W Prime and Garmin Stamina

Training
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Hello,

Just sharing an interesting finding I made regarding W prime and Garmin Stamina.

I was asked by one of the readers of our “Tracking Cycling Fitness With Intervals ICU” ebook

([EBook] Tracking Cycling Fitness with Intervals.icu)

about the W’ (W prime) option in the settings menu that was not mentioned in the ebook, because at the time I was not using it at all. So, I started to find out what this is all about.

A very simplified summary of my findings is:

There are 2 power training models that I will call FTP and CP respectively.

FTP comes from the Coggan et all authors, creators of Training Peaks and authors of the Training and Racing with a Power Meter Book. This is the method I was familiar with and have used since I started training with power. It is the most known and used methodology.

The second method CP, meaning Critical Power, which I had heard of but not really given it a look, seems to be more recent and is getting more adopters as, per the information I got, has more scientific support than FTP.

Both establish a reference target threshold value obtained with different approaches that I will not talk about in detail in this post but that are defined as follows:

FTP is defined as the maximal sustainable power for 60 minutes.

For CP I found several definitions but all of them seem to agree that it is the sustainable high intensity power that can be maintained for 30 to 40 minutes.

According to the research I made, FTP and CP are not the same from the physiological point of view, but may be very close in value, and are often used interchangeably.

When CP is tested for, 2 parameters are obtained, the value of the Critical Power as well as what is known as W prime or Anaerobic Capacity which is the amount of energy that an individual can use in anaerobic efforts, that are above CP (or above FTP if you consider them to have the same value).

W prime is the parameter that should be entered into the Intervals.icu settings page.

There are several options to get this value, one being a proper CP test but also may be taken from the intervals.icu power page under the Power Curve graph, which is what I did.

I also added the W’ chart in my activities page to get an idea of the information it provides.

After a few rides, I realized I had seen that type of performance data before in my Garmin. It looked very close to the Stamina chart available in recent devices and I thought would be interesting to compare them, both during and after a ride.

Turns out there is a W prime data field in Connect IQ called W’ Balance (W Prime Balance) that can track it during a ride in real time as well as generate a graph showing its performance upon completing the activity. The parameters required by the field to work properly can be taken from intervals, so I used my FTP as CP (as intervals.icu does), entered my W prime value and set the “differential” method to calculate it, which is the one Intervals.icu uses as well.

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Then I rode and compared the performance of both the Stamina and W prime along the ride. Often they were very close together, with differences in the recovery times but eventually getting to very close values. The W prime recovered faster than Stamina for the most part. At the end of the ride they showed different values on my 1040.

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But looking at the data in Garmin Connect, that allows to overlay the W prime curve with the Stamina one, their behavior is quite similar. The red curve is from the data field and the yellow one is Garmin’s Stamina

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And it seems same behavior can be seen in the W prime balance graph in interval.icu.

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It would be interesting to overlay the 3 curves to further compare them.

So, if you have a Garmin device that does not support Stamina and you are interested in tracking it, you may get and add the the W’ Balance (W Prime Balance) data field, use the W’ value from the intervals.icu power chart (or do a proper CP test) and have control of your available anaerobic energy tank, especially if you plan to do anaerobic interval training.

Greetings

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No, those are not the original definitions. Most of your research sounds like something ChatGPT would regurgitate from scraping websites.

I’ll stick my neck out and regurgitate what I learned over 8 years, from reading Coggan’s original white paper, books from Coggan&Allen and Skiba, and reviewing key references from the books/paper.

Coggan & Allen in Training and Racing with a Power Meter

  • FTP is highest power that a rider can maintain in a quasi-steady state without fatiguing
  • FRC is Coggan’s version of Skiba’s W’
  • Coggan alone is credited with FTP (his 2003 paper pre-dates the book and is a must read if you want the Coggan only version)

Skiba in Scientific Training for Endurance Athletes

  • (CP) represents a dividing line between exercise you can do for a long time, and exercise that is so hard that you have to quit much sooner
  • Skiba is credited with W’ (Scherrer and others published CP concept in 1954)

Both Skiba and Coggan are describing a narrow range of power that divides stable and unstable physiology.

Same concept.

Both FTP and CP are estimated using power data.

FTP can be estimated different ways, The “best estimate of performance is performance itself” approach is to go long and do a long TT. But its not the only way, Coggan even lists CP as a way to estimate (using efforts between 3 and 30 minutes). Coaches believe most trained cyclists can sustain FTP from 30 to 70 minutes.

