After analysing 40,000 games of basketball, hockey and American football (college and professional), Aaron Clauset of the University of Colorado and colleagues have found that a random walk model provides a remarkably good description for the dynamics of scoring in competitive team sports(1):
The emergent behaviour of these highly trained athletes in a well-regulated environment is basically equivalent to a random number generator. (“Winning formula reveals if your team is too far ahead to lose”)
The celebrated arcsine law closely describes the distribution of times for: the total amount of time a team holds the lead, the time of the last lead change in a game, and when the maximal lead in the game occurs. For basketball, in particular, the agreement between the data and the theory is quite close, with a typical game effectively viewed as repeated coin-tossings.
Just like efficient stock markets
C’mon. Don’t tell me you didn’t figure it out.
(1) Clauset, A., M. Kogan, and S. Redner. “Safe Leads and Lead Changes in Competitive Team Sports.” Physical Review E 91, no. 6 (June 25, 2015): 062815. doi:10.1103/PhysRevE.91.062815.