Running head: SHOOTING STATISTICS
Shooting Statistics
Ivan N. Mix
Mesa Academy for Advanced Studies
SHOOTING STATISTICS
Purpose
The question that this project is trying to answer is how can an equation be made to
represent the degree in which you see the goal change in relation to distance and angle from the
goal. If this project is successful, it can supply information to soccer teams to develop strategies
that would place the shooter in a higher percentage area of success. This same approach can also
be used to calculation the angle of departure for future space craft to travel at light speed or
greater. Basically, this project will create an equation that will be able to calculate the minimum
angle of degree in which you have for success. With this question and the importance of this
study, the hypothesis that was came up with was if there is a relationship between all the data,
then an equation will be able to be made, because an equation can always represent a group of
ideas that link together.
Entity
During the background research it was learned that in order to conduct the experiments in
a correct manner, you would need to understand all the different parts of the soccer field and its
dimensions (see picture #1 and picture #2). A soccer field must be in the form of a rectangle and
marked with lines. These lines determine the boundary, in which you can play. And the two long
boundary lines that make the rectangle are called the touch lines, and the two short lines that
appear on the same side of the goal are called the goal line. The touch lines are anywhere
between 100 to 130 yards long, but for this experiment we will be using 130 yard long touch
lines. The goal line can be anywhere between 50 to 100 yards but for this experiment we will be
using 80 yard long goal lines. Within this field of play there is a goal, goal area and the penalty
area. The goal consists of two upright posts that are joined at the top by a horizontal bar, and it
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must be placed in the very center of the goal line. This goal is 8 feet tall and 8 yards long (see
picture #3). The goal area is when two lines are drawn at right angles from the goal line, 6 yards
away from each of the goal posts. Then these lines extend 6 yards into the field, and are joined
by a line that is parallel to the goal line. The penalty area is drawn with two lines that form right
angles with the goal line, 18 yards from each of the goalposts. And these lines extend 18 yards
into the field of play, and then they are connected with a line that is parallel to the goal line.
Trigonometry is also equally as important as the names and dimensions of the soccer
field, because it will be used to calculate the angle in which you see the goal width and height
wise. Trigonometry is the branch of mathematics dealing with the relations of the sides and
angles of triangles and with the relevant functions of any angle. The work trigonometry comes
from the Greek words trigonon (“triangle”) and metron (“to measure”). And in order to do
trigonometry you need a right angle, and need to be able to identify the hypotenuse, opposite and
adjacent (see picture #4). The hypotenuse is the longest side on a right angle, the opposite is the
angle that is opposite of angle 0 and the adjacent is the angle that is next to angle 0. And the six
commonly used functions that tie with the hypotenuse, opposite and adjacent are known as sine
(sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). And to create
right angles when you are located in between the goal posts, you need to draw lines from where
you’re standing to both of the goal posts. Then you would draw a line that is perpendicular to the
goal line to where you are standing, causing two right angles to form. In this circumstance the
hypotenuse would be the line that you drawed from your location to either post, the opposite
would be equal to half of the goal, and the adjacent would be the distance from the goal. When
you are not in between the goal posts, you need to draw lines from where you’re standing to both
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of the goal posts. Then you would draw a line that is perpendicular to the goal line to where you
are standing, causing two right angles to form. In this circumstance the hypotenuse would be the
line that you drew from your location to the far post, the opposite would be the distance between
you and the goal line, and the adjacent would be the distance from the far post and to the point
where the perpendicular line crosses the goal line.
Independent Variable
The independent variable that was chosen for this project was the location that you are on
a soccer field. This was chosen because in professional soccer, free kicks can be given anywhere
on the soccer field and my project needs to address all of these locations. But since it isn’t
logical to calculate all of the different places on the soccer field, the points that will be used are
points on the 90, 60, 30 and 0 degree line that depends on the goal line and the middle of the
goal. And on those lines you will be using 3 points that are located 5, 10 and 15 feet away from
the goal. If these 3 points on each line is not enough to determine a relationship in the output to
come up with an equation, then add more points on the line as needed. I will not be calculating
all of the outputs that could be made from the lines, because it is only necessary to calculate
enough points that will be needed to make an equation. The errors that can be conducted in this
experiment is very small, because since it is math only arithmetic errors can be made.
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Dependent Variable
The dependent variable of the degree in which you see the goal width and height wise
was chosen, because this form of qualitative data represents the degree in which you have an
opportunity for success. And free kicks for soccer all depend on this degree of success, because
everyone taking the free kick wants to score a goal. And to calculate the degree that you see the
goal, we will be using trigonometry. This is because you can create a right angle anywhere on
the field that would be able to calculate the angle in which you see the goal using sin and tan.
Methods
It was originally thought to draw the soccer field on a graphed paper, so that each square
represents one square foot of the soccer field. But this method has many places where human
error can come into effect, so the project turned to trigonometry to solve this problem.
Trigonometry is more effective than the drawing method, because it is more exact and there is
not a lot of places where you can have human error. Trigonometry is more exact than the
drawing method because it works with numbers and theorems that have already been proven to
work by the past’s mathematicians. The only errors that can occur with trigonometry is
arithmetic errors, but since each solution will be checked over and over, this error will most
likely not occur.
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Appendix
Picture #1:
Picture #2:
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Picture #3:
Picture #4:
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References:
2015-2016 LAWS OF THE GAME. (2015). Zurich, Switzerland: Federation International de
Football Association.
Soccer (FIFA) Field Dimensions & Layout. (2015). Retrieved September 25, 2016, from
http://www.sportscourtdimensions.com/soccer/
Trigonometry. (2016, April 18). Retrieved September 25, 2016, from
https://www.britannica.com/topic/trigonometry
Introduction to Trigonometry. (2014). Retrieved September 25, 2016, from
https://www.mathsisfun.com/algebra/trigonometry.html