In this project, we analyzed the NBA history with the parameters of players age, the winning percentage of teams, PER (players efficieny rating), minutes played between 1986-2017 and used Python jupyter notebook for creating codes.
- Can the Team Four Factor Rating of Basketball help in accurately determining the team’s winning percentage? Does the data set we are using needs to be adjusted for accurate analysis?
- How does age of the player affect PER (Player Efficiency Rating)?
- How does a player’s move (Top 10 only based on overall points) affect the new team’s winning percentage?
- Is the Minutes Played variable positively correlated with a players core performance variables? (i.e: 3pts, 2pts, blocks, steals, ect.)
| Parameters | Against |
|---|---|
| Four Factors Ratings | Team's winning percentage |
| Age | Players Efficiency Ratings (PER) |
| Player's Move | New Team's winning percentage |
| Minutes Played | 3pts, 2pt, Stl, Blk, Drb, Orb, Ft |
- (https://www.sportsgamblingpodcast.com/2020/04/20/nba-most-valuable-statistic/)
- (https://pypi.org/project/nba-api/) Notes: Limiting our project between 1986-2017.
To get our data in a format that was needed, we had to merge teamData (contains Year, Team, Record, and Winning Percentage information) with playerData (contains Index, Year, Player, Pos, Age, Tm, G, GS, MP, PER, TS%, 3PAr, FTr, ORB%, DRB%, TRB%, AST%, STL%, BLK%, TOV%, USG%, blanl, OWS, DWS, WS, WS/48, blank2, OBPM, DBPM, BPM, VORP, FG, FGA, FG%, 3P, 3PA, 3P%, 2P, 2PA, 2P%, eFG%, FT, FTA, FT%, ORB, DRB, TRB, AST, STL, BLK, TOV, PF and PTS) in Resources folder. In order to get the winning percentage by Year and Team (teamData) to be combined with the PlayerData, we did some data cleansing in Python as well as created the complete_nba_data database, this file combines that information. This is what we used to do all of our analysis except for Question 4. In addition, we had to identify if we had any NaN in our data. The NBA Team Data had many players that had this occur. This was due to the data in those fields were not calculated at the time these players played, or the data needed was not available for that time period. We were able to identify that for a 30-year period (1986 - 2017) the data was clean (had no fields with NaN).
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complete_nba_data: Merged team data with city data and added players data in csv files to work on first question and related visualizations and arranged the data between 1986 to 2017 and cleaned up dataset to use as main data.
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age_player_data: Create a data frame using complete_nba_data to find age effects PER (Player Efficiency Rating). Gathered the data from complete_nba_data and use "Year", "Player", "Age", "G", "MP","PER" as column to find out top players.
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player_move_data: Create a data frame using complete_nba_data to find the effect a players move had on his new team. In order to make sure we only used the best players based on total points for each year (1986-2016). We did several queries to get to this data (see code). In addition we needed to make sure that we were able to capture the New Team and the Year it happened from the output. To do this, we used the team, year and winning percentage information from the output to get the teams winning Percentage for the prior year from the complete_nba_data database (see code). We then compared the prior year to the year the trade happened (see code).
As we compared different players from top 10 players list, we saw some difference between old winning percentage and new winning percentage when player’s team changed.
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Impact of Four Factor Ratings on Winning Percentage: Analyzed the impact of Four Factor ratings on team's Winning Percentage by performing linear regression and scatter plot. We also calculated Coefficient of Correlation (r) to see how Four Factors and Team's winning percentage are correlated. We calculated residuals and plotted residuals with predicted values to see if the data that we are working on needs adjustment or not.
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Impact of age based on PER: Analyzed players age data and found the quartiles, IQR, upper and lower bound to compare the players who would be on top 10 based on players median.
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Impact of players move based on points: Analyzed players move based on points and winning percentage using player_points_data. Found top 10 players based on points and impact of their move to other team.
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Impact of minutes played on key varibles: Took the natural log of all varibles in order to see elasticity through regression analysis.
We understand from these scatter plots that individual factors have a very weak correlation with the winning percentage as Coefficient of Correlation (r) is very low in all the cases.
Hence, we then perform linear regression on the Four Factor Rating to see if we get better correlation to Team’s winning percentage compared to individual factors.
From Scatter Plot and Linear Regression analysis, we can observe that Four Factor Rating has a better correlation to the team’s winning percentage than individual factors.
For a healthy positive correlation, it is important to have Coefficient of Correlation (r) = 0.9.
r is 0.377 in this case which indicates that it is a weak positive correlation. This indicates that Four Factor Rating is not an efficient parameter in determining the winning percentage of the team. There are several other external factors that needs to consider to accurately predict the winning percentage.
We calculate residuals which are difference between predicted winning percentages and observed winning percentages. Residuals are essentially errors in our predictions. A positive residual indicates that our prediction was lower than expected while negative residual indicates that our prediction was higher than expected.
We then plot a scatter plot of predicted values against residuals to check for the pattern. If we get any kind of pattern in this scatter plot, it means that we can predict our residual based on our predicted values. This means that our data model is not accurate, and it will require some transformation of the data.
