Losing faith in normalized power...



acoggan

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Tom Anhalt said:
Here's the way I think of it: TSS isn't "additive" over segments because the total NP is not equivalent to the average of the NPs of the segments.

This is because taking the "4th root of the average of the sum of the powers^4" over the whole range is NOT equivalent to the average of the sum of any subsets of "4th root of the average of the sum of the powers^4". For example:

(( a^4 + b^4 + c^4 + d^4)/4 )^0.25 does NOT = (((a^4 + b^4)/2)^0.25 + ((c^4 + d^4)/2)^0.25)/2

Since TSS is calculated from the NP, FTP and time....you can see that the only way TSS could be "additive" is if the NP of the whole ride was equal to the average of the NP of the segments. Make any sense?

Yes, which is why I replied to beerco as I did (think about it).
 

SolarEnergy

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JohnMeyers said:
Has anyone looked at that other file that goofy "JohnMeyers" fellow posted as further evidence to his point?

:p

Seriously though, this is all in good fun--a learning experience (hopefully) for everyone.
Yesterday I began taking a closer look to one of the file.

As I said earlier. I find the max 20s at 1043w, 97rpm, acceleration from 21 to 27mph (over 20s) a bit suspect.

Take the minute at 1hr35m something seconds... Power goes from 118w, to 1180w (instantaneous) down to 0w

Total time spent over 1000 is 65 seconds
Total time spent over 800w is more than 2 minutes

You were either very fresh, or some of the >1000 numbers (like the ones occuring at 1hr35m) are example of garbage data. Kilo garbage number hurt NP very very bad.

On the other hand, you spent 2665secs between 1 and 99watts. More than 60minutes between 1 and 150w.

Not saying your complain is not justified, but keep a eye on the global picture. It's hard to evaluate a ride by RPE for this ride only. Sometimes, during a workout, I finger tap on my display. Stop. Zero the torque. In other words, I even question AP.

I'll continue this "learning experience" tonight.
 

frenchyge

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doctorSpoc said:
"Correct me if I am wrong, but I interpreted normalized power to be an estimation of what power I would have to keep at a steady state to emulate the same percieved level of exertion." ...and no one corrected him, that would have likely went a long way in setting him on the right path..

but anyways...
Yeah, I saw that too as I was flipping back. Physiological strain and perceived level of exertion sound pretty similar, but it probably would have helped to have clearly made that distinction.
 

frenchyge

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JohnMeyers said:
Has anyone looked at that other file that goofy "JohnMeyers" fellow posted as further evidence to his point?
I'm seeing a 55min effort at 336w NP (281w AP) with 11 30-sec attacks of 600-800w in that file. Notes say "decently tough little workout!" That's compared to the other file with 283w NP (191w AP) and 10 attacks over 600w over 2.5 hours real time, where the noted exertion was much lower.

I'm really not trying to be a jerk here, but I don't see how the 10/27 file helps show that NP doesn't reflect the physiological cost of a variable power ride well. In that ride, the strength of your attacks (and even the steady power in between) is diminishing steadily between 20-45 minutes, until the final push, so it appears that you were having a pretty tough time of it (and certainly tougher than the 281w AP would suggest), but still found something for a 2.5 min leadout into the final sprint.

The final ride NP says you were 3.8% over your estimated steady state 1 hr power for a variable ride with a 1.2 VI, which I don't think is bad, considering the nature of this ride. How have you been determining FTP?

JohnMeyers said:
Seriously though, this is all in good fun--a learning experience (hopefully) for everyone.
Definitely. No worries. :)
 

Uhl

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I'm with SolarEnergy, I think the power meter was acting up on the 11/22 ride. In addition to the odd spikes mentioned, there are tons of data dropouts. Maybe the batteries were going?

Just curious, what kind of power meter was it?
 

ahaile

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Tom Anhalt said:
Here's the way I think of it: TSS isn't "additive" over segments because the total NP is not equivalent to the average of the NPs of the segments.

