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Science | Technology | Engineering | Math
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Texas Legends: STEM Book
Table of Contents
Rules of the Game
The Basketball Court
Physical Characteristics
Force
Jumping
Dribbiling
Shooting
Passing
Defense
The Box Score
Advanced Concepts
Answer Key
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Introduction
Welcome to the Texas Legends STEM Booklet brought to you by Raytheon. This booklet takes a look at basketball and how it can be explained through math and science. It begins with basic concepts and rules suitable for
all school-aged students, and advances to concepts for middle school-aged students. The content is organized to
present science and math concepts first, and then brings them together to explain how they can be applied to different aspects of basketball; Jumping, Dribbling, Shooting, Passing, and Defense. The more advanced sections teach
students how to utilize and analyze a box score, and provide an introduction to more in depth and highly developed
statistics that have become a major part of the game today.
The booklet uses basketball to help students better understand math and science concepts that they are learning. It
is intended for all students, no matter how familiar they are with the game of basketball. Using a fun and familiar
game as a platform for learning allows students to relate to the new information that they are taking in, and demonstrates the connection between math and science theory and everyday scenarios.
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Rules of the Game
Points
• In a basketball game, points are used to keep track of the score.
Points are given to teams for making either a field goal or a free throw.
• A made basket can be worth 1, 2, or 3 points depending on how it was
scored.
Field Goals
• A field goal is a basket scored in any way other than a free throw.
• A field goal can be a jump shot, a layup, a dunk, a tap in, or any other
shot.
• Field goals are worth either 2 or 3 points depending on where the shot
is taken.
• On a basketball court there is a curved arc that sets the difference between 2 and 3 point baskets. If a player shoots from behind the line and
makes a basket, their team gets 3 points. If a shot is taken from inside
the line and is made, the team is awarded 2 points. If a basket is made
when the shooter’s foot is touching the three point line, the shot is worth
2 points.
Free Throws
• A free throw is a shot taken at the designated free throw line that
counts for 1 point if it is made.
• During a free throw no other players are allowed to move or stand in
the way of the shooter.
• A free throw is given to a player if they are fouled by an opponent.
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Time of the Game
• Basketball games are normally divided up into either four quarters or
two halves.
• If the game is made up of quarters, two quarters would be equal to one
half of the game.
- NBA basketball games are made up of four 12 minute quarters.
- NCAA basketball games are made up of two 20 minute halves.
• High level basketball games also use a shot clock to keep the game
moving and keep it entertaining to fans.
• The clock shows how much time a team has to shoot the ball on
offense.
• The shot clock starts when a team gains possession of the ball and will
reset either when the team shoots and the ball hits the rim, or when the
opposing team gains possession of the ball.
- The NBA shot clock is 24 seconds long
- The NCAA shot clock is 35 seconds long
Possessions
• In basketball, a possession begins when a team gains possession of
the ball and ends on either a made shot, a defensive rebound, or a
turnover.
• The “Lowest common denominator” is a term used in math when
dealing with fractions. The “Lowest common denominator” or LCD is the
smallest number that can be used for the denominator of more than one
fraction.
• In basketball, the LCD is one possession. That means that of all the
ways to compare numbers and statistics in basketball, (Per Game, Per
Minute, etc) a possession is the way to compare these numbers on an
equal playing field.
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The Basketball Court
Court Measurements
• A basketball court is the shape of a rectangle.
• Court sizes can vary based on the level of competition playing.
- An NBA court is 94 feet by 50 feet.
- A high school court is 84 feet by 50 feet.
• One dimension of the court that does not change from high school
basketball all the way up to NBA basketball is the height of the rim,
which is always 10 feet above the floor.
• The backboard, which is also a rectangle, is another dimension of the
court that does not change. The backboard measures 6 feet by 3.5 feet.
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Area
• Area is the size of a surface, or the amount of space inside a flat
object.
• Area is calculated by multiplying Length X Width and is expressed in
terms of a unit square
- Area = L x W
- Ex. L = 1ft W = 1ft
- Area = 1ft x 1ft = 1 ft2 or 1 square foot
Unit Conversion
• 1 foot is made up of 12 inches
• 1 inch is made up of 2.54 centimeters
Test Your Skill
• What is the area of an NBA court in square feet?
- Area = ____ x ____ = ______
• What is the area of a high school court in square feet?
- Area = ____ x ____ = ______
• What is the difference in area between a high school and NBA court in
square feet?
- Difference = _____ - ______ = _______
• What is the area of a backboard in square feet?
- Area = ____ x ____ = ______
• What are the length and width of an NBA court in inches?
- Length = ____ x __ = ______
- Width = ____ x __ = ______
• What are the length and width of an NBA court in centimeters?
- Length = ____ x ____ = ______
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- Width = ____ x ____ = ______
• What is the area of an NBA court in square inches?
- Area = ____ x ____ = ______
• What is the area of an NBA court in square centimeters?
- Area = ____ x ____ = ______
More Court Measurements
• The diameter of a circle is a straight line going through the center of a
circle meeting the surface on each end.
• The radius of a circle is a straight line from the center of the circle
meeting the surface on one end.
• The radius is always equal to one half of the diameter.
• The basketball rim has a diameter of 18 inches or 1.5 feet.
• The diameter of a basketball is 9 inches.
• Now that we know the diameter of a basketball and of the rim:
- How many basketballs can fit in the rim at one time? _____
- What is the radius of a basketball? _____
- What is the radius of the rim? _____
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Three Point Line
• The distance to the three point line from the center of the basket
changes for different levels of competition
- The high school line is 19.75 ft from the basket
- The NCAA line is 20.75 ft from the basket
- The NBA line ranges from 22 ft to 23.75 ft from the basket.
