Math in football - Grade: A PDF

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How math is implicated in football...

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Many individuals are unaware of how often math is used in our everyday lives, especially in sports. The game of football is a prime example of how sports and math are intertwined. According to Merriam Webster, the sport of football is defined by several games played between two teams on a usually rectangular field having goalposts or goals at each end and whose object is to get the ball over a goal line, into a goal, or between goalposts by running, and passing. There are many ways math is used in football, such as; the field, angles, yardage, and statistics. The football field itself is lined with numbers representing geometry. A football field is rectangular, with 120 yards long and 160 ft wide with two 10-yard end zones (Elert). NFL goal posts are 10 ft and 18ft and 4 inches wide. The football field has a sideline, which is marked with a solid white line that is a 6ft border where the teammates benches are located. There are two end-zones, both 10-yards wide and this is where a touchdown is scored and where the goal posts are located. This area is usually decorated with the home team’s name or symbol. The goal-line is 8-inches wide and is the line located in front of the end-zone. There are dashes in between every 10-yards represents a single yard. In the game of football, the score is the most important. There are many ways for the players to receive points. If a player runs the ball into the end-zone they receive 6 points and this is called a touchdown. Then, they are given an opportunity for extra points. The players can either kick the ball into the goal post for 1 extra point or they can go for another 2 points and get the ball back into the end zone ("Mathematics Matters Every Day - M2 ED.”). The use of simple addition is helpful when calculating the score. Angles play a large role in the game of football, especially for the players. This is seen in all aspects of the game from catching, pursuit angles, and tackling. The majority of football passing routes involve angles. “A passing route is a play driven by the quarterback to allow the receiver to open up and get the ball (Lampkin)”. For example, an out route is a play where the

receiver runs a few yards and cuts at a 90-degree angle and heads towards the sideline with the ball. Similarly, a post route is when the receiver runs towards the goal post at a 45-degree angle looking to get the ball (Lampkin). After the receiver catches the ball, all defensive players are taught to follow their own pursuit angle. This is the best angle that puts the defender on the right trajectory to meet the ball carrier in attempt to stop him or her. In addition to the main two phases of football, offense and defense, the third part of special teams highly regards the use of angles. Similar to the defenders following their pursuit angle to the ball carrier, those on the kickoff coverage unit have a direct angle that the play calls them to follow. Additionally, every time a ball is kicked, whether on kickoff or for a field goal, the angle that the ball travels in determines an outcome. This translates to the kick either going through the uprights or missing them completely. The use of angles is extremely important in football because they are used in every play throughout the game. Each football play involves a calculation of either positive or negative numbers, depending on the call of the referees. For example, if a player gets a penalty, the team gets negative yardage and the next play begins where the team was pushed back. On the other hand, if a player has an offensive “explosive play,” which is a pass or run greater than 20 yards, then the team would add yardage to the play. Mathematically, using a number line helps to provide a visual of the gains and losses the team received on each play. When each team gains possession, they have four plays to make a first down. If they don’t get a first down within the four plays, the team with possession tends to punt the ball to the other team and the process repeats itself. A football player is also a statistical model. Before coaches scout and look for potential players, they have to view the player’s statistical model. A statistical model is defined as, “a simplified, mathematically-formalized way to approximate reality (i.e. what generates your data) and

optionally to make predictions from this approximation” ("What Is Statistical Modeling?”). The statistical model of a player can consist of various data, such as; their height, weight, their speed, how much weight they can lift and more. Since the first game in 1869, football has developed into a sport that regards and makes a great emphasis on the use of statistics. One of the most influential statistics in football is the turnover ratio and its correlation to winning. In Zach Barnett’s article, “One Statistic That Virtually Guarantees a Winning Season,” he examines college football and how important forcing turnovers are: “53 teams that forced an average turnover margin of greater than one per game, 52 of them posted winning seasons. Fifty-two out of 53. Force a fraction more than one turnover per game than your opponent and your team has a 98.11% chance of a winning season.” Since the objective is to win the game, this reinforces the importance of forced turnovers in a game as they almost always result in a winning season. Of the teams that averaged at least 1.01 forced turnovers a game, 94.33% won at least 8 games, 75.47% won 9 games, and 60.38% won ten games. The use of statistics are prevalent now more than ever. They show coaches what areas their team needs to focus on as well as help predict the outcome of a game. This is a great tool to analyze and is only one of the many ways to gauge the outcome, or reason as to why a team won. Football is more than a game, it is filled with intricate parts that represent math in every aspect. When looking at the field itself, it is covered with numbers and hash marks that culminate to 100 yards. This large playing ground is home to 22 athletes competing for their team to win the game. The importance of angles in the sport is vast and can be seen in every play. From the flight of the ball being perfectly thrown in between defenders and falling into the receiver's hands, angles play a great role in the sport of football. Defenders and those tracking down the ball follow their designated pursuit angle to make a play. Without understanding angles, a player

will never be the best he or she can be. Aside from the numerical and mathematical areas that can be seen during the game, statistics are a huge area of the game. Statistics allow coaches to understand areas of improvement, but also how to win the game. There are various statistics that indicate how a game is won or why the turnout happened the way it did. The beauty in football does not solely lie on the competitive nature and tendency of the game, rather it is also in the math and statistics that often go underlooked despite the gravity they hold on the game.

Barnett, Z. (2015, March 04). One statistic that virtually guarantees a winning season. Retrieved April 10, 2017, from http://footballscoop.com/news/one-statistic-virtually-guarantees-winningseason/ Elert, G., & Rozovskiy, A. (2008). Length of a Football Field (American). Retrieved April 5, 2017, from http://hypertextbook.com/facts/2001/NinTam.shtml

Football. (n.d.). Retrieved April 10, 2017, from https://www.merriamwebster.com/dictionary/football

Lampkin, B. (2015, November 09). 10 Football Passing Routes Explained. Retrieved April 5, 2017, from http://mentalfloss.com/article/70831/10-football-passing-routes-explained...