A Nba Player Scoring Per Game Statistics Biology Essay

Published: 2021-06-20 17:45:04
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The main purpose of this report is to work out factors affecting the points players get per game in the NBA. The report comprises the best opencast and opencast & underground mining strategy, sensitivity analysis on the optimal strategy for a specific site and a generalised model for opencast mining with sites of similar properties.
2.0 Background
When talking to the unbreakable records in the NBA history, it is unbelievable that Wilt Chamberlain got 100 points in a single game and average more than 50 points in a season. Thus, what affect points players score in each game? Here, I consider 8 factors: games played, playing time per game, field goals attempted per game, field goal percentage, 3-point field goals attempted per game ,3-point field goal percentage ,free throws Attempted per game and free throws percentage that may affect points player get per game.
3.0 Data
I take data of top 50 scores per game leaders in the NBA 2012-2013 regular season into consideration.
PLAYER
GP
MPG
FGA
FG%
3PA
3P%
FTA
FT%
PTS
Kevin Durant
47
39.5
18.5
0.516
4.7
0.414
9.5
0.904
29.6
Carmelo Anthony
38
37.8
22
0.447
6.6
0.409
7.4
0.822
28.5
Kobe Bryant
47
38.7
21.1
0.466
5.7
0.341
7.5
0.838
27.9
LeBron James
43
38.7
18.7
0.547
3.3
0.403
6.4
0.734
26.5
James Harden
48
38.3
17.4
0.44
5.6
0.328
10.1
0.859
25.8
Kyrie Irving
37
35.6
18.6
0.471
4.8
0.412
5.3
0.851
24
Russell Westbrook
47
36.3
18.9
0.419
4.1
0.325
6.7
0.801
22.6
Stephen Curry
43
38
16.7
0.44
7.1
0.457
3.6
0.902
21.1
Dwyane Wade
39
34
15.4
0.508
1.2
0.319
6.3
0.738
20.6
LaMarcus Aldridge
45
38.2
17.6
0.47
0.2
0.1
4.9
0.801
20.5
Tony Parker
47
32.7
15.1
0.534
1.1
0.396
4.4
0.808
20.1
Jrue Holiday
42
38.4
17
0.463
3
0.354
3.3
0.779
19.4
David Lee
46
37.8
15.6
0.514
0.1
0
4.2
0.802
19.4
Brandon Jennings
46
36.8
16.6
0.406
5.7
0.374
3.8
0.828
18.7
Brook Lopez
40
29.4
14.2
0.526
0
0
5.1
0.734
18.7
Paul Pierce
46
33.7
14.8
0.422
5
0.346
5.5
0.788
18.6
Monta Ellis
46
36.4
17.4
0.4
3.5
0.252
4.7
0.799
18.6
Blake Griffin
48
32.6
13.9
0.531
0.3
0.188
5.6
0.658
18.5
Damian Lillard
47
38.6
15.4
0.423
6.3
0.362
3.6
0.845
18.4
O.J. Mayo
47
35.9
13.9
0.461
4.8
0.427
3.7
0.847
18
Kemba Walker
46
35.2
15.3
0.432
3.8
0.349
4.3
0.797
18
DeMar DeRozan
47
36.7
15
0.44
1.6
0.28
4.7
0.826
17.4
DeMarcus Cousins
44
31.9
14.7
0.444
0.2
0.2
5.6
0.762
17.4
Luol Deng
42
40
14.9
0.436
2.9
0.336
4.1
0.82
17.3
Paul George
46
37.3
15.1
0.427
5.7
0.382
2.8
0.808
17.3
Rudy Gay
43
36.6
16.4
0.411
3.1
0.319
3.7
0.772
17.3
Tim Duncan
43
29.8
13.7
0.505
0.1
0.4
4
0.828
17.3
Al Jefferson
47
32.9
15.4
0.477
0.2
0.2
2.9
0.837
17.1
Chris Bosh
42
33.9
12.2
0.54
0.8
0.25
4.6
0.818
17.1
Danilo Gallinari
47
32.9
13.1
0.424
5.4
0.37
4.9
0.811
17
David West
47
33.6
14.5
0.485
0.3
0.214
3.9
0.739
17
Joe Johnson
47
38
15
0.425
5.5
0.381
2.6
0.82
17
Ryan Anderson
48
31.3
14.1
0.434
7.6
0.396
1.9
0.878
16.9
Josh Smith
43
35.5
15.7
0.451
2.2
0.302
4.1
0.497
16.9
Deron Williams
46
36.4
13.5
0.415
5.3
0.34
4.4
0.858
16.8
Klay Thompson
47
35.3
14.5
0.418
7
0.391
2.1
0.888
16.7
Arron Afflalo
43
36.7
14.1
0.442
3.8
0.346
3.4
0.857
16.7
Jamal Crawford
46
29.4
13.5
0.417
5
0.362
4
0.863
16.5
Dwight Howard
43
34.7
10.3
0.577
0.1
0.25
9.3
0.496
16.5
J.R. Smith
45
33.4
15.1
0.402
4.9
0.338
3.1
0.793
16.3
Al Horford
43
37.3
13.4
0.532
0
0
2.9
0.602
16
Nicolas Batum
46
38.9
12.5
0.425
6.5
0.362
3.5
0.849
15.9
Carlos Boozer
44
31.2
14.1
0.475
0
0
3.5
0.699
15.8
Greg Monroe
47
32.6
12.8
0.483
0
0
4.9
0.685
15.7
Zach Randolph
44
35.2
13.6
0.472
0.4
0.125
3.5
0.75
15.5
J.J. Redick
46
32
11.7
0.452
6.2
0.399
2.6
0.892
15.3
Thaddeus Young
46
36
13
0.522
0.1
0.2
2.6
0.57
15.1
Raymond Felton
33
33.5
15.3
0.401
4.2
0.365
1.7
0.782
15.1
Kevin Martin
46
29.8
10.6
0.45
5.2
0.435
3.6
0.904
15.1
Ty Lawson
47
34.3
13.1
0.431
2.9
0.36
3.6
0.737
15
http://espn.go.com/nba/statistics/player/_/stat/scoring-per-game
GP: Games Played
MPG: Minutes Per Game
PTS: Points Per Game
FGA: Field Goals Attempted Per Game
FG%: Field Goal Percentage
3PA: 3-Point Field Goals Attempted Per Game
3P%: 3-Point Field Goal Percentage
FTA: Free Throws Attempted Per Game
FT%: Free Throws Percentage
4.0 Analysis
4.1 Correlation
Firstly, I use scatterplot with regression to show the links between points per game and the 8 factors respectively.
