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  1. #1
    Killing Rabbits
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    Power Normalizations- Lies, Damn lies and Stats

    A recent thread got me interested in power normalization algorithms so today I decided to compare a couple for myself. I used Coggan’s normalized power (CNP) as well as an exponentially weighted moving average (EWMA). For the EWMA I used a time constant that yields a half-life value of ~30s (alpha =0.0465).

    CNP
    1) starting at 30 seconds, calculate a 30 second rolling average for power
    2) raise the values obtained in step 1 to the 4th power
    3) take the average of all the values obtained in step 2
    4) take the 4th root of the number obtained in step 3

    EWMA


    The Challenge

    Warm-up followed by a work period that includes 2x10min work periods that both average 250W -but differ significantly in the amount of strain. Furthermore, the efforts were bracketed with 5min@250W for calibration purposes. All efforts were preceded with 5min@150W to establish baseline.



    The Results – Heart rate



    Power Normalizations



    Summary Statistics

    Code:
    Workload	
    Average	198.1
    Std Dev	52.3
    %RSD	26.4
    
    30s Average	
    Average 198.1
    Std Dev	50.1
    %RSD	25.3
    
    EWMA	
    Average	198.1
    Std Dev	44.7
    %RSD	22.5
    	
    	
    Normalized Power 
    217.0
    
    Heart Rate	
    Average	139.8
    Std Dev	16.1
    %RSD	11.5
    Correlation coefficients

    Code:
    Correl HR-30s	0.673678
    Correl HR-EWMA	0.872638
    Correl HR-Workload	0.721307
    Conclusions

    Obviously a straight 30s moving average of workload does not correlate as well with physiological stress as does the EWMA. The plot of EWMA is very similar to the HR response plot indicating that this algorithm really does approximate real-time physiological strain well. Interestingly, you can see that HR remains the ultimate normalizer, as the %RSD of that measurement is the smallest. It is almost humorous that the EWMA of power seems to be a backwards calculation of HR; a measure that some power disciples want to completely ignore.

    However, Coggan’s normalized power does a very good job at increasing the strain estimate of variable workouts as confirmed by the HR-Power calibration plot show below (done last month). The entire workout yielded an average HR of 139.8bpm, which agrees well with the NP of 217W unlike the average power of 198.1W.



    Both algorithms have their advantages. EWMP better matches instantaneous strain, and is more elegant, however, CNP matches strain over the course of the entire workout very well.

    ElJ I suggest you use try the EWMA algorithm as a normalization protocol in your most excellent TT optimization program. The syntax is actually easier than NP.

  2. #2
    Royal Grand Exalted Pooba smoke's Avatar
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    bored last night?
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  3. #3
    部門ニ/自転車オタク NomadVW's Avatar
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    Well.. in order to agree with you I think I'd have to assume that HR vs Power is a constant relationship, which... well.. in my experience it is not, soooo.... therefore, all I can do is nod and look nicely at your graphs.
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    Burning Matches. ElJamoquio's Avatar
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    Quote Originally Posted by Enthalpic View Post
    ElJ I suggest you use try the EWMA algorithm as a normalization protocol in your most excellent TT optimization program. The syntax is actually easier than NP.
    Will do, thanks for the analysis. It'll be a few days until I'll be able to throw that in there, though.
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  5. #5
    Race to train jrennie's Avatar
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    You seem to spend a lot of time trying to find fault in coggan's methods and analysis software but for what reason? If you do not like his methods then do not use them. I am sure someone out there is using a philosophy you do agree with. I really don’t think anyone is going to suddenly view you as an exercise physiology messiah and hand you a grant for your tireless efforts on BF.

    *written by some one to lazy to look any further into his files than the main page of cyclingpeaks so feel free to ignore

  6. #6
    Killing Rabbits
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    Quote Originally Posted by jrennie View Post
    You seem to spend a lot of time trying to find fault in coggan's methods and analysis software but for what reason? If you do not like his methods then do not use them. I am sure someone out there is using a philosophy you do agree with. I really don’t think anyone is going to suddenly view you as an exercise physiology messiah and hand you a grant for your tireless efforts on BF.

    *written by some one to lazy to look any further into his files than the main page of cyclingpeaks so feel free to ignore
    No, I respect Coggan's work. I seek understanding, not just the ability to use his stuff. Furthermore, the EWMA idea was recently brought up by Dr P.S. in another thread, so I played around with it.

    Lastly, Coggan didn't develop a lot of this stuff. It's not like he invented math He refined and expanded some existing ideas while making them much more mainstream. Good stuff.

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  7. #7
    James
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    Quote Originally Posted by jrennie View Post
    You seem to spend a lot of time trying to find fault in coggan's methods and analysis software but for what reason? If you do not like his methods then do not use them. I am sure someone out there is using a philosophy you do agree with. I really don’t think anyone is going to suddenly view you as an exercise physiology messiah and hand you a grant for your tireless efforts on BF.

