Biomechanics Analysis

The optimal trajectory of a basketball jump-shot is influenced by several biomechanical factors. The angle of release (projection angle), backspin (Magnus force), velocity of the ball, height of ball release, angle of knee flexion, and smooth movement sequence influence the trajectory of a basketball jump shot. 

Smooth Movement Sequence  

While the majority of scientific studies explore the optimal release parameters of a basketball jump shot, many overlook the preliminary phase of the jump shot (Cabarkapa et al., 2022). A player’s capability to execute a smooth shot sequence is crucial for ensuring optimal projectile motion and the accuracy of a basketball jump shot. Such a concept involves the coordinated, sequential movement of the joints in the kinetic chain to maximise force production (Wuest & Bucher, 2011). To effectively perform a successful jump shot, an athlete must utilise a range of muscle groups which collectively contribute to the overall force applied to the basketball at the point of release (see video 1). Originating from the proximal joints of the athlete (the hips and core), the force is then transferred through the knees and ankles. This results in the accumulation of force in the distal joints (wrists and hands), allowing for the ball to be released at the optimal height and angle (see image 1).  

 

Video 1: Video example of Stephen Curry demonstrating a smooth shot sequence

Source: YouTube, 2023

Image 1: The sequential order of the kinetic chain segments of the jump shot.  

Source: Body by Reuben , n.d.

The establishment of the key joints in the kinetic chain of a jump shot, correlates with the development of optimal force and minimal applied loads, resulting in one of the most efficient methods of coordinating kinetic chain activation (Kibler, 1994). Coaches and trainers that understand the concept of kinetic chain activation can greatly influence a player’s shot accuracy. Kinetic chain activation can be further explained through the concept of mechanical energy, which involves potential and kinetic energy. Potential energy (PE) refers to the energy associated with an object before motion or stationery and has the potential to gain velocity. On the other hand, kinetic energy (KE) relates to objects that are in motion (Blazevich, 2017). In the context of the jump shot, while the lower joints of the body are flexed and in a crouch position, they store elastic PE. As the player extends their legs and jumps the PE is translated into elastic KE, which contributes to the force applied to the ball at the time of release (Blazevich, 2017). The production of greater power in the jump equates to higher vertical velocity, meaning the shot has higher elastic KE and the basketball has greater force applied.   

In the video below, player 1 demonstrates a smooth shot sequence where the kinetic chain is effectively utilized, resulting in a coordinated and accurate release of the basketball at an optimal angle (see Optimal Projectile Angle Analysis). In comparison, player 2 displays a stagnant jump shot, which provides an example of suboptimal elastic KE generation. Player 2’s shot sequence is interrupted at the knee and hip joints, which limits the transfer of KE to the upper joints of the kinetic chain and furthermore disrupts the power and accuracy of the shot.   Ellenbecker et al., (2020) highlighted that the “hip/trunk area contributes approximately 50% of the kinetic energy and force to the entire throwing motion; thus, the force and power generation in this area is compromised by altered kinematic in this area, resulting in increased stress in distal segments”. Insufficient range of motion in the hip may significantly affect the transfer energy along the kinetic chain, which results in uncoordinated movement, causing increased stress on the shoulder and elbow which may result in injury (Kibler et al., 2013).  Therefore, player 1 demonstrates the effectiveness of optimising the kinetic chain to enhance shot accuracy, while player 2 highlights the negative impact of a disrupted kinetic chain which leads to decreased energy transfer and lower accuracy.  

 

Video 2: Shot sequence comparison of Player 1 (top) and Player 2 (bottom)

Angle of Knee Flexion  

Newton’s third law states, “for every action, there is an equal and opposite reaction” (Blazevich, 2017). The law highlights that for every force applied to another object, it will have an equal and opposite force in the opposite direction. In the context of a basketball jump shot, when a player lowers their centre of mass and applies force against the ground, it will produce and equal and opposite reaction, propelling the player upwards (Benjamin, 2014). Such a concept relates to the application of ground reaction forces vertically applied through a player's feet against the floor. The upwards propulsion, which is a result of the ground reaction force, allows the player to generate the optimal elevation and height of release to successfully execute a jump shot. 

 

An aspect which is often overlooked in plyometric studies is the consideration of lower limb muscle activity in both the concentric and eccentric phase of a jump (Torres-Banduc et al., 2024). Regarding the impact of knee flexion angle on strength, power and work while performing a jump shot, a greater knee flexion angle enhances the muscle fibre’s length-tension relationship, resulting in a greater amount of force produced (Arnold et al., 2013). So, what is the ideal knee flexion angle? Torres-Banduc et al.,(2024) stated that the “mechanical advantage achieved at 90° knee flexion led to improved power generation and work output.” as well as “at 90° of knee flexion, the patella’s position enhances the leverage and mechanical advantage of the quadriceps muscles.”, which generates greater force. While the 90° knee flexion is suggested, the likelihood of a basketball player achieving a knee flexion of 90° at every shot taken is near impossible. Christensen et al., (2020) proposed that the knee flexion between 87° and 107° was shown to maximise the height of a vertical jump, which is a more appropriate range for a basketball player.  

