Training based on TSS instead of HRS



Piotr

New Member
Jan 29, 2007
794
0
0
acoggan said:
Whoever stops for a significant period of time in the middle of a training ride? :p

WKO+ calculates TSS (and average power) based on rolling time, not clock time, so stoppages have no impact on the value.
Well, those who actually train twice a day and don't even know it. :D
 

djconnel

New Member
Apr 2, 2007
94
0
0
acoggan said:
Define "considerably". ;)

As others who have been using these metrics for quite some time have observed, Frank Holt's RATSS effect has very little impact in the big scheme of things.
If I climb @ FTP for one hour, then coast back down the hill in 20 minutes:

include the descent: 115.5
exclude the descent: 100.0
(neglecting smoothing)

TSS = 100 * ((1^4 * 60 + 0^4 * 20) / 80) ^(1/2) * 80/60 if it is included
= 100 (by definition) it's excluded

15% is worth considering.

Dan
 

daveryanwyoming

Well-Known Member
Oct 3, 2006
3,857
190
0
djconnel said:
If I climb @ FTP for one hour, then coast back down the hill in 20 minutes:...include the descent: 115.5...exclude the descent: 100.0.... 15% is worth considering....Dan
So is it your contention that the ride down hill creates no stress on the system and is the same as say lying on the couch? I guess I figure if I'm on the bike and descending a 20 minute mountain pass I'm still accumulating stress. Not as much as I was during the climb, but then NP takes that into account. I don't see a problem with TSS continuing to climb(albeit at a slower rate) as long as I'm actively riding the bike.
 

djconnel

New Member
Apr 2, 2007
94
0
0
daveryanwyoming said:
So is it your contention that the ride down hill creates no stress on the system and is the same as say lying on the couch? I guess I figure if I'm on the bike and descending a 20 minute mountain pass I'm still accumulating stress. Not as much as I was during the climb, but then NP takes that into account. I don't see a problem with TSS continuing to climb(albeit at a slower rate) as long as I'm actively riding the bike.
The formula doesn't know or care if I'm descending a gravel road in the hail or lying on the couch or doing a trackstand :). It's only calculating the stress from producing watts. Of course stress can come from many factors, not just producing power.

The key point is the Ergomo's result is substantially affected by whether it decides to exclude or include zero-power or micro-power segments from reasonable rides.

BTW, in another thread, the following TSS formula was proposed, which would be immune from this anomaly:

TSS = (100/hour) integral { (P* / FTP) ^ n dt }

where P* is smoothed power (30-second rolling average). In the proposed model, n=3.

Andrew said this had been considered before, however, so there may be a limitation.

Dan
 

daveryanwyoming

Well-Known Member
Oct 3, 2006
3,857
190
0
djconnel said:
The formula doesn't know or care if I'm descending a gravel road in the hail or lying on the couch or doing a trackstand :).....
I see your point, but the algorithm(or should I say the measurement device that drives the algorithm) definitely distinguishes the difference between being in motion on the bike vs. lying on the couch. Your previous example argues a 15% error based on the algorithm continuing to accumulate TSS on a descent. That's only a 15% error if you believe that riding downhill doesn't represent training stress. The 20 minute continuous descents around here are anything but relaxation if you want to avoid going over the guard rail :)

I do see your point about deciding to include or exclude the zero wattage samples but it only introduces an error if you argue that that periods of zero power during an ongoing ride are equivalent to rest and shouldn't be counted in a training stress score. And your example of an hour long FTP climb followed by a 20 minute no pedalling descent is a pretty extreme example of an occasional zero power moment during a ride unless your power typically drops to zero for 25% of the time you're on the bike.
 

djconnel

New Member
Apr 2, 2007
94
0
0
daveryanwyoming said:
I see your point, but the algorithm(or should I say the measurement device that drives the algorithm) definitely distinguishes the difference between being in motion on the bike vs. lying on the couch. Your previous example argues a 15% error based on the algorithm continuing to accumulate TSS on a descent. That's only a 15% error if you believe that riding downhill doesn't represent training stress. The 20 minute continuous descents around here are anything but relaxation if you want to avoid going over the guard rail :)

I do see your point about deciding to include or exclude the zero wattage samples but it only introduces an error if you argue that that periods of zero power during an ongoing ride are equivalent to rest and shouldn't be counted in a training stress score. And your example of an hour long FTP climb followed by a 20 minute no pedalling descent is a pretty extreme example of an occasional zero power moment during a ride unless your power typically drops to zero for 25% of the time you're on the bike.
The real issue is the formula (BTW, I should comment that the work Andrew, Hunter Allen, and others have done with these training metrics is fantastic; I don't want to seem too critical) is that it isn't linear with time. Neglect the 30 second average. If I do an hour at 80%, that's a TSS of 0.64. If I immediately do another hour @ 80%, the TSS is doubled, to 1.28. All is well: the TSS of the total = the sum of the TSS of the parts.