Test Your Skill
• How many inches from the basket is the NCAA three point line?
Inches = ____ x __ =
• What is the difference in inches from the NCAA and High School three
point lines?
- NCAA three point line = ____ inches
- High School Line = ____ x __ = ______ inches
- Difference = ____ - ____ = ______ inches
• If an NBA player makes a shot 262 inches away from the basket, how
many points does his team get? _____
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Physical Characteristics
Height
• Height is the measurement of how tall a
person is.
• In basketball height is a very important
characteristic for a player
• Basketball players come in all shapes
and sizes.
- The tallest professional basketball
player ever, Paul Sturgess, stands 7 ft 8 in
tall
- The smallest professional player, Tyron
“Muggsy” Bogues stood 5 ft 3 in tall.
Test Your Skill
• What is the difference in height between these two players?
- Sturgess: 7 feet = ___ in + 8 in = _____
- Bogues: 5 feet = ___ in + 3 in = _____
- Difference = ____ in - ____ in = _____ inches
• How many centimeters tall is Paul Sturgess?
- Height = ____ inches x ___ = ______ cm
• How many centimeters tall is Mugsy Bogues?
- Height = ____ inches x ___ = ______ cm
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Wingspan
• Wingspan is an important measurement used in basketball in
addition to height.
• Wingspan is measured from fingertip to fingertip with both arms fully
stretched out to the side.
• A long wingspan helps a basketball player on the defensive end,
making them seem wider, longer, taller, and allows them to keep a
further distance from their opponent, while still disrupting them
defensively.
• Although it can help a player in many ways, a long wingspan mainly
helps players get rebounds, contest and block shots, get steals, and
block an offensive player’s vision.
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Standing Reach
• A player’s standing reach is almost a
combination of height and wingspan,
except only one arm is measured.
• Your standing reach is measured as the
distance from the ground to your fingertip
when standing straight up with one arm
extended vertically in the air.
• Standing reach helps you figure out how
tall a player can make themselves without
jumping.
• While height is an important
measurement, some players have long
arms that can effectively make them
“taller” while reaching than another
player who may be taller but have a
shorter reach.
Test Your Skill
• John has a standing reach of 92 inches. How high does he need to
jump to dunk the ball? _______ in
• Tim has a standing reach of 218 centimeters. He can jump 90
centimeters off the ground. Can he dunk the ball? _____
Weight and Mass
• Weight is defined as the force on an object due to gravity.
• Weight is calculated by multiplying the mass of an object and the
gravitational acceleration.
- W=M x G
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• Weight can be expressed in pounds (lb) or newtons (N).
- 1 pound = 4.44822162 Newtons
• Mass is defined as the amount of matter an object contains.
• Mass is expressed in kilogram (kg)
- 1 kilogram =9.80665 Newtons
• While weight can change based on the location of the object,
due to changes in the gravitational acceleration, mass does not.
• Gravitational acceleration (G) is equal to 9.8 m/s2
• Mass can affect players in many ways on the court, including
their
- Force
- Acceleration
Test Your Skill
• If Paul weighs 800 Newtons, what is his mass in kg?
- Mass (kg) = W/G
- M = 800N/_____ = ______kg
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Force
The Laws of Motion
• Force is a push or pull on an object.
• Force only occurs when there is an interaction between objects.
• Isaac Newton’s First Law of Motion states that:
- An object at rest stays at rest, while an object in motion stays in
motion unless acted upon by another force.
• The formula for force is
- Force (F) = Mass (m) x Acceleration (a)
• This is also known as Newton’s Second Law of motion
- Acceleration occurs when a force acts on a mass
• Newton’s Third Law of Motion, which also is applicable to basketball
states that:
- To every action there is always an equal and opposite reaction.
• That means that when force is exerted on one body, an equal force is
exerted back in the opposite direction by the second body
• These laws and how they relate to different aspects of basketball will
be examined throughout this packet.
Acceleration
• Acceleration is the change in the rate of speed of a moving object over
time.
• Acceleration affects many aspects of basketball including:
- Transition
- Fast acceleration allows a player to reach their top speed
quicker than others.
- Driving
- Quick acceleration with the ball allows offensive players to
blow by defenders on their way to the basket.
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- Defense
- Quick acceleration allows defenders to stay in front of an
opponent and keep them from getting to the basket or
finding space for an open shot.
- Cutting
- Fast acceleration allows players moving without the ball
to blow past their defender to get open and receive the
ball.
• From Newton’s Second Law of Motion we can determine that
- Acceleration (a) = Force (F) / Mass (m)
- The standard unit of measurement used for acceleration is
Meters per Second Squared (m/s2)
• In order for players or objects of different masses to generate an
equal amount of acceleration, they must produce differing amounts of
force
• In order for a player of a high mass to accelerate at the same rate as
a player with a low mass, they need to generate a much greater force.
• Whenever you see a player or object slow down or speed up, you are
watching acceleration in action.
Momentum
• Momentum is a term often used in sports.
• Many people use the term to describe a team that has been playing
well or is on a winning streak.
• The definition of momentum is the force that an object has when it’s
moving.
• The formula for momentum is:
- Momentum (p) = Mass (m) x Velocity (v)
- Velocity is the speed of something in a given direction
• This means that if an object with a large mass is travelling at the
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same velocity as an object with a low mass, the object with the large
mass will have the greater momentum.
