CP - Mean Max NP Curve

djconnel

Well, exponential averaging time constants are equivalent to a rolling average approximately twice as long, if you match the average age of the data contributing to the current average (= the time constant for exponential smoothing, = half the smoothing window for a rolling average), so the time constant in the default formula is arguably half of what it should be based on this criterion.

There's typically a transition in maximal power versus time, where it goes from steep (closer to conserved work) to gradual (closer to fixed power, gradually decaying with duration). The goal is to keep the steep part in the smoothing regime, which inhibits short intense efforts embedded within a longer workout from being extrapolated out to 1 hour and over-predicting FTP. Without smoothing, doubling the effort results in a 0.5^(1/n) reduction in power. With dominant smoothing, doubling the effort halves the available power. So the smoothing constant defines where the transition occurs.

When I get the time, I'm going to look at the effective maximal power curve consistent with different smoothing constants and exponents, and compare these with actual data.

Not now, though... I REALLY need to get back to work .

Dan

acoggan

Right...but:

1) why should my initial choice of a 30 s rolling average influence the time constant you use for an exponentially-weighted moving average if one is approaching the question anew based on first principles?

2) in practice, I've found that the use a 30 s rolling average and an exponentially-weighted moving average using a time constant of 25 s give nearly identical results. (That is, I analyzed a large number of files to determine the time constant of an exponentially weighted moving average that would most closely match the values obtained using a 30 s rolling average, and the overall mean value was 25 s.)



One factor to keep in mind when pursuing this line of reasoning is that even after smoothing, the power-duration relationship isn't very well described by a power function. So, if the goal is to empirically derive a new normalized power algorithm based on the power-duration curve (versus the original algorithm, which was developed via first-principles reasoning), you're likely to be better off using some other function.

AshesGlory

Not at all. But even the very best models cannot be universally applied, for example, general relativity. Removing this w/o from my MMNP chart provides me better representation of my maximal capabilities.

Will do. FTP from Monod spreadsheet. I'll send you the numbers.

djconnel

Interesting: when I plot smoothed power I get similar results for a 30-second rolling and a 15-second exponential average. But as you say, this is not the relevant point.
The wonderful thing about power functions, which I really like in your development, is that they require no additional scale powers. No matter what your FTP, it's just power^n. For example, if you used some sort of exponential-based parameter, like sinh, you need to determine a scale power, which then implies having to scale it with FTP, which makes for an iterative determination of FTP. So I'd prefer to stick with power functions unless they prove inadequate.

frenchyge

But they don't exceed your capabilities from a NP perspective, which is the perspective one should have while viewing a MM(NP)C.

When I want to get an idea of what NP I'm capable of generating for certain durations (such as while planning L5 workouts), then I do look at the MM(NP) chart. But in those cases I would want to know what my NP-based envelope really is. If your MMNP(60) is 10% higher than your MMP(60), then you still need to do NP-based workouts at the higher level, right?

Though if the workout NP is thought to be off by that much, then I'm not sure why the TSS should be counted either.

frenchyge

An observation here is that your approach seems one of data mining rather than one based on physical events and properties. While I have no issues with your interest in tweaking the mathematical model to more closely resemble the available data and fair-in the curve which fits best, I think that approach limits the ability to test and understand where certain elements of the model may be lacking. For example, two different mathematical expressions may both fit the available data fairly nicely, but it's tough to understand which one represents a better model for predicting future events.

djconnel

What events are you trying to predict?

This is what I am trying to predict: Given this ride I did, what other rides could I have done with the same fitness?

A subset of this question is "how hard could I have ridden in an hour"?

If you think the conventional equation optimizes the answer to this question, then fine, that's your opinion. But there's no scientific basis for claiming it does so. It's heuristic. Even Andrew claims that.

frenchyge

Well, hopefully the math predicts the physical events happening inside the body. Otherwise it's just math for math's sake.

Andy's equations are modelled from the physical processes happening within the cells (ie, the time constants and power weighting). I wouldn't say NP is the most optimal model, but it'd probably have to be a lot more complex to accurately model those complex physiological processes. If the goal is to increase the accuracy of the model, then I'd suggest adding terms which account for the processes that Andy has not explicitly included in his model, such as energy storage and recovery processes during lower power periods. Choosing different time constants and weighting may bring some outlying data back in line, but that assumes that the right answer is already known and the data is being made to conform. The mathmatical model has broken from its physical basis at that point.

djconnel

The NP equation estimates the 4th root of the lactate generated during a ride. However, it isn't at all clear that this is the limiting factor in how fast you can go. For example, I can't simply generate the same amount of lactate in half the time. If you can bring more sophisticiation to the modeling, without introducing unknown parameters like FTP, please do! I tried to do so in my proposed TSS equation, although that's obviously FTP-dependent:

TSS = integral { ((P*/FTP)^4 + (P*/FTP)) dt } * K, where K = 50/hour, and P* = smoothed power
( I added a fatigue factor to this later, a sort of ATL with a 1-hour time constant)

Here there's two stress generators: one proportional to lactate generated, the other proportional to work done (which is also a stresser).

