Power Laws, Power Laws, Everywhere, and Not a Ball to Kick

Boy reading the physics section of the arxiv sure has given me much amusement lately:

arXiv:0706.1758
Statistics of football dynamics
Authors: R. S. Mendes, L. C. Malacarne, C. Anteneodo
Abstract: We investigate the dynamics of football matches. Our goal is to characterize statistically the temporal sequence of ball movements in this collective sport game, searching for traits of complex behavior. Data were collected over a variety of matches in South American, European and World championships throughout 2005 and 2006. We show that the statistics of ball touches presents power-law tails and can be described by $q$-gamma distributions. To explain such behavior we propose a model that provides information on the characteristics of football dynamics. Furthermore, we discuss the statistics of duration of out-of-play intervals, not directly related to the previous scenario.

In related power law news, if you’ve got the data and want to know whether it’s power law distributed, you’d better read this:

arXiv:0706.1062
Power-law distributions in empirical data
Authors: Aaron Clauset, Cosma Rohilla Shalizi, M. E. J. Newman
Abstract: Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the tail of the distribution. In particular, standard methods such as least-squares fitting are known to produce systematically biased estimates of parameters for power-law distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law distribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We demonstrate these methods by applying them to twenty-four real-world data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.

Blog post about this paper at Structure and Strangeness here.

This entry was posted in Science. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *