NBA Game Data Wrangling
Tarun.S.Sarode
Summary:
The data analysis process includes many steps from defining the problem statement or the aim of the project, data collection to do analysis, data pre processing which includes getting the data ready to analyze, exploring the data to understand and extract any information from it, followed by modeling the data to obtain the results from it and finally interpreting the results.
This report provides an analysis on a NBA game data set for the season of 2019-2020 season which applies first three steps of data analysis process and the primary task of an data analysis process which is,Defining a problem statement, Data Collecting and Data pre processing.
The data collection for this analysis is retrieved from Kaggle.com and R is used to carry out the data pre processing.
The Methodology and analysis of the data set includes using the basic R packages and the functions available in them by following the pre processing steps.
The two separate data sets called “games.csv” and “games_details.csv” is imported using the ‘readr’ library .
The redundant column, for example Comments were dropped from the data set and separated the variables, an example of it would be MIN column to HOURS and MINUTES.
The two data sets were joined together to make one data set using the primary keys GAME_ID and HOME_TEAM_ID.
For analysis a new variable was created/mutated called Offensive_Rebound_To_Defensive_Rebound_Ratio, which would help in the further analysis because it indicates the impact of the offensive contribution of an NBA player with respect to defensive contributes in terms of rebounds.
The structures of the variables in the data set were converted to the right format and factored the columns respectively.
After the above steps were implemented the missing values were analyzed in the data set and were replaced or removed accordingly.
Next, outliers were found out for the numeric columns and capping and replacing were applied.
Finally, Box Cox transformations were applied to ensure the normality of the data, which makes it ready for the analysis.
From the analysis of the data set it can be concluded that the nba_games_dataset is the final cleaned data set which is free from any impurities and can be used for further analysis.
Data
The “games.csv” contains informations about NBA Games during 2019 Season. It contains 23195 observations and 21 variables. It was collected from Kaggle[https://www.kaggle.com/nathanlauga/nba-games?select=games.csv].
The “games.csv” contains the following attributes:
- GAME_DATE_EST(Data Type- Date) - This attribute contains The date when the match occured.
- GAMEE_ID (Data Type - double) - This attribute contains the game status. It is the primary key
- HOME_TEAM_ID (Data Type - double ) - This attribute contains the unique id of the home team.
- VISITOR_TEAM_ID(Data Type - double) -This attribute contains the unique id of the visitor team.
- SEASON(Data Type - double) - It contains the NBA season information of the current match.
- TEAM_ID_home (Data Type - double) - It contains the unique id of the home team.
- PTS_home (Data Type- double)- This attribute indicates the the total points scored by the home team.
- FG_PCT_home (Data Type-double)- This attribute indicates the the assists by the home team.
- FT_PCT_home (Data Type-double) - This attribute indicates the free throw percentage by the home team
- FG3_PCT_home (Data Type-double) - This attribute indicates the 3 point field goal percentage by the home team
- AST_home (Data Type-double) - This attribute indicates the assists made by the home team.
- REB_home (Data Type-double) - This attribute indicates the rebounds by the home team.
- TEAM_ID_away (Data Type-double) - This arrtibute contains the team id of the away team.
- PTS_away (Data Type-double) - This attribute indicates the total points scored by the away team
- FG_PCT_away (Data Type-double) - This attribute indicates the Field Goal Percentage by the away team
- FT_PCT_away (Data Type-double) - This attribute indicates the free throw percentage by the away team
- FG3_PCT_away (Data Type-double) - This attribute indicates the 3 point field goal percentage by the away team
- AST_away (Data Type-double) - This attribute indicates the the assists by the away team
- REB_away (Data Type-double) - This attribute indicates the rebounds by the away team.
- HOME_TEAM_WINS (Data Type-double) - This attribute shows if the home team wins or not. 1 indicates win and 0 indicates loss
#Loading the required packages
library(readr)
library(dplyr)
library(tidyr)
library(car)
library(outliers)
library(stringr)
library(forecast)
library(magrittr)Loading the “games.csv” dataset.
viewing the contents using the head().
