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.

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(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.