DA
Jacob Kuhlman, Haoxin Liu and Jarrett Hyder
4/26/2019
Introduction
The ranking of a team in the National Basketball Association, also known as the NBA, is quite simple; the more you win the better ranking you will have, and the more you lose the worse your ranking will be. The Atlanta Hawks and Houston Rockets, both teams which we will be analyzing in this report, have seen tremendous fluctuation in their ranking from the 2015-2018 seasons. The Hawks went from being in 7th place in 2015 to 27th place in 2018, whereas the Rockets went from being 17th in 2015 to 1st in 2018. What kind of variables determine how well a team is going to do in a season, and more importantly determine if they are going to win? Well, that is what we are analyzing in this report. Our goal is to understand what kind of things made the Atlanta Hawks become a worse team over the three seasons we are analyzing, and also what kind of variables made the Houston Rockets a better team over the three seasons we are analyzing. To give an understanding of what we will be looking at, here are some of the variables we will be analyzing: salary cap, salary of individual players on each team, three-point percentage for a team as a whole and also individual players, two-point percentage for teams and individuals, minutes played by individual players, distance shot from for individual players, etc. We will analyze the 2015-2016 season stats for each team, the 2016-2017 season stats for each team and also the 2017-2018 season stats for each team. Along with that, we will also analyze the stats of the individual players from the rockets and hawks for the 2015-2016, 2016-2017, and 2017-2018 seasons. This will give us a great understanding of what kind of things changed for the teams as a whole throughout these seasons, and also what kind of things changed for the individual players on these teams throughout these seasons. Note that these teams do not have the same players every year due to the trading of players throughout the NBA. We got out data set from: https://www.basketball-reference.com Here is our analysis:
Ethical considerations
There is much ethical concern when analyzing this type of data in which we are analyzing in this lab. We are analyzing the individual player stats of players on the Rockets and Hawks. We are doing this without consent from the individual players and the organization in which they play. This data could expose some players in showing that they were a reason for their team either doing better or worse in NBA league ranking. This could also put the Atlanta hawks or Houston rockets organization at risk due to us examining why the teams changed so drastically in ranking over three seasons. This analyzation is done out of good intentions and does not work to expose any individual player or the organization in which they play.
Rockets and Hawks team comparison
Analyzing the Graph
This graph is showing the rankings of the Atlanta Hawks and Houston rockets for the 2015-2016, 2016-2017, and 2017-2018 seasons. Note that the y-axis is labeled as rankings would be on an NBA site, or even NBA TV channel, with 27th place being at the top, and 1st place being at the bottom. This means that a downward trend in the graph is a positive thing and an upward trend in the graph is a negative thing. Hence the Rockets having a downward trend going from 17th place to 1st place, and the hawks having an upward trend going from 7th place to 27th place.
Analyzing strength of schedule compared to league rank
This graph is showing strength of schedule compared to league rank for the Atlanta Hawks and Houston Rockets for the 2015-2018 NBA seasons. Any positive decimal determines a more difficult schedule that the team played, whereas any negative decimal is showing that the team played an easier schedule. As we can see in the graph, as the rockets schedule got easier, their league rank started to go down (which is a good thing, because as you go down in league rank you are getting closer to being in 1st place). In the 2017-2018 season when the rockets played their easiest schedule, they were the best team in the league ranking in 1st place. Whereas when they were in 17th place in 2015-2016, they played their most difficult schedule. The Atlanta hawks are showing almost the same trend as the Houston Rockets in this graph. Except, in 2015-2016 they played one of their easiest schedules and were in 7th place, and in 2017-2018 they played their hardest schedule and were in 27th place. After examining this graph, it is very evident that a team’s strength of schedule has strong correlation with their league rank.
Base Salary comparison for Houston and Atlanta
In this boxplot we can see that the two teams pay their players relatively the same amount. This is excluding the few outliers for Houston and the one outlier for Atlanta. Overall, the players on the two teams make about the same salary except for the outliers.
Player efficiency compared to year analyzation
Player efficiency is known as how many points a player has per minute over a season. In this boxplot, we can see that Atlanta and Houston’s players are making about 0.25 to 0.50 points per minute over a season, excluding the outliers. The teams have about the same player efficiency overall, except Houston has more outliers which means they have more players making above 0.50 points per minute over a season.
Atlanta’s wins and rank ggpair
Atlanta ggpairs analysis
The first ggpairs graph examines factors that affect wins for the Hawks. There is a negative correlation (-0.77) of wins compared with three-point percentage (X3P) and three-point attempts(X3PA). Consistent with our findings before, as players’ shooting accuracy decreased, less wins were accompanied with 3 points shots. Rather, since shooters have left the team, they are getting points through 2-point shots, which showed positive relation with the wins. (X2P=0.881, X2PA=0.675). The changes for Atlanta Hawks’ scoring strategy might be due to the lack of shooters on the team. The second graph examines the relationship of 3 points shots, minute played, and age directly with the team rank. As rank declined, less three-point shots are made, and players are playing more minutes on the court. Also, the average age on the team had decreased, meaning that the Hawks were losing experienced players as their rank went down. The reason why the “minute played” factor had a small impact on the rank might be due to the fact that our dataset only contained 3 seasons, which is not enough to show strong correlations. However, given this relationship, we can conclude that as the Hawks players were playing more time on the court than before though the relationship was not significant.
Houston’s wins and rank ggpair
Houston ggpairs analysis
For the Houston Rockets, instead of shifting strategy as the Hawks did, they did better on both three-point shots and two-point shots because the result is showing strong correlation with wins. Also, when we compare the percentage free throw percentage (FT) of Houston with Atlanta, Houston is showing a strong positive relation with wins, but Atlanta showed a negative correlation (-0.348) instead. As the rank went up, we found the Rockets players’ age also went up with weak correlation with the rank, and the ‘minute played’ was also weakly related to the rank as it decreased so that more players are taking turns playing. The efficiency, which measures a player’s ability to score in one minute, also went up with the Rockets’ rank. Admittedly, though our interpretations are based on the weak correlations and may not reflect significant differences or have a good p-value, the change is actually significant when we saw subtle changes of player’s performance and team strategy as a result of rapid lift or drop of rank in only three seasons.
Rockets and Hawks top player comparison
Minutes played compared to year boxplot analysis
In this boxplot, we can see that the top players on the Atlanta hawks played the most minutes in 2015-2016 when they were in 7th place. At the same time, we can see that the rockets top players played the least amount of minutes in 2017-2018 when they were in 1st place. This brings us to the conclusion that top players minutes played does not have a strong correlation with the team’s league rank.
Year compared to total points scored for top players analyzation
Overall in this graph, we can see that Atlanta’s top players were never scoring as much points as Houston’s top players. This is weird considering when the Hawks were a better league rank than the Rockets in 2015-2016, their top players were still not scoring as many points as Houston’s players. In 2017-2018 when the rockets were in 1st place, their top players score the least amount out of all three seasons analyzed. This might correlate to the boxplot above which shows that in 2017-2017 Houston’s top players played less minutes than other seasons.
