Clearly you haven't done your homework...the time constants are drawn from scientific studies of the full-blown Banister impulse-response model:

https://www.trainingpeaks.com/...performance-manager/

That's the only thing you took issue with in my post? I'm disappointed. Anyways, 7 and 42 days were still assumptions, weren't they? I didn't read the entire link, but I don't see where it explains how they were "drawn from" and calculated based on prior studies.

See table 1 in the article, and the surrounding text. The table is blury and hard to make out. But it lists the studies that estimated the model parameters and their estimates. The article also discusses the sensitivity of the model to errors in the time constants compared to the individual, and also discusses when it might be appropriate to adjust those... Especially the 7d constant.

Clearly.

"The default time constants of the Performance Manager, i.e., 42 d (6 wk) for CTL and 7 d (1 wk) for ATL were chosen as nominal values based on the scientific literature." (see #7 under "Applying the Performance Manager concept").

I could, of course, have instead done a meta-analysis, and calculated a weighted average across every study that could be located. However, all this would have done is convey a false sense of precision, because:

1) neither Banister's model or the simpler PMC are particularly sensitive to the time constant used for CTL, and

2) while both are sensitive to the time constant used for ATL, there is considerable variation between studies (cf. Table 1), which appears to relate to the overall training load.

Because of these facts, nominal values are sufficient.

Or better still, read all of the references (which includes essentially every English-language peer-reviewed original article published when I wrote the article on August 14-18, 2006).

From a purely mathematical point of view ATL/CTL is no more sensitive to changes in TSS than TSB is, and is arguably LESS sensitive. Sensitivity in this context being rate of change in output as a function of input. Since the CTL constant is so much larger than the ATL constant, the rate of change of ATL/CTL is driven by the rate of change in ATL alone, certainly on a single day basis. ATL changes at a rate that is 6 times faster than CTL. So, when I divide by CTL all I'm really doing is scaling ATL down to a value between 1 and 2....eg, making it a SMALLER number, but the rate of change in ATL/CTL is entirely driven by the change in ATL. CTL is adding nothing new.

The above said...I did go back and model a training week as a set of fixed ratios of CTL, as I described above. I used:

Mon = 1.3
Tue = 1.5
Wed = 2.0
Thu = 1.0
Fri = 1.5
Sat = 3
Sun = 0.7

After several weeks, the ATL/CTL ratio stabilizes to:

Mon = 1.37
Tue = 1.37
Wed = 1.42
Thu = 1.36
Fri = 1.35
Sat = 1.50
Sun = 1.39

TSB is still sensitive to actual CTL values, but at a CTL of ~100:

Mon = -37
Tue = -37
Wed = -43
Thu = -37
Fri = -37
Sat = -54
Sun = -42

At this CTL value (100) this represents a CTL ramp rate of 8 CTL per week. I can tell you that I CANNOT sustain that training load at that CTL. I noted above the ramp rates that I can maintain at various CTL levels. So, directly to your point, NO I cannot train to maintain "fixed" ATL/CTL ratios per week independent of CTL state.

My current CTL is 93. the lowest TSB that I can sustain right now is about -35. That is a ROUGH day, but that would only be a ATL/CTL ratio in the 1.3x range...no where near your proposed 1.49.

Again, because my tolerable ramp rates aren't constant (and aren't constantly increasing), even the concept of FIXED ratios doesn't work.

Hey
This is really interesting, but i dont understand how you implement it to improve your everyday training, and also finding which atl/ctl number is optimum for maintaining performance while avoiding injury... I understand its different for everyone, so how do you find the number that is right for you..? Is it just trial and error or am i missing something

This approach will NOT inherently improve your everyday training. I say that because there is no NEW information in the ratio of ATL:CTL that isn't already in TSB. As described above TSB and ATL/CTL are equally sensitive to daily TSS. When one moves the other moves in the opposite direction and by the same proportion (not magnitude, but proportion).

So, everything that you know (or don't know) about how to find your "ideal" TSB applies to finding your ideal ATL/CTL and vice-versa. Also, both approaches must be scaled to your current weekly CTL. So, your ideal (or maximum) TSB or ATL/CTL ratio will be different when your CTL is 20 vs.100.