Well, total NP *Is* equal to the average of the NPs of the segments if you use a 4th-order average. I can spell it out with an example. To make it easy, lets say we have two segments, 1 and 2, and that each has just two samples:

NP1 = ((a^4 + b^4) / 2)^0.25
NP2 = ((c^4 + d^4) / 2)^0.25

Call the NP of the whole ride NP12, which would be:

NP12 = ((a^4 + b^4 + c^4 + d^4) / 4)^0.25

If we isolate the sum on the right hand side of the NP1 and NP2 equations, we get:

2 * NP1^4 = a^4 + b^4
2 * NP2^4 = d^4 + c^4

Substituting those into the equation for NP12 gives:

NP12 = ((2 * NP1^4 + 2 * NP2^4) / 4)^0.25
NP12 = ((NP1^4 + NP2^4) / 2)^0.25
NP12 = Avg^4(NP1, NP2)

If the two segments aren't of equal length, then the average needs to be weighted by their relative durations, but it works out the same.

rmur was right that the reason TSS isn't additive is b/c of the mismatch in the exponents between the NP formula (4th order) and the TSS formula (2nd order). TSS is IF^2 * T. Imagine instead that it was IF^4 * T. Then, TSS1 (using the same segment 1 as above) would be:

TSS1 = IF1 ^ 4 * T1

Substitute in IF = NP/FT:

TSS1 = NP1^4 / FT^4 * T1

Substitute in the definition of NP1 from above:

TSS1 = (((a^4 + b^4) / 2)^0.25)^4 / FT^4 * T1

Simplify the (...^0.25)^4:

TSS1 = ((a^4 + b^4) / 2) / FT^4 * T1

T1 = 2 if we assume a sample rate of 1hz (even if we don't it's just a constant difference), so:

TSS1 = (a^4 + b^4) / FT^4

By the same logic:

TSS2 = (c^4 + d^4) / FT^4
TSS12 = (a^4 + b^4 + c^4 + d^4) / FT^4

Summing TSS1 and TSS2 gives:

TSS1 + TSS2 = (a^4 + b^4) / FT^4 + (c^4 + d^4) / FT^4
TSS1 + TSS2 = (a^4 + b^4 + c^4 + d^4) / FT^4

But that's the definition of TSS12 above, so:

TSS1 + TSS2 = TSS12

Ergo, it's additive.

As for whether these equations are right or wrong or inflate or deflate, I've got no opinion. I'm just handy with the numbers ;)
 

rmur17

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Oct 5, 2004
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ahaile said:
Well, total NP *Is* equal to the average of the NPs of the segments if you use a 4th-order average. I can spell it out with an example. To make it easy, lets say we have two segments, 1 and 2, and that each has just two samples:

NP1 = ((a^4 + b^4) / 2)^0.25
NP2 = ((c^4 + d^4) / 2)^0.25

Call the NP of the whole ride NP12, which would be:

NP12 = ((a^4 + b^4 + c^4 + d^4) / 4)^0.25

If we isolate the sum on the right hand side of the NP1 and NP2 equations, we get:

2 * NP1^4 = a^4 + b^4
2 * NP2^4 = d^4 + c^4

Substituting those into the equation for NP12 gives:

NP12 = ((2 * NP1^4 + 2 * NP2^4) / 4)^0.25
NP12 = ((NP1^4 + NP2^4) / 2)^0.25
NP12 = Avg^4(NP1, NP2)

If the two segments aren't of equal length, then the average needs to be weighted by their relative durations, but it works out the same.

rmur was right that the reason TSS isn't additive is b/c of the mismatch in the exponents between the NP formula (4th order) and the TSS formula (2nd order). TSS is IF^2 * T. Imagine instead that it was IF^4 * T. Then, TSS1 (using the same segment 1 as above) would be:

TSS1 = IF1 ^ 4 * T1

Substitute in IF = NP/FT:

TSS1 = NP1^4 / FT^4 * T1

Substitute in the definition of NP1 from above:

TSS1 = (((a^4 + b^4) / 2)^0.25)^4 / FT^4 * T1

Simplify the (...^0.25)^4:

TSS1 = ((a^4 + b^4) / 2) / FT^4 * T1

T1 = 2 if we assume a sample rate of 1hz (even if we don't it's just a constant difference), so:

TSS1 = (a^4 + b^4) / FT^4

By the same logic:

TSS2 = (c^4 + d^4) / FT^4
TSS12 = (a^4 + b^4 + c^4 + d^4) / FT^4

Summing TSS1 and TSS2 gives:

TSS1 + TSS2 = (a^4 + b^4) / FT^4 + (c^4 + d^4) / FT^4
TSS1 + TSS2 = (a^4 + b^4 + c^4 + d^4) / FT^4

But that's the definition of TSS12 above, so:

TSS1 + TSS2 = TSS12

Ergo, it's additive.