    *written by some one to lazy to look any further into his files than the main page of cyclingpeaks so feel free to ignore
    Read his signature quotes.

  8. #8
    getting dropped merckx89's Avatar
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    Ok, can someone please explain what normalized power means. Preferably without using calculus as i haven't taken that class yet. I understand SD but have no idea where normalized power comes from.

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    Quote Originally Posted by merckx89 View Post
    Ok, can someone please explain what normalized power means. Preferably without using calculus as i haven't taken that class yet. I understand SD but have no idea where normalized power comes from.
    http://www.cyclingpeakssoftware.com/...11/defined.asp

  10. #10
    Euro-Trash Enzo Gucci's Avatar
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    Normalized power is a wonderful tool that allows people to brag about their numbers, while conveniently leaving out that fact that their power output was normalized rather than average, therefore giving others the false impression that their power output matches that of many pro tour riders.

    EDIT: I don't ride with a power meter, so I may very well be wrong.
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    部門ニ/自転車オタク NomadVW's Avatar
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    Quote Originally Posted by Enzo Gucci View Post
    Normalized power is a wonderful tool that allows people to brag about their numbers, while conveniently leaving out that fact that their power output was normalized rather than average, therefore giving others the false impression that their power output matches that of many pro tour riders.

    EDIT: I don't ride with a power meter, so I may very well be wrong.
    Yep... you are.
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  12. #12
    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by NomadVW View Post
    Yep... you are.
    So there is absolutely no truth to what I said, at all?

    I was being sarcastic, but I know that normalized power yields higher numbers than average power, hence my comment.
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  13. #13
    Senior Member
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    Quote Originally Posted by Enzo Gucci View Post
    ... but I know that normalized power yields higher numbers than average power, ...
    Even that's not right.

  14. #14
    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by asgelle View Post
    Even that's not right.
    It isn't?
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    Quote Originally Posted by Enzo Gucci View Post
    It isn't?
    Normalized power can be higher, lower, or equal to average power. It is true that normalized power is higher than average power much more often than it is lower.

  16. #16
    部門ニ/自転車オタク NomadVW's Avatar
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    It can, but just cause it's normalized doesn't mean it's going to. The point of normalization (whether using the oft accepted Coggan method or something you put together yourself) is to more accurately identify the physiological strain of an effort or workout.

    If you do a workout that avg's 220 watts, normalized at 225, it will be different than one that is avg 220 and normalized at 300. Anyway... if you're using normalized watts to compare yourself to pro average watts, you're an idiot. Not that there aren't enough of those around here.
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    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by asgelle View Post
    Normalized power can be higher, lower, or equal to average power. It is true that normalized power is higher than average power much more often than it is lower.
    I know it's possible for it to be lower, but in all of the real world situations I've seen it, it's always higher by a pretty significant amount. I've seen it be close to equal on uphill TT's by riders of the same weight with very close times.

    Coming off of Cross season, I know the differences can be huge in a cross race, where there is a constant fluctuation of explosive power/no power. I remember differences of 50 watts (between average and normalized) over the course of an hour long race, which is pretty significant.

    In terms of gathering race date (and again, this is only our of curisoty, since I don't have a power meter) which would be more applicable; normalized or average?
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  18. #18
    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by NomadVW View Post
    It can, but just cause it's normalized doesn't mean it's going to. The point of normalization (whether using the oft accepted Coggan method or something you put together yourself) is to more accurately identify the physiological strain of an effort or workout.

    If you do a workout that avg's 220 watts, normalized at 225, it will be different than one that is avg 220 and normalized at 300. Anyway... if you're using normalized watts to compare yourself to pro average watts, you're an idiot. Not that there aren't enough of those around here.
    I've never heard anyone do it, but I'm sure people do.

    How close are the power readings from a PowerTap and an SRM?

    I don't use a powertap, but I've strapped my bike to a Dyno before. Let me show you:


    819ft/lbs of torque at my rear wheel. Pretty impressive, no?
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  19. #19
    部門ニ/自転車オタク NomadVW's Avatar
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    Quote Originally Posted by Enzo Gucci View Post
    In terms of gathering race date (and again, this is only our of curisoty, since I don't have a power meter) which would be more applicable; normalized or average?
    Normalized power more accurately reflects the physiological strain/effort required. Average power is actual work done.

    So, we expect that two workouts with normalized power of 300 will induce the same amount of stress/fatigue on the body for the same rider. That says nothing about adaptation/muscle recruitment required to do it or gained from it - just the effect of the effort on the body in terms of stress. It will also help display for other people the type of ride done in terms of variability. You know that if I claim a ride average watts 250 and normalized 255 that it was a reasonably steady state effort. If I claim a ride average watts 250 and normalized 325 or 350, that the workout had some pretty large efforts at higher power.
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  20. #20
    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by NomadVW View Post
    Normalized power more accurately reflects the physiological strain/effort required. Average power is actual work done.

    So, we expect that two workouts with normalized power of 300 will induce the same amount of stress/fatigue on the body for the same rider. That says nothing about adaptation/muscle recruitment required to do it or gained from it - just the effect of the effort on the body in terms of stress. It will also help display for other people the type of ride done in terms of variability. You know that if I claim a ride average watts 250 and normalized 255 that it was a reasonably steady state effort. If I claim a ride average watts 250 and normalized 325 or 350, that the workout had some pretty large efforts at higher power.
    I think this is the most reasonable explanation for normalized power's application.

    In something like a 'cross race (or a mountain bike race) where an overwhelming majority of the time it's a solo effort (unlike a road race or criterium where you can sit in) yet you have huge peaks and valleys in your power due to varying terrain and corners (unlike a solo TT) would average power serve as a good representation of weak spots in your race? For example, someone who manages to hammer on the descents and pedal harder into and out of corners (as opposed to someone who coasts down the descents and doesn't get on the gas early after cornering) would obviously see a closer relation between average and normalized... Would there be any advantage of using average or normalized to analyze these types of terrain-specific races?
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  21. #21
    部門ニ/自転車オタク NomadVW's Avatar
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    I would expect that the hard pedaling in/out of corners and much more varied terrain would actually increase the variability of the power applied during race further separating the two values. (from not having raced cross, myself) Average power (for my riding at least) only really tells me valuable information about my riding in steady state intervals (of any length).

    Once you induce terrain, wind, drafting, or anything that would cause you to vary your power output between significant numbers for significant lengths of time over a longer period (20+ minutes), normalized power tends to tell me more.

    I'm not a 100% Coggan follower, but I can't find much reason to dispute/disagree with the normalized power methods or algorithm. You'd have to show me more than a HR graph from one ride to say that a different algorithm was more beneficial. On the other hand, I've found that the longer I ride with a power meter the less I depend on the resulting numbers and am back to riding a lot by feel this time of year. I still track the numbers as meticulously from week to week, I just don't get as wrapped up in them. It doesn't take a mathematical formula to tell me that the last two days of 4+ hr rides have made my legs tired and that I rode harder than I probably should have.
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  22. #22
    Burning Matches. ElJamoquio's Avatar
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    Quote Originally Posted by Enzo Gucci View Post
    819ft/lbs of torque at my rear wheel. Pretty impressive, no?
    Hm, I can only do about 200 ft-lbs. I'll have to try for some more.
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  23. #23
    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by NomadVW View Post
    I would expect that the hard pedaling in/out of corners and much more varied terrain would actually increase the variability of the power applied during race further separating the two values. (from not having raced cross, myself) Average power (for my riding at least) only really tells me valuable information about my riding in steady state intervals (of any length).

    Once you induce terrain, wind, drafting, or anything that would cause you to vary your power output between significant numbers for significant lengths of time over a longer period (20+ minutes), normalized power tends to tell me more.
    I know from experience that the difference between average and normalized during a cross race is pretty significant.

    I guess my question boils down to an unlikely scenario, but this is the best I can explain it:

    Imagine two riders of equal weight and very simmilar phsyical abilities on a 'cross course (lets just say the two riders have the same wattage-kilo but not the same bike handling skills) and both of them are using power meters. On the flats, they are probably going to be equal, but through corners/up steep climbs/and down descents the one with better handling skills is probably going to do better (pedal hard down the hill as opposed to coasting, pedal further into corners, brake late, and pedal sooner out of the corner or even pedal through the turn)

    After the race, the two riders compare their power files. I know there are so many variables to factor in, but both of them might have a very simmilar normalized power, while the rider with better handling skills probably has much higher average power. I know in a race, the riders finish probably will speak more than the power file and I would imagine the more skilled rider would have won...

    So, while analyzing race data (as opposed to training files) is there a possiblity that average power might be a better tool or indication of what type of real-world power you actualy put to the ground, rather than the physiological strain it placed on the individual? I would imagine that during training, especialy while training within certain "zones" that normalized could be a beter indication of your training, but would this still hold true for a race situation? I hope that all made sense, haha.

    Again, I don't train or race with power (although I've borrowed a bike during a few cross races with a power meter, it's pretty fun being able to compare files of consecutive races) so this is all out of curiosity.
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  24. #24
    Euro-Trash Enzo Gucci's Avatar
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    Quote Originally Posted by ElJamoquio View Post
    Hm, I can only do about 200 ft-lbs. I'll have to try for some more.
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  25. #25
    Burning Matches. ElJamoquio's Avatar
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    Won't help me at all, because I'm not doing any work at my max torque.
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