But once the power is different in different segments, this no longer applies. The total no longer equals the sum of its parts. You can't do an hour @ 80% (TSS = 0.64) + an hour @ 50% (TSS = 0.25) and get TSS = 0.89. No -- instead the TSS of that workout is 0.97. There's an "extra TSS" component which leaks in, as a result of the formula.

A result of this is adding micro-power or zero-power segments to a workout can add TSS. This creates non-intuitive results. Like if I finish the workout, then take a nap, the TSS is less than if I take the nap in the middle :). This is a pathological case (I assume!). But if we both do a century ride, and you spend an extra 2 hours at rest stops, should your TSS be higher, if we ride at the same power, and have the same FTP?

I don't doubt descending adds stress on many roads. So does weather, but weather isn't included. TSS works great, in practice, I'm sure. But it is not necessarily unique in this regard. It is possible it has potential improvement. My guess is a linear-time formula might better capture what is intended, even if TSS is already way better than miles, hours, or kJ.

Dan
 

frenchyge

New Member
Apr 3, 2005
4,687
4
0
djconnel said:
But if we both do a century ride, and you spend an extra 2 hours at rest stops, should your TSS be higher, if we ride at the same power, and have the same FTP?
I believe this has been mentioned before (probably somewhere in this very thread), but spending those extra 2 hrs sitting in the sun rolling around on the bike without additional nutritional replenishment could arguably mean more stress on the body that must be recovered from later. The person who takes 8 hrs to complete the ride probably would feel worse than the person who does it in 6 hrs. Including naps, or 8hrs spent in the office between am/pm commutes within the realm of a cycling workout seems pedantic at best.

Personally, I ctrl-x any periods of more than a few seconds of just rolling around or sitting at a long stoplight out of the file, but that's just me.
 

gvanwagner

New Member
Jan 25, 2006
134
0
0
frenchyge said:
I believe this has been mentioned before (probably somewhere in this very thread), but spending those extra 2 hrs sitting in the sun rolling around on the bike without additional nutritional replenishment could arguably mean more stress on the body that must be recovered from later. The person who takes 8 hrs to complete the ride probably would feel worse than the person who does it in 6 hrs. Including naps, or 8hrs spent in the office between am/pm commutes within the realm of a cycling workout seems pedantic at best.

Personally, I ctrl-x any periods of more than a few seconds of just rolling around or sitting at a long stoplight out of the file, but that's just me.
TSS is training stress score- and descending for 20 min isn't training. Seriously if your going to consider "zero power descending" as stressful then that opens up a whole nother load of things, weather, a long day job on your feet but none of that really should be part of trying to show the effects from your training. I think that it does changes things if your using PMC. After all different rides in different training periods will have different amounts of added TSS. If your used to doing one type of training then try to replicate your TSS in the next period then 15% represents a huge difference in the amount of actual stress your incurring.

When I do 2x20 up a local hill it works out to about 25% boost in TSS due to coasting. Whereas if Im doing SST it's in the under 3% range. So how do I go from one period to another without under or over training. I have to take that into account. What if you went from L3 to L4 building up for a peak thinking your keeping CTL high, when really your TSB just had a huge boost and you PMC graph isn't reflecting reality. Do you want to build your whole season based on PMC without taking it into account.


Greg
 

djconnel

New Member
Apr 2, 2007
94
0
0
gvanwagner said:
When I do 2x20 up a local hill it works out to about 25% boost in TSS due to coasting. Whereas if Im doing SST it's in the under 3% range. So how do I go from one period to another without under or over training. I have to take that into account. What if you went from L3 to L4 building up for a peak thinking your keeping CTL high, when really your TSB just had a huge boost and you PMC graph isn't reflecting reality. Do you want to build your whole season based on PMC without taking it into account.
Greg
The solution, I think, is to use a different TSS.

Here's the thing with TSS:

* when considering how different parts of the workout contribute relative to each other, it uses power^4.
* when considering how one workout contributes relative to another workout, it uses power^2

Why should these be different? It was proposed on another thread a balance be striked, and use power^3 for each. This creates a very simple TSS formula, which I'll call here TSS3

TSS3 = (100 / hour) integral { (P* / FTP)^3 dt }

where P* is the smoothed power.