Checking the attributes and their data types using the str function
#Loading the dataset "games.csv"
#Stripping the white spaces where it is possible
games <- read.csv("data/games.csv", strip.white = TRUE)
#Viewing the games dataset
head(games)## GAME_DATE_EST GAME_ID GAME_STATUS_TEXT HOME_TEAM_ID VISITOR_TEAM_ID SEASON
## 1 2020-03-01 21900895 Final 1610612766 1610612749 2019
## 2 2020-03-01 21900896 Final 1610612750 1610612742 2019
## 3 2020-03-01 21900897 Final 1610612746 1610612755 2019
## 4 2020-03-01 21900898 Final 1610612743 1610612761 2019
## 5 2020-03-01 21900899 Final 1610612758 1610612765 2019
## 6 2020-03-01 21900900 Final 1610612740 1610612747 2019
## TEAM_ID_home PTS_home FG_PCT_home FT_PCT_home FG3_PCT_home AST_home REB_home
## 1 1610612766 85 0.354 0.900 0.229 22 47
## 2 1610612750 91 0.364 0.400 0.310 19 57
## 3 1610612746 136 0.592 0.805 0.542 25 37
## 4 1610612743 133 0.566 0.700 0.500 38 41
## 5 1610612758 106 0.407 0.885 0.257 18 51
## 6 1610612740 114 0.421 0.818 0.219 24 52
## TEAM_ID_away PTS_away FG_PCT_away FT_PCT_away FG3_PCT_away AST_away REB_away
## 1 1610612749 93 0.402 0.762 0.226 20 61
## 2 1610612742 111 0.468 0.632 0.275 28 56
## 3 1610612755 130 0.505 0.650 0.488 27 37
## 4 1610612761 118 0.461 0.897 0.263 24 36
## 5 1610612765 100 0.413 0.667 0.429 23 42
## 6 1610612747 122 0.515 0.900 0.371 23 36
## HOME_TEAM_WINS
## 1 0
## 2 0
## 3 1
## 4 1
## 5 1
## 6 0#Viewing the attributes in the "games.csv" dataset
str(games)## 'data.frame': 23195 obs. of 21 variables:
## $ GAME_DATE_EST : chr "2020-03-01" "2020-03-01" "2020-03-01" "2020-03-01" ...
## $ GAME_ID : int 21900895 21900896 21900897 21900898 21900899 21900900 21900901 21900887 21900888 21900889 ...
## $ GAME_STATUS_TEXT: chr "Final" "Final" "Final" "Final" ...
## $ HOME_TEAM_ID : int 1610612766 1610612750 1610612746 1610612743 1610612758 1610612740 1610612744 1610612752 1610612737 1610612748 ...
## $ VISITOR_TEAM_ID : int 1610612749 1610612742 1610612755 1610612761 1610612765 1610612747 1610612764 1610612741 1610612757 1610612751 ...
## $ SEASON : int 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 ...
## $ TEAM_ID_home : int 1610612766 1610612750 1610612746 1610612743 1610612758 1610612740 1610612744 1610612752 1610612737 1610612748 ...
## $ PTS_home : num 85 91 136 133 106 114 110 125 129 116 ...
## $ FG_PCT_home : num 0.354 0.364 0.592 0.566 0.407 0.421 0.472 0.553 0.548 0.451 ...
## $ FT_PCT_home : num 0.9 0.4 0.805 0.7 0.885 0.818 0.708 0.697 0.864 0.833 ...
## $ FG3_PCT_home : num 0.229 0.31 0.542 0.5 0.257 0.219 0.321 0.4 0.429 0.368 ...
## $ AST_home : num 22 19 25 38 18 24 25 29 34 27 ...
## $ REB_home : num 47 57 37 41 51 52 52 50 36 45 ...
## $ TEAM_ID_away : int 1610612749 1610612742 1610612755 1610612761 1610612765 1610612747 1610612764 1610612741 1610612757 1610612751 ...
