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a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS
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Over on the " Graphical Representation of Training Load & Adaptation" thread, a few people have been critical of Dr. Steve McGregor's normalized graded pace (NGP)/rTSS calculation (http://home.trainingpeaks.com/...rmalized-graded-pace). As it so happens, he and I chatted for about an hour yesterday, during which he made the point that rolling NGP should be essentially equivalent to Stryd's estimated running power. Since I'm doing a free webinar tonight on the use of WKO4 to analyze running data (https://attendee.gotowebinar.com/.../6892692532430862082), I thought I'd throw together a new chart to test Steve's hypothesis.

The pic below shows some typical results. As you can see, generally speaking rolling normalized graded speed (i.e., the inverse of rolling NGP, shown as a purple line) and power-to-weight ratio (shown as a yellow line) parallel each other rather nicely. The biggest difference would seem to be during the long, gradual downhill between ~27 and ~38 min, during which NGP seems to give more credit to the effects of gravity than does Stryd's algorithm. Based on the heart rate response, you could argue that the directly-measured power may be closer to the truth, but I'm not sure that is really a valid conclusion, given the influence of cardiac drift, etc.

So what does this mean for rTSS? As a first approximation/corollary to TSS, I think these data suggest that Steve's approach is actually rather good (note that rTSS also includes a correction or adjustment for VO2 drift, i.e., the formula is a bit more complicated than for plain ol' TSS). IOW, for a pure runner, using rTSS as an input to the PMC definitely has merit (as Steve has shown: https://www.ncbi.nlm.nih.gov/pubmed/19910822). However, this still doesn't mean you can or should add TSS and rTSS, since the stresses created by cycling and running are not equivalent.

ETA: Note that I smoothed the power/weight data using an exponentially-weighted moving average. I don't know if NGP uses a rolling or exponentially-weight average, but for visual comparison at least it doesn't really matter.


Last edited by: Andrew Coggan: Apr 28, 16 12:49
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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Andrew Coggan wrote:
I smoothed the power/weight data using an exponentially-weighted moving average.

I find this exceptionally ironic.
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
Andrew Coggan wrote:
I smoothed the power/weight data using an exponentially-weighted moving average.

I find this exceptionally ironic.

Why? I've always pointed out that 1) it makes more sense from a physiological perspective, but 2) practically-speaking, a simple rolling average works just as well.* The only reason I used an exponentially-weighted moving average in this case is that I thought that was how NGP was calculated (turns out it is calculated just like NP).

ETA: *As I determined when developing the original NP algorithm back in 2003.
Last edited by: Andrew Coggan: Apr 29, 16 5:28
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
Andrew Coggan wrote:
I smoothed the power/weight data using an exponentially-weighted moving average.


I find this exceptionally ironic.

Why? An EMWA is just an IIR filter to remove high frequency sampling noise.

Checkout http://www.iotexpert.com
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [alanhawse] [ In reply to ]
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I know what it is.

See: Skiba's xPower exponential moving average vs. Coggan's Normalized Power linear moving average
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
I know what it is.

See: Skiba's xPower exponential moving average vs. Coggan's Normalized Power linear moving average

Yes. Phil utilized an exponentially-weighted moving average to differentiate his xPower from the original normalized power, which had been trademarked by TrainingPeaks.

As I've said before (and above), though, I tested both approaches when developing normalized power, and it doesn't really make a significant difference.
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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I still don't understand why I can go for a really
Hilly run at 5:40/km average and it gives me the same NGP and rTSs as 5:40/km for the same amount of time in a flat course.

Am I being dense?
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [T1mbro] [ In reply to ]
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T1mbro wrote:
I still don't understand why I can go for a really
Hilly run at 5:40/km average and it gives me the same NGP and rTSs as 5:40/km for the same amount of time in a flat course.

Am I being dense?

How long does it take to run up and down each hill?
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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Not sure if that response is trying to make me realise I am seeing it all wrong or a genuine question but on my route normally it's a 15min up and another 15min up and a 15min down with some rolling terrain in between.
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [T1mbro] [ In reply to ]
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Your barometric altimeter is broken? What does the elevation in your file say?
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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It says 700m up 700m down (roughly) which looks accurate
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [T1mbro] [ In reply to ]
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T1mbro wrote:
Not sure if that response is trying to make me realise I am seeing it all wrong or a genuine question but on my route normally it's a 15min up and another 15min up and a 15min down with some rolling terrain in between.