It would be interesting to see how TSS3 compares to TSS for, for example, Robert Chung's sample data.
 

frenchyge

New Member
Apr 3, 2005
4,687
4
0
gvanwagner said:
Do you want to build your whole season based on PMC without taking it into account.
Not really, that's why I snip out any significant periods of noodling within an otherwise productive workout. I don't have any 20min descents to worry about here, but we do occassionally have to stop for a coal train. ;)
 

acoggan

Member
Jul 4, 2003
3,047
18
0
djconnel said:
in another thread, the following TSS formula was proposed, which would be immune from this anomaly:

TSS = (100/hour) integral { (P* / FTP) ^ n dt }

where P* is smoothed power (30-second rolling average). In the proposed model, n=3.

Andrew said this had been considered before, however, so there may be a limitation.

Only:

1) physiological responses seem to scale more rapidly than X^3; and

2) the current formulae for normalized power and TSS are in widespread use, such that (IMHO) any modifications have to represent a truly significant improvement to justify changing them.
 

acoggan

Member
Jul 4, 2003
3,047
18
0
djconnel said:
The real issue is the formula (BTW, I should comment that the work Andrew, Hunter Allen, and others have done with these training metrics is fantastic; I don't want to seem too critical) is that it isn't linear with time. Neglect the 30 second average. If I do an hour at 80%, that's a TSS of 0.64. If I immediately do another hour @ 80%, the TSS is doubled, to 1.28. All is well: the TSS of the total = the sum of the TSS of the parts.

But once the power is different in different segments, this no longer applies. The total no longer equals the sum of its parts. You can't do an hour @ 80% (TSS = 0.64) + an hour @ 50% (TSS = 0.25) and get TSS = 0.89. No -- instead the TSS of that workout is 0.97. There's an "extra TSS" component which leaks in, as a result of the formula.

A result of this is adding micro-power or zero-power segments to a workout can add TSS. This creates non-intuitive results. Like if I finish the workout, then take a nap, the TSS is less than if I take the nap in the middle :). This is a pathological case (I assume!). But if we both do a century ride, and you spend an extra 2 hours at rest stops, should your TSS be higher, if we ride at the same power, and have the same FTP?

I don't doubt descending adds stress on many roads. So does weather, but weather isn't included. TSS works great, in practice, I'm sure. But it is not necessarily unique in this regard. It is possible it has potential improvement. My guess is a linear-time formula might better capture what is intended, even if TSS is already way better than miles, hours, or kJ.

Dan

1) a 2 h nap in the middle of a century would have no impact on your TSS, as it is (again) calculated based on rolling time, not clock time.

2) if you check out the presentation that I recently gave to UK Sport, you'll see a slide towards the end titled "how long is long?". The point that I used it to illustrate is that all current means of quantifying training load assume that the latter increases linearly with duration.* However, there is plenty of physiological data to show that this is incorrect, i.e., the weighting should be non-linear with respect to duration (i.e., the last hour of a long ride hurts more than the first hour, even if done at the same intensity). In that regard you could actually consider the tendency of TSS to creep up over time due to periods of extended coasting to better reflect reality than a formulation that was mathematically more appealing (even though that wasn't my intent).

*Ignoring the RATSS effect in the case of TSS, that is.
 

acoggan

Member
Jul 4, 2003
3,047
18
0
gvanwagner said:
TSS is training stress score- and descending for 20 min isn't training.

It's called "training stress score" and not "training performance score" for a reason.
 

acoggan

Member
Jul 4, 2003
3,047
18
0
djconnel said:
The solution, I think, is to use a different TSS.

Here's the thing with TSS:

* when considering how different parts of the workout contribute relative to each other, it uses power^4.
* when considering how one workout contributes relative to another workout, it uses power^2

Why should these be different?

Because:

1) blood lactate (an excellent marker for global metabolic strain) scales with power^4, but

2) nobody - including me - really knows precisely how duration and intensity interact with one another, so I took the parsimonious approach of simply multiplying them together (just as a statistician would attempt to account for interactions between variables by, e.g., including their product in an ANOVA model). The fact that TSS scales with IF^2 instead of IF was merely an unintended consequence of my further decision to attempt to place everyone on the same scale (by equating things to 1 h @ functional threshold power).

As you probably realize, Dan, you are far from the first to raise these issues. What you may not realize, however, is that there are people on the other end of the spectrum who complain that normalized power and hence TSS routinely overestimate the things they are meant to measure. I therefore feel that I must have come pretty close to hitting the dead-center of the population, since I get negative feedback from both directions. ;)
 

RChung

New Member
Sep 12, 2006
306
2
0
acoggan said:
(just as a statistician would attempt to account for interactions between variables by, e.g., including their product in an ANOVA model).
I'm not sure how many modern statisticians think that this is a good way to account for interactions. When Fisher started doing things like this around 1925, he did it for practical reasons: the computational demands for doing anything more complicated were huge.
 

rmur17

New Member
Oct 5, 2004
1,066
0
0
acoggan said:
It's called "training stress score" and not "training performance score" for a reason.
wow-wee I'm staying out of this round!! I'm getting too old to argue :D
 

acoggan

Member
Jul 4, 2003
3,047
18
0
RChung said:
I'm not sure how many modern statisticians think that this is a good way to account for interactions. When Fisher started doing things like this around 1925, he did it for practical reasons: the computational demands for doing anything more complicated were huge.

