I’d agree. I’m still looking at TR plans with an eye on the hours and TSS I’ve done in previous years to get a sense of confidence.
But only because Garmin make it difficult to analyse/manipulate EPOC load data. Which I suspect is much better. I also look at active kcal.
I outperform Friel/Couzens predictions on hours and bike TSS for a mid pack Ironman triathlete, by about 30%. I put that down to indoor structured training.
That’s kind of a funny story. When Andy first came up with TSS, he was trying to mimic the formulation of TRIMPS. He had a long series of steps which he posted to the old Wattage List. Then maybe a day later he decided to revise the definition with a slightly different weighting scheme, and revised the long series of steps. A couple of hours after he posted, someone posted with “Um, don’t all those new steps reduce down to 100 * duration in hours * IF^2 ?”
Hahaha. If that’s true, then that’s too funny. I’m a math and physics guy, so these manipulations are completely intuitive and immediate.
Recently, someone posted a review by researcher of Loughborough University that compared the Cricital Power model to a power law. I was surprised by the state-of-the-art. One or two of the authors were from their math department and they included (mathematical) propositions and had proofs in the Supplementary Material. (These were things you could ask math undergraduates and they should know the answer.) When I interviewed for a position there, I was told that the sport sciences department was quite good.
Yeah, I have never gotten into thinking of my training in terms of CTL ramp rates and the like, so this sounds quite alien (and indeed, archaic) to me.
Do you have any alternative that is better? I’m seriously asking.
I am not aware of another metric that is as universal as FTP (feel free to lump in CP). For most athletes, i. e. those that are not on the shallow part on the top-right of the S-curve, FTP (however you want to define/measure it) does strongly correlate with all other performance metrics. Whenever I hear replacements, refinements or some such bandied about, I almost always think “The juice is not worth the squeeze.” — except in certain select circumstances.
Perhaps a stupid question but, where in the TR pages can I find my CTL values?
You can’t, they don’t track/display it. You’ll need to use intervals.icu, TrainingPeaks or other similar services. Strava has their version as well.
I mean at the end of the day if you use Strava’s or intervals.icu’s or CTL or just TSS, it doesn’t really matter, what matters is that the number goes up over time meaning you have increased your training load. And that you achieve via riding more and/or riding harder.
So the question is, why do you want to reach 100 ‘fitness’? Because it’s a nice number?
Yeah, I saw that. I thought they set up a straw man and knocked it down.
As Sam Karlin used to say, “the purpose of models is not to fit the data but to sharpen the questions.” CP/W’ isn’t meant to fit the data–you can fit the data more closely with lots of different models. CP/W’ is useful because it helps you sharpen the questions. A power law fits, but what are the questions it prompts?
It wasn’t just that the fit was worse, the range of validity isn’t clear either. Apparently, it is significantly shorter than what I thought CP to be, the power you can hold for 49ish minutes. (Why 40?)
Ditto for anaerobic capacity, it it does not have predictive value of the work you can do above CP ≈ FTP, what is the point?
It seems to me that the ideas underlying the CP model are not borne out by the data. So perhaps the ideas and questions were interesting, but now we seem to know better.
Physics is all about models. The purpose of models can vary, but one core job is to make testable predictions It ideally contains some mechanisms, but there are plenty of disciplines where phenomenological laws exactly like the power law are used successfully (e. g. in parts of astronomy). And models should always come with an explicit range of validity.
Does it, though? If the range of validity is 15–25 minutes as claimed, what does CP predict? If the model isn’t accurate, I don’t quite see how it can be used to sharpen questions.
