How Math Is the Foundation of Football

The Super bowl, the Game of Games, the Battle of the Pigskin is fast approaching, and we know you will likely be watching, even if it is only for the Puppy Bowl or the commercials in between play. So, in honor of this fun and exciting American sports day in February, we wanted to share with you some educational insights on how football is actually a very mathematical and calculated game.

The Rules

The objective of the game of football is to gain possession of the ball and advance the ball down the field towards the opponent’s goal line or goal posts. Each team has 4 plays to move the ball 10 yards or more before the ball is turned over to the other team. Each time the team succeeds in moving the ball 10 yards or more, they either get a first down which starts their 4 chances over again, or they score!

The Field

Mathematical concept: Geometry

The field is an example of a rectangle; 120 yards long and 53 and 1/3 yards wide. The field has two end zones at either end where points can be scored. When moving from one end of the field to another, the yardage count goes up to 50 and then back down to 10. This can make for some interesting addition and subtraction challenges once the offense and defense start moving up and down the field!

General Game Play

Mathematical concept: Basic Addition and Subtraction

In football, each play is made up of either yardage gain or yardage loss which is a calculation of a negative or positive number.

With each pass or run that the offense attempts, you must add the yardage that they made together to understand where they have advanced to on the field.

However, at the same time, the defense is working to stop the offense from scoring. So, if the defense pushes the ball back past the line of scrimmage which is where ever a set of 4 downs began, the offense loses those yards, and they are subtracted from the offenses’ yardage.

Don’t forget about penalties! They can affect the yardage count for both the offense and the defense. Sounds like a lot of addition and subtraction practice in the works!

Last but not least, what we mentioned about the field affects how this addition and subtract goes. If a team is moving towards their opponents end zone and is at the 20 yard line, they need to move 20 yards to score. But what if they only gain 10 yards? Where are they at on the field?

At the 10 yard line! So gains and losses in the game can actually be subtraction and addition respectively!

Play Calling/Routes

Mathematical Concept: Angles

Since the goal of the game of football is to get 10 or more yards, teams have to be very strategic on how they plan to outplay the defense. Teams practice plays which include a variety of routes for the wide receivers, running backs, and corner backs to run in order to get the ball down the field. All of these routes make up different angles to maximize the chances of getting the ball and taking it down the field. In most plays, these angles compliment each other to utilize the full field while trying to outsmart the defense.

In addition, the defense also has to think about angles. In an effort to slow down or stop the movement of the offense, the defense has to constantly be thinking about intercepting the ball from their opponent. This requires an understanding of the best angles to ensure they can beat their opponent to the spot and still have the ball in a place where they can advance the other way down the field.

Individual Player Stats

Mathematical Concept: Statistics

In football, statistics are used to understand how a player is performing and how to compare one player to another. Without statistics, this can be difficult in a team sport like football.

Using one of the main positions as an example, quarterbacks on evaluated on the following statistics:

  1. Pass completion percentage

  2. Yards per pass attempt

  3. Quarterbacks efficiency rating

  4. Yards per game

  5. Touchdown to interception ratio

When calculating a quarterback’s pass completion percentage, all you have to know is how many passes they attempted and how many passes they completed. Let’s say a quarterback attempted 30 passes in a game but only completed 20 passes. We would calculate 20/30 = .666 X 100 = 66.6% as their pass completion percentage.

All of these statistics can be calculated using addition, subtraction, multiplication, and division.

Applying This Knowledge

Now that you know how math plays a part in the game of football, use these facts to mathematically track the progress of the Super Bowl yourself! Block the portion of the TV during the game they gives the yardage and score, and check in with your progress every now in then to see if you are on track with your calculations!

We recommend only doing this if there is not an avid football fan in the room!

Another way to practice your math during the Super Bowl is to try and calculate the yardage and score before it appears on the screen. This can be tough though as they are fast so be ready for some speed math!

Happy Super Bowl Sunday!

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