Change in top scorers over the three seasons
| Year | Player | Total.Points | efficiency |
|---|---|---|---|
| 2015-2016 | Dennis Schroder | 879 | 0.5422579 |
| 2015-2016 | Jeff Teague | 1239 | 0.5494457 |
| 2015-2016 | Paul Millsap | 1385 | 0.5232338 |
| 2016-2017 | Dennis Schroder | 1414 | 0.5690141 |
| 2016-2017 | Paul Millsap | 1246 | 0.5317968 |
| 2017-2018 | Dennis Schroder | 1301 | 0.6260828 |
| Year | Player | Total.Points | efficiency |
|---|---|---|---|
| 2015-2016 | James Harden | 2376 | 0.7603200 |
| 2016-2017 | Eric Gordon | 1217 | 0.5238915 |
| 2016-2017 | James Harden | 2356 | 0.7994571 |
| 2017-2018 | Chris Paul | 1081 | 0.5852734 |
| 2017-2018 | Eric Gordon | 1243 | 0.5770659 |
| 2017-2018 | James Harden | 2191 | 0.8588789 |
Analyzation of tables
From these tables, we are able to see that the hawks had three highly efficient players in 2015-2016, but just one highly efficient player in 2017-2018. Whereas, the rockets had one highly efficient player in 2015-2016 and three highly efficient players in 2017-2018. The hawks were in 7th place in 2015-2016 and 27th place in 2017-2018 and the rockets were in 17th place in 2015-2016 an in 1st place in 2017-2018. The increase and decrease of efficient players on each team is seen to have a huge effect on the teams’ overall league rank.
Top players for rockets and hawks total points comparison
Total points analyzation for Houston
This is a pie chart showing Houston’s top players total points percentage from three seasons. Top players are labeled as players who scored more than 1000 points in a season. As you can see in this pie chart, James Harden has been the leading scorer for the Rockets the three seasons we analyzed. We can see that Eric Gordon was the second highest scorer on the team for two seasons, and the rest were among the highest scorers for one season. A tentative conclusion we can come to from this is that without James Harden, the Rockets would not have been able to become the best team in the NBA.
Total points analyzation for Atlanta
This is a pie chart showing Atlanta’s top players total points percentage from three seasons. Top players are labeled as players who scored more than 1000 points in a season. There are no outliers for who has scored the highest percentage of points the past three seasons for the Hawks as there was for the Rockets. It seems that over the three seasons we have analyzed, the top scorers have been distributed among the team.
Distance shot at for top players comparison
Average distance shot at for top scorers on the rocket’s analysis
A top player is one who has over 1000 points a season. In this graph we can see that overall, except for Clint Capella, the average distance shot at for Houston’s top players increased from 2015 to 2017. This means they were shooting more threes which could ultimately have a great effect on the teams win percentage and league rank.
Average distance shot at for top scorers on the hawk’s analysis
In this graph, compared to Houston’s above, we can see that the hawks are shooting at a shorter distance than the rockets. (The y-axis is different) Although the teams average distance shot at for top players did increase a little from 2015 to 2017, they are still not shooting at as great of a distance as the rockets. This could be a cause for them not being as good as the rockets in overall league rank.
Distance shot compared with total points for the hawks and rockets
Rockets analyzation
This graph is showing the change of total points when the average distance shot from the basket has increased for the Houston Rockets in three seasons, and the numbers on top of the graph are showing their rank in the different seasons. As we can see from the fitted lines, the Houston Rockets have an uprising trend in distance shot from, and also, in total points scored. The gradient of the fitted line increased the most when the Rockets climbed up from 17th place to 3rd place, and they still maintained their long-distance shooting accuracy when they finally reached first place. As an NBA superstar for the Rockets, James Harden stood out in total points scored which could have a large impact on the slope of the lines. However, he cannot affect the accuracy of the team alone. His teammates improved a lot on accuracy in 2016-2017 season, which might be due to their successful change of training strategy made by the Rockets’ head coach.
Hawks analyzation
This graph is showing the change of total points when the average distance shot from the basket has increased for the Atlanta Hawks in three seasons, and the numbers on top of the graph are showing their rank in the different seasons. For the Atlanta Hawks, as their average distance shot increased, their total points decreased. As time went on, in the season 2016-2017, the performance of players was starting to decrease with Dwight Howard as a boundary line, which means players with total points less than 500 points were losing their accuracy as shooting distance increased. When we proceed to the 2017-2018 season, though the stratification problem was solved, the data points, as a whole, were showing a decreasing accuracy for most players. Closer distance means less 3-point shots were made. As a contrast, Houston’s improvement is wholesome, and each individual on the team was improving to make more scores with higher accuracy.
