# Football strikers and midfielders: Goals and Salaries

Violetta Vylegzhanina, Nithin Kumar
Application Project: Part 1
Math 216
March 26, 2012

Football strikers and midfielders: Goals and Salaries

European football leagues are one of the wealthiest of all sports clubs, second only to the NFL, and the salaries of their players are often extravagant, as detailed in the Forbes article, “The world’s most valuable teams,” published in 2010. Strikers and midfielders are the players who generate the maximum interest and excitement in a match since they have the ability and opportunities to score goals. Furthermore, this will cause them to rake in profits for their respective leagues from advertising endorsements due to their popularity. As a result, it would be logical to assume that these strikers and midfielders who score more goals are better paid than those who rarely do so. Therefore, we hypothesize that there is a strong linear relationship between the number of goals scored by strikers and midfielders during matches of the European football leagues and their respective annual salary.

Since the average football striker scores roughly 5-6 goals per season it would be impractical to simply tabulate the number of goals scored by every player in 1 season. Since the sample size and variation in goals scored would not be large enough to justify a relationship between goals scored and annual salary, the data for the number of goals scored from Jan 2009 till Nov 2011 (a duration of close to 3 years) of various strikers and midfielders in European football leagues will be used in this project (along with their annual salary in 2011). The independent variable is the number of goals scored by strikers and midfielders in European football leagues from Jan 2009 to Nov 2011 and the dependent variable is their respective annual salary in 2011.

After obtaining a statistically large sample (n > 50), descriptive statistics of the number of goals scored from official websites (“Spanish la liga,”), (“Player statistics: EPL,”) and the annual salary of football players in 2011 (“Os 100 maiores,” 2011) will be analyzed. These statistics will include measures of center (mean, median), and measures of variation (standard error, standard deviation, and the range of observations). A line of best fit, which minimizes the sum of the square of the residuals (between all data points and the line), will also be created.

Regression analysis will be performed using Microsoft Excel. The coefficient of determination R2 will indicate how well the regression fits the data. The value of R2 will essentially determine how much of the variation in the annual salary of football players (the dependent variable) can be explained by the variation of the number of goals scored by these players (the independent variable). A low R2 value would indicate a weak linear relationship between goals scored and the salary earned by a football player while a large coefficient of determination value would indicate a strong linear relationship between the variables.

To further support the validity of results, a hypothesis test will be undertaken to determine if there is a relation between the number of goals scored and the annual salary of football players. The null hypothesis would be that the slope of the line of best fit (β1)is zero, which is indicative of no relation between the variables. The alternative hypothesis would be that β1 is greater than zero (there is a positive association between the variables). Testing at the 5% significance level, if the p-value of the corresponding test has a value less the 5%, the null hypothesis will be rejected in favor of the alternate hypothesis and we would conclude that there is a positive linear relationship between the two variables.

In conclusion, we propose that European football strikers and midfielders who score more goals are paid better than their teammates. Regression analysis and hypothesis testing will be performed to validate this claim. Possible factors and observations that could provide additional insight into the results will also be discussed.

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