The temptation of the exact fit
Two maximal efforts give exactly one hyperbola, and with two efforts that is simply the solution: the line runs through both, which is why a cleanly ridden protocol matters. Three efforts give exactly one more complex curve. That looks precise, but it isn't: an exact fit of a more complex curve through a few points has no room for what real life always brings along. Form on the day, fuelling, pacing, yesterday's leftover fatigue. Every one of these deviations goes one to one into the parameters. In the worst case, one additional effort lowers the calculated Critical Power by more than 30 watts, not because you are weaker, but because the model tolerates no error.
What we do instead
Our analysis follows a simple physiological fact: on a given day you can stay below your true performance limit, but never go beyond it. That is why we first judge every effort on its own: only what lies on your personal maximal power curve counts as maximal and goes into the model. Then we do not fit “through the middle”, but weight asymmetrically: an effort above the model curve is impossible and forces the model upwards; an effort below it can be explained and carries only little weight. The curve follows your best efforts, not the average. With two efforts the line runs exactly through both; the asymmetric weighting applies from three efforts on.
When a sprint completes the picture
The standard model has two parameters and one known weakness: in the sprint range it becomes unrealistic. Morton's 3-parameter model fixes that, but only when a short, maximal effort of 30–60 seconds anchors the curve at the bottom end. Without this anchor the model would have to guess the sprint range, and in doing so it would push Critical Power down. So our rule is: with three or more maximal efforts plus an anchor, the full Morton model is fitted; otherwise it stays with the proven 2-parameter model. And if the data do not fit together, for example because the sprint was not ridden rested, the algorithm discards the extension and tells you why in the report.
What this means for you
Choose one of the two protocols (3′ + 12′ or 5′ + 20′), ride it cleanly, and stick with it for retests. Coaches who want more upload three or more maximal efforts plus a sprint: the tool recognises automatically which model the data support. Either way, the report shows you which model was fitted, which efforts were used, and which were not, with the reason.
Evidence, not hype: The models come from the peer-reviewed literature (Monod & Scherrer 1965; Hill 1993; Morton 1996; Mattioni Maturana et al. 2018). This article explains why we apply them the way we do.
References
- Monod, H. & Scherrer, J. (1965). The work capacity of a synergic muscular group. Ergonomics, 8(3), 329–338.
- Hill, D. W. (1993). The critical power concept. A review. Sports Medicine, 16(4), 237–254.
- Morton, R. H. (1996). A 3-parameter critical power model. Ergonomics, 39(4), 611–619.
- Mattioni Maturana, F., Fontana, F. Y., Pogliaghi, S., Passfield, L. & Murias, J. M. (2018). Critical power: How different protocols and models affect its determination. Journal of Science and Medicine in Sport, 21(7), 742–747.