## $ PTS_away : num 93 111 130 118 100 122 124 115 117 113 ...
## $ FG_PCT_away : num 0.402 0.468 0.505 0.461 0.413 0.515 0.488 0.461 0.5 0.465 ...
## $ FT_PCT_away : num 0.762 0.632 0.65 0.897 0.667 0.9 0.889 0.696 0.714 0.739 ...
## $ FG3_PCT_away : num 0.226 0.275 0.488 0.263 0.429 0.371 0.667 0.486 0.286 0.364 ...
## $ AST_away : num 20 28 27 24 23 23 24 26 14 30 ...
## $ REB_away : num 61 56 37 36 42 36 34 33 42 44 ...
## $ HOME_TEAM_WINS : int 0 0 1 1 1 0 0 1 1 1 ...#Checking the dimension of the "games.csv" dataset
dim(games)## [1] 23195 21The “games_details.csv” contains extensive game details information about NBA Games during 2019-2020 Season. It contains 576782 observations and observations and 28 variables.It was collected from Kaggle[https://www.kaggle.com/nathanlauga/nba-games?select=games_details.csv].
The “games_details.csv” contains the following attributes:
- GAME_ID (Data Type- double) - The primary key of dataset. This indicates the game id of the match.
- TEAM_ID (Data Type- double) - This attribute indicates the team id of the player.
- TEAM_ABBREVIATION(Data Type- character) - This attribute indicates the abbreviation of the team.
- TEAM_CITY- This attributes indicates the city of the team.
- PLAYER_ID - This attribute indicates the player id.
- PLAYER_NAME (Data Type - Character)- This attribute indicates the players name.
- START_POSITION(Data Type - Character) - This attribute indicates the starting position of the player.
- COMMENT(Data Type-character) - This attribute is unnecessary. It contains the comments about the player.
- MINS(DATA TYPE - S3:hms)- This attribute contains the total minutes player. But this attribute is untidy because hours and minutes are 2 different attributes.
- FGM (Data Type- double)- This attribute indicates the field goals made by the player.
- FGA (Data Type- double) - This attribute indicates the field goal attempted by the player.
- FG_PCT (Data Type- double) - This attribute indicates the field goal percentage of the player.
- FG3M (Data Type- double)- This attribute indicates the 3 point field goal made by the player.
- FG3A (Data Type- double) - This attribute indicates the 3 point field goal attempted by the player.
- FG3_PCT (Data Type- double)- This attribute indicates the 3 point field goal percentage of the player
- FTM (Data Type- double) - This attribute indicates the free throw made by the player.
- FTA (Data Type- double)- This attribute indicates the free throw attempted by the player.
- FT_PCT (Data Type- double) - This attribute indicates the field goal percentage of the player.
- OREB (Data Type- double) - This attribute indicates the offensive rebounds made by the player.
- DREB (Data Type- double) - This attribute indicates the defensive rebounds made by the player.
- REB (Data Type- double) - This attribute indicates the total rebounds made by the player.
- AST (Data Type- double) - This attribute indicates the total steals made by the player.
- STL (Data Type- double) - This attribute indicates the total steal made by the player.
- BLK (Data Type- double)- This attribute indicates the total number of blocks made by the player.
- TO (Data Type- double)- This attribute indicates the total turnovers made by the player.
- PF - (Data Type- double) - This attribute indicates the total personal fouls made by the player.
- PTS (Data Type- double) - This attribute indicates the total points made by the player.
- PLUS_MINUS (Data Type- double) - This attribute indicates the plus/minus attribute to quantify the team’s performance when the player was on the team.
Loading the “games_details.csv” data set and viewing the contents using the head() function.
Using the str() function to attributes and their data types.
Using dim() function to see the number of rows and columns in the dataset.
