Based on past and current research we noted that it has been an interest statistically throughout the world to try to analyse and determine the factors that influence National Basketball Association (NBA) player’s salary rate. It is of great importance in light of financial constraints to denote whether it will be their skills, scoring, wins, loose and even fouls that may significantly contribute to determine a NBA player’s salary. The purpose of this investigation report is to identify the variables that are most likely to contribute to NBA player salaries. There is an acute insufficiency of empirical literature and evidence regarding the topic of NBA player salary determinants as the battle of these factors have been mostly forcefully accused with player’s discrimination, performances and so on. And in the past there have been quite a lot of articles written on NBA player salary discrimination, the lack of empirical evidence as it associates to the player’s performance and its impact on their salary.

Therefore on this report we analyse and try to describe these factors that may contribute to the NBA player’s salary rate using the SAS data that we have been given which consist of a sample of 335 NBA players observed with 23 variables associated with different statistic based on their games played, goal points, game player total, losses player in, etc. throughout the report’s description we observed on the data and we noticed that to make analysis about the sample players we have to make the salary of NBA players (in millions) the target variable in other to further conclude about our research question which is based on identifying whether the NBA player’s physical capabilities influence their salaries but most of this is described further on the descriptive analysis. Most of the output and results of the PROCs procedure we used to analyse the data will be discussed on the Results and Discussion section which gives us a broad view of how the data set is and ehre it puts us based on our hypothesis.

Introduction

There is a powerful software program designed to give researchers a wide variety of both data management and data analysis capabilities. SAS has two main concepts which are how to get data into SAS and how to perform analysis. The steps we are going apply to our data are: Enter SAS data, tell SAS what analysis to perform and then observe the output. Then from the output of our data we will conclude about which variables affect our data. The method we are going to use to read our data into SAS is the free point form, because it’s easy with very little to specify. The analysis that we will use to analyze our data is multiple Regression which is an extension of linear regression. It is used when we want to predict the value of a variable based on the value of two or more variable. The dependent variable is the Salary. The procedure we are going to use is PROC REG, and the independent variables are Age, Time, Loses, Fouls. Further analysis based on these concept is conceptualized on the following sub headings giving further knowledge and research found on the data.

Descriptive Analysis

Based on the sample data that we have been given of all the 335 NBA players in the season between 2016 -2017, the hypothesis is that there more a player has more GP (Game Player Total) and less L (Losses player in) then that player will have higher salary rate. The objective is to check whether there is sufficient evidence to accept or reject the hypothesis base on the sample data. The SAS data that we have been given consist of a sample of 335 NBA players observed with 23 variables associated with different statistic based on their games played, goal points, game player total, losses player in, etc. As we observed on the data we noticed that to make analysis about the sample players we have to make the salary of NBA players (in millions) the target variable in other to further conclude about our research question which is based on identifying whether the NBA player’s physical capabilities influence their salaries. To make the analysis about the data we used the SAS system which is a powerful software program designed to give researchers like us a wide variety of both data management and data analysis capabilities. So making the analysis on the data set we make the salary of NBA players (in millions) the independent variable and the other 22 player statistic will be the dependent variables. Since we have a variety of SAS analysis (PROCs, for procedures) to perform, in this case we will use a few to make analyse the data set by manipulating the data to get it ready for our analysis. But since this is a large data set we may subset most of the variables because some are not going to be quite helpful to the research we are conducting and there are a lot of SAS statements we will use to do so.

The initial analysis we observed on the data set is that looking at each players GP (Game Player Total) with minutes played the more a player plays in a game or the more minutes a player has the GP also was greater so based on that we first made the assumption that this was based on the time, but with the output of the analysis we didn’t have enough evidence to conclude that was true because most of these players with the first theory we created the salary rate was not supporting the theory. In addition, changing the theory we used explanatory variables such as height, weight, games played, minutes and etc. to take a different approach to understanding salaries. Therefore using these variables at least a more broad realistic view came out about which is more efficient in making an inference on the data. Most of the output and results of the PROCs procedure we used to analyse the data will be discussed on the next session which is Results and Discussion. In this section it will mostly be a break-down of the output we observed and analysis of it interpreting the results. The guide on this initial analysis is to give the reader some insight of the data and SAS analysis procedures that we used for reaching the point of concluding about the NBA player’s game statistics, physical athletic skills etc. and indicating whether they Influence their salary rate based on the given sample statics. But through all the above mentioned the further steps that we will take to get more evidence concluding about the research question is using different variables by the subset method and observing which output results we will observe.