As for whether these equations are right or wrong or inflate or deflate, I've got no opinion. I'm just handy with the numbers ;)
Now why couldn't I have posted that :) ? How about we just use ^3 for both and call it even? :)
 

Las Montanas

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Dec 19, 2005
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Uhl said:
I'm with SolarEnergy, I think the power meter was acting up on the 11/22 ride. In addition to the odd spikes mentioned, there are tons of data dropouts. Maybe the batteries were going?

Just curious, what kind of power meter was it?
He uses a PowerTap SL, if I'm not mistaken.
 

RipVanCommittee

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Nov 3, 2005
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acoggan said:
I would say that my experience agrees with yours: to be able to generate an 'NP buster', you need to have a high neuromuscular power and a high anaerobic capacity.
Well, I wonder how much the neuromuscular component contributes to it, and how much is just a byproduct of people with high 30-40 second power typically having high neuromuscular power? I ask for 2 reasons:
1) the rider I've seen produce the most NP busters has relatively low neuromuscular power (15.5 w/kg), but relatively high 30 second power (12 w/kg). He's regularly able to produce rides of over an hour that are 12 to almost 15% over his FTP (I've actually sent you a couple a while back).
2) I actually have relatively (to him at least) high neuromuscular power (18.5 w/kg), and quite low 30 second power (9.6 w/kg). I have never produced an NP busting file--as a matter of fact, a really hard hour race tracks with 2-3% of my actual FTP. This, despite doing the same races as the previous rider.

Lastly, at least according to the monad model, using durations of 3 and 12 minutes, my "AWC" is actually relatively high (350+ or so)--but my AWC is 'high' based more on the fact that my values at 1.5-3 minutes are high. In other words, if one has a "long-burning" AWC, verus a "big burst" AWC, it doesn't seem to affect the algorithm in the same way? (sorry to confuse you with these highly scientific terms:D).


Moreover, by necessity the algorithm must be "one size fits all", as no other approach is really workable...
Is it, though? I'm just thinking out loud here--so feel free to tell me if I'm being an idiot. Wouldn't there be some way to do one of the follows things:

1) Allow the user to put in their peak values (just as they put in FTP) over certain short durations, and have the algorithm weight short efforts differently depending on those values?

2) Kinda like those 'smart transmissions', could the program have an option (in addition to the above) to LOOK at past files say from the last 30 and 90 days (weighted differently, of course, placing more weight on the more recent ones), and estimate peak power at the shorter durations, then incorporate that logic into the differential weighting of shorter efforts??

Just some thoughts.

Again, as you said, and with which I agree: "just because something isn't perfect, doesn't mean it isn't useful".

A corrolary to that would be "just because something is useful, doesn't mean we can't work to improve it".

Oh yeah, for the buck a copy you're getting, I'm leaving the heavy lifting to you.:D:D:D
 

doctorSpoc

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RipVanCommittee said:
...He's regularly able to produce rides of over an hour that are 12 to almost 15% over his FTP (I've actually sent you a couple a while back)...
then by definition, his FTP is 12-15% higher than he thinks it is... may be more since you said more than an hour.
 

RipVanCommittee

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doctorSpoc said:
then by definition, his FTP is 12-15% higher than he thinks it is... may be more since you said more than an hour.
Umm..no, it isn't. By 12-15% over his FTP, I meant the normalized power not the ave. power was 12-15% over his FTP. Sorry I wasn't more clear on that part.

He's done enough solid 1 hour efforts that I have a pretty good handle on his FTP. His 20 minute test power isn't even as high as the NP from some 90 minute races.
 

doctorSpoc

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RipVanCommittee said:
Umm..no, it isn't. By 12-15% over his FTP, I meant the normalized power not the ave. power was 12-15% over his FTP. Sorry I wasn't more clear on that part.

