Scaling properties of marathon races

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 marathonerʹs ranking behaves as a power-law, which may be suggesting the presence of critical phenomena. Elite marathoners with racing times below 2:15 h 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 marathonerʹs 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.