Mathematical Elegance for Xert: Integrating Freshness into the Signature

[Craigol (Hans Meier)]

I’ve been delving into Xert on a theoretical level over the past few days and I’m fascinated by both the concept and the implementation. I’m almost enjoying it more than cycling itself But seriously, I look forward to analyzing each workout in Xert.

I have a suggestion or thought for future versions:

If I understand correctly, Xert relies (among other things) on two separate systems that operate independently: the Fitness Signature (i.e., the trio of TP, HIE, and PP, along with derived values like LTP or X-minute Power) on one hand, and the Training Status + Freshness indicators on the other. These two systems are not connected.

So when I do a hard workout, my star status might turn yellow or red, but my fitness signature doesn’t change: my TP, HIE, and PP stay untouched (aside from minor increases through XSS accumulation or a breakthrough).

But that doesn’t reflect reality. After a hard session, my signature should actually drop — at least one of those parameters, if not all three. That’s how physiological adaptation works: only after several hours or even days do I fully recover — or perhaps even become fitter than before (keyword: supercompensation).

Idea: Instead of running two separate systems — the fitness signature and the training status/freshness — why not integrate the latter into the signature itself? This way, the three signature parameters would ideally reflect actual performance potential at any given moment — even immediately after a hard workout or the day after.

There would be several advantages: First, it would be much more elegant and would push the Xert concept of the three-parameter model further toward a unified theory (keyword: grand unified theory, rather than multiple models). Some contradictions that are often discussed here on the forum could be resolved more elegantly. And it would also be a fascinating mathematical challenge to incorporate freshness into the fitness signature in such a way that it changes hourly — a sort of meta-MPA.

As someone with a master’s degree in mathematics, I would absolutely love such an approach — it feels completely natural to me. Data nerds would definitely appreciate it And on top of that, it would take Xert’s unique selling point to an entirely new, unmatched level.

What do you think?

[xertedbrain (Armando Mastracci)]

A person after my heart…

Training loads (TL or training status) and fitness signatures are currently loosely tied. As TL’s go up, so do your Fitness Signature values. But we don’t adjust your signature values with recovery load (RL). That is something we originally considered but since it added a great deal of complexity to an already fairly difficult algorithm to implement, we did not include it.

But now that we’ve introduced Durability Scores, we’re sort of backing into this anyways. Durability calculations, in effect, take into account your accumulated strain (or KJs, carbs, etc.) into account in predicting your performance during a ride. One could harmonize Durability with TL/RL to create a fully dynamic fitness signature that rises and falls with TL/RL/XSS in 3 dimensions before and during rides. That’s cool! But also challenging because a key factor in durability (as well as recovery) is replenishing the carbs you burn. This data isn’t in the power data we collect and would require out-of-band data collection at the moment. Having said that, it would be quite an accomplishment to have a model that predicts performance on a 24-hour basis inclusive of accumulated strain, recovery and perhaps accounting for food intake and other biological contributors to performance. Combining the additional data collection, with a robust exercise model and applying AI-based methods could likely get us pretty close.

I’d love to venture down this road in the tuture. We have several fairly big improvements to the exercise model that we are working on and think these new models will form a better foundation as a more universal exercise model. There are applications outside of cycling too such as weight-training and other sports activities. A fully universal exercise and fitness 24-hour model isn’t as pie-in-the-sky as one might think.

Xert was originally imagined as a way to showcase what is possible with exercise modeling, beyond where the current science is. With more and more people like yourself recognizing the potential, we hope we might see even greater advancements and contributions from scientists, mathematicians and AI experts as time goes by.

Thanks for making my day.