Salary distribution for top players of the hawks and rockets
Pie Chart analyzation
This is a pie chart showing Houston’s top players salary percentage from three seasons. Top players are labeled as players who scored more than 1000 points in a season. We can see in this that the top two highest paid players are James Harden and Eric Gordon. They are the highest paid, therefore they are labeled as the team’s most efficient players. We can see this on the pie chart with top scorers. James harden is the highest paid and is the top scorer on the rockets, whereas Eric Gordon is the second highest paid and is the second highest scorer on the team. This would help us come to the assumption that for the Rockets organization, players are based on their ability to score points.
Analyzing the Pie Chart
This is a pie chart showing Atlanta’s top players salary percentage from three seasons. Top players are labeled as players who scored more than 1000 points in a season. This pie chart relates to the Rockets pie chart up above. The two highest scorers on the team are Paul Millsap and Dennis Schroder, whereas the two highest paid players on the team are Paul Millsap and Dennis Schroder. We can see that the Hawks also pay their players based on how efficient they are and how many points they score.
Top scorers for Houston and Atlanta over three seasons
Houston’s top players efficiency pie chart
This is a pie chart showing Houston’s top players scoring efficiency from three seasons. Top players are labeled as players who scored more than 1000 points in a season. Scoring efficiency is how many points a player has per minute over a season. We can see that the highest paid players and top scorers James Harden and Eric Gordon also have the highest scoring efficiency. This is showing us that without Eric Gordon and James Harden, the rockets would not have improved to be one of the best teams in the NBA.
Atlanta’s top players efficiency pie chart
This is a pie chart showing Atlanta’s top players scoring efficiency from three seasons. We can see that the highest paid players and top scorers Paul Millsap and Dennis Schroder also have the highest scoring efficiency. A thing that can be said from this is that the Hawks do not have a top player as good as James Harden. This could be a reason that the Hawks went from 7th to 27th place in the league rankings.
Atlanta and Houston total points t.test
| Season.Comparasion | Team | t.test.p.value |
|---|---|---|
| 2015-2016/2016-2017 | ATL | 0.4099 |
| 2016-2017/2017-2018 | ATL | 0.8155 |
| 2015-2016/2017-2018 | ATL | 0.5513 |
| 2015-2016/2016-2017 | HOU | 0.8703 |
| 2016-2017/2017-2018 | HOU | 0.9312 |
| 2015-2016/2017-2018 | HOU | 0.3714 |
##
## Welch Two Sample t-test
##
## data: Atlanta$Total.Points[Atlanta$Year == "2015-2016"] and Atlanta$Total.Points[Atlanta$Year == "2016-2017"]
## t = 0.47897, df = 33.444, p-value = 0.6351
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -237.2803 383.4979
## sample estimates:
## mean of x mean of y
## 496.0588 422.9500##
## Welch Two Sample t-test
##
## data: Atlanta$Total.Points[Atlanta$Year == "2016-2017"] and Atlanta$Total.Points[Atlanta$Year == "2017-2018"]
## t = 0.29465, df = 36.932, p-value = 0.7699
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -221.6976 297.1430
## sample estimates:
## mean of x mean of y
## 422.9500 385.2273##
## Welch Two Sample t-test
##
## data: Atlanta$Total.Points[Atlanta$Year == "2015-2016"] and Atlanta$Total.Points[Atlanta$Year == "2017-2018"]
## t = 0.79572, df = 29.7, p-value = 0.4325
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -173.7452 395.4083
## sample estimates:
## mean of x mean of y
## 496.0588 385.2273##
## Welch Two Sample t-test
##
## data: Houston$Total.Points[Houston$Year == "2015-2016"] and Houston$Total.Points[Atlanta$Year == "2016-2017"]
## t = -0.45768, df = 34.996, p-value = 0.65
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -508.8241 321.6065
## sample estimates:
## mean of x mean of y
## 513.9412 607.5500##
## Welch Two Sample t-test
##
## data: Houston$Total.Points[Houston$Year == "2016-2017"] and Houston$Total.Points[Atlanta$Year == "2017-2018"]
## t = 1.2882, df = 29.423, p-value = 0.2077
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -126.1216 556.0581
## sample estimates:
## mean of x mean of y
## 525.4444 310.4762##
## Welch Two Sample t-test
##
## data: Houston$Total.Points[Houston$Year == "2015-2016"] and Houston$Total.Points[Atlanta$Year == "2017-2018"]
## t = 1.2401, df = 28.356, p-value = 0.2251
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -132.4379 539.3679
## sample estimates:
## mean of x mean of y
## 513.9412 310.4762Total points t-test analysis
In the table, we can see the p-values for all of the t-tests on total points compared to year for the Houston rockets and Atlanta hawks. There are no significant values in this t-test. This means that the data would not be able to be published.
