CP - Mean Max NP Curve

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I have an old workout which if I understand the term correctly is a "NP buster". It has made my Mean Max NP Curve for the season pretty useless. Is there any way I can exclude just this single workout from my season mean max np curve?

re-asign it to a new athlete, such as yourself #2.

So your default athlete (yourself #1) does not contain this workout.

re-asign it to a new athlete, such as yourself #2.

So your default athlete (yourself #1) does not contain this workout.Alternatively you could redefine the workout as Cross Training, or Other and then filter your Mean Maximal Graph to exclude that type of workout.

-Dave

Alternatively you could redefine the workout as Cross Training, or Other and then filter your Mean Maximal Graph to exclude that type of workout.
How about assigning it to the 'NP Buster' workout category? :D

How about assigning it to the 'NP Buster' workout category? :DThat's sort of what I was thinking with "other" I mean it might screw up an NP based MMC, but it's still valid TSS for the Performance Manager. It seems ashame to assign it to a fictitous athlete and not get credit for the work done :)

That's sort of what I was thinking with "other" I mean it might screw up an NP based MMC, but it's still valid TSS for the Performance Manager. It seems ashame to assign it to a fictitous athlete and not get credit for the work done :)Excellent. That worked like a charm. I reassigned the sport category of the offending workout to an unused category, and then in the options for the MMNP curve selected only the "Bike" sport under "sports to include". All other charts are unaffected. Thanks.

I have an old workout which if I understand the term correctly is a "NP buster". It has made my Mean Max NP Curve for the season pretty useless. Is there any way I can exclude just this single workout from my season mean max np curve?
I'm curious how the NP from that one workout makes all the other NPs in the MMC (NP) worthless? Is there some reason to believe that you couldn't generate that same NP again under similar conditions, so that it needs to be thrown out as a false reading?

The MMC represents history of what you have done, and assuming the data aren't really old it's relevant to what you can do. Why do you think that one workout is not representative of what you can do?

I'm curious how the NP from that one workout makes all the other NPs in the MMC (NP) worthless? Is there some reason to believe that you couldn't generate that same NP again under similar conditions, so that it needs to be thrown out as a false reading?

The MMC represents history of what you have done, and assuming the data aren't really old it's relevant to what you can do. Why do you think that one workout is not representative of what you can do?The normalized powers from the workout exceeded my capabilities for a large range of durations so masked my real capabilities. For example the MMNP(60) was more than 10% higher than my FTP, and corresponded to my MMP(10). The VI for the w/o was 2.58 and comprised L6 intervals.

First, I'll assume here NP is for pacing and for predicting FTP. I separate it from an NP used for determining TSS. TSS can be calculated with a separate formula, if necessary.

NP is calculated from smoothed power w/ a 30 second smooth. I'll call smoothed power "P*". Basically integrate P*^4 over time (I'll call this meta-work -- work is the integral of power over time).

If, at constant power, I can generate more meta-work in a short interval than I can in a longer one, at an appropriately reduced constant power, I can get an NP buster.

Another possible NP problem is, if optimizing pacing based on a fixed NP for a given duration, I will tend to over-predict how much harder I can go for a shorter interval, for example to go extra hard on a climb and less hard on the descent. This is sort of the opposite problem. NP should be tuned to avoid NP busters, and to avoid over-predicting what I can do at shorter efforts.

There are two components to the NP formula: the smoothing time and the exponent. Defaults are 30 seconds and 4.

Now, NP uses a rolling average: the first thing I change in my calculations is to use an exponential average, as is used in ATL and CTL, as this is more physiologically representative (for example, representative of blood lactate levels, or ATP levels, following time-variable power). With exponential smoothing, a 15 second time constant (the CTL time constant is default 42 days, for example) is about the same as a 30-second running average (the conventional NP). This time constant marks the transition from "short-duration" efforts, which are primarily anaerobic, and "long-duration efforts", which are more dominated by aerobic capacity, and are valid predictors of FTP. If I set the smoothing time to 0, and have a massive jump, I can do a bunch of jumps then forecast a high 1-hour power. This may well be an invalid prediction: an "NP buster".

The second thing to be tuned is the exponent. The exponent of 4 says: if I halve the duration, I can supply 2^(1/4) - 1 = 19% more power. I know I can't supply 19% more power at 10 minutes than at 20 minutes, for example. So for me, an exponent of 4 is obviously too low. Maybe I can supply 6% more power. 2^(1/12) =~ 1.06, so for me, an exponent of 12 makes more sense.

I've looked at several NP busters folks have sent me, and using an exponent of 12, a time constant of 60 seconds seems to work fairly well. I got two files of one guy with really high anaerobic capacity but low aerobic capacity, and for him, I used 90 seconds, and nailed his FTP on both files, but with 60 seconds, I overpredicted FTP. So to me this suggests at least a 90 second time constant for him. But for others, the same 90 second time constant predicted well under FTP in what were reportedly brutally hard 1-hour race files. 60 seconds worked better at getting close to FTP. So I think the time constant needs to be tuned a bit based on an individuals ratio of aerobic to anaerobic capacities.

