W-tau: why your recovery doesn't come from an app
Every training app knows how much power you have. Almost none knows how quickly you get it back — and the app that does claim to, uses an average that probably isn't yours.
Rob Bohte, physician and coach · updated
You know the feeling: after a hard effort above your limit it takes a moment before you can go again. That “battery above your line” is called W′ in training science — a finite amount of work you can deliver above your Critical Power before you blow up. As soon as you drop below your CP, that battery recharges. How fast that goes is the question a race turns on.
What an app does: one curve for everyone
Most apps use one standard formula for that recovery — the same curve for you, for your teammate and for a pro. That formula (the classic W′bal model) assumes one fixed recovery rate, derived from a group of moderately trained cyclists.
It isn't one formula either, but a handful: some five are in circulation by now, each with its own assumption about how fast you recharge, and they give different answers. (Skiba 2012 and 2015; Bartram 2018; Pugh 2022) What they share: they don't measure your recovery. They derive it from your CP and from how far below CP you are riding.
In 2025 all five were laid against real data. Thirteen competitive cyclists rode intervals until they truly blew — if the model is right, the battery reads zero at that moment. Not one formula landed there: one calculated there was plenty left, another that the battery should have run out long before. The individually determined recovery time in that group ranged from roughly 100 to 190 seconds. The researchers' own conclusion: you need an individual value, not an average. (Welburn et al., 2025)
What the science actually shows
Two things a standard curve leaves out.
Translated: two riders with the same FTP can have completely different recovery, depending on their aerobic engine. An app that sticks one curve on both of you misses exactly that difference.
That's why your recovery doesn't come from an app
An app doesn't know your recovery — it estimates it with an average. And science now says three things at once: recovery is individual, it is two-phase, and it is linked to your specific fitness. None of those three sit in a standard formula.
What can be done: measure it on you. With a single targeted test session — recording your recovery after a short and a longer rest period — your personal recovery profile can be estimated. That rarely happens; usually it stops at the estimated value from the formula. That personal recovery time is what I call your W-tau. (individualisation method: Chorley et al., 2023)
Honest about what W-tau is and isn't
W-tau is a model estimate, not an absolute physiological constant. Even a personally measured value doesn't predict your exhaustion to the second — the research admits that honestly itself. But a value measured on you is demonstrably better than an average from an app you've never seen. That's the difference: not perfect, but yours.
And the good part: once you know your W-tau, you also know what you can do about it. The research points towards your aerobic engine — VO₂max and CP — as keys to improving your recovery. Not a guess, but a foothold you can train.
Want to know your W-tau instead of guessing it?
Start with the CP test: your Critical Power and W′ mapped, with a conversation about what it means for your races. No app average — your number.