• In basketball, you could view this as two players with different
masses. If they are moving at the same speed, the player with a larger
mass will have more momentum, and will take more force to stop it.
• The more momentum an object has, the more force it takes to slow
down or stop the object.
• Force is the rate that momentum changes with time.
• So, we can also calculate momentum using:
- Momentum (p) = Force (F) x Time (t)
- The standard unit for momentum in the N s
• Assuming equal force is used to stop both objects, an object with a
greater momentum will take more time to stop than an object with a
lower momentum.
• Momentum also relates to Newton’s Third Law of Motion in what is
called the Conservation of Momentum.
• In a closed system (where objects are not affected by external forces)
momentum is conserved. For a collision with 2 objects, the total
momentum of the two objects before the collision occurred is equal to
the total momentum of the two objects after the collision.
- This demonstrates Newton’s Third Law that for every action
there is an equal and opposite reaction.
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Test Your Skill
• John is sprinting to catch a loose ball. He has a mass of 80kg and is
accelerating at a rate of 3.25m/s2, how much force is he producing?
- Force (N) = ______ x _______ = _______ N
• John produces this force for 1.8 seconds. What is John’s momentum?
- Momentum (p) = _______ x 1.8s = _______ N s
• Given all of this information, what was John’s velocity over this time?
- Velocity (v) = ______ / ________ = _________ m/s
• If John is moving with a momentum of 415 N s and collides with a
player that is setting a pick, standing still with no momentum. They
both fall backward after this collision. What is the total momentum of
these two players after the collision? _______ N s
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Jumping
Jumping and Force
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• Jumping is a big part of the game of basketball
• The ability to jump high gives players an advantage when performing
acts such as:
- Shooting
- Rebounding
- Defending
• In order to begin a jump, a force has to be generated by the jumper to
launch themselves off of the ground.
• Newton’s Third Law of Motion is demonstrated on the launch.
- You generate a force pushing against the ground, and that force is
projected upwards, launching you into the air.
• When you see someone jump, you might notice that they seem to hang
in the air for the longest time at the highest point of the jump.
• This is an example of projectile motion.
• Projectile motion occurs due to the downward pull of gravitational
acceleration, and states that:
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- When an object is thrown or launched into the air that it will
move in a curved path.
• Gravity is a downward force only, so it does not affect horizontal
movement during a jump.
• Because gravitational acceleration is a constant force, a player can
increase their vertical leap by strengthening the muscles they use to
generate the force to jump.
• The more force you generate to launch yourself from the ground, the
higher and longer you will stay in the air.
• Hang time, a term used a lot in basketball, describes the amount
of time that someone stays in the air following a jump. This time is
recorded from the time the feet first leave the ground, until the feet
reach the ground on the landing.
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Energy
Dribbling
• The dribbling and bouncing of a basketball can be a great example of
some of the physics concepts that we’ve touched on in this packet.
• When a ball is dropped from a certain point, for example 4ft in the air,
it will bounce back to that 4ft height on it’s first bounce, but will begin to
bounce lower on each bounce after that. Why is this?
• Without a hand to keep pushing the ball downwards it will not bounce
at a consistent height.
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• As the ball bounces, energy is being transferred, causing the heights of
each consecutive bounce to decrease.
• A basketball begins with what is called potential energy
- Potential energy is the energy stored in a physical object
- In this example, the ball has gravitational potential energy,
due to the ball being held at a height above the ground. The
force of gravity will act on the ball.
• When the basketball begins to fall, potential energy begins to transfer
into kinetic energy.
- Kinetic energy is the energy an object possesses due to it’s
motion.
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- In this example, as the ball accelerates towards the
ground, it gains kinetic energy.
• The law of conservation of energy states that the total energy in a
system cannot change if it is not affected by outside forces.
• The Law of Conservation of Energy can be related to Newton’s Third
Law, where a force in one direction causes and equal but opposite
force in the other direction.
• If this law held true for our bouncing ball example, the ball would
keep bouncing back to the height it was dropped from. What causes
the ball to reach a lower height on each bounce?
Friction
• Friction is the reason that the ball does not keep bouncing back to
it’s original height.
• When the ball hit’s the ground, it loses energy to the floor due to
friction.
- Friction is the resistance that occurs when two objects rub
against each other.
• Each time the ball hits the ground some of it’s energy is lost to
friction with the ground, therefore causing the ball to bounce to a
lower height each time.
• When the ball reaches the top of it’s bounce, it has less potential
energy than it began with when it was originally dropped.
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Air Pressure
• In order to keep the ball bouncing back to a consistent height, a
player needs to give the ball a downward push on each bounce to offset
the energy lost to friction.
• Another factor in the bouncing of the ball is the air pressure inside the
ball.
• A ball that has more air pressure, meaning it is filled up with more air,
will exert a larger force on the floor when it bounces.
• This is because the ball is more firm and will lose less energy to
friction when it hits the ground.
• A ball with high air pressure is more tightly filled with air particles.
When the ball collides with the ground, the tightly packed air particles
collide at a high speed, causing the ball to inflate back to it’s original
volume at a greater speed and retain more of it’s kinetic energy.
• If a ball isn’t filled with much air, the air particles inside have more
room to move around without colliding when it hits the ground. The air
particles collide at a slower speed, causing the ball to inflate back to it’s
original volume at a slower speed, causing the ball to lose more energy
to friction.
• The higher the air pressure in the ball, the less downward force is
required for the ball to bounce back to it’s original height.
• That is why is it easier to dribble a ball that is fully inflated, rather than
a ball that has lost air. You don’t need to use as much force to bounce
the ball when it is full of air.
