What factors influence 3 point shooting performance?

3 Point shooting is a crucial skill within basketball. Players who can score from long range are valuable assets to any team. Bio-mechanically sound technique is key to shooting a high percentage.  Physics allows athletes to understand why some techniques are efficient, and others aren’t.  Newtons 3 Laws, projectile motion, Levers , Magnus effect and the coefficient of restitution are applied to 3 point shooting to understand contextual factors that influence optimal technique. Knowing the mechanics behind the shot enables players, coaches and spectators to understand and appreciate the skill more.

What is the 3 point shot?

The 3 point shot is performed outside the arc. It is 23 feet and 9 inches from the basket (Bartlett, 2014). Due to distance athletes must generate greater amounts of force to reach the target. To perform the skill successfully athletes must follow several components in sequence.

  • Shoulders Squared towards basket
  • Have dominant foot slightly in front of other
  • Knees bent, eyes on rim
  • Jump high and bring ball in front of face
  • Extend arm at highest point
  • Follow through

Execution of this skill is demonstrated in this clip.

Summation of force

Utilizing force effectively is key to shooting 3 pointers. Athletes want a fluid motion  that can be repeated throughout a game. Techniques that over exert onset fatigue and reduce effectiveness (Sewell, Watkins and Griffin, 2013). Correct force summation prevents this from occurring. Force summation adds forces produced by each body segments, allowing maximum force to be exerted by the muscles and transferred (McGinnis, 2013). In the context of a basketball shot, generation of force starts at the feet, works its way up the body until it is exerted upon the ball.

summation of force

Stephen Curry demonstrating summation of force – http://www.espn.com.au

As shown above, force is generated through the bending of the knees. This engages lower leg muscles, thighs, glutes, calve and foot tendons. As the athlete jumps force is pushed up through the torso, through the arms and ending at the fingertips. This sequence is known as the kinetic chain (Zatsiorsky, 2008). The combination of these muscles generated force impacts on the ball, enabling it to be projected further (McGinnis, 2013). Stephen Curry is known for his deep threes which requires summation of force to propel the ball long distances.

Why is Summation of Force important?

Athletes cannot shoot the ball without generating large amounts of force.The more body parts involved, the greater possible force can be generated. Utilizing summation of force enables athletes to perform skills that require large amounts of force, distributed to different muscle groups, enabling them to repeat them throughout a game (Bartlett, 2014). Athletes who understand how to apply this principle will succeed compared to those who don’t, as they will have imbalanced generation that causes fatigue, inaccuracy and inconsistent technique (McGinnis, 2013).

Centre of Mass
Bodies consist of many individual particles of mass, the centre of mass in a human body is the point in where the mass of the body is evenly distributed in all directions (Blazevich, 2013). To increase vertical velocity for a jump shot, the centre of mass may be manipulated through movement of the body by applying force to jump off the ground, bringing the legs up and behind, and rapidly extending the legs downwards (Blazevich, 2013). Raising the centre of mass can assist with improving the accuracy of the shot as it contributes to upper body stability (Blazevich, 2013). In conjunction with raising the centre of mass, keeping the head and eyes still throughout the execution of the shot can further improve the accuracy (Blazevich, 2013).

Figure 2. Manipulation of centre of mass during jump-shot
Manipulation of centre of gravity is useful when being defending. Gaining extra hang time allows the athlete to get a better look at the basket, thus improving his accuracy (Bartlett, 2014). The defender may be in a position to block the shot, however the extra time provides an opportunity to score.


Newtons 3 Laws – How do they affect shooting?

Isaac Newton developed 3 laws of physics that allow us to understand the world we live in today. They are known as:

  1. Law of Inertia
  2. Law of Acceleration
  3. Law of Action / Reaction

Application of these laws can assist athletes in improving their shooting mechanics.

1)  An object will remain at rest, until acted upon by another force. The force of gravity is constant (9.81 newtons) (McGinnis, 2013). This force is applied downwards. Athletes must be aware of gravity’s effect on the ball when it is in the air. Understanding the balls flight path assists with accuracy.

When playing outdoors the effect of wind can impact the basketball. Accommodating for this factor increases shooting performance, and will be covered under Magnus Effect (Zatsiorsky, 2008).

2) Force acting upon mass produces acceleration. Larger mass requires more force to accelerate. In a basketball context, a Men’s size 7 basketball requires more acceleration than a Women’s size 6. Heavier objects have more inertia, requiring more force to move. Therefore athletes should be careful to practice only with equipment that replicates the game. Otherwise incorrect force will be applied to objects, causing over or under acceleration.