Step 1 in the normalized power algorithm (and also in the normalized graded pace algorithm) is to first smooth the data using a 30 s rolling average. The logic for that is described in this post:

http://lists.topica.com/...ort=d&start=9353

but the effect would be to make any really short ups-and-downs "disappear." Turns out that's not the explanation, but it is why I asked.
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [T1mbro] [ In reply to ]
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T1mbro wrote:
I still don't understand why I can go for a really
Hilly run at 5:40/km average and it gives me the same NGP and rTSs as 5:40/km for the same amount of time in a flat course.

Am I being dense?

So, next honest question: are you analyzing your data using TrainingPeaks, or WKO4?
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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Ah thanks! Good to know that too
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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Andrew Coggan wrote:
T1mbro wrote:
I still don't understand why I can go for a really
Hilly run at 5:40/km average and it gives me the same NGP and rTSs as 5:40/km for the same amount of time in a flat course.

Am I being dense?

So, next honest question: are you analyzing your data using TrainingPeaks, or WKO4?

Wko4
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [T1mbro] [ In reply to ]
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T1mbro wrote:
Andrew Coggan wrote:
T1mbro wrote:
I still don't understand why I can go for a really
Hilly run at 5:40/km average and it gives me the same NGP and rTSs as 5:40/km for the same amount of time in a flat course.

Am I being dense?

So, next honest question: are you analyzing your data using TrainingPeaks, or WKO4?

Wko4

Well then something's not right, because it works just fine for me. Possible explanations might be:

1. You've got an old build of the program, which perhaps didn't handle NGP properly (not that I'm aware that that was ever an issue);

2. You've got a recent build of the program (build 280 just came out today), but your chart files is dates/munged; or

3. There is something wrong with your file(s), such that WKO4 can't do the calculation of NGP properly.

Your best bet would be to put in a support ticket to TrainingPeaks, or reach out to Tim Cusick directly via the WKO4 FB page, and let them take it from there.
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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Andrew Coggan wrote:
T1mbro wrote:
Not sure if that response is trying to make me realise I am seeing it all wrong or a genuine question but on my route normally it's a 15min up and another 15min up and a 15min down with some rolling terrain in between.

Step 1 in the normalized power algorithm (and also in the normalized graded pace algorithm) is to first smooth the data using a 30 s rolling average. The logic for that is described in this post:

http://lists.topica.com/...ort=d&start=9353

but the effect would be to make any really short ups-and-downs "disappear." Turns out that's not the explanation, but it is why I asked.

And this is precisely why NGP is going to be next to be really misleading in helping you quantify the training stress associated with your 200m interval workout. As well as any sort of punch my hills, short bursts, and other elements common in trail running and other types of highly stochastic running. Not to mention I could be running in quicksand or a running track and the training stress would read the same if the quicksand was flat.

30 second linear moving average or 25 second EWMA: both make a lot of sense just because of the nature of power meter single second data. They make less sense in running. Just my opinion
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [T1mbro] [ In reply to ]
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Your BEST bet would be to sign up for Strava premium and use their Grade Adjusted Pace algorithm (GAP). It's not perfect, particularly on steep descents and quick rollers, but IME it is significantly better than NGP
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
Just my opinion

...which is based on? Feel? Gut instinct? Scientific research using high-resolution tri-axial accelerometers and some fancy math?
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
Your BEST bet would be to sign up for Strava

Ah, yes, Strava, that icon of novel thinking and accurate algorithms. ;)
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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Andrew Coggan wrote:
kileyay wrote:
Your BEST bet would be to sign up for Strava

Ah, yes, Strava, that icon of novel thinking and accurate algorithms. ;)

Since you are fond of replying to me with abstruse scientific journal articles, here is the basis for Strava's algorithm....just sayin

[1] Davies, C.T.M. et al. (1974). The Physiological Responses to Running Downhill. Journal of Applied Physiology 32, 187-194.

