Superstar Magic Johnson topped the 1984-1985 NBA earnings list with a salary of 2.5 million dollars. However, for the 2013-2014 season, Kobe Bryant became the highest paid NBA player when the Lakers paid him 30.4 million dollars. It is evident that throughout the years the salaries of NBA players have skyrocketed. The glamorous lifestyle of NBA superstars today catches the attention of millions across the world. But according to the NBA data set for years 2019-2020, there exists large disparities in the salaries of NBA players. Some players make up to forty times the amount of others. We want to investigate whether or not points scored is the biggest factor in determining the scope of NBA salaries. We will use the data to find out the effect that amount of points scored has on players’ salary. Second, we will examine if other variables have an influence on players’ salary, such as minutes played and their age. The data analysis focused on the 2019-2020 NBA season. We will create scatter plots to determine how each of the different variables are correlated with each player’s salary, as well as histograms to measure the distribution of salaries in the league. The reason this matters is because it is important to determine if all NBA players are being paid what they’re worth or if they’re being cut short of the money they deserve. The dataset nba20 (provided by professor Stoyanov) included variables such as: age, points per game, minutes played, salaries, team name etc. of 464 NBA players.
Figure one and Figure Two analysis As evident in figure one and figure two, there appears to be a correlation between the percentage of NBA players who score 2,000+ points and the percentage of players who earn over $40 million. The fact that the densities of both histograms significantly decrease as you move further along the right, suggests that the fewer number of players who can score 2,000+ points places a higher monetary value on the players who CAN put up these points. That could potentially be the result of the scarcity of these prolific players. NBA teams want to keep players who are very effective on offense, so they will offer them really large paychecks to incentivise their stay. It also suggests that the players who score 2000+ points are more irreplaceable than those who’s scored points are closer to the min value. As a result, they are paid more.
In analyzing the graph displaying the relationship between age and salary, we see that there is a weak positive correlation (r=0.39), and we can attribute that to a number of reasons. Men usually enter their physical prime around the age of 26-28, which in athletic competition is conducive to a greater level of output. Furthermore, due to the high level of competition, over time players are often weeded out of the NBA and replaced by younger players, causing the NBA to be skewed towards having younger members. Lastly, just like in any job, the more years you have in the NBA the greater your minimum pay; however, professional basketball is a job that highly incentivizes personal performance, and as a result, it is not uncommon to see young players with large contracts and older players with relatively small contracts.
Our group wanted to explore if the amount of minutes played by NBA players had an influence on their salaries. We used a scatter plot to test the correlation and to answer the question: “Does more minutes associate to a higher salary?” According to figure4 , the points are distributed with no clear pattern, suggesting that minutes and salary are not truly related. According to the data set, several players played far less minutes but got paid several millions more. Specifically, Alex Len played 895 minutes and earned $4.1 million dollars, and Reggie Bullock made $4 million while playing 684 minutes. In contrast, Devonte’ Graham makes only a quarter of their salaries at a mere $1.4 million, but he played 2211 minutes! Lebron did not even have that many minutes! These numbers prove that there are several confounding factors such as the team you play for and what role you have, and more minutes does not associate to a higher salary.
Using the information from the dataset, we wanted to use a simple scatterplot to analyze the association between the points scored by players and their salary form 2019-2020. The x variable is points scored, and the y variable is their salary. We believed that NBA players who scored more points would have a higher salary, and that points would have the largest effect on how much money they earned than all of the other variables. There is a correlation coefficient of r=0.567 which is moderately positive: As number of points increase, annual salary generally increases. There were a few extreme outliers, however, and I was curious to why they did not fall into the pattern. The dot seen on top left of the plot indicates that a player scored very few points but earned one of the highest salaries in the league. How is that so? That dot represented superstar Stephen Curry, as he suffered a broken left early in the season that forced him to stay on the sidelines for several months. He had already signed the contract for that salary, explaining why his lack of points due to being injured did not affect his pay. Thus, confounding factors such as injuries (which occur to a significant number of players) weaken the correlation, but out of all the variables we studied, points scored has the strongest correlation to salary.
Points SD: 394.9901 SE: σ/√n = 394.9901/√464 = 18.34 points Salary SD: $8,826,911 SE: σ/√n = 8826911/√464 = $19,023.51
Null Hypothesis: An NBA player’s salary will be determined by how many points they score. Alternative Hypothesis: An NBA player’s salary is not entirely dependent on amount of points scored; rather, it is due to chance.
We conducted a hypothesis test for the significance of a correlation coefficient.
Ho: p = 0
T = (r - p) √1 - r^2 √n-2
T = (0.567 - 0) √1 - (0.567)^2 √464 - 2
T = 14.8
Since the value is bigger than the critical value on a two-sided table, and more than a standard significance level of 5%, we accept the null hypothesis.
We are accepting the null hypothesis. Reason here.
In conclusion, we sought to determine what criteria most influenced the salary of NBA players; in this investigation we hypothesized that the more points a player scores, the greater their earnings. In our exploration of this hypothesis, we took data from the 2019-2020 NBA regular season to determine averages in both points scored as well as wages earned. The data has negated our alternative hypothesis or and supported null hypothesis that points scored by an NBA player does in fact have an influence on their salary. The hypothesis tests prove that, and all the other plots we made with other variables showed no correlation as strong as the relationship that the points scored had.
I“Stephen Curry Has Surgery on Hand, Out At Least 3 Months.” Around the League. National Basketball Association. https://www.nba.com/article/2019/10/30/stephen-curry-exits-wrist-warriors-suns
“Determinants of NBA Player Salaries.” The Sport Journal.
https://thesportjournal.org/article/determinants-of-nba-player-salaries/