Atlanta and Houston top players total points t.test
| Season.Comparasion | Team | t.test.p.value |
|---|---|---|
| 2015-2016/2016-2017 | ATL | 0.4099 |
| 2016-2017/2017-2018 | ATL | 0.8155 |
| 2015-2016/2017-2018 | ATL | 0.5513 |
| 2015-2016/2016-2017 | HOU | 0.8703 |
| 2016-2017/2017-2018 | HOU | 0.9312 |
| 2015-2016/2017-2018 | HOU | 0.3714 |
##
## Welch Two Sample t-test
##
## data: ATLtop$Total.Points[ATLtop$Year == "2015-2016"] and ATLtop$Total.Points[ATLtop$Year == "2016-2017"]
## t = 0.90906, df = 4.4484, p-value = 0.4099
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -173.8032 353.3032
## sample estimates:
## mean of x mean of y
## 1291.00 1201.25##
## Welch Two Sample t-test
##
## data: ATLtop$Total.Points[ATLtop$Year == "2016-2017"] and ATLtop$Total.Points[ATLtop$Year == "2017-2018"]
## t = -0.25125, df = 3.5489, p-value = 0.8155
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -356.716 300.216
## sample estimates:
## mean of x mean of y
## 1201.25 1229.50##
## Welch Two Sample t-test
##
## data: ATLtop$Total.Points[ATLtop$Year == "2015-2016"] and ATLtop$Total.Points[ATLtop$Year == "2017-2018"]
## t = 0.71835, df = 1.8789, p-value = 0.5513
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -330.5868 453.5868
## sample estimates:
## mean of x mean of y
## 1291.0 1229.5##
## Welch Two Sample t-test
##
## data: HOUtop$Total.Points[ATLtop$Year == "2015-2016"] and HOUtop$Total.Points[HOUtop$Year == "2016-2017"]
## t = 0.18301, df = 2.1953, p-value = 0.8703
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2731.579 2996.579
## sample estimates:
## mean of x mean of y
## 1919.0 1786.5##
## Welch Two Sample t-test
##
## data: HOUtop$Total.Points[ATLtop$Year == "2016-2017"] and HOUtop$Total.Points[HOUtop$Year == "2017-2018"]
## t = 0.089981, df = 5.9903, p-value = 0.9312
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -890.9448 958.9448
## sample estimates:
## mean of x mean of y
## 1419.25 1385.25##
## Welch Two Sample t-test
##
## data: HOUtop$Total.Points[ATLtop$Year == "2015-2016"] and HOUtop$Total.Points[HOUtop$Year == "2017-2018"]
## t = 1.0195, df = 3.4453, p-value = 0.3741
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1016.955 2084.455
## sample estimates:
## mean of x mean of y
## 1919.00 1385.25Top players total points t-test analysis
In the table, we can see the p-values for all of the t-tests on top players total points compared to year for the Houston rockets and Atlanta hawks. There are no significant values in this t-test. This means that the data would not be able to be published.
