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Grad student uses physics to analyze basketball | ‑ The Minnesota Daily

OCTOBER 1, 2012



Grad student uses physics to analyze basketball Brian Skinner’s use of Nash equilibrium has intrigued the basketball community.

By Jayme

By Brent Renneke



April 26, 2010

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‑student‑uses‑physics‑analyze‑basketball


10/1/12 Athletics

Grad student uses physics to analyze basketball | ‑ The Minnesota Daily Authors



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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 offense’s 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 he’s taken season-to-season. According to Skinner, Allen was the most effective when he took fewer shots. Using the theory, Allen’s effectiveness reached its highest level when he took 20 percent of his team’s shots. “The result of limiting Allen’s shots keeps the defense from focusing too intently on him, and it pays off,” 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. “It is the job of the coach to prevent this from happening,” Skinner said. “Allen was the primary scorer, but he was also the second and third option,” Skinner said. “Over his career, he had a wide range of shot volume.” With the team’s offense continuing to utilize Allen as their best scoring option, the team reaches the Nash equilibrium with Allen shooting 40 percent of his team’s shots. John Hollinger, writer for ESPN Insider on, uses quantitative analysis to analyze basketball. Hollinger, who was in attendance for Skinner’s presentation, said the representatives from NBA teams and others involved in basketball strategy were very interested in the premise behind the presentation. “The presentation got noticed,” Hollinger said. “There are teams that are going to be looking at this.” Jim Peterson, assistant coach for the Minnesota Lynx and former NBA player, said things like the positioning of Allen’s shot attempts are more important than the actual number attempted. “If you are having Ray Allen take shots on the floor where he is not effective, he will not be as good,” Peterson said. However, having a star player’s shot attempts be proportionate to the rest of the team does have some value, Peterson said. Peterson’s own effectiveness as a player was influenced by his talented teammates getting the majority of the shot‑student‑uses‑physics‑analyze‑basketball



Grad student uses physics to analyze basketball | ‑ The Minnesota Daily

attempts, he said. “If 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,” Peterson said. Hollinger said it is tough for former and current NBA players to accept Skinner’s research in the way he intended, because they are not used to looking at it that way. “They are not in the NBA because they are mathematicians,” Hollinger said. However, Hollinger said former NBA players like Brent Barry, a 14-year NBA veteran, were very receptive of the presentation. “I think he would find a surprising number of converts even if he made that presentation to a room full of NBA players,” Hollinger said. Skinner and Hollinger both said statistical analysis is becoming more popular in the NBA. “Right now, basketball is sort of a revolution of analyses,” Skinner said. “More and more statistical analysts are going into the game.” Peterson agreed and said “higher math” does have a place in basketball and is becoming popular in how organizations think. “Teams are crunching numbers and trying to quantify player effectiveness,” Peterson said. “They try to make players see the statistics are trying to make them become better.” Skinner said it is this group of people he had hoped his paper would stir up interest in. “All I intended to do was get people talking,” Skinner said. “Then maybe some smarter people would find out how to run with it.” Hollinger said one way Skinner’s 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. “Brian’s paper does a great theoretical premise in that coaches are hurting themselves by doing that,” Hollinger said. Printer-friendly version Share‑student‑uses‑physics‑analyze‑basketball



Grad student uses physics to analyze basketball | ‑ The Minnesota Daily


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