This is a review of the basketball research conducted by Brian Skinner, applying networks and Braess’s paradox.
A basketball game can be seen as a series of intertwined networks. Each possession has a starting point, a path to follow, and an ending point. Each possession, or pathway, would have its own unique probability of scoring points. A pathway that is used more regularly would naturally have a lower probability as the more often one type of play is used the easier it is for the opponent to be prepared. In order to describe the entire offense of a team in a basketball game as a network, every possible pathway would need to be created along with its unique efficiency, a process that is impossible in practical terms.
However, a network can provide useful information regarding a basketball offense, especially in looking at the difference between a team’s efficiency and maximum possible points. In this case, a basketball game is compared to a simplified traffic network.
The difference between a team’s efficiency and maximum possible points can be described as the price of anarchy, which measures how the efficiency of any system degrades due to selfish behavior.
Braess’s paradox is a proposed explanation for the situation where an alteration to a road network to improve traffic flow actually has the reverse effect and impedes traffic through it.
In basketball, a possession is like a car on the road and the different plays are different roads that can be chosen to reach the destination. The more often a play, or road, is used the lower its efficiency. If all cars take the fastest route, the route will be clogged and time increases. However, if some cars take a slower route the average speed for all cars increases. This is the difference between selfish and unselfish behavior. Likewise, in basketball, always implementing the play with the highest probability of scoring can lead to an overall decrease in efficiency.
A simplified network can be created for a basketball offense with each line in the network connecting the beginning of a possession to the shot attempt. Each player is assigned a scoring efficiency dependent on how often that particular play is used. In this network the efficiency of a player is defined as the player’s true shooting percentage as a function of the fraction of the team’s shots he takes while he is on the court.
The optimal strategy for a team would be the one that maximizes the team’s overall efficiency. This optimal strategy can be calculated using Lagrange multipliers for constrained optimization.
Coaches and analysts could take this information to determine how often each player should take possession of the ball and how often a particular play should be utilized in order to maximize the overall team’s efficiency. This may indicate that star players should not be given the ball as often as they currently are as such ‘selfish’ behavior may actually decrease the team’s overall scoring potential. If a star player makes fewer plays, he will receive less defensive attention, leaving him more open to make the points when he does have the ball.
In fact, in a traffic network removing a road can actually increase efficiency, indicating that removing a player could also increase efficiency. This obviously is not logical and is referred to as Braess’s Paradox.
Analytics Used: Price of Anarchy, Network, Braess’s Paradox.
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