#Loading the "games_details.csv" data set
games_details <- read.csv("data/games_details.csv", strip.white = TRUE)
head(games_details)## GAME_ID TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID
## 1 21900895 1610612749 MIL Milwaukee 202083
## 2 21900895 1610612749 MIL Milwaukee 203507
## 3 21900895 1610612749 MIL Milwaukee 201572
## 4 21900895 1610612749 MIL Milwaukee 1628978
## 5 21900895 1610612749 MIL Milwaukee 202339
## 6 21900895 1610612749 MIL Milwaukee 1626192
## PLAYER_NAME START_POSITION COMMENT MIN FGM FGA FG_PCT FG3M FG3A
## 1 Wesley Matthews F 27:08 3 11 0.273 2 7
## 2 Giannis Antetokounmpo F 34:55 17 28 0.607 1 4
## 3 Brook Lopez C 26:25 4 11 0.364 1 5
## 4 Donte DiVincenzo G 27:35 1 5 0.200 0 3
## 5 Eric Bledsoe G 22:17 2 8 0.250 0 1
## 6 Pat Connaughton 24:52 2 5 0.400 1 4
## FG3_PCT FTM FTA FT_PCT OREB DREB REB AST STL BLK TO PF PTS PLUS_MINUS
## 1 0.286 0 0 0.000 4 4 8 2 2 0 0 0 8 11
## 2 0.250 6 7 0.857 2 18 20 6 1 0 3 2 41 22
## 3 0.200 7 9 0.778 2 5 7 0 0 3 0 2 16 16
## 4 0.000 0 0 0.000 1 6 7 5 0 1 2 0 2 14
## 5 0.000 0 0 0.000 1 0 1 2 1 0 3 2 4 6
## 6 0.250 1 2 0.500 2 3 5 1 0 0 1 2 6 0#Viewing the attributes in the "games_details.csv" data set
str(games_details)## 'data.frame': 576782 obs. of 28 variables:
## $ GAME_ID : int 21900895 21900895 21900895 21900895 21900895 21900895 21900895 21900895 21900895 21900895 ...
## $ TEAM_ID : int 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 ...
## $ TEAM_ABBREVIATION: chr "MIL" "MIL" "MIL" "MIL" ...
## $ TEAM_CITY : chr "Milwaukee" "Milwaukee" "Milwaukee" "Milwaukee" ...
## $ PLAYER_ID : int 202083 203507 201572 1628978 202339 1626192 201577 1628425 101107 201588 ...
## $ PLAYER_NAME : chr "Wesley Matthews" "Giannis Antetokounmpo" "Brook Lopez" "Donte DiVincenzo" ...
## $ START_POSITION : chr "F" "F" "C" "G" ...
## $ COMMENT : chr "" "" "" "" ...
## $ MIN : chr "27:08" "34:55" "26:25" "27:35" ...
## $ FGM : num 3 17 4 1 2 2 1 1 0 4 ...
## $ FGA : num 11 28 11 5 8 5 5 2 1 11 ...
## $ FG_PCT : num 0.273 0.607 0.364 0.2 0.25 0.4 0.2 0.5 0 0.364 ...
## $ FG3M : num 2 1 1 0 0 1 0 1 0 1 ...
## $ FG3A : num 7 4 5 3 1 4 0 2 1 4 ...
## $ FG3_PCT : num 0.286 0.25 0.2 0 0 0.25 0 0.5 0 0.25 ...
## $ FTM : num 0 6 7 0 0 1 0 0 0 2 ...
## $ FTA : num 0 7 9 0 0 2 0 0 0 3 ...
## $ FT_PCT : num 0 0.857 0.778 0 0 0.5 0 0 0 0.667 ...
## $ OREB : num 4 2 2 1 1 2 1 0 0 2 ...
## $ DREB : num 4 18 5 6 0 3 2 3 2 3 ...
## $ REB : num 8 20 7 7 1 5 3 3 2 5 ...
## $ AST : num 2 6 0 5 2 1 0 0 2 2 ...
## $ STL : num 2 1 0 0 1 0 0 0 1 2 ...
## $ BLK : num 0 0 3 1 0 0 1 0 1 0 ...
## $ TO : num 0 3 0 2 3 1 2 1 1 3 ...
## $ PF : num 0 2 2 0 2 2 1 0 1 1 ...
## $ PTS : num 8 41 16 2 4 6 2 3 0 11 ...
## $ PLUS_MINUS : num 11 22 16 14 6 0 -12 -8 -11 2 ...#Checking the dimension of the "games_details.csv" data set
dim(games_details)## [1] 576782 28Renaming the column TEAM_ID to HOME_TEAM_ID in “games_details.csv” data set , so that it becomes parts of the primary key, before performing the join operation.
