Reliability of time to exhaustion analyzed with critical-power and log-log modeling

Med Sci Sports Exerc. 2005 Apr;37(4):696-701. doi: 10.1249/01.mss.0000159023.06934.53.


Purpose: The large variability of time to exhaustion between repeated tests at constant power output or speed gives an impression that these tests are unsuitable for monitoring athletic performance. We have addressed this issue using critical-power and log-log models of the speed-duration relationship to analyze treadmill runs.

Methods: Application of differential calculus to the models provided factors for converting variability in time to exhaustion into variability in equivalent time-trial time. We estimated values for the factors and variabilities from a reliability study. Eight male competitive runners performed a test consisting of three constant-speed runs to exhaustion lasting approximately 2, 4, and 8 min, with a 30-min rest between runs. A pair of such tests 5 d apart was repeated 7 and 14 wk later within a summer competitive season. We also used the models to predict times for fixed distances from each set of three runs. Repeated-measures analysis of log-transformed times provided estimates of variability expressed as coefficients of variation.

Results: Variabilities of time to exhaustion were 9.2, 13, and 16% (shortest to longest runs). Converted to their equivalents in time-trial time, the variabilities were 2.6, 1.7, and 1.0% via critical-power modeling, and 1.3, 1.7, and 2.2% via log-log modeling (90% likely limits x//1.2). The conversion factors varied typically by 28% (x//1.5) from runner to runner. Variabilities in times predicted for fixed distances were similar, but more uniform, for the log-log model.

Conclusion: Runs to exhaustion are inherently reliable, but conversion of changes in time to exhaustion at a single fixed speed into changes in equivalent time-trial time is model and individual specific, and therefore only approximate. Combining runs at several speeds with log-log modeling provides accurate conversion.

MeSH terms

  • Adult
  • Exercise Test
  • Humans
  • Least-Squares Analysis
  • Male
  • Models, Biological*
  • Physical Endurance / physiology*
  • Physical Exertion / physiology
  • Reproducibility of Results
  • Running / physiology*
  • Time Factors