Towards Quantifying Training Loads Using CP

[Coach_Ron]

Following up from a highly interesting discussion thread : https://forum.intervals.icu/t/ftp-and-cp-interchangeability-some-notes/2665

David has made available an FTP model and several CP models to choose from. The athlete can choose the model that comes closest to reality. In other words, the number that most closely resembles a “maximum” steady state. If they don’t like it, they adjust it as they see fit and form their own custom power zones under “Settings”.

I take it that the metric “load” in a cycling activity is proxy for TSS. If yes, its likely tied up to FTP. Since we want a distinction between derived metrics associated with these terms, I suggest Dr. Skiba’s “xPower” & “BikeScore” as CP based analogues.

This is an open-source computation but unfortunately I can’t find the original documentation from Dr. Skiba’s webpage. However, I’ll list out the steps required to do this below :

1. Calculate Critical Power (as per the method of Monod & Scherrer (1965), or Morton 3P method)
2. From raw time series data, compute a 25-s exponentially weighted moving average for power.
3. Raise the values in step 2 to the 4th power.
4. Average the values from step 3.
5. Take 4th root of step 4. Define it as xPower.
6. Divide xPower by Critical Power from step 1 to get the Relative Intensity (RI).
7. Multiply the xPower by the duration of the workout in seconds to obtain a “normalized work” value in Joules.
8. Multiply value obtained in step 7 by the RI to get a raw BikeScore.
9. Divide the values from step 8 by the amount of work performed during an hour at Critical Power.
10. Multiply the number from step 9 by 100 to obtain the final BikeScore.

I’m not sure it is possible for most people to ride at CP for an hour, given a reliable value of CP (i.e an intensity that is the boundary between heavy and severe regions). Perhaps pegging the score to an hour would be incorrect in that case. Maybe the modification to step 9 should be the amount of work at CP tolerable for the duration associated with that intensity in the athlete’s PD curve. Going down this path would deviate from the original Skiba BikeScore definition. So probably best to leave it as it is until further guidance from Dr. Skiba. I could try reaching out to him.

I suggest a “cog wheel” option to user to facilitate changing the load metrics based on CP or FTP as they desire.

What does the rest of the community think?

Background reading for computation : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.564.9255&rep=rep1&type=pdf

[david]

Tx. There have been previous requests for BikeScore. I would probably still need to call it “Load” to avoid trademark issues but have something in settings to decide how the athlete’s load should be calculated and what “threshold” is (FTP or CP). Choosing CP would just change the “FTP” label to “CP” everywhere and use “eCP” instead of “eFTP”. Likewise would need a setting for the load calc (TSS/BikeScore) relative to threshold (FTP/CP).

Time to upgrade TSS?

I would need to be working from a published paper to do something different. BikeScore (Skiba) has already been suggested on this forum as an alternative. TSS certainly has limitations but it also has a huge ecosystem behind it. Lots of people joining Intervals.icu look very closely at the training loads and want a very close match with other tools, which is understandable. I think the whole polarised training thing helps with TSS chasing.

[Coach_Ron]

Thanks.

Agree with IP/ trademark. You can continue to call it Load to keep things consistent. In the background, just the computation changes using either CP or FTP.

I got a fairly helpful response from Dr. Skiba when I asked him about the use of a score of “100” to peg work for an hour.

Here’s what he states, quoting him directly

“In terms of the computation, I only made it compatible with the 100 point scale so that it would fit with the (very useful) TSS. There’s no reason it needs to be so. It just made it easier for people to go between the scales and to be able to talk to each other. You could (and I have experimented with) making 100 points equal to the time the person can ride “at” CP.”

My question followed, whether someone can ride at CP for an hour as I highly doubt so. He agreed with me that only in the rarest of cases. In most cases, CP corresponds to an intensity sustainable for around 20-30 minutes.

It really depends upon how good the athlete is, how good the estimate of CP is, and how closely they adhere to their pacing. If athletes are careful to approach CP from below, not exceed it, etc… I’ve seen athletes approach an hour, but only rarely. You are correct in your estimation that most motivated people can hang at CP for 20-30min.

However, it’s important to realize that you can’t ride “at” CP. Every estimate has an uncertainty associated with it, based upon the quality of the tests, the accuracy of the power meter, etc. So really, CP training in the practical sense involves being in a zone of probably several percent in real world terms. I like to tell athletes that CP is the “center” of the bullseye, which you can never really hit dead on, but as long as you are in the black, you are doing ok.

So basically what Dr. Skiba is saying is that there is no reason physiologically speaking to peg the score of 100 to a time duration of 1 hour and we are free to model it as per a more realistic scale. So David, its upto you what is the approach you want to take. I would say refer to the PD curve and pick out the time duration corresponding to the 2-P CP value.

Lastly, can Bikescore (or Load) be calculated from the 3-P model? I had a doubt as he seems to prefer the Monod 2-P model.

You can do anything, but the question is if you should. I would say no. I get into this in my forthcoming book, but the reason is that the 2 parameter model seems best correlated with the actual change in physiology. If you go above CP as calculated by the 2 parameter model, you enter into a metabolic instability that forces you towards vo2max, and you quit. (in other words, riding at any power above CP, causes VO2 to rise and eventually reach VO2max, even if you ride the same power the whole time). The 3 parameter model may fit short duration power better, however, it gives you a lower value for CP, which may not be high enough to reflect the boundary between stable and unstable metabolism…and THAT’s what you really want to know about.

Dr. Skiba’s views on what model to use aligns with what the research world seems to prefer and this is the Monod 2-parameter model. So David, this is something to watch out for. The computation needs to pick the 2-P CP value, not the 3-P CP value.

Finally, the Load value then feeds into the Fitness & Fatigue management charts.

Thank you,
-Ron

[david]

Thanks for this. I went with the 3P model because it was “newer” and seemed well supported in reading I did and it didn’t have the “infinite” short duration problem.

I am going to have to make some time to tackle this soon. Not the sort of thing you can do after working all day