colnames(games_details)[2] <- "HOME_TEAM_ID"
head(games_details)## GAME_ID HOME_TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID
## 1 21900895 1610612749 MIL Milwaukee 202083
## 2 21900895 1610612749 MIL Milwaukee 203507
## 3 21900895 1610612749 MIL Milwaukee 201572
## 4 21900895 1610612749 MIL Milwaukee 1628978
## 5 21900895 1610612749 MIL Milwaukee 202339
## 6 21900895 1610612749 MIL Milwaukee 1626192
## PLAYER_NAME START_POSITION COMMENT MIN FGM FGA FG_PCT FG3M FG3A
## 1 Wesley Matthews F 27:08 3 11 0.273 2 7
## 2 Giannis Antetokounmpo F 34:55 17 28 0.607 1 4
## 3 Brook Lopez C 26:25 4 11 0.364 1 5
## 4 Donte DiVincenzo G 27:35 1 5 0.200 0 3
## 5 Eric Bledsoe G 22:17 2 8 0.250 0 1
## 6 Pat Connaughton 24:52 2 5 0.400 1 4
## FG3_PCT FTM FTA FT_PCT OREB DREB REB AST STL BLK TO PF PTS PLUS_MINUS
## 1 0.286 0 0 0.000 4 4 8 2 2 0 0 0 8 11
## 2 0.250 6 7 0.857 2 18 20 6 1 0 3 2 41 22
## 3 0.200 7 9 0.778 2 5 7 0 0 3 0 2 16 16
## 4 0.000 0 0 0.000 1 6 7 5 0 1 2 0 2 14
## 5 0.000 0 0 0.000 1 0 1 2 1 0 3 2 4 6
## 6 0.250 1 2 0.500 2 3 5 1 0 0 1 2 6 0Performing the join operation operation of the two datasets: “games.csv” dataset and “games_details.csv”. The merged data set contains 288643 observations and 47 attributes found using dim() function before any kind of data preprocessing.
#Performing the Join operation of the data section
nba_games_dataset <- games_details %>% inner_join(games, by = c('GAME_ID','HOME_TEAM_ID'))
head(nba_games_dataset)## GAME_ID HOME_TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID PLAYER_NAME
## 1 21900895 1610612766 CHA Charlotte 1628970 Miles Bridges
## 2 21900895 1610612766 CHA Charlotte 1629023 P.J. Washington
## 3 21900895 1610612766 CHA Charlotte 202687 Bismack Biyombo
## 4 21900895 1610612766 CHA Charlotte 1628984 Devonte' Graham
## 5 21900895 1610612766 CHA Charlotte 1626179 Terry Rozier
## 6 21900895 1610612766 CHA Charlotte 1628998 Cody Martin
## START_POSITION COMMENT MIN FGM FGA FG_PCT FG3M FG3A FG3_PCT FTM FTA FT_PCT
## 1 F 35:15 3 13 0.231 1 7 0.143 0 0 0
## 2 F 31:52 5 14 0.357 1 8 0.125 1 1 1
## 3 C 22:07 2 8 0.250 0 0 0.000 4 4 1
## 4 G 32:21 7 18 0.389 3 8 0.375 0 1 0
## 5 G 36:05 6 18 0.333 0 3 0.000 1 1 1
## 6 29:08 4 8 0.500 2 5 0.400 1 1 1
## OREB DREB REB AST STL BLK TO PF PTS PLUS_MINUS GAME_DATE_EST GAME_STATUS_TEXT
## 1 1 3 4 2 2 2 2 2 7 -4 2020-03-01 Final
## 2 1 5 6 3 0 2 2 3 12 -13 2020-03-01 Final
## 3 4 5 9 2 0 2 1 3 8 -15 2020-03-01 Final
## 4 0 2 2 3 1 0 0 2 17 -14 2020-03-01 Final
## 5 2 1 3 4 1 0 2 2 13 -20 2020-03-01 Final