Methodology

The methodology that we going to follow is based on the SAS data that we have been given which consist of a sample of 335 NBA players observed with 23 variables associated with it. We are going to make a data analysis using the SAS essentials software to build a multiple regression model, predicting the salary of NBA players (in millions) as the target variable. Following this methodology will lead us to a point whereby we will look into it and decide whether we reject or do not reject the hypothesis that’s been predicted. This is the most appropriate methodology to effectively answer the research question because we will have a visual view using a powerful tool to conclude about the hypothesis. As in this research we are basically working with NBA (basketball players) players for the season which is between the years of 2016 and 2017. Our interest is to find the primary determinant of an NBA player during the above mentioned season. In this examination we want to examine 335 NBA players and 23 possible determinants. To do the analysis of this data we will use one of the most popular statistical programming languages called SAS. We will kindly use multiple linear regression model which is mathematically represented as where the error is assumed to be zero and our estimate equation will be the same as the above mentioned linear regreation model equation accept that the estimate has no error since the error is zero, We assume that our data is normally distributed with mean denoted as and variance. Using this model we are now allowed to examine more than one determinant at the same time and this model is useful in giving us the mean and variance of each determinant (independent variable). This could even allow us to identify some outlier’s points in the grid (plane). In our predictions we will use SAS built in function called PROG REG for multiple linear regression. Testing this we will use hypothesis test. Our hypothesis from this statistical model if it happened that the determinant of salary amounts players is insignificant in predicting the salary of the players. For this test if it happened that the p-value is less than 0. 05 then we will not reject our null hypothesis in favour of our alternative otherwise we reject our null hypothesis. There are a lot of other models we can use like, Hierarchical clustering. This model processes unknown patterns. Hierarchical clustering is used to place similar variables in one group and assign none identical variables to a different group. The algorithm of this model however cannot replace what was done previously. It is also hard/tricky to identify the correct number of clusters by dendrogram.

Results and Discussion

Basically, the purpose for this study was to identify the variables that were most likely to contribute to NBA player salaries. The existing literature on strategic behaviour in the context of the National Basketball Association showed inconsistent results using different empirical variables hence stated in the above initial analysis that the output of the analysis based on time did not give us sufficient evidence to support the time theory, then we had to utilise other explanatory variables stated on the above analysis. Our findings have the potential to benefit NBA teams in their player evaluation process, mostly in salary determination of how much a player should be paid, as it allows them to more accurately determine contract cycle effects on player performance. By the way of illustration, when trying to decide whether to sign a player to a new contract who is currently in his contract year, my model of player productivity could offer insight into how much of the player’s productivity is explained by his being in a contract year, and how much is a function of his individual characteristics by looking at the feedback given by SAS analysis procedures and their variables. The inclusion of both age and experience as variables in estimating player’s productivity should allow for greater accuracy in predicting future productivity and the salary that the player deserves, especially of players who do not follow the typical path to the NBA. These players might not exhibit the usual correlation between age and experience, so modelling the two as separate effects will be much more accurate in these cases. With greater success in player evaluation, teams would be able to save money that they previously would have spent on unworthy players, and parity and competitiveness in the NBA would likely increase.

When age variable is used to account for the effects of both age and experience, the increases in experience that begin upon the player entering the NBA have a monotonically increasing effect on production, so it is not until the player is older that the negative effect of aging begins to overcome the positive effect of gaining experience. In the base model, age variable does not captures the pure physical effect of aging, the player with the most age of 32 earns more salary than young players as He earns R30. 96 million and the player with the least age earns R1. 45 million. Moreover, this study found that older players receive larger salaries relative to their marginal revenue product compared to younger players and their MRP. Also this study found that general managers do tend to pay players more for points scored versus other statistics variables. Win and points per game, age as well as min proved to be the most statistically significant variables in determining player salary; however, fouls, and assists were significant contributors as well, also the assists per season are one of the key variables in determining the salary. The research we did based on our research question; we found that teams prefer oversized players. “In the past, tall players were considered less talented than shorter ones in some aspects of the game, such as dribbling the ball or shooting efficiently from long range. In the last twenty seasons, these statements do not longer exist. There are some players who are pretty tall for their position, such as the point guard Jason Kidd, the shooting guard Tracy McGrady and the power forward Kevin Garnett, whose height is 193 cm, 203 cm and 211 cm respectively, who dominated the league in the late 1990’s and 2000’s and earned hundreds of millions of dollars in their entire career, won multiple individual and team awards and are considered as future hall of famers. Nowadays, the point guard John Wall is considered to be one of the NBA’s greatest guards, the small forward Kevin Durant has multiple scoring titles and a MVP award and the small forward Giannis Antetokounmpo is considered as one of the biggest prospects of the league and recently signed a $ 100, 000, 000 contract. It should be noticed that height is the only personal characteristic which is statistically significant in all our models”. This does not contradict with our research but our research showed Age as the leading variable in salary determination. The result showed that signing an old player or having an old player in the team comes with the risk of overpaying him. It might be true, but I suppose the story should be more like this: old players cannot run as fast and jump as high as before, it is because their physical condition decreases with age growing, and that is true. However, old players also have more experience than the young players; they are more familiar with the rule and have more useful skills in playing court like “flop”, which means acting as he was fouled, or just some little tricks to protect their bodies from getting injured by opponents. Most of these abilities cannot be shown by performance stats, but it is really useful. Precisely, when there is an old player in a young team with a lot of young players, that particular player could be a teacher to his young teammates, sharing his experience from his long career to the rookies can help them improve faster, gaining young some experience from the legend.

Summary and Conclusion

Results indicated that points per game, age, and minutes played contributed significantly to a player’s salary rate. Implications on some sort of other statistical inferences of these results are mainly discussed in the results and discussion section. Through all the studies for determining the significant statistics in explaining the salary for NBA players our results have shown that players are paid for points scored (GP) but with also research that we made it show that also NBA players seem to receive salaries based on their years in the league, goal points, experience, fouls and field goal percentage also affects the salary rate. Therefore on this report as we analysed we found that these factors that contribute to the NBA player’s salary rate using the SAS data that we have been given which consist of a sample of 335 NBA players observed with 23 variables associated with different statistic is mainly caused by the number of games played, goal points, game player total, losses play and fouls.