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Shooting
Jump Shots
• Newton’s laws of motion are very important when it comes to shooting
the basketball.
• All three of the laws need to be considered when trying to shoot the
perfect shot.
• Newton’s First Law of Motion explains why the ball doesn’t keep
moving through the air forever after it is shot.
• The ball is in motion but is affected by outside forces, mainly the
downward acceleration of gravity.
• The pull of gravity is very important, since it causes the ball to move in
an arc, similar to what we discussed about jumping.
• Because gravity creates movement in an arc shape, the shooter needs
to understand the correct force to shoot the ball with and the correct
angle to shoot the ball so that their shot will go in the basket.
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• The shooting angle is particularly important, because it determines the
angle at which the ball will fall into the hoop.
• Because the ball is never going to be falling straight down into the
hoop from a 90o angle, the rim takes the shape on an ellipse from the
ball’s perspective.
- An ellipse is an oval shape and not perfectly round like a circle
• The basket seems larger for the ball when it falls in at a greater angle
closer to 90o
• A flat shot without much arc has a small
chance to go in the basket.
• Although a higher arc makes the hoop seem
larger for the ball, you also have to consider the
force it takes for the ball to reach the hoop.
• For example:
- If you are shooting from 20 feet away from
the basket, a shot taken at an angle of 60o
is going to require more force behind it than
a shot taken at a 45o angle.
- If the shots were taken with the same
force, the shot at a 45o angle would reach
the basket, but the 60o shot would fall
short.
- Shooting at a 60o angle requires the
ball to go higher in the
air, trading off with the horizontal distance it will travel.
- If you want the 60o shot to travel the same horizontal
distance as a 45o shot, it will need more force behind it.
• A 45o angle has been determined as the optimal release angle for a
jump shot because it has the right trade off between horizontal distance
and entry angle to the hoop.
• When shooting, it is important to practice your release angle
consistently.
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- Because different release angles require different amounts of
force to reach the hoop, a consistent release angle means that you
will be using a consistent amount of force for each shot.
- If your release angle keeps changing, you’ll need to keep
changing the force you put behind the shot.
- Consistent mechanics become key for a consistent shot
• The force that the shooter applies to the ball when shooting brings us
to Newton’s Second Law.
• As we know, Force is equal to mass times acceleration.
• From this equation we can determine that in order to shoot the ball
with a consistent force, we need to shoot the ball at a consistent
velocity, since the mass of the ball remains constant.
• Newton’s Third Law is demonstrated when the ball that has been shot
collides with a surface.
• In most cases there are three types of collisions that can occur
- The ball hits the rim and bounces off
- The ball hits the backboard and bounces off, either into the basket
or out of the basket
- The ball goes through the next and hits the floor
• We have already discussed how Newton’s Third Law works when the
ball hit’s the floor
- The ball will generate a force on the ground, causing an upward
force that makes the ball bounce.
• This concept holds true to when the ball bounces off the backboard or
rim.
- The ball will generate a force on the object it collides with,
creating an equal and opposite force that causes the ball the
bounce off of that object.
• Newton’s Third Law can be used in this situation to help with
rebounding.
• A ball colliding with the backboard or rim with a high force will bounce
back with a high force. A ball with a low force that collides with these
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objects will bounce back with a low force.
• Generally, shots from a longer distance or shot with a high angle used
more force to reach the basket. Therefore, the ball will bounce back
with a greater force, usually causing it to bounce to a point further away
from the basket.
• If a player shoots the ball from just a few feet away from the basket,
the rebound shouldn’t bounce back very far from it’s collision point.
• So, when rebounding, be aware that most of the time the rebound from
a missed 3pt shot will usually fall further from the basket than the
rebound from a missed two point shot.
Rotation
• Shooting the ball with backspin, or a backwards rotation, can also
make a difference in the outcome of a shot.
• Backspin affects shooting positively for a few reasons.
• First, backspin on the ball can help change the direction the ball
bounces when it hits the backboard.
• If a ball has no spin on it and hits the rim, it will most likely bounce
back at an angle similar to the one that it hit the rim.
• If the ball has backspin, there will be a downward velocity at the point
of the collision due to the ball’s momentum, causing the ball to bounce
down towards the rim.
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• Backspin also helps soften the bounce a ball makes after a collision
due to friction.
• When a ball with backspin hits the backboard, more friction is
created because more of the ball’s surface makes contact with the
backboard.
• When more friction is created, more energy is lost from the system,
sending the ball bouncing back with a lower force.
• This means that the ball will not bounce back as far, making it more
likely that the ball will fall into the rim.
Free Throws
• Just like a jump shot, the arc of a free throw has a big affect on the
ball’s chances to go in the basket
• The release angle and the force on the shot are the determining
factors
• Unlike a jump shot, when a free throw is taken, the shooter is not
moving and their feet do not leave the ground. Enough force to generate
a high arc on the ball must be created.
• The free throw incorporates the shoulder, elbow, wrist, hips, knees,
and ankles to generate the necessary force to shoot the shot.
• The body of the shooter begins with potential energy that turns into
kinetic energy to be transferred to the ball.
• All of the shooter’s motion, starting the bending of the knees and
ending with their arm movements and follow through, transfer kinetic
energy to the ball.
• The energy is first sent downward towards the floor when the shooter
bends their knees.
• Because of Newton’s Third Law of Motion, we know that the force
projected onto the floor is sent back up with the same force.
• The upward force that is generated, along with an extra push from the
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leg and arm muscles of the shooter as
they go through their shooting motion,
give the ball the force it needs to make it
to the hoop.