CP can be estimated different ways, using field data and plugging into a mathematical equation. Skiba’s book says 2 to 4 efforts, between 2 min and 20 minutes. (comment: this seems too short given I “blow up” at unstable vo2max HR/breathing at the end of 20-min max effort). Skiba states its the best power most cyclists can hold from 20 to 40 minutes, although he also says its close to power on a 40km TT (50-70 minutes).

The basic argument of the modern CP crowd is using a handful of 2 to 20 minute efforts with a mathematical model (fit a straight line to work performed at each test point). A critical review from ~25 years ago suggested using 6 to 30 minute efforts. Coggan suggests using 3 to 30 minutes.

Examples of estimates from my data

Season A

  • CP of 280 and W’ 12.3 kJ (3, 5, and 20-min)
  • CP of 276 and W’ 13.1 kJ (3, 5, and 30-min)
  • FTP of 276 and FRC 14.2 kJ
  • FTP-vs-CP: basically the same
  • W’-vs-FRC: 7% difference
  • shortly after I did 15.6 kJ over ftp/cp on a 4-min near max effort, so both underestimated but FRC was “better”

Season B

  • CP of 277 and W’ 11.2 kJ
  • FTP of 273 and FRC 16.9 kJ
  • FTP-vs-CP: basically the same (for long effort I only had 21-min this season)
  • 33% difference between W’ and FRC
  • shortly after I did 14 kJ over ftp/cp effort (2-min very hard but not max) effort, and all-time PR max 15.5 kJ on a 60-sec effort, so FRC estimate was “better”

My data looks like that season after season after season.

So this is what I’ve learned from doing this over 8 years:

  • CP and FTP are thresholds dividing stable and unstable physiology
  • How well you are able to execute tests will impact the results
  • For myself, FTP and CP estimates are basically the same when using at least 20-min efforts in the CP model
  • Anaerobic capacity modeling always falls short in my data, because ALL OUT / MAX EFFORTS are REALLY REALLY HARD for me to execute but when I’m motivated by a Strava KOM then I can exceed W’ and FRC estimates
  • very very happy that I bought WKO5 over 5 years ago

You don’t need to agree, thats what I learned.

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@WindWarrior Take it easy my friend, we are just sharing information and learning in the process. Maybe I should have been more specific with the FTP definition I used. I should have quoted it from the Training and Racing with a Power Meter book that I have read in detail (the definition is on page 27 of my copy), instead of writing it by memory.

As for CP, being relatively new to me, I read about it in several sites, including High North Performance you mention ( Critical Power and W’ Explained For Cyclists (inc. Critical Power Calculator) — High North Performance

as well as others such as:

Road Cycling Academy:
Critical Power vs FTP for Cyclists: What You Need to Know

The Threshold Coach
thethreshold.coach

Working Triathlete
Critical Power Testing: How to dial in your intensity zones

I found that the CP definition in these sites is not consistent among them, so what I wrote was my way to summarize it.
If you are aware of the official definition, I would appreciate if you can direct me to it so that I can learn more.
And no, I did not use chatgpt for any of this.

The purpose of this thread was not to discuss FTP vs CP but rather to give some basic context to show a finding I came through about comparing the W prime performance in intervals.icu with Garmin’s Stamina.
The context was needed because in the second post of this thread
forum.intervals.icu
@david explains that

“I decided to use FTP instead of CP because from what I could tell they would usually be close together and setting training zones relative to FTP is so popular.”

so, strictly speaking, he is combining the 2 methods using FTP as CP and the W prime value obtained from the power chart.
In order to properly compare Stamina to W prime in the 1040 I had to be sure that the same parameters were used to properly compare the output.

Thanks for your comments.

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For what it’s worth, my 530 gave good estimates of FTP. Even from endurance and tempo rides. Sadly the 840 does not, and the Stamina info is not useful. I’ll run out of Stamina on easy long endurance rides. Stamina on x40 works for some people, just not me!

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This may be the best CP definition I have seen so far:

“The CP may be functionally defined as the highest power output that can be sustained without progressively drawing on W ′, where the latter represents, at the onset of exercise, a fixed amount of work that can be done when CP is exceeded.”

Taken from

The ‘Critical Power’ Concept: Applications to Sports Performance with a Focus on Intermittent High-Intensity Exercise - PMC.

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That’s a reverse definition of W’ and not a definition with any utility.

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@Cleansoap thanks for your comment. Are you aware of a better definition you can share?

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You could start your research back at the beginning with Monod and Scherrer. Or go back even further and read A.V. Hill’s seminal work.

Jones, Skiba, Poole, Clarke, Vanhatalo, Maturana, Burnley, and several others have been working on CP for many decades and provide a wealth of knowledge on the topic. Ignore pretty much all the blogs.