[2] Davies, C.T.M. (1980). Effects of wind assistance and resistance on the forward motion of a runner. Journal of Applied Physiology 48, 702-709.

[3] Minetti, A. E. et al. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology 93, 1039-1046.
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
Andrew Coggan wrote:
kileyay wrote:
Your BEST bet would be to sign up for Strava

Ah, yes, Strava, that icon of novel thinking and accurate algorithms. ;)

Since you are fond of replying to me with abstruse scientific journal articles, here is the basis for Strava's algorithm....just sayin

[1] Davies, C.T.M. et al. (1974). The Physiological Responses to Running Downhill. Journal of Applied Physiology 32, 187-194.

[2] Davies, C.T.M. (1980). Effects of wind assistance and resistance on the forward motion of a runner. Journal of Applied Physiology 48, 702-709.

[3] Minetti, A. E. et al. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology 93, 1039-1046.

Yup, read 'em all. You'll note, however, that #2 isn't particularly important in this context, because the effects of wind on the energetics of running are rather small. Similarly, I wouldn't put too much faith in Minetti's equations, which have been questioned by, e.g, Kram. It doesn't surprise me, though, that Strava thinks that they can link the two, and thus come up with an accurate algorithm (Strava is obviously strong on coding, but weak on science).
Last edited by: Andrew Coggan: Apr 29, 16 11:16
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [kileyay] [ In reply to ]
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kileyay wrote:
I know what it is.

See: Skiba's xPower exponential moving average vs. Coggan's Normalized Power linear moving average

I guess Im surprised that there would be a hill of beans difference in two low pass filters.

I didn't look... what is the cut-off frequency of the two filter configurations?

I remember a few years ago Dr. Coggan said that there was some PM that he thought was better because it could sample at 100hz? instead of 60hz? At the time I thought maybe that was curious because both of those sampling frequencies are way down on the edge of human perception. But maybe.

What is the fundamental frequency of the power signal?

Checkout http://www.iotexpert.com
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [alanhawse] [ In reply to ]
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alanhawse wrote:
kileyay wrote:
I know what it is.

See: Skiba's xPower exponential moving average vs. Coggan's Normalized Power linear moving average

I guess Im surprised that there would be a hill of beans difference in two low pass filters.

There isn't.

alanhawse wrote:
I didn't look... what is the cut-off frequency of the two filter configurations?

Normalized power uses a 30 s rolling average. xPower uses an exponentially-weighted moving average with a 25 s time constant.

alanhawse wrote:
I remember a few years ago Dr. Coggan said that there was some PM that he thought was better because it could sample at 100hz? instead of 60hz? At the time I thought maybe that was curious because both of those sampling frequencies are way down on the edge of human perception. But maybe.

That wouldn't have been me, unless perhaps I was comparing the event-based SRM (which happens to sample at 200 Hz) to the time-based PowerTap (which happens to sample at 60 Hz) on other criteria?

alanhawse wrote:
What is the fundamental frequency of the power signal?

I'm not sure how to answer that question. Or, rather, perhaps that's not the question to be asked?
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Re: a few semi-random thoughts on Dr. Steve McGregor's normalized graded pace and rTSS [Andrew Coggan] [ In reply to ]
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alanhawse wrote:
What is the fundamental frequency of the power signal?


Quote:
I'm not sure how to answer that question. Or, rather, perhaps that's not the question to be asked?


In digital signal processing, the Shannon-Nyquist Theorem says (from the very nicely written Wikipedia page) "Sampling is a process of converting a signal (for example, a function of continuous time and/or space) into a numeric sequence (a function of discrete time and/or space). Shannon's version of the theorem states:[2] If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart. A sufficient sample-rate is therefore 2B samples/second, or anything larger. Equivalently, for a given sample rate fs, perfect reconstruction is guaranteed possible for a bandlimit B < fs/2."

In hindsight I think that i should have said "What is the maximum frequency of the human power "signal"?

So, my question is... for a human power... what is "B"? It is bound to be less than a few hundred hz.

Checkout http://www.iotexpert.com
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