Trust me, I've dealt with plenty of statisticians, and every one that I have ever met has modeled interactions that way. It's also how the commonly accepted software packages - SAS, SPSS, etc. - routinely deal with interaction effects.
 

acoggan

Member
Jul 4, 2003
3,047
18
0
rmur17 said:
wow-wee I'm staying out of this round!! I'm getting too old to argue :D

I'm not arguing, I'm making a point (in my best R. Chung cryptic style).
 

djconnel

New Member
Apr 2, 2007
94
0
0
acoggan said:
Because:

1) blood lactate (an excellent marker for global metabolic strain) scales with power^4, but

2) nobody - including me - really knows precisely how duration and intensity interact with one another, so I took the parsimonious approach of simply multiplying them together (just as a statistician would attempt to account for interactions between variables by, e.g., including their product in an ANOVA model). The fact that TSS scales with IF^2 instead of IF was merely an unintended consequence of my further decision to attempt to place everyone on the same scale (by equating things to 1 h @ functional threshold power).

As you probably realize, Dan, you are far from the first to raise these issues.
As I noted, it was mentioned here in another thread:
http://www.cyclingforums.com/showpost.php?p=3103388&postcount=86

Inertia imposed by existing infrastructure aside (I'm wirting my own Perl script for my own use, so for me there's no inertia), it's still interesting and fun to consider how the metric may be improved. The "obvious" approach would have been TSS = (100/hour) integral { (P/FTP)^4 dt }, but I you note this seems to over-weight high intensity, short time, versus long time, lower intensity. (P/FTP)^3 may be a reasonable "compromise".

Another option might be a history dependence. There's already history dependence from the 30-second rolling average, but something longer-term, something in the style of ATL For example, This would also address your point that doubling the duration of a workout at the same power may more than double the stress, while TSS only doubles, neglecting the 30 second average.

For example, introduce a parameter, F:

F(t + dt) = F(t) * (1 - dt/T) + dt/hour * (P(t)/FTP)^4

where T is some time constant (1 hour?) . If you'd been producing 100% FTP work for many T, F would approach 1.

Then you could generate an F-dependence to training stress. For example:

TSS(t + dt) = TSS(t) + (K/hour) (1 + F(t))^2 (P(t) / FTP)**4

where K is a normalization constant (for T=1hour, K=52.5). The power 2 there is just an example.

This results in the following TSS scores for 100% FTP work starting fresh:
15 minutes: 16.4
30 minutes: 39.0
60 minutes: 100.0
2 hours (!!!) : 264.2

A result of this is given two interval workouts,one with more soft-pedaling between identical intervals, the one with less recovery will have a higher TSS, as opposed to the present definition, in which the one with more recovery has the higher score.

Of course, I'm hardly bold enough to claim this is a suitable formula. It's probably highly flawed. Any added complexity needs to be justified against scientific data. But following the lead of the ATL-CTL model may be a good approach to handling interactions between components of a given workout.

Dan
 

acoggan

Member
Jul 4, 2003
3,047
18
0
djconnel said:
it's still interesting and fun to consider how the metric may be improved.

Well sure...and given your penchant for math, I'm a bit surprised that you've only recently jumped on the bandwagon with the rest of us. ;)

djconnel said:
Another option might be a history dependence. There's already history dependence from the 30-second rolling average, but something longer-term, something in the style of ATL For example, This would also address your point that doubling the duration of a workout at the same power may more than double the stress, while TSS only doubles, neglecting the 30 second average.

For example, introduce a parameter, F:

F(t + dt) = F(t) * (1 - dt/T) + dt/hour * (P(t)/FTP)^4

where T is some time constant (1 hour?) . If you'd been producing 100% FTP work for many T, F would approach 1.

Then you could generate an F-dependence to training stress. For example:

TSS(t + dt) = TSS(t) + (K/hour) (1 + F(t))^2 (P(t) / FTP)**4

where K is a normalization constant (for T=1hour, K=52.5). The power 2 there is just an example.

This results in the following TSS scores for 100% FTP work starting fresh:
15 minutes: 16.4
30 minutes: 39.0
60 minutes: 100.0
2 hours (!!!) : 264.2

That's an interesting, and rather novel, idea...you could choose T such that the weighting with respect to time reflects, e.g., the increase in catecholamine levels (as a marker of overall physiological strain) over time during exercise at a constant intensity.