But lacking a more sophisticated model, I propose to go fully heuristic, and try to more closely match the maximal power curve. For example, if I can ride maximally for 30 minutes, then collapse, exhausted, for 30, the NP equation should give me a reasonable estimate for how hard I could have ridden with more optimal pacing: uniform power for 1 hour.

Dan

acoggan

Point of clarification: I relied on blood lactate data simply to define (mathematically) the degree of non-linearity in physiological strain in response to increases in exercise intensity. I did so because 1) such data were readily available, and 2) changes in blood lactate with increasing exercise intensity parallel numerous other physiological (esp. metabolic and neurohormonal) responses (e.g., cellular "energy charge", catecholamine - esp. epinephrine - levels). IOW, don't make the mistake that, e.g., Kirk Willett did, and read too much into the fact that the algorithm is based on blood lactate - the latter is just a marker, not something that is mechanistically important.

acoggan

Keep in mind that the original - and I would say still primary - purpose of the normalized power algorithm was to account for the additional physiological strain resulting from a non-constant power output when calculating TSS. That the algorithm turned out to be accurate enough to also be useful in other contexts - e.g., for estimating functional threshold power, for planning interval training sessions, for devising pacing strategies for TTs, etc. - was an unexpected side benefit. "Tweaking" the algorithm may in fact make it even more accurate in the latter context(s), but if such modifications entails changes that run counter to the physiological principles/knowledge upon which the algorithm is based, they may very well make it less accurate when used in its original context. Indeed, as I indicated before, I think attempting to optimize the algorithm to describe the power-duration relationship is incorrect, as it forces you to adopt a smoothing/weighting approach that is non-physiological. Presumably, this is because 1) the power-duration relationship isn't described very well by a power function, and 2) perhaps more importantly, fatigue during exercise is always multi-factorial, whereas training stress/strain is, at least in cycling, largely metabolic in nature.

frenchyge

No problems there, and here's the reason I even make the point: in my local criteriums (mostly flat, 4-corners) where the hard efforts are typically <15 seconds long, I personally feel that NP underestimates the physiological cost of the ride. For a killer 50-min crit, I typically see an IF around .90-.92 when I get home, which would be a walk in the park (well, a moderate effort at least) on a normal road ride.

Another example would be riders who complain of being dropped by a series of repeated hard surges, or 'running out of matches', even though each individual effort might be within their ability.

I just wonder if changing the algorithm to bring 'NP Buster' rides back into line wouldn't potentially make NP worse for a different set of ride conditions. While I can't personally add any sophistication to the model, I do think that'd be what's necessary in order to improve it over all possible scenarios.

rmur17

Just for fun here's an example of an actual planned 40k TT workout on the CT in which I went out too hard and died at the 21k point. I had to spin easily for 5-min then went as hard as I felt like could for the remainder (only tempo power left in the tank at that point).

Duration Power
30 390
5 190
25 320
60 356 NP _Exp: 4

If I increase the NP exponent to have that workout match FTP of 380, I'd have to get up around ^26!

I wouldn't even call that workout a "collapse" after 30-min. It wasn't pretty though!

It may be an easy way out but I don't expect NP to handle extreme cases like that any longer. One of my fav. example was a mountainous ride say 30-min climbs and 10-min free-wheeling descents. Same goes for extended warmups & cooldowns wrapped around a high-power 'core' ride.

My current POV is that NP is meaningful only when attached to a specific duration. Rides with very long climbs and free-wheeling descents --- well the overall NP for that ride isn't of much interest. It's the power on the climbing segments only that really makes any difference. Same goes for a hard threshold workout followed by an easy spin home. NP for the entire ride just isn't meaningful IMHO.

For my workouts I log what I call Pc or 'core' average power and normalized power and track Power-duration curves for both. that's minus any easy warmup and cooldown and if I happen to have a ride with some sloppy/easy riding in the middle, I'll break the stats in two around that point.

I don't know if this adds anything to the discussion. Another point would be is what % of overall rides actually fall into the NP-buster (or NP outlier) category. Must be pretty darned small?

__________________
rmur

acoggan

Obviously that's hard to say, since 1) any survey is potentially subject to response bias, and 2) even if everyone who has ever used the algorithm were to respond, you're still left with the question of whether they simply underestimated their functional threshold power. That's why, e.g., I find the experiences of coaches such as John V. worth noting: he's somebody who 1) has no potential conflict-of-interest, 2) truly understands the concepts at hand (thus minimizing the probability that an IF of >1.05 is just due to setting functional threshold power too low), and 3) sees lots of files from lots of people. So, when he says that in his experience true NP busters are rather rare, I think it says something about the accuracy of the algorithm.