3) Action reaction is prevalent in basketball. In the motion of shooting a ball, force generated in summation of force (action) manifests itself in shooting the ball (reaction). Understanding what actions cause what reactions is unconsciously learned through practice. Application of too much force in the action can cause an unwanted reaction of air balling or bricking a shot.

All 3 laws are constant in all forms of life, and basketball is no exception. Application and understanding of these laws is beneficial to athletes who wish to succeed.

Coefficient of restitution

The coefficient of restitution refers to the amount of energy that remains in an object after collison with another object (Blazevich, 2013). Experiments involving a basketball with proper inflation bouncing off a hard floor resulted in a coefficient restitution measurement of 0.91 (Blazevich, 2013). The backboard however, is less rigid than the floor and therefore resulted in a coefficient of restitution that ranged from 0.85 to 0.88 (Blazevich, 2013). Evaluation of these results determined that when a basketball bounces off the backboard, the energy that is absorbed may provide a compensation for shooting error, where the degree of compensation is relative to the flexibility of the backboard, i.e. greater compensation for shooting error can be associated with greater flexibility of the backboard (Blazevich, 2013).

Understanding an objects coefficient of restitution assists with shooting performance. Players attempting a bank shot need to know how much force will be absorbed and exerted during the skill. Energy cannot be created or destroyed, it can only be transferred or changed from one form or the other (Bartlett, 2014). Understanding the relationship between force, energy and the objects that utilize it benefits athletes as they can predict if a shot will go in or not by measuring the force. Using less force when throwing the ball against the backboard generates a higher coefficient of restitution, relative to starting position. Manipulating physics to ones advantage separates good players from great players.

Projectile Motion

Projectile motion measures the motion of an object released at an angle. Understanding the movement of the basketball in the air is required for shooting performance, as adjustments can be made based upon the balls flight path. 4 factors influence Projectile Motion:

  1. Projection Speed
  2. Projectile Angle
  3. Relative Release Height
  4. Ratio of Muscular force applied to an object (Summation of Force)( McGinnis, 2013)

Projectile Angle

Optimal angle of release is contextual based upon an athletes physiological characteristics. Typically 45 degrees is cited as optimal, however this caters for the average human being (Zatsiorsky, 2008). Identifying ones anthropometric features reveals how one should shoot the ball to have the greatest chance of success. For the purpose of this blog, Stephen Curry will be analyzed, as he is arguably the best shooter in the game today (2017). The video below analyzes why he is so efficient.

Why is Projection angle important?

Releasing the ball too low or high causes problems in efficiency. Releasing the ball between 50-55 degrees has a greater chance of success due to the increased surface area of the basket (Bartlett, 2014). The flatter the shot, the less surface area the ball has, thus making it harder to score. All basketball shots have a negative release height. This is due to the release height being lower than its landing level. This is seen in the image below.

negative release.png



Limb length influences shooting performance. Athletes with longer levers are able to generate more force compared to those with shorter ones.  This is due to the mechanical advantage that can be expressed in the equation (McGinnis, 2013) :

Force x Distance

50 (F) x .10 (D) = 10

50 (F) x .20 (D) = 20



As with most human body movements, the basketball shot is a level 3 lever. This is because the force is applied between the load and the axis. A level 1 has the fulcrum between the load and the force, whereas level 2 has the load is in the middle of the fulcrum and force (McGinnis, 2013).

Force generated is increased with greater distance. In a basketball context this is incredibly useful as long levers are capable of generating more force, while applying the same force as someone with shorter levers (Bartlett, 2014). Kevin Durant is an excellent example of an athlete with long levers. His height is 6,10 with a wingspan of 7,4. He is considered one of the best scorers in the league, which is aided considerably by his length. Defenders cannot contest his shots, he is able to achieve greater power with less effort, and has a greater launch velocity scoring the ball quickly. The graph below demonstrates his superiority in comparison to players with shorter levers.player release height.png


