title: Safe leads and lead changes in competitive team sports.
abstract: 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 "safe" 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 semiprofessional team sports, and are more accurate than popular heuristics currently used in sports analytics.
authors.affiliation: Department of Computer Science, University of Colorado, Boulder, Colorado 80309, USA.|BioFrontiers Institute, University of Colorado, Boulder, Colorado 80305, USA.|Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: A
authors.initials: A
authors.lastname: Clauset
authors.affiliation: Department of Computer Science, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: M
authors.initials: M
authors.lastname: Kogan
authors.affiliation: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.|Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: S
authors.initials: S
authors.lastname: Redner
mesh_terms: D001490:Basketball; D003163:Competitive Behavior; D008962:Models, Theoretical; D011336:Probability; D013177:Sports; D013997:Time Factors