Analyzation of three-point percentage to wins
This graph is showing three-point percentage compared to wins for the Houston rockets and Atlanta hawks. There is an evident trend showing in both of these graphs. For the rockets, we can see that as the teams three-point percentage increases, the amount of wins they have also increased. We can see their three-point percentage was highest in the 2017-2018 season when they got 1st place, and their three-point percentage is lowest in the 2015-2016 season in which they got 17th place. For the Hawks on the other hand, as their three-point percentage increased their wins decreased. This is the opposite of what we saw for the rockets. One thing we can take from these graphs is that an increase in three-point percentage for the rockets was a major contributor to their increase in league rank.
## Start: AIC=149.87
## Rank ~ X3P. + MP + Avg..Distance.Shot + Age + X2P. + FT.
##
## Df Sum of Sq RSS AIC
## - FT. 1 1.42 1850.9 147.90
## - Avg..Distance.Shot 1 4.58 1854.0 147.96
## - X2P. 1 8.49 1857.9 148.03
## - MP 1 48.45 1897.9 148.75
## - X3P. 1 66.27 1915.7 149.07
## <none> 1849.5 149.87
## - Age 1 319.98 2169.4 153.30
##
## Step: AIC=147.9
## Rank ~ X3P. + MP + Avg..Distance.Shot + Age + X2P.
##
## Df Sum of Sq RSS AIC
## - Avg..Distance.Shot 1 5.83 1856.7 146.01
## - X2P. 1 9.07 1859.9 146.07
## - MP 1 47.09 1898.0 146.75
## - X3P. 1 68.22 1919.1 147.13
## <none> 1850.9 147.90
## + FT. 1 1.42 1849.5 149.87
## - Age 1 320.25 2171.1 151.33
##
## Step: AIC=146.01
## Rank ~ X3P. + MP + Age + X2P.
##
## Df Sum of Sq RSS AIC
## - X2P. 1 8.77 1865.5 144.17
## - MP 1 41.41 1898.1 144.76
## - X3P. 1 66.70 1923.4 145.21
## <none> 1856.7 146.01
## + Avg..Distance.Shot 1 5.83 1850.9 147.90
## + FT. 1 2.67 1854.0 147.96
## - Age 1 359.42 2216.1 150.02
##
## Step: AIC=144.17
## Rank ~ X3P. + MP + Age
##
## Df Sum of Sq RSS AIC
## - MP 1 34.71 1900.2 142.79
## - X3P. 1 61.81 1927.3 143.28
## <none> 1865.5 144.17
## + X2P. 1 8.77 1856.7 146.01
## + Avg..Distance.Shot 1 5.53 1859.9 146.07
## + FT. 1 3.38 1862.1 146.10
## - Age 1 354.50 2220.0 148.08
##
## Step: AIC=142.79
## Rank ~ X3P. + Age
##
## Df Sum of Sq RSS AIC
## - X3P. 1 77.64 1977.8 142.16
## <none> 1900.2 142.79
## + MP 1 34.71 1865.5 144.17
## + X2P. 1 2.06 1898.1 144.76
## + FT. 1 0.25 1899.9 144.79
## + Avg..Distance.Shot 1 0.22 1900.0 144.79
## - Age 1 368.46 2268.6 146.82
##
## Step: AIC=142.16
## Rank ~ Age
##
## Df Sum of Sq RSS AIC
## <none> 1977.8 142.16
## + X3P. 1 77.64 1900.2 142.79
## + MP 1 50.54 1927.3 143.28
## + FT. 1 23.05 1954.8 143.76
## + Avg..Distance.Shot 1 22.64 1955.2 143.76
## + X2P. 1 15.10 1962.7 143.90
## - Age 1 447.12 2424.9 147.09## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## Rank ~ X3P. + MP + Avg..Distance.Shot + Age + X2P. + FT.