The test of an NP formula isn't just if it over-predicts FTP, but whether it over-predicts critical power at any duration. So if I plot NP^n * t, where NP is the near-optimal maximal NP at duration t, n is the NP exponent, versus duration t, for t of at least a few smoothing constants, I shouldn't see any long-term rises or drops. If I see a significant drop, I'll get an "NP buster" for some duration. If I see a sharp rise, I'll produce unobtainable optimization strategies. (my maximal power curve currently has a sharp dip at 20 minutes.... this is because this is close to my slower times up Old La Honda Road, not because of physiology, so it's for these criteria, the curve needs to be relatively optimal: ie there need to be maximal efforts over a range of durations spanning the curve).

So in summary, this is what I use for myself: a 60 second (optionally up to 90 for some riders) exponential smoothing along with an exponent of 12. I haven't done enough testing on this yet, and would be curious to see if others find it generates less of an "NP buster" problem.

Dan

Anyway to change the NP to avg power?

Using average power instead of NP would certainly solve the NP buster problem, but would result in a huge over-prediction of available power at shorter durations. For example, if I can average FTP for 1 hour, it would suggest averaging 2 FTP for half an hour up a hill, then coasting downhill for half an hour at zero power, is also possible (obviously I'd coast further than I climbed, but let's not sweat the small details :)). Of course, doubling power going from 1 hour to 30 minutes isn't possible.

First, I'll assume here NP is for pacing and for predicting FTP. I separate it from an NP used for determining TSS. TSS can be calculated with a separate formula, if necessary.

NP is calculated from smoothed power w/ a 30 second smooth. I'll call smoothed power "P*". Basically integrate P*^4 over time (I'll call this meta-work -- work is the integral of power over time).

If, at constant power, I can generate more meta-work in a short interval than I can in a longer one, at an appropriately reduced constant power, I can get an NP buster.

Another possible NP problem is, if optimizing pacing based on a fixed NP for a given duration, I will tend to over-predict how much harder I can go for a shorter interval, for example to go extra hard on a climb and less hard on the descent. This is sort of the opposite problem. NP should be tuned to avoid NP busters, and to avoid over-predicting what I can do at shorter efforts.

There are two components to the NP formula: the smoothing time and the exponent. Defaults are 30 seconds and 4.

Now, NP uses a rolling average: the first thing I change in my calculations is to use an exponential average, as is used in ATL and CTL, as this is more physiologically representative (for example, representative of blood lactate levels, or ATP levels, following time-variable power). With exponential smoothing, a 15 second time constant (the CTL time constant is default 42 days, for example) is about the same as a 30-second running average (the conventional NP). This time constant marks the transition from "short-duration" efforts, which are primarily anaerobic, and "long-duration efforts", which are more dominated by aerobic capacity, and are valid predictors of FTP. If I set the smoothing time to 0, and have a massive jump, I can do a bunch of jumps then forecast a high 1-hour power. This may well be an invalid prediction: an "NP buster".

The second thing to be tuned is the exponent. The exponent of 4 says: if I halve the duration, I can supply 2^(1/4) - 1 = 19% more power. I know I can't supply 19% more power at 10 minutes than at 20 minutes, for example. So for me, an exponent of 4 is obviously too low. Maybe I can supply 6% more power. 2^(1/12) =~ 1.06, so for me, an exponent of 12 makes more sense.

I've looked at several NP busters folks have sent me, and using an exponent of 12, a time constant of 60 seconds seems to work fairly well. I got two files of one guy with really high anaerobic capacity but low aerobic capacity, and for him, I used 90 seconds, and nailed his FTP on both files, but with 60 seconds, I overpredicted FTP. So to me this suggests at least a 90 second time constant for him. But for others, the same 90 second time constant predicted well under FTP in what were reportedly brutally hard 1-hour race files. 60 seconds worked better at getting close to FTP. So I think the time constant needs to be tuned a bit based on an individuals ratio of aerobic to anaerobic capacities.

The test of an NP formula isn't just if it over-predicts FTP, but whether it over-predicts critical power at any duration. So if I plot NP^n * t, where NP is the near-optimal maximal NP at duration t, n is the NP exponent, versus duration t, for t of at least a few smoothing constants, I shouldn't see any long-term rises or drops. If I see a significant drop, I'll get an "NP buster" for some duration. If I see a sharp rise, I'll produce unobtainable optimization strategies. (my maximal power curve currently has a sharp dip at 20 minutes.... this is because this is close to my slower times up Old La Honda Road, not because of physiology, so it's for these criteria, the curve needs to be relatively optimal: ie there need to be maximal efforts over a range of durations spanning the curve).

