Safe leads and lead changes in competitive team sports

A. Clauset, M. Kogan, S. Redner
2015 Physical Review E  
We investigate the time evolution of lead changes within individual games of competitive team sports. Exploiting ideas from the theory of random walks, the number of lead changes within a single game follows a Gaussian distribution. We show that the probability that the last lead change and the time of the largest lead size are governed by the same arcsine law, a bimodal distribution that diverges at the start and at the end of the game. We also determine the probability that a given lead is
more » ... fe" as a function of its size L and game time t. Our predictions generally agree with comprehensive data on more than 1.25 million scoring events in roughly 40,000 games across four professional or semi-professional team sports, and are more accurate than popular heuristics currently used in sports analytics.
doi:10.1103/physreve.91.062815 pmid:26172762 fatcat:xdzbcsewqnhpph426k7tt5g2ui