Grad student uses physics to analyze basketball

Brian Skinner’s use of Nash equilibrium has intrigued the basketball community.

Grad student uses physics to analyze basketball

Brent Renneke

A graduate student in physics at the University of Minnesota recently had a research paper recognized at a Massachusetts Institute of Technology conference, and it had nothing to do with matter, forces or energy. It was about the game of basketball and used theory rooted in the heart of physics to analyze the game in a truly unique way. Brian Skinner, graduate student in the physics and astronomy departments, presented a research paper last month at the 2010 MIT Sloan Sports Analytics Conference. The paper compared a basketball offense to a traffic network in a way that rethinks basic offensive strategy. In the research paper, Skinner said the most talented offensive player benefits his or her team by shooting less, because concentrating the offensive production on one player lessens the offenseâÄôs efficiency as a whole. To make this point, Skinner looked at the phenomenon in traffic where jams occur because each vehicle is taking the path of their best interest. Skinner found that a similar phenomenon occurs in basketball when teams repeatedly run the play with the highest percentage of success by having the player with the best chance of scoring shoot the majority of the time. He made this argument using Nash equilibrium, which describes a point in a game where each player looks for the best possible outcome, which, according to Skinner, does not lead to the best outcome overall. For an example, Skinner looked at Boston Celtics shooting guard Ray Allen and the variation in the amount of shots heâÄôs taken season-to-season. According to Skinner, Allen was the most effective when he took fewer shots. Using the theory, AllenâÄôs effectiveness reached its highest level when he took 20 percent of his teamâÄôs shots. âÄúThe result of limiting AllenâÄôs shots keeps the defense from focusing too intently on him, and it pays off,âÄù Skinner said. Nash equilibrium shows that the more Allen shot the basketball, the more his effectiveness fell, until he was as effective as his less-talented teammates. Thus, the decision of who shoots no longer matters. âÄúIt is the job of the coach to prevent this from happening,âÄù Skinner said. âÄúAllen was the primary scorer, but he was also the second and third option,âÄù Skinner said. âÄúOver his career, he had a wide range of shot volume.âÄù With the teamâÄôs offense continuing to utilize Allen as their best scoring option, the team reaches the Nash equilibrium with Allen shooting 40 percent of his teamâÄôs shots. John Hollinger, writer for ESPN Insider on ESPN.com, uses quantitative analysis to analyze basketball. Hollinger, who was in attendance for SkinnerâÄôs presentation, said the representatives from NBA teams and others involved in basketball strategy were very interested in the premise behind the presentation. âÄúThe presentation got noticed,âÄù Hollinger said. âÄúThere are teams that are going to be looking at this.âÄù Jim Peterson, assistant coach for the Minnesota Lynx and former NBA player, said things like the positioning of AllenâÄôs shot attempts are more important than the actual number attempted. âÄúIf you are having Ray Allen take shots on the floor where he is not effective, he will not be as good,âÄù Peterson said. However, having a star playerâÄôs shot attempts be proportionate to the rest of the team does have some value, Peterson said. PetersonâÄôs own effectiveness as a player was influenced by his talented teammates getting the majority of the shot attempts, he said. âÄúIf I had the same courage to take shots without regard, I think I would have been a more effective player and help the team more,âÄù Peterson said. Hollinger said it is tough for former and current NBA players to accept SkinnerâÄôs research in the way he intended, because they are not used to looking at it that way. âÄúThey are not in the NBA because they are mathematicians,âÄù Hollinger said. However, Hollinger said former NBA players like Brent Barry, a 14-year NBA veteran, were very receptive of the presentation. âÄúI think he would find a surprising number of converts even if he made that presentation to a room full of NBA players,âÄù Hollinger said. Skinner and Hollinger both said statistical analysis is becoming more popular in the NBA. âÄúRight now, basketball is sort of a revolution of analyses,âÄù Skinner said. âÄúMore and more statistical analysts are going into the game.âÄù Peterson agreed and said âÄúhigher mathâÄù does have a place in basketball and is becoming popular in how organizations think. âÄúTeams are crunching numbers and trying to quantify player effectiveness,âÄù Peterson said. âÄúThey try to make players see the statistics are trying to make them become better.âÄù Skinner said it is this group of people he had hoped his paper would stir up interest in. âÄúAll I intended to do was get people talking,âÄù Skinner said. âÄúThen maybe some smarter people would find out how to run with it.âÄù Hollinger said one way SkinnerâÄôs research could be used is the predictable behavior of teams late in the game. Teams are very predictable about getting the shot to their best player, according to Hollinger. âÄúBrianâÄôs paper does a great theoretical premise in that coaches are hurting themselves by doing that,âÄù Hollinger said.