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Scaling properties of marathon races

Author

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  • Alvarez-Ramirez, Jose
  • Rodriguez, Eduardo

Abstract

Some regularities in popular marathon races are identified in this paper. It is found for high-performance participants (i.e., racing times in the range [2:15,3:15]h), the average velocity as a function of the marathoner's ranking behaves as a power-law, which may be suggesting the presence of critical phenomena. Elite marathoners with racing times below 2:15h can be considered as outliers with respect to this behavior. For the main marathon pack (i.e., racing times in the range [3:00,6:00]h), the average velocity as a function of the marathoner's ranking behaves linearly. For this racing times, the interpersonal velocity, defined as the difference of velocities between consecutive runners, displays a continuum of scaling behavior ranging from uncorrelated noise for small scales to correlated 1/f-noise for large scales. It is a matter of fact that 1/f-noise is characterized by correlations extended over a wide range of scales, a clear indication of some sort of cooperative effect.

Suggested Citation

  • Alvarez-Ramirez, Jose & Rodriguez, Eduardo, 2006. "Scaling properties of marathon races," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 509-520.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:2:p:509-520
    DOI: 10.1016/j.physa.2005.09.066
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    Cited by:

    1. Kwong, Hok Shing & Nadarajah, Saralees, 2019. "Modelling dynamics of marathons – A mixture model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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