The Physics of Steph Curry's Killer Jump Shot

Do jump shots give a significant advantage to the player? Here is a look at jump shots using projectile motion physics.
Image may contain Stephen Curry Human Person People Sport Sports Team Sport Team and Basketball

Stephen Curry of the Golden State Warriors has a jump shot that can’t seem to not drop into the basket. But that’s weird—because it doesn’t look like a successful shot. So why is Curry so good? Well, physics.

Perhaps Curry is thinking about a jump shot like this:

OK, I am 14 feet away from the basket. I know the ball size and the basket size so that there is a range of ball trajectories that will still get two points. I can throw the ball with a speed of 5 to 7 m/s. What angle should I throw the ball? If I jump, I can increase the ball’s starting position by 1 meter. Should I shoot or take a jump shot? What should I do?

Ok, it’s clear that humans don’t go through a thought process like this during a game. They just don’t have enough time to calculate these things. In fact, that’s what makes sports like basketball so fascinating. Humans can succeed even without fully understanding the physics. Stephen Curry just happens to be better at the jump shot than most humans.

The Advantage of a Jump Shot

Instead of looking at all basketball shots, let’s consider the jump shot. The basic idea is to throw the ball at the top of a jump trajectory. Ask a basketball player and they can give you excellent reasons why this jump shot is useful.

  • The jump shot raises the starting position of the ball such that it is more likely to clear defending players.

  • In order to properly defend a jump shot, an opposing player must also jump. This means that there is a possibility that a defender could jump too early or too late to block a shot.

  • The player has the option to release at various points during the jump giving more options to evade a defender.

  • A jumper can move away from a player during the jump to give more room for a shot (fade).

  • Finally, the ball can be released at a location that is closer to the same height as the goal.

It’s this last point that I wish to explore. Does the jump shot give a player a better opportunity to score a goal? If so, how significant of a gain is it?

Here is the plan. I will use a basic projectile motion model to determine the motion of a thrown basket ball. I will pick a starting location as either a jump shot or a standing shot. Since I know the size of the basketball goal and the basket ball (23.8 cm vs. 45.7 cm), the ball could be anywhere in a zone of 21.9 cm and still make it through the hoop. This of course assumes that I don’t have to worry about “side-to-side” aiming which would probably be the same for both a standing and jump shot.

If you want more details about projectile motion and basketball shots, check out this older post with all of the kinematic equations and steps to calculate the trajectory of a basketball.

OK, let’s do it. Suppose the ball is shot from a range of 6 meters. What initial ball velocities would make it into the basketball goal? Here is a plot of all the starting velocities (x and y velocities) that score a goal for both standing and a jump shot. For simplicity, I only included shots that went right into the hoop. No bouncing shots allowed (because then it gets crazy complicated).

Jump Shot vs. Standing Shot What does this mean? If you look at the for the jump shots, there are two important things to notice. First, look at the range of horizontal velocities for the jump shot to score a goal. They go all the way from 3.7 m/s to 6 m/s. The horizontal velocities for the standing shot must be much greater from 5 m/s to 7 m/s. So you have to throw the ball faster while standing. Second, look total velocity space (the area on the graph that would score a goal). There is a much larger space of scoring goals for the jump shot. You have more options of initial velocities that would score if the ball starts and ends at the same height (as it would in a jump shot).

This all seems to suggest that shooting the ball closer to the same height as the goal is a better shot. Wouldn’t that imply that taller players would be better at jump shots (since they don’t have to jump very high)? Maybe, or maybe not.

For example, let’s get back to Steph Curry. He is “only” 6 feet 3 inches tall (the average NBA height is 6 ft 7 inch) and yet he is regarded as one of the best jump shooters in the league. Curry’s skill shows that the jump shot is more than just a simple physics problem. Perhaps his advantage isn’t just from his release height but also in the quickness of his shot. It’s also possible that he could be releasing the ball as he moves upward in the jump to add to the initial velocity of the ball. Either way, it’s clear that whether Steph Curry knows any physics or not, he’s a jump shot expert.