And it would be a good idea to understand the various formulations of critical power, e.g., 2 parameter, 3 parameter, OmPD to better understand the assumptions that go into things.

Some papers:
Monod and Scherrer, 1965
https://www.tandfonline.com/doi/abs/10.1080/00140136508930810

And further
Moritani, et al, 1980
https://www.tandfonline.com/doi/abs/10.1080/00140138108924856

Jones, et al, 2010
https://www.researchgate.net/publication/283651849_Critical_Power_Implications_for_the_Determination_of_VO2max_and_Exercise_Tolerance

Vanhatalo, et al, 2011

Clarke and Skiba, 2013
https://journals.physiology.org/doi/full/10.1152/advan.00078.2011

Maturana, et al, 2017
https://www.sciencedirect.com/science/article/abs/pii/S1440244017302621

Maturana, et al, 2018
https://www.sciencedirect.com/science/article/abs/pii/S1440244017318170

Jones, et al, 2019 (I don’t agree that CP is the gold standard, but this is a good paper)

Caen, et al, 2024

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That’s some good detective work and plotting of W’ vs stamina.

From my understanding, W’ stays “full” until you hit your CP. If you set a smart trainer for 1W below your CP, your W’ would never decrease, but I suspect your Garmin Stamina would decrease. On the other hand, again, from my understanding, Garmin Stamina is based off of some HR algorithm. I’m not sure if they use power in that calculation. So, although they tracked pretty well in your chart, if you did the experiment I suggested above (steady state ride at 1W below CP), your W’ would not change, but your Stamina would decrease.

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@GarageLab
Thank you for the links. I think I have read most of them already but will double check to make sure.
I now have a very clear understanding of what critical power and W Prime are as well as how they compare to FTP, how they could be used for training, particularly when your type of riding includes anaerobic efforts needed for high intensity sudden efforts such as in criteriums, MTB races and so forth. Might not be that critical for long endurance events where high intensity surges are not that critical.
Thanks all for the feedback

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@Gregory_Yourek
Thanks for the comments. According to the Garmin documentation, both heart rate and power are needed to get accurate readings. Several times, before installing a power meter in my MTB, I used the heart rate monitor only and the Stamina performace did not make any sense, so I guess both power and HR are needed.
What it is not clear to me yet is whether Stamina measures just the available energy above threshold as W Prime does, or if it also considers energy use below threshold.
Maybe doing the test you suggest using both W prime and Stamina would help to find out.
Not sure if I want to make a CP test…

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I´ll dig up some examples but I can already tell you that Stamina goes down, even for activities where you get nowhere even near FTP/CP.
I have been pleasantly surprised on long events that Stamina is a pretty good indicator on how much is still left in the tank. That is for rides over 6 hours at mostly Z2 intensity. Lowest I saw it was around 8% and I was really happy to get to the finish line. Not completely wasted, but I had to dig deep.
I´m pretty sure that Garmin uses your recent activity history, HR and Power.
Haven´t done any further investigation around it, but I have it on one of my device screens and keep an eye on it for longer events.

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@MedTechCD
In those long rides, do you use both the HR monitor and power meter?

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I always record both, but I use HR for steady riding. On short climbs, I keep my eye on power.

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Mentioned earlier it hasn’t corresponded like that for myself, here is a 5.5 hour climbing ride (6500’) at 305 TSS and 0.75 IF:

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where my post ride notes:

“Did all the climbs by feel, didn’t look at power meter data. The day got better as I rode.”

climbs were mostly low to mid tempo.

More reasonable stamina results on shorter rides with all-out efforts under 20 minutes.

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Interesting. Stamina is a topic with very contradictory opinions both in Garmin forums as well as comments in my youtube channel. For some people it works very well but for others it does not.
Thanks all for your comments.

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My 530 was eerily accurate estimating ftp, even on sub-maximal efforts. The 840 hasn’t, unfortunately.

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For what it is worth, I gave ChatGPT the following input:

Context cycling and power training, what is the relation between W’ (W prime), Garmin stamina, FTP, Critical Power, FRC. What is the definition of FTP, what is the definition of CP?

Here is what ChatGPT had to say:

In the context of cycling and power training, several metrics are used to measure and analyze a rider’s performance, including W’ (W prime), Garmin Stamina, FTP (Functional Threshold Power), Critical Power (CP), and FRC (Functional Reserve Capacity). These metrics help in understanding endurance, power, and stamina during cycling. Here’s how they are related and what they mean:

Key Definitions:

1. FTP (Functional Threshold Power):

  • Definition: FTP is defined as the highest average power a rider can sustain for one hour without fatiguing. It represents the power output that separates endurance-based efforts from high-intensity efforts that lead to fatigue more quickly.
  • Use: FTP is commonly used to set training zones and gauge cycling fitness. It’s a critical measure for determining long-duration endurance capacity.
  • Relation: It is related to a rider’s ability to sustain a steady effort over a long period and is often used as a basis for setting power zones for training.