From this Scatter plot, we can see that slope is 0 and linear regression is a horizontal line. This means that there is no correlation in the predicted values and residuals. The occurrences or residuals are in a randomized order. This concludes that the data model we were working is an accurate data model.
From this scatter plot and the value of r, we can conclude that there is a very weak positive correlation between Age and PER. This is not a sufficient data to predict that age of the player affects his PER.
But we can see it here that more datapoints are recorded between the age 20 and 30 and a very few datapoints are recorded after the age of 30. This also infers a player’s PER will reach a peak between these years.
Our expectation would be the new team would improve.
- In most cases that is exactly what happen.
- In the cases they did not, some of the players like Tracy McGrady were traded / moved several times in a year and his teams did not improve.
- The Top 10 had 2 players Kobe Bryant and Russell Westbrook that did not move. If we had more time, we could have replaced them with the next best player that had a move. This would have help in verifying the outcome to back up out Theory.
- The Top 10 had 1 player Kevin Durant that did had a move to a brand new team OKC. This caused a bug that if we had more time we would have fixed, Due to OKC being a new team we had no data on new team's previous winning percentage. The query should have returned only on Team change with a message that "This is a New Team and no winning Percentage was found". The code displays the current year data for the new team instead.
- The Top 10 had 2 players Alex English and Dwayne Wade that did not have a positive outcome. When they went to the new team they were both at the end of their careers.
- The Top 10 had 1 player Dominique Wilkins that had mixed results. He was on 2 different teams in 1994 he was traded from and to the same team the Atlanta Hawks. He also was traded again at the end of his career to Seattle, and they were an awfully bad team before he got there.
Based on the finding we would need more Data to deal with the outliers.
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If we had more time, we could have tried to a line series plot for each player with years on the bottom and age on side.
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If we had more time, we could have used Points as well as winning % to see how many more or less points they averaged.
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If we had more time, we could of we could have looked at Player Efficiency Rating over that time
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If we had more time, we could have used a Confusion Matrix to help Validate the outcome.
Here is the process and an example
- You need a test dataset or a validation dataset with expected outcome values.
- Make a prediction for each row in your test dataset.
- From the expected outcomes and predictions count:
- The number of correct predictions for each class.
- The number of incorrect predictions for each class, organized by the class that was predicted.
Q4: Is Minutes Played positivly correlated with key factors chosen to represent a players basketball skill?
- On average, minutes played is positively correlated to a player's three point score, two point score, free throw score, offensive rebound score, defensive rebound score, block score, and steal score.
- The more minutes you play the more chances you have to either score a point or prevent the other team from scoring a point.
In order to run this regression smoothly, there were many steps I had to take to clean my data frame. To start off I created a subset data from my original that contained all basketball statistics between the year 1986 and the year 2017. After this I created yet another subset including only the variables described in the hypothesis. Then I created a function that would drop all outliers using quantiles. Once this was completed I decided to log transform every variable in order to compress the data and make my model linear. This arose a problem within the data as some of these log transformed variables contained inf and na values. I modified the dataset to drop all rows with either a na or inf value inorder to get my working data frame.
- My dependent variable for this regression analysis will be minutes played as I wish to see the effects it has on three point scores, two point scores, free throw scores, offensive rebounds, defensive rebounds blocks, and steals. These will be considered my independent variables.
After close analysis of this regression I am able to confirm that all of the variables I have chosen are positively correlated except for blocking stats and offensive rebounds. Since all of these variables are log transformed, I am now looking at the elasticity between variables. I am able to tell that a ten percent increase in minutes played results in a 0.3% decrease in a players blocking stats. Even though this is a negative correlation, It has a very small correlation which tells me that even though this is statistically significant (low p value) minutes played does not affect a players blocking stats in a largely impactful way. The other negative coefficient is similar in that minutes played has a very small impact on it. For a ten percent increase in minutes played, a player's offensive rebounds decrease by 0.2%. The independent variables with the strongest correlation to minutes played are defensive rebounds, steals, and two point shots. Respectively, a ten percent increase in minutes played yields a 3.6% increase in defensive rebounds, a 2.5% increase in steals and a 2.6% increase in 2 pointers.
My insight as to why these are more highly correlated is that these aspects of a basketball game are more likely to happen than the negatively correlated aspects. For example, a defensive rebound is much more likely to occur vs an offensive rebound since when a team is on defense, they usually have more players under the basket than the opposing team. Similarly, blocking a shot in the NBA is considered very hard to do which makes sense as to why on average, the more a person plays the less blocked shots he has. The R squared value sits high at 0.9546 meaning that my data is highly correlated. Also with a very low p value my data is considered statistically significant.
With all that being said I am forced to reject my null hypothesis since there are negatively correlated variables however, my logic in creating that hypothesis was correct since the majority of variables are highly correlated and the variables that are negatively correlated are so in a very minor manner.
Required dependencies:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as statsCreated by: