Rider model fundamentals

CP is where hard riding changes. Below CP, the body can settle into a hard rhythm. Above it, fatigue keeps accumulating until power has to fall. On the modeled power-duration curve, CP is the value the curve approaches as duration grows—the power asymptote. It is not a promise that CP can be held forever.

W′ estimates how much work the rider can do above CP before having to back off. At a constant power above CP, the difference between the rider’s power and CP is the rate at which the model uses W′. Twenty watts above CP costs 20 joules per second; 200 watts above it costs ten times as much. Riding below CP lets Gritmo estimate how W′ recovers.

FTP solves a practical problem: it gives a rider one threshold number that can be estimated outside a laboratory. The trouble starts when that number is treated as a complete rider model. Depending on the protocol, FTP may come from a sixty-minute effort or be estimated from a shorter test. Change the protocol and the number may change.

CP begins with a different question. Instead of choosing one threshold from one test, it fits a relationship across several maximal durations. The fit returns two parameters: CP, the power asymptote, and W′, the finite modeled work available above it.

On a power-duration chart, FTP is one horizontal reference line. CP and W′ describe a curve. Two riders can have the same FTP and still be very different over three, five, or ten minutes. A single threshold cannot express that difference.

This does not make FTP useless or CP ground truth. CP also depends on the efforts, duration range, and mathematical model used to fit it. But CP and FTP should not be treated as interchangeable. They may be close for one rider and materially different for another.

Gritmo uses CP and W′ because the product needs the shape, not only the line. It has to account for work above CP and distinguish riders whose threshold power looks similar but whose response above it does not.

Extending the two-parameter equation below its fit range treats the full W′ as accessible at every duration. Because W′ is divided by time, predicted power rises without limit as duration approaches zero. Gritmo does not use that extrapolation as a physiological prediction.

Below three minutes, Gritmo can add a separate Short-Power Model when the rider’s evidence supports it. The model keeps the active CP and W′ fixed, then estimates tau from observed short efforts. Tau controls how quickly the model allows the rider to use W′ as the effort gets shorter.

Percentage-based training places every rider on one relative scale. A target at 120% of FTP or CP tells us how far the target sits above a reference power. It does not tell us how much above-CP work the rider can perform.

Two riders can therefore receive the same target while taking on very different modeled costs.

Power bests you enter and measured Ride data contribute evidence to the same Rider Model. Their origin remains visible, but Gritmo does not turn them into competing models.

For its current CP/W′ fit, Gritmo needs one eligible effort from each of three ranges: 3:00–6:00, 6:30–10:00 and 10:30–15:00. The separation matters because three nearby efforts cannot describe the shape of the power-duration relationship.

Short efforts have a different job. Evidence from ten to 150 seconds may estimate tau, but it does not refit CP or W′. At 180 seconds, the Short-Power Model meets the active CP/W′ curve by construction.

An observed effort proves what the rider achieved, not their absolute limit. Gritmo treats ordinary ride bests as lower bounds and looks for the smallest plausible frontier that can explain them. Repeated ride evidence can narrow what remains plausible, but lower bounds alone cannot identify tau from both sides. Without a credible maximal anchor, Gritmo keeps confidence low.

The observed efforts remain points. The continuous curve is modeled. When stronger compatible evidence supports an update, Gritmo promotes one current Rider Model for the rest of the product to use. A mathematically valid curve is not automatically a physiologically reliable one, so duration coverage, recency, residual error and consistency still matter.

CP and W′ describe the core power-duration relationship in a relatively fresh state. They do not fully describe sprint delivery, what remains after accumulated work or what can be produced again after incomplete recovery.

Gritmo interprets the Rider Model through five performance capabilities. They describe what the rider can do, not five isolated systems inside the body. Each capability uses the evidence that belongs to its own question.

CP/W′ earns its place by making a small number of claims that can be checked against observed efforts. Its compactness is also its limit: two parameters cannot describe every duration, fatigue state, or recovery pattern.

Its estimates depend on the durations and quality of the efforts used for fitting. W′ is generally more sensitive than CP to input error and model choice. Predictions also become less reliable outside the duration range supported by the evidence, particularly for very short or very long efforts.

Gritmo treats every output as an estimate. Confidence describes the support behind that estimate, not the ability or value of the rider.

I cite these papers for specific parts of the explanation: what CP and W′ mean physiologically, whether field efforts can estimate them, and where their predictions fail. They do not validate Gritmo’s implementation; that still has to survive observed data.