• Because a free throw is an
uninhibited set shot, it is much easier to
achieve consistent results.
• Players are able to take thousands of
free throw repetitions from the same spot
and using the same motion,
allowing them to perfect their technique
and achieve the right launch angle on
each attempt.
Shooting Form
• Correct shooting form can be crucial in basketball.
• Proper shooting form helps players:
- Achieve their desired force on the ball with the least amount of
work necessary
- Aim their shot
- Shoot the ball at the optimal trajectory or angle
- Put backspin on the ball
- Develop consistency in their shot
• We have discussed why these factors are an important part of
shooting, but how are they achieved?
• The shot begins with proper footwork
- You want to have a balanced base
- Feet shoulder width apart
- The correct footwork is very important for aiming the shot
• When you shoot, you want to know your target
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- Keep your eyes fixated on the middle of the rim
- When using the backboard, your target should be the top corner
of the inside square, on whatever side you are shooting from
• Keep your shooting hand behind the ball and your elbow behind your
shooting hand
- The non-shooting hand should cover the side seams, with your
thumbs forming a T shape
• Knees should be bent to generate power
- As mentioned earlier, the knee bend generates much of the force
that will be used to get the ball to the target
• Maintain a high chest with shoulders up
- Your shoulders should never be in front of your knees
• As you elevate, the ball goes above the forehead
- With the elbow kept in, the shooter should look though the
“window” created by the arms
• Release the shot at the highest point of the jump
- For a free throw, the ball should just be released at the highest
point
• Finish with the shooting arm elbow above the eyebrow and a relaxed
shooting wrist
- This helps release the ball at the correct angle
• The index and middle fingers are the final body parts to touch the ball
- This helps create rotation and the backspin on the ball
• The non shooting hand should end up at forehead level
- Palm to the face
- Fingers to the sky
• The follow through on a shot is very important for increasing the
acceleration and force on the ball
- When you increase the distance that your arm moves, that
increases the time it takes to shoot the ball, therefore increasing
the momentum of the ball
• The movements for a shot require simultaneous work between the
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feet, knees, arms, and hands
• All momentum should be going towards the rim
- This helps give the ball a straight trajectory to the target
- It also helps transfer some of the body’s momentum to the shot
• Consistency and repetition are key to developing a good jump shot
• There are a lot of body movements that occur at the same time and
small details can make a big difference
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Passing
Passing Form
• Passing is another key component to the game of basketball
• Passes keep the ball moving around the court, allowing for
advancement of the ball, while also keeping defenders moving.
• Accurate passes are very important
• Passes that are not accurate can lead to not only turnovers, but they
can affect the play of the player that receives the ball
• If a player is waiting to receive the ball so that they can shoot, and
they receive a bad or inaccurate pass, it will affect the shot that is taken
and sometimes keeps the player from taking the shot
• The same can be said for a player who is cutting towards the rim, or
expecting the ball so that they can make a quick move to the basket
• An inaccurate pass can prevent the player receiving the pass from
getting the ball in the right position to score
• When passing the ball, you want to use a complete follow through with
your arms
• The reason for the follow through on a pass is the same reason you
use a follow through on a shot
- Increasing the distance that your arms moves increases the time
it takes for the pass, which will increase the momentum that the
ball has
• This concept can be used when receiving a pass, except in the
opposite way
• To make a pass easier to receive, you want to decrease it’s momentum
- If you allow your hands to move back with the ball while making
the catch, cushioning the ball, it will decrease the ball’s momentum
and make for an easier catch
• There are three different types of passes in basketball
- Chest Pass - Bounce Pass - Overhead Pass
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Chest Pass
• The chest pass is delivered from the chest by the hands and arms
• The pass is made with the elbows facing out, driving the ball towards
the target
• Hands should be placed on either side of the ball with the thumbs
down
• The thumb placement should help give the ball backspin upon release
• The pass moves due to the force created from the arm movements
• Because the mass of the ball stays the same, the acceleration on the
ball determines how much force the pass is thrown with
• As previously mentioned, accuracy is a big part of passing
• Because of the downward pull of gravity, the pass should be aimed at
a point higher than the intended target.
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- The force of gravity will pull the ball downward during it’s time
in the air
• If you are passing to a moving target, you also have to take into
consideration the velocity of the target
- Remember, velocity is the directional change in motion
• The passer must anticipate the point at which the pass will be
received and apply the proper force and direction for the pass to get
there.
Bounce Pass
• A bounce pass is a pass that bounces on the ground on the way to
it’s target.
• The ball should still be released with two hands, and thumbs down,
using the arms and elbows to generate the force behind the pass
• Instead of aiming the pass in the air, the pass should be aimed
forward and towards the ground
• Backspin helps the bounce pass lose more friction when it touches
the ground, making the pass easier to catch
• Because the pass loses more energy, it reaches the target with less
force than it was thrown with
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• You should aim your pass to bounce roughly two-thirds of the way to
the target
- You want to aim past the halfway point, because energy is lost
to friction when the ball hits the ground
Overhead Pass
34
• An overhead pass is made with two hands while the ball is held
above the head.
• The overhead pass is generally used for passes that need to travel a
longer distance
• An overhead pass will travel a further distance than other passes
because
- You are able to generate more force with your arms
- It begins with a higher release point
• You are able to generate a greater force and acceleration for an
overhead pass because there is more room for the arms to move and
build momentum for the ball
• With a chest or bounce pass, the arms do not have room for a wind
up, and have a starting point closer to the target
• Because an overhead pass comes above the head, your arms can
start moving with the ball for a longer distance before the release
point, giving the ball a greater momentum when it leaves your hands
• With an overhead pass, the ball has already built up momentum by
the time it gets to the point where a bounce or chest pass begins.