The test of a model is how well it fits the data, but that’s not the purpose of models. I’d say that the nice thing about CP/W’ is really when you look at it in work (i.e., duration vs. joules) rather than in power (duration vs. watts). That paper seemed predicated on a watts-time hyperbola as if that were the key (which they subsequently easily shoot down), when we know from the Work view that it’s surprisingly linear over a reasonably wide range of durations, though not for very short or for longer durations. A linear fit lets us think about the intercept and the slope – but also about the areas of poor fit, and why. The curvature at longer durations makes me think that it can be used as a way to parameterize fatigue, and when it sets in. The curvature at short durations makes me think about a throttle on how quickly we can empty the tank, so it’s not only about battery capacity (W’) but also about the size of the resistance–and why. (I see this most clearly when I looked at Team Pursuit, where the riders are always above their CP, so the simple CP/W’ model shouldn’t let them recharge W’, but they can definitely recover something by rotating off the front). Perhaps this is just me, but I still teach Taylor Series expansions to the students but it makes the most sense when I can put some interpretation to the terms. I can often add extra terms to the expansion to reduce the size of the remainder, but from a pedagogical point of view, the lower order terms often suffice to improve their intuition–and their questions.
Phew. More than I wanted to type, and more than you wanted to know.
Like I wrote, you have two purposes for models, predicting outcomes and providing insights into the mechanism. Models that propose a mechanism, but which are found to describe outcomes not very well simply propose the wrong mechanism or leave other important factors out. And that means, these models either need to be revised or abandoned.
The criticism in the paper implies that the authors think the mechanism implied by the CP/W’ model is not a good description of reality. Put another way, the picture of W’ as the size of capacity of an athlete’s battery or the size of their gas tank does not seem to be compatible with observation. Or, rather, there are better models out there with the same number of parameters (2).
There is nothing surprising about the linear relationship between work and time-to-exhaustion since this is mathematically equivalent to the hyperbolic power-to-time-to-exhaustion curve, i. e. you can start with one and obtain the other. In that sense, the hyperbolic relationship between power and time-to-exhaustion is the key feature of that model.
The article actually considers fatigue (equations (2) and (5)) and shows that this leads to false predictions by the model. Any model that allows you to predict power and time-to-exhaustion allows you to parametrize “fatigue”.
Not everything in life can be explained by a Taylor expansion. 
For one, Taylor expansions are around a particular point, so the farther you get away from that point, the worse the error typically becomes.
I don’t. I use FTP quite a bit to define threshold and sub-threshold targets. I use the athlete’s performance curve to lay out intervals above threshold (rather than a fixed % of FTP). I was referring to people who say VLAmax or FatMax or whatever are the newer better way to train. Usually the people telling you that are the ones that want you to buy their testing protocol or be coached by their coaches, whereas FTP was defined by a guy that doesn’t coach or do anything related to his FTP definition for profit.
The reality is you can base your training off of any metric you want, % VO2max, lactate measurements, blood O2 concentration, heart rate… whatever. FTP (and CP or really anything based on a sustained power) is superior in my opinion because it is easily obtainable with field testing and directly measurable on a day to day basis in real time with nothing but a power meter and a bike computer. As you said, most of the other available methods are “juice not worth the squeeze” when compared with using FTP/CPwhatever.
The point Karlin was making was not that a model should be kept or rejected because it does or doesn’t fit, it’s that you can learn a lot by asking where and why it fails, and an explicit model helps in structuring thinking about the failure. (As it happens, I just recently gave a series of lectures on using models of various simple types to refine or expand research questions).
Although from a mathematical point of view the linear and hyperbolic models are equivalent, from a statistical estimation point of view the way we treat the errors very much aren’t. And perhaps that’s part of the reason I don’t think goodness-of-fit is the primary decider of a model (That said, my wife’s research definitely depends more than mine on the quality of projections her models make, so I definitely see the value in that since it helps pay our mortgage. No one really cares about the quality of my projections so there’s that).
I’m sure you know that we usually pick a sensible point around which to do Taylor expansions, and that we pay attention to the size and behavior of the remainder. (Actually, that’s one of the homework problems I give the students).
I find them only to be fun numbers to look at, and nothing more.
Maybe if I REALLY wanted to dig in I could find a pattern that works for me. But I don’t care enough.