Magnus Effect

When the ball is travelling through the air, the friction between the ball and air creates a flow of air that the ball ‘grabs’ on to resulting in the particles of air to spin with the ball, this is known as the Magnus effect (Blazevich, 2013). The spin or rotation of the ball is a crucial component to a successful three-point shot. In basketball, a shot is typically shot in a manner that enables backspin on the ball. Correct grip and vertical alignment of the forearm allows the shooter to apply the backspin to the ball. Research suggests that the vertical alignment of the arm to the basket is crucial, as letting the arm drift laterally takes the arm out of alignment with the basket, resulting in the ball to spin with a to the side that may deflect it off the rim (Knudson, 1993). There are two main techniques used to generate backspin, they are; wrist action and the vertical angle of the forearm (Knudson, 1993). Backspin raises the arc of the ball as it lifts the ball forward and decreases the velocity of the ball as it’s descending, this can be beneficial as it allows for minimal impact off the backboard which in turn can tip the ball to fall into the net (Knudson, 1993). Applying backspin to the ball can also generate height allowing for a successful shot that may have otherwise been too low (Knudson, 1993).
An example of the Magnus effect can be seen in the following video of a 3-point shot taken by Stephen Curry.

The Answer

Shooting 3 pointers requires a fluid motion, practice and consistency. Knowledge of the factors that influence this shot can assist athletes who wish to improve their ability.

Utilizing Summation of Force correctly greatly aids athletes. Correctly applying force reduces fatigue and propels the ball forward. Poor use of the Kinetic Chain puts too much demand on specific body parts, which leads to decreased shooting percentage.

Manipulating Centre of Mass benefits athletes, particularly when they are being defended. Extra hang time improves shooting percentage as the defender cannot manipulate his body the same way without causing a foul.

Comprehension of Newtons 3 Laws can aid in multiple ways. Particularly the third law which is linked with Coefficient of restitution. Players who understand an objects coefficient when impacting upon surfaces will have a greater chance at scoring shots, as they know what shots will be successful, raising their shooting percentage.

Projectile motion / Angle of release is useful. Understanding the optimal release point for an athlete is crucial. Depending on an athletes Levers they have the potential to generate more force due to increased distance. Those with longer arms can do more with less, vice versa.

Indoor basketball negates the wind, but for those playing outside the Magnus Effect is a considerable influence. Identifying which way the wind is blowing and how it will curve through the air is necessary for those shooting from long range. Air pressure moving from high to low grabs the ball and manipulates it into a certain direction. Those who can cater for this effect are at a great advantage, and will have a higher shooting percentage compared to those that don’t.

Taking these factors into account, optimization of technique can occur by:

  • Bending Knees lower (Poor Summation of force, levers doing too much work)
  • Jump Higher (Increase angle of release, give higher percentage of scoring)
  • Straighten body (Off balance leaning after landing)
  • Hold follow through longer

How else can we use this information?
The biomechanical principles surrounding the shooting technique of the 3-point shot can be applied to a variety of different sports where the accuracy of the shot is critical for success. Principles of summation of force, Magnus effect and projectile motion can assist with improved performance outcomes. An example of this can be seen with the Magnus effect in volleyball, unlike the 3-point shot where backspin is applied to decrease the speed of the ball as it’s descending, topspin is applied to the volleyball to decrease the amount of time spent in the air forcing the ball downwards and therefore allowing it to land quicker. The biomechanical principle of the summation of force can be seen in netball, where the force applied to the ground influences the height of the jump essential to increase release height and velocity for optimal skill execution.
An understanding of the biomechanical principles that underpin a particular sport are beneficial for athletes, coaches, teachers and students. For athletes, an understanding of biomechanical principles allows for continuous improvement of their performance. For coaches, a deep understanding of biomechanics allows for the implementation of appropriate training programs to reach an outcome that is desirable for an athlete’s improvement for optimal skill execution to meet the increasing demands of sport. Along with skill improvement, injury prevention is another important aspect of a biomechanical understanding. Furthermore, teachers and educators can benefit from an understanding of biomechanics where lessons can be created to assist with the development and improvement of skills, and provide opportunities for assessment that are essential for the students learning


Bartlett, R. (2014). Introduction to sports biomechanics. London: Taylor & Francis Ltd.

Blazevich, A. J. (2013). Sports Biomechanics The basics: Optimising Human Performance . London: Bloomsbury Publishing.

McGinnis, P. (2013). Biomechanics of sport and exercise. Champaign, IL: Human Kinetics. 

Knudson, D. (1993). Biomechanics of the Basketball Jump Shot – Six Key Teaching Points . Journal of Physical Education, Recreation & Dance , 64(2), 67-73.

Sewell, D., Watkins, P. and Griffin, M. (2013). Sport and Exercise Science. Hoboken: Taylor and Francis.

Zatsiorsky, V. (2008). Biomechanics in Sport. Chichester: John Wiley & Sons.

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