Is the salary of a player dependent of the position he plays in the game?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. Introduction

With millions of fans worldwide, the National Basketball Association (NBA) is now one of the most popular and successful professional sports leagues. Huge profits have led to the superstars in the NBA being paid lavishly: in the 2018-19 season, Steph Curry earned over 37.4 million and LeBron James made over 35.6 million on the court……..

In our project, a dataset containing the salaries of NBA players from the 2016-17 season is used, with other variables such as career statistics, draft picks and physical measurements. Based on this dataset, we seek to answer the following popular questions around the NBA:

1. Is the salary of a player dependent of the position he plays in the game?

2. Does the salary depend on the height of the player?

3. Does the salary depend on the draft-pick and draft-year of the player?

4. Is there a single performance measure that is more important in affecting the salary than the others?

5. ……

This report will cover the data descriptions and analysis using R language. For each of our research objectives, we performed statistical analysis and drew conclusions in the most appropriate approach, together with explanations and elaborations.

2. Data Description

The dataset, titled “NBA Salaries”, is obtained from the online data science community data.world. The original data consists of 2 csv data frames, titled “players.csv” and “salaries_1985to2018.csv”. The dataset was originally posted on basketball-reference.com, the official database partner of the National Basketball Association (NBA), and is open to the public for study and research.

Before proceeding to data analysis, we first performed a preliminary data cleaning to ensure that:

- Irrelevant columns are eliminated, e.g. “birthplace” and “highschool”;

- Players with fewer than 10 games played are treated as unrepresentative anomalies and excluded;

- Redundant information is cut out, e.g. the word “overall” under “draft_pick” column as we only need the number for analysis;

- Only 2016-17 season’s data are included in our dataset

- ……

 

After all the preparation, 513 observations (players) with 11 variables are retained for analysis:

1. Sno: serial number

2. X_id: player identity, abbreviated player name

3. AST: career average assists per game

 

4. FGpct: career field goal percentage

5. PTS: average career point scored per game

6. TRB: average career rebound per game

7. height: height of the player

8. draft_pick: draft-pick position of the player, indicating the perceived value of the player before joining NBA

9. draft_year: draft-pick year of the player, indicating the seniority of the play in NBA

10. position: primary position played by the player (PG, SG, SF, PF or C)

11. salary: total salary in US$ of the player for the 2016-17 season

3 Description and Cleaning of Dataset

In this section, we shall look into the data in more detail. Each variable is investigated individually to look for possible outliers, and/or to perform a transformation to avoid highly skewed data.

3.1 Summary statistics for the main variable of interest, salary

The following plots show the overall distribution of the variable 𝑠𝑎𝑙𝑎𝑟𝑦.

It appears that the variable 𝑠𝑎𝑙𝑎𝑟𝑦 is highly skewed, hence we apply a log-transformation (base

𝑒) to the variable. The log-transformed data appears to have some outlying values at the left tail. Upon further investigation, we notice that some players were on short-term contracts (a few weeks) during the season. Therefore, we remove those players whose salary are below US$100,000, approximately 4% of the data.

The histogram and boxplot of the log-transformed variable, with the outliers removed are shown below with summary statistics. The dataset is now more symmetric and does not have any outliers.

We shall proceed to the next section with this trimmed dataset.

 

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