 

In the Image 2 below, player 1, 2 and 3 performed a jump shot. Following the proposed optimal knee flexion angles (Christensen et al., 2020, Torres-Banduc et al., 2024), player 2 with a knee flexion angle of 108° falls near the ideal knee flexion angle of 87° and 107° for maximising the height of a vertical jump. Despite player 2 being slightly above the optimal range, their knee flexion is close enough to demonstrate the use effective force generation resulting in a higher release point. In comparison to players 1 and 3, they demonstrate significantly different knee flexion angles when performing a jump shot. Player 1, with a knee flexion angle of 145°, displays a shallow knee bend, resulting in the reduced ability to generate force from the quadriceps, which is caused by a suboptimal length-tension relationship. Player 3 on the other hand, with a knee flexion angle of 69°, exhibits a knee bend that is too deep. When a player’s knee flexion is too low, there is reduced mechanical leverage and so the patella positioning cannot optimize the leverage of the quadriceps muscles resulting in suboptimal force production (Torres-Banduc et al., 2024).  

 

Image 2: Comparison of player's 1, 2 and 3 angle of knee flexion

Angle of Release 

In basketball, a key factor that influences the trajectory of a jump-shot is the angle of release. The angle of release of an object is a key factor that influences the range of a projectile. This is due to its impact on the projectile’s initial velocity which transitions into horizontal and vertical displacement (Blazevich, 2017). An object can be projected at angle between 0° and 90° (Blazevich, 2017). The angle of release on a basketball jump-shot is the reference point for when the ball is released from the players’ hand relative to the horizontal plane (Kambic et al., 2022). According to Kambic et al. (2022), the optimal shooting trajectory of the ball in basketball should be between 44° and 52°. When the angle of release is within this optimal range, the trajectory of the jump-shot holds a greater parabolic trajectory (Kambic et al., 2022). A higher parabolic trajectory allows for a greater entry angle into the hoop and more room for error (Kambic et al., 2022). However, if the angle of release is lower than the optimal trajectory than the likelihood of the jump-shot being successful is decreased. This is evident with Player 1’s angle of release for their jump-shot being 43° (Image 4). This lower angle of release led to a ‘flatter’ arc and a non-successful jump-shot. Conversely, Player 2’s angle of release was 50° (Image 5). Player 2’s jump-shot was successful which is supported by the angle of release being between the range of the optimal shooting trajectory. The greater the angle of release indicates the higher the relative vertical displacement of the jump-shot. Image 6 indicates both relative vertical displacement and the release height to the top trajectory of Player 2’s jump-shot. The relative vertical displacement calculated was 596.23cm (red line) and the release height to the top trajectory was 334.72cm (yellow line). This indicates that Player 2’s jump-shot had a nice extended arc which is evident with the success of their shot. However, it should be noted that both players faced no pressure (opponents) when shooting. The optimal trajectory range is influenced by two dynamic influences which include shooting distance and the opponent’s height being more than 1.95m (Rojas et al., 2000). Tall defenders are prominent in the NBA and players such as Steph Curry must extend their angle of release to clear the defender. This is evident in Image 7 with Curry’s angle of release being greater than the optimal trajectory. Steph Curry is famously known for his successful deep jump-shots. According to Okazaki & Rodacki (2012), the greater the distance from the basket, the greater the angle of release must be which adds to the dynamic approach of a jump-shot. The angle of release significantly influences the trajectory of a jump-shot in basketball. 

Back Spin (Magnus Force)

When shooting a jump-shot in basketball, a key factor that influences the trajectory of the shot is the back spin. The back spin of the basketball is produced by the snapping action of the wrist. A basketball jump-shot is impacted by the air pressure proximate to the ball which is the result of the Magnus effect (Blazevich, 2017). By exerting a downward force on the basketball when shooting, a greater curve and height on the trajectory of the ball is produced due to air rotating the ball in a clockwise direction (Hamilton & Reinschmidt, 1997). The downward rotation of the ball during the flight equals with the air surrounding the ball which pushes the air up and over the ball (Hamilton & Reinschmidt, 1997). When an object receives a downward rotation then the pressure of the air is higher (Blazevich, 2017). Once the high air pressure travels underneath the ball and lifts on the ball, the ball’s trajectory and flight time is increased (Hamilton & Reinschmidt, 1997). Magnus force that is created from the snap of the wrist positively influences the trajectory of a jump-shot which leads to greater success. Significant back spin of the ball increases the shooting accuracy and trajectory by increasing the angle that the ball will enter the hoop in (Blazevich, 2017). The Magnus force generated also softens the shot by slowing the ball down as it descends from its flight path (Blazevich, 2017). This allows for the basketball jump-shot to rebound better and have increased odds for the ball to drop into the hoop rather than bounce of the rim (Hamilton & Reinschmidt, 1997). To identify the impact of back spin on a professional jump-shot, see Video 3. This video highlights NBA Sixth Man of the Year candidate Bogdan Bogdanovic’s wrist motion to generate back spin on the ball to positively influence his jump-shot. He talks about how his wrist motion allows for him to produce a quick release which is effective and successful in the NBA. The back spin that his jump-shot creates produces a high parabolic trajectory which influences the success in his shooting percentage. Overall, back spin has significant influence on the trajectory of a jump-shot. 