So in summary, this is what I use for myself: a 60 second (optionally up to 90 for some riders) exponential smoothing along with an exponent of 12. I haven't done enough testing on this yet, and would be curious to see if others find it generates less of an "NP buster" problem.

Dan

1. Exponential smoothing is more physiologically plausible, but in practice I haven't found it to really make any difference.

2. If you're going to use exponential smoothing, the appropriate time constant from a physiological perspective is something in the 25-30 s range - 60-90 s is clearly far too long.

3. An exponent of 12 is simply implausible from a physiological (metabolic) perspective).

Bottom line: I think that your search for an improved algorithm has led you to oversmooth the data, then overweight it to compensate.

the MMNP(60) was more than 10% higher than my FTP, and corresponded to my MMP(10). The VI for the w/o was 2.58 and comprised L6 intervals.

Man, that ol' normalized power algorithm really sucks, eh? ;)

Would you mind sending your file (along with a brief description of how you arrived at your functional threshold power) to me at acoggan at earthlink dot net? I'd like to add it to my collection of NP busters.

1. Exponential smoothing is more physiologically plausible, but in practice I haven't found it to really make any difference.

2. If you're going to use exponential smoothing, the appropriate time constant from a physiological perspective is something in the 25-30 s range - 60-90 s is clearly far too long.

3. An exponent of 12 is simply implausible from a physiological (metabolic) perspective).

Bottom line: I think that your search for an improved algorithm has led you to oversmooth the data, then overweight it to compensate.What is the shortest trial which has been demonstrated to predict FTP?

For example, I don't have my Allen and Coggan handy, But a quick web search turned up:
http://www.springerlink.com/content/76tuhlu02a80j9mx/

From Fig B, an example, for one subject:
power = 15371 J / t + 205.4 W.

From which I get a characteristic time for anaerobic power:

tau = 15371 J / 205.4 W = 74.83 seconds

In other words, it takes an effort of at least 75 seconds before most of the power is guaranteed to come from the aerobic component. This is basically the average of the range I proposed. The shortest duration in this particular trial was approximately 130 seconds. For much shorter durations than "tau", the critical power model suggests total work is conserved, consistent with being in the "smoothing regime".

It would be interesting to see how closely various smoothing constants come to reproducing the published critical power data, taking "meta-work" as a constraint (ie integral P*^n dt).

Again, the lower bound on the exponent was based on pacing strategies for durations well above the smoothing time constant. Using 4 gives me extremely optimistic results for shortening the duration of the effort.

Dan

What is the shortest trial which has been demonstrated to predict FTP?

I don't understand the nature of your question/how it relates to the issue at hand?

For example, I don't have my Allen and Coggan handy, But a quick web search turned up:
http://www.springerlink.com/content/76tuhlu02a80j9mx/

From Fig B, an example, for one subject:
power = 15371 J / t + 205.4 W.

From which I get a characteristic time for anaerobic power:

tau = 15371 J / 205.4 W = 74.83 seconds

In other words, it takes an effort of at least 75 seconds before most of the power is guaranteed to come from the aerobic component. This is basically the average of the range I proposed.

75 s = three times a tau of 25 s = 87.5% of the way to plateau. IOW, the data you cite is consistent with my statement that the approriate tau (based on muscle PCr/ADP kinetics, and hence cellular and eventually whole-body VO2, etc.) is on the order of 25-30 s. The question, though, is why you would be desirous of applying an exponential smoothing with a time constant that is three times that of the underlying processes??

I don't understand the nature of your question/how it relates to the issue at hand?



75 s = three times a tau of 25 s = 87.5% of the way to plateau. IOW, the data you cite is consistent with my statement that the approriate tau (based on muscle PCr/ADP kinetics, and hence cellular and eventually whole-body VO2, etc.) is on the order of 25-30 s. The question, though, is why you would be desirous of applying an exponential smoothing with a time constant that is three times that of the underlying processes??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

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.

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.)

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.

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.

Man, that ol' normalized power algorithm really sucks, eh? ;) Not at all. But even the very best models cannot be universally applied, for example, general relativityhttp://cyclingforums.com/images/smilies/smile.gif. Removing this w/o from my MMNP chart provides me better representation of my maximal capabilities.

Would you mind sending your file (along with a brief description of how you arrived at your functional threshold power) to me at acoggan at earthlink dot net? I'd like to add it to my collection of NP busters.Will do. FTP from Monod spreadsheet. I'll send you the numbers.

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.)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.
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.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.

The normalized powers from the workout exceeded my capabilities for a large range of durations so masked my real capabilities. For example the MMNP(60) was more than 10% higher than my FTP, and corresponded to my MMP(10). The VI for the w/o was 2.58 and comprised L6 intervals.
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.