How do employers decide the salary payout to their employees every year? In a sales and consulting firm the salary can be based on the number sales or clients serviced. How do the National Basketball Association (NBA) team owners decide the players' salaries? The general consensus of basketball fanatics is that the wages are based on points scored. Others will argue that it is determined by other measurable statistics such as rebounds, assists, and games played. It is also possible that the salary payout is affected by the player's popularity and non-game issues. Therefore, I felt the need to run a series of statistical testing to determine the cost driver of the players' salaries.
First, I gathered data on the top 35 players based on total points scored in 2007. Throughout this article I will frequently refer to the term cost driver, which is an independent variable that drivers or affects the dependent variable of salary. Basically, the cost driver is on the x-axis and the salary will be on the y-axis. The different cost drivers I chose for testing are points scored, rebounds, assists, and games played. I used two different methods which are regression analysis and high-low costing to test the effectiveness of the cost drivers.
The high-low method is a relatively easy method since I will only be using the high and low points of the cost drivers and salary. If you are using Microsoft Excel, you can simply use the "MIN" and "MAX" functions for each column to determine the high-low values. However, I am only observing two data points for each cost driver and the salary. Below are the results from running the minimum and maximum functions on the cost drivers and salaries:
Points: High 2,430
Assists: High 884
Low 1,350 Low 68
Games: High 82
I can perform the high-low cost function of Y=a + (bx), however, it is not necessary to perform that equation. I noticed that the player with 2,430 points had a lower salary than $23,750,000. I also discovered that the player that earned only $1,808,120 scored more than 1,350 points. These numbers are not good or strong enough to develop a reasonable estimate for salary compensation. Usually, if the high-low method does not work then the regression is not likely to work either. I still chose to do the regression analysis since I am motivated to find what determines a player's salary exactly.
A regression analysis is a statistical method for obtaining the cost estimate that best fits the set of data points. Basically, the regression observes all the data points within each cost driver and dependent variable to develop the most reliable cost equation. After performing the regression, there are two crucial measures that I will observe closely. These measures are the R-squared and t-value statistic. The R-squared is a number between 0 and 1 to measure the explanatory power of the regression. The R-squared is a way of determining to what extent a change in the dependent variable can be predicted by a change in the independent variable. Most statisticians look for an R-squared that is at least 0.51. The t-value statistic is a measure of the reliability of each independent variable, or the degree to which an independent variable has a valid, stable, long-term relationship with the dependent variable. Typically, statisticians desire a t-value statistic greater than 2 when running a regression analysis. Below are the results from my regression:
Points: R-square 0.105, t-value 1.97
Assists: R-square 0.004, t-value 0.36
Rebounds: R-square 0.055, t-value 1.38
Games: R-square 0.055, t-value -1.94
Based on the results of the regression, the numbers are too weak to develop an effective equation to determine the salary for each player. Example, the R-squared of 0.105 means the all the data in the points column only explains 10.5% of the salary that was paid to the players. The other R-square values are less than 0.10 which is extremely weak. Also, all the t-value statistics are below 2.0, which indicate little or no statistical relationship between the independent and dependent variables.
I decided to conduct a multiple regression on the points, assists, rebounds, games played, and salary as a final attempt to determine the validity and reliability of the data. Previously, I was running a regression using one independent variable. In the multiple regression analysis I included all the independent variables to help strengthen the explanatory power of the regression. After completing the multiple regression analysis, I had an R-square of 0.42 and a t-value statistic of 2.10 for independent variable 1(points). The other independent variables had t-values lower than 2.0. When considering points, assists, rebounds, and games played combined as one giant cost driver, the regression is able to explain 42% of the salaries paid. There are still 58% of the salaries that are statistically unexplained. The 58% can be attributable to non-statistic measures such as exposure and popularity.
To conclude, one cannot determine with absolute certainty that an NBA player's salary based on statistic analysis of measurable statistics such as points scored, assists, rebounds, and games played. I was able to learn that a player's salary is not solely based on the measurable performance stats. A player's true worth to the team is sometimes determined by immeasurable factors such as popularity, exposure, loyalty, and leadership. Through my statistical analysis or investigation, I state that no player's salary can be reasonably determined on the basis of performance on the court.
NOTE: The salaries and statistics were gathered from NBA.com and SportsCity.com.
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