In this work, we will analyze NBA players’ salary data (for the season 2017 – 2018) and NBA team performance (for the season 2016 – 2017). Our workbook contains two sheets named
“PlayerSalaries17-18” (this sheet contains an information about players’ salaries for the season 2017 –
2018) and “TeamStats16-17 (this sheet contains an information about team performance such as Team
Names, number of games, Number of wins and losses, number of points, etc.).
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According to analysis, the minimum salary in season 2017 – 2018 is $25,000, maximum salary is
$34,682,550, and the mean salary is $5,985,488. The standard deviation is $7,080,216, which means that there is a large difference between salaries (Table 1).
Table 1. Salary Descriptives
Salary 2017-18
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
$5,985,488.36
$297,866.92
$2,422,560
$815,615
$7,080,215.82
$50,129,456,038,957
2.160994982
1.694083243
$34,657,550
$25,000
$34,682,550
$3,381,800,925
565
According to the analysis, there are 11 outliers. Thus, there are 11 players, who earn more than
$27,226,136 (more than 3 standard deviations from the mean). Among these 11 players, 2 players are from Toronto Raptors and 2 players are from Boston Celtics. Stephen Curry has the maximum salary of
$34,682,550 (Golden State Warriors).
According to the analysis, we have next data about average salary by the team (see Table 2):

Table 2. Average Salaby by Team
Row Labels
Atlanta Hawks
Boston Celtics
Brooklyn Nets
Charlotte Hornets
Chicago Bulls
Cleveland Cavaliers
Dallas Mavericks
Denver Nuggets
Detroit Pistons
Golden State Warriors
Houston Rockets
Indiana Pacers
Los Angeles Clippers
Los Angeles Lakers
Memphis Grizzlies
Miami Heat
Milwaukee Bucks
Minnesota Timberwolves
New Orleans Pelicans
New York Knicks
Oklahoma City Thunder
Orlando Magic
Philadelphia 76ers
Phoenix Suns
Portland Trailblazers
Sacramento Kings
San Antonio Spurs
Toronto Raptors
Utah Jazz
Washington Wizards
Average of Salary 2017-18 Average 2016-17 Salary
$4,575,886 $5,845,557
$5,957,331
$5,166,784
$6,698,843
$5,251,858
$3,641,612
$6,424,331
$4,146,919
$7,615,551
$4,524,237
$6,460,306
$6,504,632
$6,265,548
$8,405,658
$5,330,733
$4,303,945
$6,078,095
$7,784,448
$6,726,871
$4,660,071
$5,593,486
$5,685,102
$6,603,748
$7,211,870
$6,117,967
$6,881,343
$6,967,893
$5,069,624
$6,626,715
$6,593,855
$5,869,875
$6,457,641
$6,655,795
$6,204,768
$5,737,338
$7,013,350
$5,036,072
$6,523,581
$6,055,882
$7,624,328
$5,457,815
$4,505,440
$4,950,031
$6,557,409
$4,782,720
$6,199,199
$6,721,217
$6,268,493
$7,184,622
$6,681,750
$8,063,418
$3,304,257
$5,056,311
$6,688,123
$5,641,101
$6,037,653
$6,692,496
$5,235,885
$6,142,478
We can compare average salaries for seasons 2016 – 2017 and 2017 – 2018 by using the graph
(see Figure 1):
2

3
$8
$7
$6
$4
$3
$1
$0
Average Salary 2017-18 vs. 2016-17
Average of Salary 2017-18 Average 2016-17 Salary
Team
Figure 1. Average Salary by Team (for two seasons)
As we are able to see from the graph, there is no some tendency in average salaries, i.e. salaries for the season 2017 – 2018 increased for some teams (Golden State Warriors and Miami Heat, for example) and decreased for others (Dallas Mavericks and Atlanta Hawks, for example).
According to the results, 95% of all salaries for the season 2017 – 2018 are in range from
$5,400,424 to $6,570,552.
By using one-sample t-test, we tested the hypothesis that the average salary of the Golden State
Warriors players is greater than $5,593,908:
The level of significance is = 0.05
.
: ≤ $5,593,908
: > $5,593,908
As a result, we’ve received that test statistics is:

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∗ =
$7,784,448 − $5,593,908
$9,901013
√18
= 0.9387.
P-value equal to:
− = 0.1805.
We are able to see that − = 0.1805 > = 0.05
. It means that we fail to reject the null hypothesis. There is insufficient evidence, at the = 0.05
level, to conclude that the average salary of the Golden State Warriors players is greater than $5,593,908.
Descriptive statistics for the variables Age, Average 2016-17 Salary, ORtg, DRtg, Total Points from 2P, Total Points from 3P, and Total Points from FT shows that there are 30 teams: 16 playoff teams and 14 non-playoff teams. The variable Averag2016-17Salary has the highest variation and the DRtg has the lowest variation. The variable DRtg has the lowest (absolute value) skewness and kurtosis coefficients. The variables Age, ORtg, PTS, Total Points from 3P are skewed right or positively skewed as their skewness is positive. The variables Average 2016-17 Salary, DRtg, Total Points from 2P, and Total
Points from FT are skewed left or negatively skewed as their skewness is negative.
The same result for skewness are shown below: variable Age is right skewed (Figure 2), variable
Average2016-17Salary is left skewed (Figure 3), and variable TotalPointsfrom3P is right skewed (Figure
4).

Box-plot for Age
35.00
30.00
25.00
20.00
15.00
10.00
5.00
0.00
Age
Figure 2. Box-Plot for Age
Box-plot for Average Salary 2016 - 17
90
80
70
60
50
40
30
20
10
0
Average Salary
Figure 3. Box-Plot for Average 2016-17 Salary
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Box-plot for Total Points from 3P
50.00
45.00
40.00
35.00
30.00
25.00
20.00
15.00
10.00
5.00
0.00
Total Points from 3P
Figure 4. Box-Plot for Total Points from 3P
According to the results, we are able to see, that playoff teams have higher average salary, average age, ORtg, PTS, Total Points from 3P, and Total Points from FT (Table 3).
Table 3. Playoffs Teams
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Average Values
Playoff Team?
No Yes
Average of Average 2016-17 Salary 5560890.71 6375825.61
Average of Age 25.86 27.23
Average of ORtg 106.86 110.52
Average of DRtg
Average of PTS
110.10
104.11
107.63
106.88
Average of Total Points From 2P
Average of Total Points from 3P
Average of Total Points from FT
59.16
27.62
17.32
58.45
30.11
18.28
According to the results, we have that the average salary for the season 2016-17 is greater for both non-playoff teams and playoff teams in Eastern Conference (see Table 4 and Figure 5).

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Table 4. Salary Comparisons
Conference
Playoff Team?
No Yes
Eastern $ 5,614,990 $ 6,477,763
Western $ 5,506,791 $ 6,296,541
$60
$55
$50
Average Salary by Conference and Playoff Teams
(No/Yes)
Eastern Western Conference
$70
$65
Non-Playoff Playoff
Axis Title
Figure 5. Salary Comparisons
According to the analysis, the correlation coefficient between Win% (percentage of wins) and
Total points from 3P is 0.4468. It means that there is relatively weak positive relationship between these variables. The same conclusion we are able to see on the scatterplot: there is a positive relationship between wins percentage and total points from 3P (Figure 6).

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Win% vs. Total Points from 3P
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 10 20 30
Total Points from 3P
40 50
Figure 6. Win% vs. Total Points from 3P
After conducting a regression analysis for the variables Average 2016-17 Salary (independent variable) and Win% (dependent variable), we received that the Win% can be predicted from the average
2016-17 Salary by the equation (Figure 7):
% = 0.22 + 4.68 ∙ 10 ∙ .
The intersection coefficient is = 0.22
, which means that the wins’ percentage will be 0.22 or
22% if the average salary will be $0. The p-value for the intercept is − = 0.1350
. The coefficient = 4.68 ∙ 10 means that each additional dollar in average salary increases the Win% by
4.68 ∙ 10 . The p-value is − = 0.0439
.
The p-value for the regression model is − = 0.0439 < = 0.05
, which means that the model is statistically significant. At the same time, the coefficient of determination is = 0.1372
, which means that the model is quite bad and only 13.72% of variance in dependent variable is predictable from the independent variable. Thus, the model is very weak.

Win% vs. Average Salary 2016-17
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
$y = 5E-08x + 0.2195
R² = 0.1372
$2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000
Average Salary 2016-17
Figure 7. Win% vs. Average Salary
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