Yes, its a trial and error process. But, since every single day is a trial and an opportunity for error. If you pay attention to it, and how you feel every day, and how you perform on "key" workouts. It doesn't take long to determine what works and what doesn't. The key there is probably to start somewhere REASONABLE, and then scale up or down based on how you feel (too easy, or too hard). Also know that it takes about 3+ weeks for things to really settle in.

Also as I noted above, the ATL/CTL ratio approach is exactly analogous to planning by scaling factors of CTL. If every day is planned as a scale of CTL (eg, 1.4 * CTL), and adjusted weekly to the ever climbing CTL, and that week scaling is repeated 3-6 times in a row the ATL/CTL values will stabilize to a fixed set. I gave one example above, which stabilizes to a set of values similar to what Miles suggests.

This CTL scaled approach (or the equivalent ATL/CTL approach, since they are equivalent) works best for me in the mid-range of my training...when my CTL value spans from about 40-80. Below a CTL of 40 it leaves me undertrained....applying the same scaled week above a CTL of 80, I would quickly end up over-trained. That is not to say that you couldn't have a different set of scaling factors for CTL<40, 40<CTL<80, and CTL>80. You just need to determine what those are. Again, its not hard...one week will quickly tell you that you've (under)overdone it, and you can scale (up)down the next week.

A TSB at a low CTL is much different than the same TSB at a high CTL according to my perception, so TSB is not sensitive over a range of CTL's.
Your CTL*[x] does not factor in ATL; I think that's pretty important, as I can take a week off and still be over 80 CTL but then be at an extremely low ATL/CTL, say, approaching 0.60, in which case your CTL*[x] would not be anything at all reflective of ATL/CTL of 1.4+ at 80 CTL at a different point in time where my training load had been pretty heavy leading up to that point, so your statement on their equality is false.
ATL/CTL has felt the same at low CTL compared to at high CTL and I did not feel undertrained and I am not feeling overtrained; that's my perception.
I appreciate your input, but I'm not convinced it's a voice of authority you are sharing. My voice definitely is not a voice of authority, but I guess the difference is that I've made the clear up front and continuously in the thread. I'll leave that to Coggan. I'll leave my spreadsheet live for people to look at, and know that I'm feeling good and report back otherwise.
1.49 ATL/CTL days are hard... but not harder at a higher CTL than they were at a lower CTL.
And to Kiley's point, if he were to calculate ATL/CTL for his monster workouts that he claims won't be captured outside of HR variability, I wager that ATL/CTL for those workouts will break 1.5. Also, I tried the formula he provided and the ATL, CTL and TSB figures in my chart, which currently match TrainingPeaks spot on, began to diverge wildly, so I'll stick with the current formulas in the spreadsheet unless Coggan weighs in and sets me straight (and I guess TP for that matter....?)

Here's an image showing how CTL and TSB are highly (inversely) correlated while ATL/CTL is not when training volume is ramping up which is when injury and overtraining are most likely:

I've updated the initial post with a video; also posted here:

and another comment. Filliol has stated that he thinks peaking is overrated and he doesn't focus on peaking. He then went on to say that his athletes have a standard rest and race prep week they do before each ITU race. My big hunch is that his athletes's ATL/CTL is probably about 0.65 the day before the race, so they are peaking, but they have large enough fitness and their CTL gains are curvlinear, allowing for a 5-7 day 'taper', as I discussed in that video.

Now standard on Garmin 965 and named Load Ratio: https://www.dcrainmaker.com/...in-depth-review.html

This might be neither here nor there anymore since the rest of this discussion is so old, but I do not believe that the rolling windows used by CTL/ATL is the correct approach. I think the model would be improved if a much longer history of training stress were used for each and an exponential weight was applied to them (faster decay for ATL than CTL, obviously). With the rolling windows you can get some wonky base effects, especially with ATL. I also think this is more how it works in real life . . . lifetime miles matter.

---

Dimond Bikes Superfan

Yeah, I agree about longer history. Or maybe even a separate metric. Training Peaks' use of the term "fitness" for CTL is kinda silly anyways, but if they are going to use that term, X CTL/fitness for someone who has been training consistently for 20 years is not the same as X CTL/fitness for someone who has been training for 1 year.

Where my head has been for some time is the power of ATL/CTL to be a strong proxy for the overall training effects with regard to how the training affects the person's immune system.

