anonoftheinternets
08-19-2009, 03:09 PM
link -- http://www.wired.com/wiredscience/2009/08/basketballphysic/
Sorry, Lakers fans, Kobe could be holding your team’s offense back.
Elite players could be taking too many shots for optimal offensive efficiency, according to new mathematical analysis using network theory.
Treating each player like a pathway to get the ball into the basket, a physicist has deduced that the most efficient path to a basket does not always run through star players like Kobe Bryant, Lebron James, or Ray Allen, even though they are better shooters than their teammates.
“The idea that a team could improve after losing one of its best players may in fact have a network-based justification, and not just a psychological one,” wrote Brian Skinner (http://www.physics.umn.edu/people/bskinner.html), a physicist at the University of Minnesota, Minneapolis, in a paper posted to the arXiv.org (http://arxiv.org/abs/0908.1801). (Skinner is no relation to the other Brian Skinner (http://en.wikipedia.org/wiki/Brian_Skinner), Baylor standout, Los Angeles Clippers power forward and 22nd pick in the 1998 NBA Draft.)
First, Skinner explains how people making the best decisions for themselves can hurt the efficiency of a total system. Let’s say that there are two roads, a highway and an alley shortcut. The alley takes up to ten minutes, but sometimes less depending on traffic, and the highway always takes ten minutes. Individuals realize they could save time by taking the alley, so they do. Unfortunately, when everyone takes the shortcut, it ends up taking the full ten minutes.
It’s a suboptimal arrangement that statisticians call “the price of anarchy.” If you force some cars to take the highway to give other cars a faster alley commute, then the average commute time goes down.
In more complex simulations, even closing down some roads actually leads to reduced traffic — and some real-world evidence (http://stat.kaist.ac.kr/%7Ehjeong/PRL2008.pdf) [pdf] from cities like San Francisco appears to agree with theory, Skinner wrote.
By analogy, perhaps, getting rid of Kobe Bryant could actually make things better by dispersing the “cars” (i.e. possessions) more evenly. Offensive balance could reduce “traffic,” making putting the ball in the basket easier.
The key assumption is that a player’s real shooting percentage goes down as they take a greater percentage of a team’s shots. Skinner’s stats show this appears to be the case with Allen — and it stands to reason, too. As a player dominates an offense more, the defense adjusts. They double the player, devote more attention to him, and likely deny him high quality shots that are likely to go in. (We might call this the Iverson effect (http://www.associatedcontent.com/article/22860/20_shots_why_the_sixers_will_never.html?singlepage =true&cat=14).)
So, if one were to distribute the number of shots a player takes on the basis of their shooting skill, the math says the team’s overall shooting percentage would go down. If Ray Allen takes only as many shots as the rest of his teammates, he will make more of them than he would if he put it up on 40 percent of the possessions.
By distributing shots more evenly, then, the team’s overall shooting efficiency could go up, even if the other players on the team are only average shooters. For the star player, it’s a bit like that old adage, “You’re promoted until you’re incompetent.”
Of course, Skinner’s analysis doesn’t take defense into account and the interplay between the shooting skills of the best players versus the worst players could change the results somewhat, but it will probably add fuel to the barbershop debates of Brooklyn over whether or not the Knicks really would have been better without Patrick Ewing.
Via arXiv blog (http://www.technologyreview.com/blog/arxiv/23997/)
Sorry, Lakers fans, Kobe could be holding your team’s offense back.
Elite players could be taking too many shots for optimal offensive efficiency, according to new mathematical analysis using network theory.
Treating each player like a pathway to get the ball into the basket, a physicist has deduced that the most efficient path to a basket does not always run through star players like Kobe Bryant, Lebron James, or Ray Allen, even though they are better shooters than their teammates.
“The idea that a team could improve after losing one of its best players may in fact have a network-based justification, and not just a psychological one,” wrote Brian Skinner (http://www.physics.umn.edu/people/bskinner.html), a physicist at the University of Minnesota, Minneapolis, in a paper posted to the arXiv.org (http://arxiv.org/abs/0908.1801). (Skinner is no relation to the other Brian Skinner (http://en.wikipedia.org/wiki/Brian_Skinner), Baylor standout, Los Angeles Clippers power forward and 22nd pick in the 1998 NBA Draft.)
First, Skinner explains how people making the best decisions for themselves can hurt the efficiency of a total system. Let’s say that there are two roads, a highway and an alley shortcut. The alley takes up to ten minutes, but sometimes less depending on traffic, and the highway always takes ten minutes. Individuals realize they could save time by taking the alley, so they do. Unfortunately, when everyone takes the shortcut, it ends up taking the full ten minutes.
It’s a suboptimal arrangement that statisticians call “the price of anarchy.” If you force some cars to take the highway to give other cars a faster alley commute, then the average commute time goes down.
In more complex simulations, even closing down some roads actually leads to reduced traffic — and some real-world evidence (http://stat.kaist.ac.kr/%7Ehjeong/PRL2008.pdf) [pdf] from cities like San Francisco appears to agree with theory, Skinner wrote.
By analogy, perhaps, getting rid of Kobe Bryant could actually make things better by dispersing the “cars” (i.e. possessions) more evenly. Offensive balance could reduce “traffic,” making putting the ball in the basket easier.
The key assumption is that a player’s real shooting percentage goes down as they take a greater percentage of a team’s shots. Skinner’s stats show this appears to be the case with Allen — and it stands to reason, too. As a player dominates an offense more, the defense adjusts. They double the player, devote more attention to him, and likely deny him high quality shots that are likely to go in. (We might call this the Iverson effect (http://www.associatedcontent.com/article/22860/20_shots_why_the_sixers_will_never.html?singlepage =true&cat=14).)
So, if one were to distribute the number of shots a player takes on the basis of their shooting skill, the math says the team’s overall shooting percentage would go down. If Ray Allen takes only as many shots as the rest of his teammates, he will make more of them than he would if he put it up on 40 percent of the possessions.
By distributing shots more evenly, then, the team’s overall shooting efficiency could go up, even if the other players on the team are only average shooters. For the star player, it’s a bit like that old adage, “You’re promoted until you’re incompetent.”
Of course, Skinner’s analysis doesn’t take defense into account and the interplay between the shooting skills of the best players versus the worst players could change the results somewhat, but it will probably add fuel to the barbershop debates of Brooklyn over whether or not the Knicks really would have been better without Patrick Ewing.
Via arXiv blog (http://www.technologyreview.com/blog/arxiv/23997/)