Mathematics Of When To Shoot Basketballs.

 

Basketball can be a fast paced game with the players running up and down the court.  At any time, they have a split second to make the decision to try for a basket or wait for a better opportunity,  Sometimes they try for it and make it, other times they try and miss, or they blow past what looks like a perfect opportunity to the spectator.  It doesn't matter if it is a neighborhood, high school, or professional game, the decision is there.

Back in 2011, graduate student Brian Skinner created a model to help shooters to determine the best time to shoot based on mathematics.  In 2007, he heard a talk on traffic flow where every driver attempt to minimize their individual travel time rather than trying to reduce the average travel time for all drivers.  

This talk reminded him of the Patrick Ewing theory applied to basketball in which it was noticed by analysts that when Patrick Ewing and other high scoring players were absent, the team was more likely to win. In fact, it was noticed that the diagrams showing the movement of the players resembled traffic flow. Brian Skinner suggested that every equation and variable used in traffic flow theory could as easily be applied to basketball.  He took the routes in the traffic models and transformed them into different places.

Then he took his equations and made them follow the ball from the inbound pass to the hoop.  He factored in the probability a specific shot would make it into the basket, the quality of future shots the team is likely to make, and the number of seconds left for a player to make the shot or forfeit the ball to the opposing team. He found that the more time left for the play, the choosier the player should be in selecting which shots to make. 

In the situation where you have two teams and both have the same chance of making a certain shot but the first team passes twice as fast as the second team, one assumes that the first team should shoot twice as often as the second team to win.  According to Brian's model this is not correct.  He calculated that the first team should shoot every 13 seconds to the second team taking a shot every 20 seconds because those extra three shots allow the first team to be more selective about the shots they take.  This gives them a better chance of winning. 

In addition, he has probabilities and scenarios for all sorts of situations. Unfortunately, the shooter trying to take a bit more time to determine when to shoot is very difficult to do because it  requires split second responses and not everyone can do it. On the other hand, players can look at their stats after the game is over to compare their their actual decisions to theoretical ones to see how well they choose the best time to shoot.  

There you have it.  Applying traffic flow equations to basketball plays to get a better idea of when to shoot the ball.  Let me know what you think, I'd love to hear.  Have a great day.