
TSS = IF² x t/h x 100, with t/h the time in hours. Seems easier to me.)

NP is basically the 4-norm (p-norm for p=4) (the 30 s average is negligible here) and therefore the overall NP of the session is NP=((a^4+b^4)/2)^(1/4), where a = 100% x FTP is the power for the first hour and b = 50% x FTP the power in the second hour.
--> NP=(1+0.5^4)^(1/4) x FTP=0.8537 x FTP
--> IF = NP/FTP = 0.8537
--> TSS = 0.8537² x 2 x 100 = 145.8

The second case (two seperate files) is easy to calculate: An hour at FTP gives TSS=1 x 1 x 100=100 by definition and for 50%, IF=0.5 and therefore TSS=0.5² x 1 x 100=25.


Well, at first glance, you are doing your math wrong. NP should be ((1+1+.5^4)/3)^(1/4)xFTP = .91058xFTP

And then, TSS = (5400*.91058*FTP*.91058)/(FTP*3600)x100 = 124.37
TSS = (sec x NP® x IF®)/(FTP x 3600) x 100

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Ed O'Malley
www.VeloVetta.com
VeloVetta is developing AERO cycling shoes with CFD and wind tunnel testing.
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Last edited by: RowToTri: Mar 3, 19 17:24
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [knighty76] [ In reply to ]
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knighty76 wrote:

Shouldn't it read NP = ( ( (1xFTP)^4 + (0.5xFTP)^4 )/2 )^(1/4)

Nope. NP = ((FTP^4+FTP^4+(.5FTP)^4)/3)^(1/4)

-------------
Ed O'Malley
www.VeloVetta.com
VeloVetta is developing AERO cycling shoes with CFD and wind tunnel testing.
InstagramFacebook
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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It's too bad the search function for the Wattage List sucks so bad (especially since it's a Google product). We went through all of this 15 years ago so if you could search (which you can't) you'd find your exact argument from around 2003 or so.

So, to address some of your points:
1. The idea of TSS was based on TRIMPS, so the odd formulation is a heuristic form based on TRIMPS' heuristic. The simplified analytical form (IF^2*hours) is easier to calculate but harder to explain.

2. You (and many others) have been puzzled that TSS isn't additively linear. There are lots of things that aren't (for example, variance: if you took the variance of 1 hour of constant power at FTP you'd get zero, if you took the variance of another hour of constant power at 50% of FTP, you'd get zero -- but if you concatenate the two into one long ride, the variance *isn't zero!*). Likewise, if you multiply everything in that sequence by a constant, the variance doesn't change by the same constant! These may seem like odd examples, but the variance is the p-norm where p=2; and as you point out, NP is the p-norm where p=4.

3. It's sort of useful, especially given what we had available at the time, but it wasn't then nor is it now magic. And, it's sort of not useful, if you expect a single number to really tell you everything you need to know about how a ride fits into the bigger picture of training. There are lots of different measures of central tendency, including means, medians, modes, weighted means, truncated measures, etc. We don't think (at least, we shouldn't) that any single one is "right" and tells us everything. In fact, we often look at several measurements of central tendency and evaluate them in unison and in context. That's a long way of saying that TSS can be useful, but not always, and sometimes you have to consider it in the context of other measures of training load.
Last edited by: RChung: Mar 3, 19 17:33
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [RChung] [ In reply to ]
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Thanks for the answers so far.
knighty76 wrote:
Shouldn't it read NP = ( ( (1xFTP)^4 + (0.5xFTP)^4 )/2 )^(1/4)

Yes I forgot to type the "/2", but did include it in the calculation

RowToTri wrote:
Nope. NP = ((FTP^4+FTP^4+(.5FTP)^4)/3)^(1/4)


Why? One hour 100% FTP, one hour 50% FTP in my example

JasoninHalifax wrote:
Why do you think that 2 one hour sessions should be given the same score as a single 2 hour session?

Not necessarily, but if they are at the same intensity, they do exactly that. If they are at different intensities, they don't. It's just not consistent.

RChung wrote:
You (and many others) have been puzzled that TSS isn't additively linear. There are lots of things that aren't (for example, variance


Okay, I'll take this argument. But what's the point of TSS then? If it should be of any use, there should at least be some kind of consistency (not necessarily linear of course).
People do use it to track their training load, so in my understanding the same amount of training at the same intensity distribution should always lead to the same TSS, which it clearly and signficantly doesn't.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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vps wrote:

RowToTri wrote:
Nope. NP = ((FTP^4+FTP^4+(.5FTP)^4)/3)^(1/4)


Why? One hour 100% FTP, one hour 50% FTP in my example

My bad, I thought it was one hour, half an hour. Reading comprehension fail.

