Introduction
The quarterback serves as the offensive head of a football team. He is responsible for setting up the plays in order for the team to gain yards. His plays can be seen in different ways such as passing or running (Strauss, n.d). Depending on the decision of the team during huddle, the quarterback must be the one to ensure the success of their plays.
Unfortunately, not all the plays made by the quarterback are successful. There are several factors which contribute to the failure of the plays, such as failure of execution of the designated roles, being outsmarted by the opponent, or lack of coordination. Regardless of the reason, the skills of the quarterback can be reflected on how he successfully execute his trump card, and how often the success occurs.
In this study, the group will focus on the passing attempt of the professional quarterbacks in the National Football League (NFL). Specifically, the passing attempt of NFL quarterbacks will be related to the number of yards gained. In football terms, the passing attempt is defined as an offensive move wherein the ball must be completedly passed to the teammate (Sporting Charts, n.d). Moreover, yards gained is defined as the amount yards which are gained either by running or passing; the play in which was orchestrated by the quarterback from the line of scrimmage. In passing, yards will be gained if the pass attempt is completed (Sporting Charts, n.d).
The significance of this study can be related to the efficiency of the quarterbacks in their roles. However, the relationship between the passing attempts and the yards gained will be sufficient enough to determine the intelligence of the quarterbacks, which is a fundamental requirement for the role. According to Mirabile (2005), intelligence is the most important factor for playing the quarterback role. However, his study revealed that intelligence cannot be determined by the passing performance of the quarterbacks (Mirabile, 2005). The implication of this will be that the study will only cover the possible factors of passing in the number of yards gained. This might be compared to the number of yards gained when a running play is initiated. As such, the limitation of the study is only to the efficiency of the passing plays of the quarterbacks, but not their intelligence.
Hypothesis
An attempt to make a pass increases the opportunity to gain yards, especially when the play is properly and accurately executed. In relation with this, the hypothesis for the study is that there will be a direct relationship between the passing attempts and the amount of passing yardage
Data Gathered
The data was gathered using a random sampling method. Ten quarterbacks from the NFL was chosen from their respective teams. In order to determine whose statistics will be considered, the NFL teams were designated by numbers and the name of their respective quarterbacks were designated by letters. A number and a letter will be drawn by draw lots. The representative quarterback of the number-letter combination that will be drawn will be chosen as part of the sample population. Afterwards, their statistics regarding their passing attempt and passing yardage was recorded, and was subjected to analysis. Note that the statistics were obtained from the NFL 2015 season, which can be found at the NFL website.
Summary of Data
As stated earlier, the players above were obtained through random sampling method. It is random because the number-letter combination was selected through draw lots and as such, all combinations have equal chances of being drawn. Moreover, only the players who have recorded statistics in the 2015 NFL season were the ones that were recorded. There are circumstances where a certain player does not have statistics on both the passing attempts and passing yardage. In those cases, the drawn combination was discarded and another one was drawn thereafter. The statistics were then plotted in a scatter-plot graph with the passing yardage in the vertical axis, while the passing attempt is on the horizontal axis, as shown in Figure 1.
Figure 1. Passing Yardage vs. Passing Attempts of the 10 Randomly
Selected Quarterbacks
As Figure 1 indicated, the graph follows a near linear relationship. As the number of passing attempts increases, the amount of passing yardage generally increases as well. By drawing the best-fit line for the scatter-plot data, most of the values are situated near the line. As such, the graphical representation of the data suggests a strong relationship between the two variables.
Regression Analysis
For further and specific determination of the relationship between the two variables, different statistical analysis methods will be used. The first analysis is the determination the linear relationship of the two variables using the regression analysis. The independent variable for this data set is the number of passing attempts, while the dependent variable is the passing yardage, because as stated in the earlier definition, the yards cannot be gained if a pass will not be attempted (Sporting Charts, n.d). The governing equation for the linear regression is:
(passing yardage) = [m*(passing attempts)] + b, where:
m = slope of the line
b = y-intercept
Using the linear regression function of the calculator, the general equation of the line formed by the set of variables is:
(passing yardage) = [7.530036546* (passing attempts)] – 6.133622659
The equation obtained does not give the exact value, but the deviation of the obtained value from the value that can be obtained from the equation determines the strength of relationship between the two variables, which will be determined in the latter part. Moreover, the equation also shows that on the average, a quarterback will be able to gain at least 8 yards for every passing attempt made.
Correlation Coefficient
In order to determine the strength of the relationship of the two variables, the correlation coefficient r must be determined (The Correlation Coefficient, n.d). The governing equation for the determination of the correlation coefficient r is:
r= ∑[X-Xaverage] [Y-Y(average)](n-1)(Sx)(Sy); where
X = number of passing attempts
Y = number of passing yardage
n = number of sample
Sx = Standard deviation of X
Sy = Standard Deviation of Y
Using the calculator, the standard deviation of the variables will be accurately computed. From that, the correlation coefficient r will be directly obtained. In these data given, r is found to be +0.96314, which, according to Rumsey (2016), indicates a strong positive linear relationship. The direct relationship between the number of passing attempts and the number of passing yardage inly implies that the frequency of attempts actually increases the number of yards that will be gained by a quarterback. Looking back at the scatter-plot graph, the positive increase of the values can be actually seen. Though it already denotes a positive relationship, the correlation coefficient only proves the strength the linear relationship. As a result, the hypothesis is accepted and statistically true.
Conclusion
There is a very strong positive linear relationship between the number of passing attempts and the amount of passing yardage. With a correlation coefficient equal to 0.96314, it can only be concluded that the increase in passing yardage can be largely attributed to how frequent does a quarterback pass the ball. Moreover, this can also mean that the amount of playing time has something to do with the increase in the number of passing attempts. In a football match, offensive and defensive plays constitute a game. During those times, a quarterback only played the most on the offensive. Moreover, passing is not always an option. As such, the passing yardage can also be attained depending on how skilled the quarterback is, in terms of strategy and use of time (Mirabile, 2005). As such, the study also implies that passing attempts also determine the efficiency of a quarterback. The implication of this study is not to give utter importance to passing as way of executing plays, but to give importance to the quality of passing, which is needed for a more efficient teamplay and better passing communication.
References
Strauss, E. (n.d). What is the Job of a Quarterback? Chron. Retrieved 12 July, 2016, from http://work.chron.com/job-quarterback-9164.html
Mirabile, M. (2005). Intelligence and Football: Testing for Differentials in Collegiate Quarterback Passing Performance and NFL Compensation. The Sports Journal. United States Sports Academy.
National Football League. (n.d). Statistics. Retrieved 12 July, 2016, from http://www.nfl.com/stats/player?seasonId=2015&seasonType=REG&Submit=Go
Rumsay, D. (2016). How to Interpret a Correlation Coefficient r. Dummies. Retrieved 12 July, 2016, from http://www.dummies.com/how-to/content/how-to-interpret- a-correlation-coefficient-r.html
Sporting Charts. (n.d) Pass Attempt. Retrieved 12 July, 2016, from http://www.sportingcharts.com/dictionary/nfl/yards-gained.aspx
Sporting Charts. (n.d) Yards Gaineed. Retrieved 12 July, 2016, from http://www.sportingcharts.com/dictionary/nfl/yards-gained.aspx