• The higher release point on a bounce pass also allows it to travel a
further distance horizontally.
• The force of gravity pulling the ball down will always be equal, so it
will take a longer time for the ball to hit the ground from a higher point
in the air.
• That means that while it takes longer to drop and hit the ground, it
will travel a further horizontal distance during that time.
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Defense
Defensive Stance
• Lateral movement is a key
part of the defensive stance
• Keeping a wide stance with
your feet will maximize your
lateral quickness
• Wide feet allow you to push
off of the ground with more
force in the lateral direction
you are moving
• Feet that are not wide
and are aligned inside of
the shoulders give more of
a vertical push of force, as
opposed to the lateral push of wider feet.
• Generating vertical force wastes takes away from the lateral force
you are generating, causing the need to work harder to produce an
equal amount of lateral force to when you are in a wide stance
• The next step in the defensive stance is to keep low hips and
shoulders
- Keeping low hips allows for quicker movements and shift of
direction
- Low shoulders keep your center of mass lower to the ground
• Low hips follow the same concept as a wide stance
• Keeping hips low allows for quicker movements (acceleration)
because you are closer to the ground.
• Since your mass is going to stay the same whether you have low or
high hips, the faster acceleration of keeping low hips produces more
force to move laterally.
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• Keeping a low center of gravity with low shoulders allows you to
have greater control over your movements
• Keeping a high center of gravity puts more strain on the body due to
gravity. The body needs to generate slightly more force to move at the
same rates of acceleration.
• Because defense is all about quick, explosive movements, you want
to allow your body to accelerate as quickly as possible.
• A low center of gravity will also give you more balance
• Moving feet are also key to defense.
• In the defensive stance, the body will accelerate slower with flat,
stationary feet
• If you are a standing still, you have potential energy that requires
work the be converted into kinetic energy
• When the feet are already moving, you already have kinetic energy
and will require less work to create more
• With your feet already in motion, you are already creating force
against the ground, which is being sent back at you
• Because you are already moving with some force, it takes less
acceleration to reach your desired force than it would starting with 0
force.
• Inertia is a term used to describe the resistance of an object to a
change in it’s motion
- It takes more force to make an object that is at rest move
- It is easier for a moving object to stay in motion
- It takes more force to make a moving object to stop than for it to
stay in motion
• Wide arms are the last component of the stance.
• Wingspan was already touched on previously in the packet, and
comes into play here
• Keeping wide arms makes your body as wide as possible to keep
opponents from driving by you
• As a defender, you want to take up as much space as possible so
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that the offensive player cannot use it
• Wide arms at your side allow you to get them straight up quicker
than you could if your arms were down at your side
• Remember, quick movements are key on defense, so the faster you
can get your arms up to contest a shot, the better your defense will be.
Balance
• Balance is an important defensive concept
• Maintaining balance gives a player more control over their
momentum and will allow them to make quicker movements
• As discussed in the defensive stance section, keeping a low center of
gravity will help a players’ balance
• You will often hear offensive players talking about getting a defender
off balance
• Players with the ball will use dribble moves such as crossovers, in
and out dribbles, and spin moves to get their defender off balance
• The goal of the offensive player is for the momentum of the
defensive player to be moving in the opposite direction that the
offensive player wants to go.
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• If a defender’s momentum is going in the opposite direction as the
offensive player, the defender needs to create more force to stop that
momentum and get it moving in the opposite direction
• Maintaining balance puts the defender in the best position
possible to make a quick movement and react to what the offensive
player does.
• Balance also helps the defender stay upright and not fall over when
faced with quick movements or physical contact
• If you have good balance, it takes more force from a colliding object
to move you or make you fall
• You can’t defend anyone from the ground, so maintaining balance to
stay upright is crucial to defending.
The Box Score
• You’ve seen them in the newspaper or on-line, the box score is a
chart that shows you statistics for each player’s performance in a
game
• The box score can tell you all kinds of information about an individual
basketball game, a basketball team, and individual players
• To understand how to read and utilize the box score correctly, you
must understand the math behind it
• On the next page is an example of an NBA box score
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• First, let’s go over each of the column headings
- NO - The player’s jersey number
- Player - The player’s name
- Min - Minutes played
- FG - Field Goals Made
- FGA - Field Goals Attempted
- 3P - Three Point Shots Made
- 3PA - Three Point Shots Attempted
- FT - Free Throws Made
- FTA - Free Throws Attempted
- OR - Offensive Rebounds
- DR - Defensive Rebounds
- TOT - Total Rebounds
- A - Assists
- PF - Personal Fouls
- ST - Steals
- TO - Turnovers
- BS - Blocked Shots
- PTS - Points Scored
• The box score also tells us the team totals for each of these statistics,
along with:
- Team FG%
- Team 3P%
- Team FT%
- Team Rebounds - Rebounds not credited to an individual
- Points off Of Turnovers
• At the bottom of the box score there is additional information about the
game:
- Team Scoring by Quarter
- Technical Fouls
- Points in the Paint
- 2nd Chance Points
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- The number of lead changes
- The biggest lead of the game for each team
• While the box score lists team field goal, three point, and free throw
percentages, the box score doesn’t show the percentages for
individuals.