2. CP (Critical Power):

  • Definition: Critical Power is the power output a rider can theoretically sustain indefinitely (though in practice, it’s often closer to a 30-60 minute effort). It represents the boundary between sustainable efforts and unsustainable efforts that lead to exhaustion.
  • Use: CP is a more precise, mathematically derived metric that stems from performance tests across a range of time durations. It divides efforts into sustainable (aerobic) and unsustainable (anaerobic) efforts.
  • Relation: CP is conceptually similar to FTP, but FTP is often based on a one-hour effort, while CP is derived from various shorter-duration efforts.

Additional Metrics:

3. W’ (W prime):

  • Definition: W’ is the finite amount of anaerobic work capacity above Critical Power. It’s essentially the “battery” of energy available for high-intensity efforts that exceed CP, and once depleted, the rider must recover below CP to recharge it.
  • Use: W’ is useful for understanding how much high-intensity effort a rider can put out before fatigue sets in. It measures the amount of energy available for surges, sprints, or climbs beyond CP.
  • Relation: W’ works in conjunction with CP—when you ride above CP, you deplete W’, and when you ride below CP, W’ is recharged. It’s analogous to the “anaerobic capacity” a rider can draw from for short bursts of effort.

4. FRC (Functional Reserve Capacity):

  • Definition: FRC is similar to W’ and represents the total amount of work a rider can do above FTP. It’s typically expressed in kilojoules (kJ) and relates to the ability to perform high-intensity efforts beyond the threshold.
  • Use: FRC is a broader measure of the rider’s capacity for anaerobic efforts, including surges, attacks, or climbs, often in races or high-intensity training sessions.
  • Relation: FRC is effectively a more generalized version of W’, typically calculated with a focus on FTP rather than CP. Both FRC and W’ measure anaerobic capacity, but they are derived from slightly different models.

5. Garmin Stamina:

  • Definition: Garmin’s Stamina is a real-time metric available on some Garmin devices that estimates how much endurance (stamina) a rider has left during an activity. It’s based on a combination of heart rate, power, and performance data, showing both “available stamina” and “potential stamina.”
  • Use: Garmin Stamina helps athletes pace their efforts during longer rides by giving them feedback on how much energy they have left.
  • Relation: Stamina, in this context, is a more simplified, real-time interpretation of a rider’s endurance, influenced by metrics like FTP, CP, and W’. It acts as a dynamic indicator of remaining energy during a workout or race.

Relationships Between These Metrics:

  • FTP and CP: These two are closely related and represent the threshold between sustainable and unsustainable efforts. While FTP is more of a practical estimate used in many training programs, CP is based on a more mathematical approach.
  • W’ and FRC: These measure the rider’s anaerobic capacity above CP or FTP. Both represent how much energy a rider can expend when they exceed these thresholds, with slight variations in calculation methods.
  • Garmin Stamina: This metric integrates aspects of FTP, CP, W’, and FRC to provide a real-time estimation of the rider’s remaining endurance, but it’s more of a high-level summary rather than a precise scientific measure.

Example Use in Training:

  • FTP/CP: Used to set training zones. Efforts below FTP/CP can be sustained for long durations, while efforts above FTP/CP will deplete anaerobic reserves.
  • W’/FRC: These come into play when assessing high-intensity intervals or surges in races. Understanding W’ allows a rider to manage these efforts strategically.
  • Garmin Stamina: Useful for pacing during long events, giving insight into how much overall effort remains.

By combining these metrics, cyclists can better understand how their body responds to different intensities, how long they can sustain certain power levels, and how to pace themselves during different types of rides.

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I put my new SRM pedals on my e-MTB yesterday. Figured I’d see if the Garmin Stamina feature would have any value with my Edge 540 so I went to the Reddit and the Forums.Garmin to see what I could see. Searched all Garmin forums for Stamina and went back a year in Garmin’s Reddit channel. Found no positive useful experiences and plenty of negative. Lots of jokes about it, none complementary.

I’ve run across two pro cyclists on YouTube lately whose coaches have run them through testing periodically to judge their abilities. But, the real work is done grinding the race results it appears. W and Stamina might be a fun mathematical metric to play with, but doesn’t appear to replace real world results?

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@Akizhuzhu
Thanks for the ChatGPT info. Seems to be a good summary.