Video 3: Bogdan Bogdanovic's wrist motion to generate back spin.

Ball Velocity

Ball velocity plays a critical role in the outcome of whether a jump shot is effective in sinking the basket. A player needs to form an ability in finding the right balance of velocity to ensure the distance is made, at the same time ensuring that the force behind the ball isn’t too great thus still allowing for a soft landing. A softer landing results in the ball being less likely to bounce out of the ring causing a failed attempt (Penner, 2021).

To achieve this, players can flex their wrist on the balls release which produces spin on the ball (magnus force). This skill has been observed in the shooting performances of expert players (Knudson, 1993; Okazaki et al., 2006; Satern, 1988). Elbow extension also plays a key role in ball velocity upon release. The combination of both wrist flex and elbow extension effects the ball’s velocity at release (Button et al., 2003; Miller & Bartlett, 1993). The distance a jump shot is taken from also effects ball velocity. Changing the distance that the shot is taken from the basket influences the required velocity of ball release. Once shooting distances increase, the shooter must generate greater ball velocity at ball release to make the required distance (Miller & Bartlett, 1996, 1993).

Player 1.

Here in images of player one, a smooth transition which allows for lower velocity being placed on the ball of load up to ball release from player 1. Between images we can see the extension of the elbow with the flick of the wrist creating lower velocity on the ball, leading to the magnus effect. Player one is allowing the ball to float out her hand having used a smooth extension of the elbow and a neat flex in the wrist to impart spin on the ball creating low velocity enabling a soft landing on the ring.

Player 2

In comparison to player one, player 2 shows a much more forceful load up even though they are shooting from the same distance. From images 2-3 we can see the flatter technique used to release the ball. Player ones elbow extension of 119-168 degrees at release point creates a higher trajectory, greater shooting arc and lower velocity on the ball. Instead, player 2 is seen pushing the ball forwards with a much flatter angle with a lower release point creating a lower shooting arc, lower trajectory and higher velocity being placed on the ball. Although there is a flex of the wrist involved in the shooting action from player 2 it is coming from a much lower point on the ball, creating greater spin and more revolutions on the ball which also leads to a higher velocity at ball release.

Height of Ball Release

The optimal trajectory for a jump shot depends on both the shooter and the equipment with the height of release (Hamilton and Reinschmidt). The height of ball release is personalized for everyone. A player's standing height, jump height are variables that influence release height of the ball (Miller & Bartlett, 1996). Height of ball release also plays a part in release angle. The higher the ball release reduces the release angle and velocity being placed on the ball (Hamilton &Reinschmidt, 1997; Malone et al., 2002; Miller & Bartlett, 1993).

Video 4.

In video four, we can see an ideal jump shot technique. Player 1 uses their knee flex in the load up to drive force down into the floor through the legs to spring up into the jump shot position. The release point of the ball is slightly before the peak height reached during the jump. This is ideal as ball release should often occur either slightly before or after the instant of peak height of the jump (Elliott, 1992; Okazaki et al., 2006; Rojas et al., 2000). The follow through momentum of the jump is forward in the direction of the hoop mixed with the height of the release point also allows the shooter to transfer velocity on the ball helping ensure the distance is made on the shot (Elliott, 1992). All this combined through a smooth transition of forces gives the best opportunity to reach the optimal ball trajectory.

 Video 5.

Movement of the lower limbs and trunk can also influence release height (Okazaki et al.). In comparison to video 5, player two offers minimum bend in the knees with far less force being pushed down through the floor, as a result you can see the shooter does not get off the ground. Higher ball release heights require less vertical distance for the ball to travel, thereby requiring a lower release angle and velocity to produce accurate shots (Knudson, 1993; Satern, 1988). Without this jump upwards and in the direction of the hoop the height of release is clearly being effected and much lower than player one. Shooter two must now generate more force on the ball. Again, explaining the lower angle of elbow extension imparting greater velocity on the ball to make the distance which as previously described is not inline with allowing for an optimum ball trajectory nor a soft landing when hitting the backboard or ring.