I have historically used that ratio as follows: don't go over an ATL/CTL of 1.49, Don't stay at 1.49 for too long, Don't change ATL/CTL from day to day by more than 0.2, Be at 0.65-0.7 ATL/CTL the night before a race. When CTL plateaus, ATL/CTL drops and drops: this is a sign it's time to race.

Rappstar has suggested that ATL/CTL might be more closely related to the area under the CTL or ATL curve. I've felt that ATL/CTL feels like an effect on the immune system. I actually don't know if that's fully accurate.

With supplementary exercise such as using a Vasa trainer, strength training, Lever/Alter G treadmill running/aqua jogging, I don't get the same suppressed immune system feeling that is captured by the ATL/CTL ratio when I do swim, bike, run workouts.

I could examine the relationships between atl/ctl, the area under the ctl curve, and hrv (as a proxy for humoral and cellular immunosuppressive effects via increases in cortisol and blood pressure), and use these coefficients to weight the TSS of swimming, biking, running and different supplementary workouts.

I could then build a model, similar to the spreadsheet in the video I included in a prior post, that uses atl/ctl for next-day training planning and then use post workout hrv to update the day’s cumulative TSS, which would then auto update the next day's planned training based on atl/ctl. The TSS coefficients used for weighting workout types would be updated based on a model of the prior 45 days’ on a rolling basis.

———-

My next thought is that a top level triathlete could break down training into two types of training:

Activities that do not significantly raise ATL/CTL:

• Swim Form: swim in endless pool with video screen on bottom and ear piece in receiving constant feedback from coach and having visual feedback.
• VasaTrainer for swim strength and very low heartrate.
  
• Run Form: run on treadmill with Lever/AlterG with very low body weight with video screen in front of runner and camera from the side and a coach present to provide constant feedback.
• Bike Form: on trainer with video screen in front of rider, camera from the side, pedaling in very slow motion and display of where the rider is applying force during the pedal stroke, the ratio of quad engagement to power output on the screen (muscle sensors on quads), with coach providing constant feedback.
• Strength training: varying and low volume/time

Activities that significantly increase ATL/CTL:

• Endurance training: 1.0-2.0 mm/L, high volume
• AeT training: 2.5-3.0 mm/L, medium volume using fartlek intervals to lower strain (Canova)
• AT training: 3.5-4.0 mm/L, low volume using fartlek intervals to lower strain (Canova)

And now here's how that could look during a week of pro training where they typically already S/B/R daily, and the purpose would be to

• minimize ATL/CTL effects/suppressed immune system responses
• maximize gains from training that does not raise ATL/CTL
• lots of biomechanics work. analogy: don't just increase the power applied to the wheel, make the wheel rounder

Monday:

• Swim Form
• Bike Form
• Run Form
• Strength

Tuesday:

• Swim Form & Swim AeT
• Bike Form & End Bike
• Run Form & End Run
• Strength

Wednesday:

• Swim Form & VasaTrainer
• Bike Form & End Bike
• Run AeT
• Strength

Thursday:

• Swim AT
• Bike Form & End Bike
• Run Form & End Run
• Strength

Friday:

• Swim Form & VasaTrainer
• Bike Form & End Bike
• Run AT
• Strength

Saturday:

• Swim Form & Swim End
• Bike AeT & AT -includes A/B aerosensor testing during intervals.
• Run Form & End Run
• Strength

Sunday:

• Swim Form & VasaTrainer
• Bike Form & End Bike
• Run AeT
• Strength

Have you updated your original google doc (from your original post) to reflect any changes?

jeremyebrock wrote:

Have you updated your original google doc (from your original post) to reflect any changes?

I pulled down the google sheet in the original post, but here's a view-able sheet which you can copy and see the formulas and basic structure used. I did not add the hrv idea above to create a feedback loop - that's just a curiosity at this time.

The example training in this sheet is someone starting with a pretty high existing CTL, so there is no ramping up of training. When not ramping up, ALT/CTL and TSB are pretty correlated. During a period of ramping up training, they diverge quite a bit as seen in the youtube video, and I contend that's what many of us are doing a lot of the time and it's during that ramp up period that the chance of immunosuppression and injury increase and where ATL/CTL is very helpful. You can play with and see if you copy and edit this sheet:

https://docs.google.com/...mCM/edit?usp=sharing

Gotcha thanks, really interesting.