To shoot, or not to shoot, that is the question. Whether ’tis nobler to try to score right away or wait for a better chance.

Professional basketball players face that quandary multiple times in every game. And in an article posted at arXiv.org on 29 July, Brian Skinner, a graduate student in theoretical physics at the University of Minnesota, Twin Cities, provides some mathematical guidance for the best time to take aim.

Skinner, an avid basketball fan, was inspired to analyze the game when he heard a talk at an American Physical Society meeting in 2007 on the flow of traffic. Every driver tries to minimize his or her commuting time rather than reduce the average travel time of all drivers, resulting in a paradoxical situation: Closing a road may actually reduce congestion by forcing drivers to take a route many had avoided, speeding up the average commute.

That paradox reminded Skinner of the Patrick Ewing theory in basketball, named after the high-scoring player for the New York Knicks. Analysts had noticed that in games from which Ewing or other big scorers on a team were absent, that team was more likely to win. In addition, the diagrams and flow of players in basketball also resembled the traffic models Skinner had seen.

to read more, go to:    http://news.sciencemag.org/sciencenow/2011/08/the-mathematics-of-basketball.html?ref=hp