He's done enough solid 1 hour efforts that I have a pretty good handle on his FTP. His 20 minute test power isn't even as high as the NP from some 90 minute races.
oh.. ok... i was kinda scratching my head without that NP in there.. sp NP for a highly variable intensity ride of 1hr+

i guess one usually thinks of high neuromuscular power and good AWC as going together but... i would agree too that it's seem like it's really AWC that would make for a good NP buster.. not neuromuscular power per se, even though neuromuscular power proably helps in the AWC department..
 

otb4evr

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RipVanCommittee said:
Umm..no, it isn't. By 12-15% over his FTP, I meant the normalized power not the ave. power was 12-15% over his FTP. Sorry I wasn't more clear on that part.

He's done enough solid 1 hour efforts that I have a pretty good handle on his FTP. His 20 minute test power isn't even as high as the NP from some 90 minute races.
Would it make more sense to do a MAP test on this individual to get a handle on their FTP?

http://www.cyclingnews.com/fitness/?id=powerstern

Jim
 

acoggan

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doctorSpoc said:
i would agree too that it's seem like it's really AWC that would make for a good NP buster.. not neuromuscular power per se, even though neuromuscular power proably helps in the AWC department..

FWIW, that's not evident in any of the data I've collected. For example, my wife has (had) an anaerobic work capacity that would put everyone else's to shame, yet she never generated an 'NP buster', despite, e.g., doing lots of interval training sessions that would apparently enhance this possibility.
 

acoggan

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RipVanCommittee said:
Well, I wonder how much the neuromuscular component contributes to it, and how much is just a byproduct of people with high 30-40 second power typically having high neuromuscular power?

As I have always tried to emphasize, there is no duration at which the power one can generate is a 'pure' measure of anything. In particular, ~30 s is a duration that is really neither here nor there, in that it is clearly impacted by both neuromuscular power and anaerobic capacity (and in my experience at least, roughly equally). So, what you refer to as a 'big burst' anaerobic work capacity I tend to think of as really reflecting neuromuscular power, at least in the context of the normalized power algorithm, since individuals with a very high anaerobic work capacity defined using critical power approach (which is the next best thing to lab testing) but with a low neuromuscular power (e.g., my wife) don't seem to have a propensity for 'busting the algorithm'. OTOH, being able to generate a high power for only a few seconds doesn't mean you can bust the algorithm either...you need to be able to maintain the power for longer than that, and repeat that effort quite frequently.

Anyway, I think we're seeing/saying the same thing here...just labeling it differently.

(BTW, who are you? It would be helpful to me to be able to associate your comments with the files you've sent me.)

RipVanCommittee said:
I'm just thinking out loud here--so feel free to tell me if I'm being an idiot.

Okay, you're an idiot. ;) (Kidding!!)


RipVanCommittee said:
Wouldn't there be some way to do one of the follows things:

1) Allow the user to put in their peak values (just as they put in FTP) over certain short durations, and have the algorithm weight short efforts differently depending on those values?

2) Kinda like those 'smart transmissions', could the program have an option (in addition to the above) to LOOK at past files say from the last 30 and 90 days (weighted differently, of course, placing more weight on the more recent ones), and estimate peak power at the shorter durations, then incorporate that logic into the differential weighting of shorter efforts??

Just some thoughts.

Again, as you said, and with which I agree: "just because something isn't perfect, doesn't mean it isn't useful".

A corrolary to that would be "just because something is useful, doesn't mean we can't work to improve it".

Oh yeah, for the buck a copy you're getting, I'm leaving the heavy lifting to you.:D:D:D

Almost anything is possible provided you throw enough resources at it. To date, however, no one (myself included) has really come up with a significant improvement on the original algorithm that clearly works better across the board, and I don't see the point in changing things just for the sake of change.
 

gza

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acoggan said:
For example, my wife has (had) an anaerobic work capacity that would put everyone else's to shame
Have you tested your kids yet to see which parent they take after most of all? ;-)
 

RipVanCommittee

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otb4evr said:
Would it make more sense to do a MAP test on this individual to get a handle on their FTP?

http://www.cyclingnews.com/fitness/?id=powerstern

Jim
No, having complete files for 2 years, along with 40K TTs and hour long hill climb TT's is really the most solid predictor of FTP, IMO. After all, a MAP test is still a 'predictor' of performance, where as a 55 minute hill climb is, well, pretty close to the definition of FTP.

p.s. to Andy--I send an e-mail to you with the info on the files I sent.