Long-Range Correlations and Complex Regulation of Pacing in Long-Distance Road Racing

in International Journal of Sports Physiology and Performance
Restricted access

Purchase article

USD  $24.95

Student 1 year subscription

USD  $107.00

1 year subscription

USD  $142.00

Student 2 year subscription

USD  $203.00

2 year subscription

USD  $265.00


To analyze time-domain, spectral, and fractal properties of speed regulation during half-marathon racing.


In 21 male experienced runners, high-resolution data on speed (V), stride frequency (SF), and stride length (SL) were assessed during half-marathon competition (21,098 m). Performance times, timeand frequency-domain variability, spectral-scaling exponent (beta), and fractal dimension (FD) of V, SF, and SL were analyzed.


V of 3.65 ± 0.41 m/s, SF of 1.41 ± 0.05 Hz, and SL of 2.58 ± 0.25 m occurred with higher (P < .05) individual variability in V and SL than in SF. Beta and FD were always 1.04–1.88 and 1.56–1.99, respectively. Beta and FD differed (P < .05) in SF and SL compared with V and were correlated in V and SL (r = .91, P < .05). Spectral peaks of V, SF, and SL occurred at wavelengths of 3–35 min, and those of V and SL were interrelated (r = .56, P < .05). Mean SF and mean SL were significantly correlated with performance (r = .59 and r = .95, P < .05). SL accounted for 84% ± 6% and SF for 16% ± 6% of speed variability.


The observed nonrandom fluctuations in V, SF, and SL correspond to nonstationary fractional Brownian motion with inherent long-range correlations. This indicates a similar complex regulation process in experienced runners that is primarily mediated via SL.

Hoos is with the Faculty of Philosophy II, Julius Maximilians University Wuerzburg, Wuerzburg, Germany. Boeselt, Steiner, and Beneke are with the Dept of Medicine, Training and Health, Philipps-University Marburg, Marburg, Germany. Hottenrott is with the Dept of Sports Science, Martin Luther University Halle-Wittenberg, Halle, Germany. Correspondence concerning this article should be addressed to Olaf Hoos. E-mail: olaf.hoos@uni-wuerzburg.de