Tracking Performance Limits Using Multi-Timescale Maximal Mean Power Ratios

This study introduces a multi-timescale mechanical model to quantify proximity to performance limits during endurance exercise. The model represents power output using a set of rolling averages, each associated with a characteristic time constant, and identifies the dominant component as the one approaching its historical maximum at any given time. To demonstrate this framework, real-world data were collected from 21 male professional cyclists during an 11-day training camp. Data from the first 10 days were used to construct individual maximal mean power (MMP) profiles across multiple time scales. On the final day, cyclists completed a fatiguing protocol (∼2000 kJ of work) followed by 3-min and 12-min maximal time trials. During exercise, the ratio between each exponentially weighted component and its corresponding historical maximum was computed, and the maximum ratio was used to track proximity to performance limits. At the end of the time trials, this ratio reached 98.6% (94.3%-101%) and 101% (98.5%-103%) for the 3-min and 12-min efforts, respectively (median and interquartile range), indicating convergence toward maximal performance capacity. Notably, in both trials the dominant component corresponded to a slower time scale (∼1 h), rather than to components matching the nominal duration of the efforts. These findings suggest that performance limits emerge from the interaction of multiple time scales and are not solely dictated by the duration or intensity of the task. This framework extends the traditional use of MMP from a post hoc descriptive tool to a real-time dynamical measure of performance capacity.