-------------
Ed O'Malley
www.VeloVetta.com
VeloVetta is developing AERO cycling shoes with CFD and wind tunnel testing.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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vps wrote:
Okay, I'll take this argument. But what's the point of TSS then? If it should be of any use, there should at least be some kind of consistency (not necessarily linear of course).
People do use it to track their training load, so in my understanding the same amount of training at the same intensity distribution should always lead to the same TSS, which it clearly and signficantly doesn't.

I don't think that was quite the idea -- which is a separate question than whether it successfully accomplishes what it was intended to do.

Back then we very much were concerned about how to balance off quantity and quality (or duration and intensity), and to quantify that load over time. One way to do that is simply to convert to kilojoules of work, and that's one of the first things that we tried. (That has the advantage of additivity.) It turns out that people reported that kJ of work seemed like a blunt tool, and that intense workouts both seemed harder, and also that one could see "equivalent" improvements by mixing up short intense workouts with longer less intense workouts. Part of this was in response to HIT workouts, where the kJ's of work could be (surprisingly?) low. Look at the classic original Tabata interval workout for an example, but there are others.

So that was the context. We had kJ of work, but they didn't seem to capture either the "hurt" or the "returns" of short high-intensity workouts.

Does TSS capture that well? I have mixed feelings about that (but then I have mixed feelings about Tabatas).

By the way, another discussion we had back then was about two-a-days. This might have even more applicability to triathletes, but back then we were only concerned about cyclists who did two-a-days. As you've noticed, concatenating two rides gives you different TSS than two separated rides. I don't think that has ever been satisfactorily handled, nor have 24-hour rides that cross over midnight. We did come up with a rule of thumb that if the two workouts were separated by enough time that significant (we never determined exactly what that might mean) recovery could have occurred, then they should be separated into two rides. Empirically, that meant that if you stop for a stop light or to wait for your riding partner to catch up, you don't split your ride into two. On the other hand, if you do a ride at 8 am and another at 4pm, they should count as two rides. That became known as "the beer and burrito" rule.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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Let me go the non Math route.

A parameter is more helpful when you use it regularly and are familiar with it. If we have chosen or relied on other parameters before coming to TSS, then TSS might not seem all that informative. TSS seems to be a cumulative measurement (in that it combines many elements of a ride without really detailing the nature of the ride). Rides of xxx TSS can vary greatly.

For me, miles plus detailing the workout (hills, surges, weather, group ride or solo) is worth more than recording a TSS number. I am way more familiar with the parameters of miles, time and conditions.

Parameters that I am getting to appreciate more are: FTP, IF, Cadence, Pedal balance.

TSS is a parameter that I am less familiar with so, after a ride, It's a nice to know and not a got to know. Yet, like mileage it's a number that measures a cumulative so maybe I will appreciate it over time if I start using it daily.

Indoor Triathlete - I thought I was right, until I realized I was wrong.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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I am sorry I kind of disagree with you. I am going to compare it to running as I have more experience there.

Lets say I was to do a hard tempo run maybe 1 hr 15 min total length. something in the range of 2x20 min main set of something. This hard run will equate to some TSS value. Now I also want to add more miles in for the week, so instead of doing another 30 minutes easy after the tempo run I do it later at night. That run having its own TSS value.

In my eyes a 1 hr 45 min run with tempo for 1:15 then 30 min easy is more taxing and should be a high TSS then two runs split up which should result in a lower TSS.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [trifantasy] [ In reply to ]
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trifantasy wrote:
I am sorry I kind of disagree with you. I am going to compare it to running as I have more experience there.

Lets say I was to do a hard tempo run maybe 1 hr 15 min total length. something in the range of 2x20 min main set of something. This hard run will equate to some TSS value. Now I also want to add more miles in for the week, so instead of doing another 30 minutes easy after the tempo run I do it later at night. That run having its own TSS value.

In my eyes a 1 hr 45 min run with tempo for 1:15 then 30 min easy is more taxing and should be a high TSS then two runs split up which should result in a lower TSS.

I agree with this when overall IF or NP is higher versus lower. Especially with cycling.

Example: one a day 2 hours with 1 hour HIIT and 1 hour Z2 versus two-a-days with 1 hour HIIT then some length of Z2 later in the day.

It's different energy systems. I think it works OK for TSS to work that way when accumulating for like energy systems, it doesn't seem to work well with mixes in energy systems. Particularly when you're working with fat versus surgar/ATP. Makes no difference to me to do HIIT with Z2 after OR to do HIIT then do my Z2 ride after work.

Just my personal experience. My TSS/week you'd think I could never race a bike. Reality is I can do just fine.

I take TSS with a serious grain of salt. Especially when my events are a max of 2 hours anyway in duration.

I'd rather know my TSS or CTL/ATL/TSB by ZONE than overall.
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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps] [ In reply to ]
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