• If you want to know the percentages of the individuals, you can
calculate them yourself
• Let’s use Chase Budinger from the Minnesota Timberwolves for an
example. Here are his statistics from the box score and how we
calculate his percentages:
- FG: 2 FGA: 11
- FG% = 100% x (FG/FGA)
- FG% = 100% x (2/11) = 100% x .18 = 18%
- 3P: 1 3PA: 5
- 3P% = 100% x (3P/3PA)
- 3P% = 100% x (1/5) = 100% x .2 = 20%
- FT% = 100% x (FT/FTA)
- FT% = 100% x (1/2) = 100% x .5 = 50%
• Knowing each player’s shooting percentages is a good way to rate
how they performed in a game
• Shooting percentages give an insight into each player’s shooting
efficiency
- Efficiency can be defined as the accomplishment of a job with a
minimum expenditure of effort
• Shooting efficiency is the ability of a player to score the most with a
minimum expenditure of attempts.
• For example:
- James scores 10 points on 4/5 shooting
- James had a FG% of 80% and scored 2 points per shot at
tempt
- Allen scored 16 points on 7/16 shooting
- Allen had a FG% of 43.75% and scored 1 point per attempt
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- Although Allen scored more total points, James was the most
efficient player. He scored more points per shot attempt.
• Let’s practice some of this math to fill in an incomplete box score:
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Advanced Concepts
Introduction
• In recent years there has been a lot of innovation in the use of
basketball statistics
• Following a similar movement that occurred in baseball, analysts have
been making an effort to dive deeper into the numbers to find new
statistics that give an even more accurate presentation of performance
than ever before
• Many of these statistics are made up of the numbers you would find in
a box score
• One of the biggest reasons for the need for newer statistics is to be
able to judge players on an equal playing field.
• Traditionally per-game statistics were the main way that individual
players were judged. The problem with per-game numbers is that they
are affected by team playing styles, and each individual’s minutes.
• These new statistics find a way to evaluate players evenly, regardless
of how many minutes they play, or the pace that their team plays.
• Earlier we defined the possession as the lowest common denominator
in basketball.
• These new statistics rely on per-possession numbers rather than
per-game numbers, using the lowest common denominator to compare
players equally.
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Per-Possession Statistics
44
• Individual and team performance can be evaluated on a
per-possession basis
• On the team level, the most basic per-possession numbers are
offensive and defensive efficiency
- Offensive Rating (Ortg) is the amount of points per 100
possessions that a team scores.
- Defensive Rating (Drtg) is the amount of points per 100
possessions that a team allows.
• Many teams are often judged by how many points per game they score
or allow, but to achieve the most accurate reflection of their
performance they must be evaluated on a per possession basis.
• For example, here are the offensive numbers for two teams in the
2013-14 season:
- Los Angeles Lakers:
- PPG = 103
- Ortg = 104.2
- Brooklyn Nets
- PPG=98.5
- Ortg=106.7
- As you can see from these numbers, the Lakers scored almost 5
more points per game than the Nets last season. But which team
had the better offense?
- With an offensive efficiency of 1.067 points per possession, the
Nets had the more efficient offense between the two teams.
- The Lakers averaged 98.8 offensive possessions per game
- Poss=100 x (Pts /Ortg)
- Poss = 100 x (103/104.2) = 98.8
- The Nets averaged just 92.3 offensive possessions per game
- Poss = 100 x (98.5/106.7) = 92.3
• Because these teams played at a different pace, causing one to use
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more offensive possessions per game than the other team, their points
per game numbers do not give the most accurate comparison to
determine which offense was better.
• To judge a team’s overall performance you can compare their
Efficiency Differential or Net Rating
- NetRtg =Ortg-Drtg
• The point of basketball is to score more points than you give up to your
opponent. It doesn’t matter how many points you score, as long as you
give up less than you score.
• We can measure who the best teams are by looking at who has the
largest positive differential between how points that they score and how
many points they give up.
• Point differential is a very good way to judge how good a team is, but
it is not the most precise.
• Using the Net Rating gives the most accurate differential number by
eliminating the fact that teams play with different pace.
• Points per game numbers are no different than statistics such as
rebounds or assists per game in that they are affected by pace.
• Statistics such as rebounds, assists, turnovers, steals, blocks, and
personal fouls are tracked as rates.
• These rates, for example rebounding rate (TRB%), are expressed as
rebounds per 100 possessions, or the percent of possessions that the
team grabs an available rebound.
• All of these statistics can be used for individual performance as well.
• Along with pace, minutes per game make it difficult to evaluate players
on an equal playing field.
• Per possession stats allow payers to be compared at the most precise
level, just as they do for teams.
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Shooting Efficiency
46
• In addition to points per
possession, there are a few other
measures that can be used to
evaluate a player’s shooting
efficiency.
• The most simple of these
measures is points per shot.
• Points per shot is a quick and easy
way to measure how efficient
players are at scoring.
• Two more metrics that are now
used to evaluate shooting efficiency
are:
- Effective Field Goal
Percentage (eFG%)
- True Shooting Percentage
(TS%)
• Effective Field Goal Percentage is a Field Goal Percentage that is
adjusted to account for the extra point given to three point shots.
• The formula for eFG% is:
- eFG%=(FG + .5*3P)/FGA
• Here is an example of how Effective Field Goal Percentage works:
- Paul scores 10 points. He is 4/10 with 2 3pt shots made
- eFG%=(4 + .5*2)/10
- eFG%=5/10=50%
- Jeremy scores 10 points. He is 5/10 with 0 3pt shots made
- eFG%=(5 + .5*0)/10
- eFG%=5/10=50%
- Even though Paul had a lower FG% than Jeremy, he had an equal
eFG% and scored equally as efficiently as Jeremy.