From the picture, we can observe FGA has the strongest relationship with PTS as the data points are closest to the line. At the same time, GP have a weakest relationship with PTS.
In addition, I use correlation coefficient to show the relationships between average points and the other 8 factors. Below is a correlation matrix for all variables in the model. Numbers are Pearson correlation coefficients, go from -1 to 1. Closer to 1 means strong correlation. A negative value indicates an inverse relationship (roughly, when one goes up the other goes down).
From the table above, we can observe field goals attempted per game(FGA) and free throws attempted per game(FTA) have a great influence on the points per game players get as the correlations are 0.840 and 0.727 respectively.
4.2 Simple linear regression
I take independent variables FGA and GP as the typical examples to show the linear relationship with PTS.
Therefore,I build the simple regression model using FGA as the independent variable and PTS as the dependent variable and get results below.
The t-values test the hypothesis that the coefficient is different from 0. To reject this, we need a t-value greater than 1.96 (for 95% confidence). In this case, t-value of FGA is 10.72, which indicates there is a linear relationship between PTS and FGA.
Two-tail p-values test the hypothesis that each coefficient is different from 0. To reject this, the p-value has to be lower than 0.05 (you could choose also an alpha of 0.10). In this case,with a p-value of 0.000, there is very strong evidence to suggest that the simple linear regression model is useful for PTS.
The r2 value listed on the output is 70.5%, which is implies that about 70.5% of the sample variation in points per game(PTS) is explained by field goals attempted per game(FGA) in a straight-line model. There are some unusual observations and thus there are likely other variables that affect PTS.
Moreover, the most important part of the ANOVA table is the probability. The probability is calculated by assuming that the independent variable in question has no effect and then gauging the likelihood that the outcome you observed would occur. The effect of the variable is called statistically significant if the P value is less than 0.05 or 0.01, with smaller numbers indicating higher significance. Since the P value above is well below 0.01, we can reasonably say that the tested factor(PGA) has a real impact on the response variable(PTS)..
The regression equation is PTS = -0.84 +1.29*FGA. For each one-point increase in FGA, scores increase by 1.29 points
A typical assumption in regression is that the random errors () are normally distributed. The normality assumption is important when conducting hypothesis tests of the estimates of the coefficients (). Fortunately, even when the random errors are not normally distributed, the test results are usually reliable when the sample is large enough. In this case, it is a well-behaved residual.
Then let me show another typical relationship by using PTS as a response and GP as a predictor.
In this case, t-value of GP is -0.67, greater than -1.96 (for 95% confidence), which indicates we have insufficient evidence to conclude that a statistically significant relationship between PTS and FGA exists. Alternatively, with the p-value of 0.509, greater than 0.05,we can also obtain there is no significant relationship between PTS and FGA. The r2 value listed on the output is only 0.9%, which is implies that nearly no sample variation in points per game(PTS) is explained by games player(GP) in a straight-line model. Moreover, the P value of the ANOVA table above is 0.509 far greater than 0.05 and there are many unusual observations, we can reasonably say that the tested factor(GP) has no impact on the response variable(PTS).
The picture illustrates that the random errors are not normally distributed, there the test results are not reliable.
Overall, there is no significant relationship between PTS and FGA.
4.3 Multiple Linear Regression
To improve the results obtained above, we can use the multiple linear regression to get the relationship between the points per game and other 8 factors.
The t-values test the hypothesis that the coefficient is different from 0. To reject this, you need a t-value greater than 1.96 (at 0.05 confidence). The t-values also show the importance of a variable in the model. In this case, FGA is the most important.
Alternatively, two-tail p-values test the hypothesis that each coefficient is different
from 0. To reject this, the p-value has to be lower than 0.05 (you could choose also an alpha of 0.10). In this case, GP, MPG, and 3P% are not statistically significant in explaining PTS. FGA, FG%,3PA,FTA,FT% are variables that have some significant impact on PTS.
Moreover, the model explains 99.0% of variances on PTS.
The P value of the ANOVA table above is 0.000 far less than 0.05, we can reasonably say that the tested factors has great impact on the response variable(PTS).
Overall, the model describes the variation in data well, however, we can still improve it as there are some factors that are not important in explaining PTS.
4.4 Improvement
As discussed before, the three factors GP, MPG and 3P% are not statistically significant in explaining PTS, therefore, I exclude the three factors and build a new multiple regression model with other 5 factors.
Similarly, we can conclude the five facotrs have some influence on PTS. Among them, FGA have the largest impact.

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