##
## Final Model:
## Rank ~ Age
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 27 1849.451 149.8736
## 2 - FT. 1 1.420159 28 1850.871 147.8997
## 3 - Avg..Distance.Shot 1 5.834177 29 1856.705 146.0067
## 4 - X2P. 1 8.766044 30 1865.471 144.1669
## 5 - MP 1 34.709275 31 1900.180 142.7937
## 6 - X3P. 1 77.639508 32 1977.820 142.1553##
## Call:
## lm(formula = Rank ~ Age, data = Atlanta)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.373 -5.867 -1.219 7.627 14.133
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.8228 8.7296 4.562 5.98e-05 ***
## Age -0.9295 0.3190 -2.914 0.00618 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.018 on 35 degrees of freedom
## (22 observations deleted due to missingness)
## Multiple R-squared: 0.1953, Adjusted R-squared: 0.1723
## F-statistic: 8.492 on 1 and 35 DF, p-value: 0.00618
##
## Shapiro-Wilk normality test
##
## data: model7$residuals
## W = 0.9369, p-value = 0.03681Analyzation
Multiple factors considered to affect the ranking of Atlanta Hawks were plugged into the stepAIC model and the best model was selected. It appeared that age is the best model. The p-value is shown to be 0.0061, which suggests that relationship exists between the Hawks’ team rank and the age of players in their team. The multiple R-squared value is 19.53% which means that the variance of the model explained 19.53% of the total variance. Though it’s not big enough to cover all the variance, the residuals are actually following a homoscedastic pattern( shapiro test, p-value =0.03681). Also, the points on the qq plot are sticking close to the gray dotted line, and only three points are skewed on the top. To test the scattering pattern of the residuals, a histogram was also made to test whether it follows normal distribution. It turns out that points are normally distributed except the residuals from 0 to 5, the normal distribution is a little bit skewed to the right but in general, it’s fairly a good model. According to the result of linear regression model, as the Hawks’ team rank declined, younger players are dominating the team. Since experienced shooter were transferred to other teams, younger players do not have enough experience to carry up the team, and decreased shooting accuracy is also important for the chief coach to consider.
Conclusion
In conclusion, we have found a lot of things that have affected the league ranking of the Houston rockets and Atlanta hawks over the three seasons we analyzed. For Atlanta, the main reasons they went from 7th place to 27th place in the matter of three seasons were: the loss of players over the seasons along with the loss of player efficiency, the lack of top scorers or stand out players, the loss of experienced players that they had in 2015, a decrease in accuracy of shots, a lack of regard for distance shot at, a decrease in three point percentage, a decrease in total points scored by top players, and a harder strength of schedule. As for Houston, the reasons they went from 17th place to 1st place in 2017 were: an improvement in shot accuracy over the years, the addition of experienced players to the roster, an easier strength of schedule, an increase in overall player efficiency, an increase in total points scored by top players, addition of standout players playing at an efficient level such as James Harden and Eric Gordon, an increase in distance shot at that correlates with points scored, a salary cap increase over the years, and an overall better and new strategy that the head coach implemented which was to shoot more three pointers. Overall, throughout this analysis we have determined that individual and team stats for the Houston rockets improved over the years leading them to be in 1st place in the 2017-2018 season, whereas the Atlanta hawks have worsened in both individual and team stats leading them to be the 27th ranked team in the NBA as of the 2017-2018 season. The limitations of this data were that we were not able to get all of the individual stats for the players on the Hawks and Rockets. We had to make our own data set which limited the type of data we were able to analyze. For future data analysis, we would love to have a bigger data set with more of the player stats. Along with this point, we would like to analyze more seasons that just the three that we analyzed. In our analysis we determined that there was a change in method for the rockets that was implemented by the head coach. This method was that the team was taking too many deep two-pointers and should just step a few feet back and take a three-pointer instead. This eventually led the team to become one of the best team in the NBA. This analysis that we determined is supported by this article on ESPN: http://www.espn.com/nba/story/_/id/9024190/moreyball-how-houston-rockets-became-nba-most-exciting-team