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• True Shooting Percentage takes evaluating shooting efficiency one step
further.
• TS% measures efficiency by adjusting for field goals, three point shots, and
free throws.
• By accounting for free throws, TS% measures all elements of scoring to
evaluate players on an equal level.
• The formula for TS% is:
- PTS/[2*(FGA + .44*FTA)]
- Why multiply FTA by .44 instead of .5?
- The coefficient to multiply by FTA is .44 because free throws do not
always take up a possession.
- Technical fouls are an example of this
- So are “and ones” or free throws given in addition to a made basket
- Statisticians have determined that 44% of free throws use a
possession, which is the reason for .44 as the coefficient, and not .5
• Here is an example of how True Shooting Percentage works:
- James scores 41 points. He is 12/28 from the field, hit 7 3pt shots, and
was 10/11 from the free throw line.
- TS% = 41/[2*(28+.44*11)]
- TS% =41/[2*(28+4.84)] = 41/65.68 = 62.4%
- Marcus scores 32 points. He is 15/31 from the field, and 2/2 from the
free throw line.
- TS%= 32/[2*(31+.44*2)]
- TS%=32/[2*(31.88)] = 32/63.76 = 50.2%
- As you can see from the comparison, even though James (43% FG%)
lower FG% than Marcus (48% FG%), James scored much more
efficiently overall than Marcus because of his three point shots and free
throws.
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Test Your Skill
• Calculate the eFG% and TS% for both players:
• Kevin Durant
- eFG% = (___ + .5*___)/____
- eFG% = (
)/
- eFG%=
- TS%= ___/[2*(___ + .44* ____)]
- TS%=___/[2*(
)]
- TS%= ___/_______
- TS%=
• Blake Griffin
- eFG% = (___ + .5*___)/____
- eFG% = (
)/
- eFG%=
- TS%= ___/[2*(___ + .44* ____)]
- TS%=___/[2*(
)]
- TS%= ___/_______
- TS%=
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Answer Key
Court Measurements
• What is the area of an NBA court in square feet?
- Area = 94ft x 50ft = 4700ft2
• What is the area of a high school court in square feet?
- Area = 84ft x 50ft = 4200ft2
• What is the difference in area between a high school and NBA court in
square feet?
- Difference = 4700ft2 – 4200ft2 = 500ft2
• What is the area of a backboard in square feet?
- Area = 6ft x 3.5ft = 21ft2
• What are the length and width of an NBA court in inches?
- Length = 94ft x 12 = 1128in
- Width = 50ft x 12 = 600in
• What are the length and width of an NBA court in centimeters?
- Length = 1128in x 2.54 = 2865.12cm
- Width = 600in x 2.54 = 1524cm
• What is the area of an NBA court in square inches?
- Area = 1128in x 600in = 676,800in2
• What is the area of an NBA court in square centimeters?
- Area = 2865.12cm x 1524cm = 4,366,442.88cm2
• How many basketballs can fit in the rim at one time? 2
• What is the radius of a basketball? 4.5in
• What is the radius of the rim? 9in
• How many inches from the basket is the NCAA three point line?
- Inches = 20.75ft x 12 = 249in
• What is the difference in inches from the NCAA and High School three
point lines?
- NCAA three point line = 249in
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- High School Line = 19.75ft x 12 = 237in
- Difference = 249in – 237 in = 12in
• If an NBA player makes a shot 262 inches away from the basket, how
many points does his team get?
Physical Characteristics
• What is the difference in height between these two players?
- Sturgess: 7 feet = 84in + 8in = 92in
- Bogues: 5 feet = 60 in + 3 in = 63in
- Difference = 92in – 63in = 29in
• How many centimeters tall is Paul Sturgess?
- Height = 92in x 2.54 = 233.68cm
• How many centimeters tall is Mugsy Bogues?
- Height = 63in x 2.54 = 160.02cm
• John has a standing reach of 92 inches. How high does he need to
jump to dunk the ball? 28in
• Tim has a standing reach of 218 centimeters. He can jump 90
centimeters off the ground. Can he dunk the ball? Yes
• If Paul weighs 800 Newtons, what is his mass in kg?
- Mass (kg) = W/G
- M = 800N/9.8m/s2 = 81.63kg
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Force
• John is sprinting to catch a loose ball. He has a mass of 80kg and is
accelerating at a rate of 3.25m/s2, how much force is he producing?
- Force (N) = 80kg x 3.25m/s2 = 260N
• John produces this force for 1.8 seconds. What is John’s momentum?
- Momentum (p) =260N x 1.8s = 468Ns
• Given all of this information, what was John’s velocity over this time?
- Velocity (v) = 468Ns / 80kg = 5.85m/s
• If John is moving with a momentum of 415Ns and collides with a
player that is setting a pick, standing still with no momentum. They
both fall backward after this collision. What is the total momentum of
these two players after the collision? 415Ns
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Box Score
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Shooting Efficiency
• Calculate the eFG% and TS% for both players:
• Kevin Durant
- eFG% = (14+ .5*3)/25
- eFG% = (15.5)/25
- eFG%=0.62 or 62%
- TS%= 36/[2*(25+.44*7)]
- TS%=36/[2*( 28.08)]
- TS%= 36/56.16
- TS%= 0.641 or 64.1%
• Blake Griffin
- eFG% = (9 + .5*1)/12
- eFG% = (9.5)/12
- eFG%= 0.7917 or 79.17%
- TS%= 22/[2*(12+.44*6)]
- TS%=22/[2*(14.64)]
- TS%= 22/29.28
- TS%= 0.7514 or 75.14%
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