## 6 0 5 5 2 0 1 1 2 11 2 2020-03-01 Final
## VISITOR_TEAM_ID SEASON TEAM_ID_home PTS_home FG_PCT_home FT_PCT_home
## 1 1610612749 2019 1610612766 85 0.354 0.9
## 2 1610612749 2019 1610612766 85 0.354 0.9
## 3 1610612749 2019 1610612766 85 0.354 0.9
## 4 1610612749 2019 1610612766 85 0.354 0.9
## 5 1610612749 2019 1610612766 85 0.354 0.9
## 6 1610612749 2019 1610612766 85 0.354 0.9
## FG3_PCT_home AST_home REB_home TEAM_ID_away PTS_away FG_PCT_away FT_PCT_away
## 1 0.229 22 47 1610612749 93 0.402 0.762
## 2 0.229 22 47 1610612749 93 0.402 0.762
## 3 0.229 22 47 1610612749 93 0.402 0.762
## 4 0.229 22 47 1610612749 93 0.402 0.762
## 5 0.229 22 47 1610612749 93 0.402 0.762
## 6 0.229 22 47 1610612749 93 0.402 0.762
## FG3_PCT_away AST_away REB_away HOME_TEAM_WINS
## 1 0.226 20 61 0
## 2 0.226 20 61 0
## 3 0.226 20 61 0
## 4 0.226 20 61 0
## 5 0.226 20 61 0
## 6 0.226 20 61 0#Checking the dimensions of the merged dataset
dim(nba_games_dataset)## [1] 288643 47Tidy & Manipulate Data I
The “games.csv” data set is not tidy because it contains 2 attributes “AWAY_TEAM_ID” and “TEAM_ID_away” which are duplicates of each other.Therefore, dropping “Team_ID_away” from the data set.
According to the Tidy Principles:Each variable forms a column, whereas variables here are forming multiple columns.
Therefore, I am dropping “Team_ID_home” and “Team_ID_away” attributes from the “nba_games_dataset” dataset.
#Dropping TEAM_ID_HOME and TEAM_ID_AWAY
nba_games_dataset <- nba_games_dataset %>% subset( select= -c(TEAM_ID_home,TEAM_ID_away) )
head(nba_games_dataset)## GAME_ID HOME_TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID PLAYER_NAME
## 1 21900895 1610612766 CHA Charlotte 1628970 Miles Bridges
## 2 21900895 1610612766 CHA Charlotte 1629023 P.J. Washington
## 3 21900895 1610612766 CHA Charlotte 202687 Bismack Biyombo
## 4 21900895 1610612766 CHA Charlotte 1628984 Devonte' Graham
## 5 21900895 1610612766 CHA Charlotte 1626179 Terry Rozier
## 6 21900895 1610612766 CHA Charlotte 1628998 Cody Martin
## START_POSITION COMMENT MIN FGM FGA FG_PCT FG3M FG3A FG3_PCT FTM FTA FT_PCT
## 1 F 35:15 3 13 0.231 1 7 0.143 0 0 0
## 2 F 31:52 5 14 0.357 1 8 0.125 1 1 1
## 3 C 22:07 2 8 0.250 0 0 0.000 4 4 1
## 4 G 32:21 7 18 0.389 3 8 0.375 0 1 0
## 5 G 36:05 6 18 0.333 0 3 0.000 1 1 1
## 6 29:08 4 8 0.500 2 5 0.400 1 1 1
## OREB DREB REB AST STL BLK TO PF PTS PLUS_MINUS GAME_DATE_EST GAME_STATUS_TEXT
## 1 1 3 4 2 2 2 2 2 7 -4 2020-03-01 Final
## 2 1 5 6 3 0 2 2 3 12 -13 2020-03-01 Final
## 3 4 5 9 2 0 2 1 3 8 -15 2020-03-01 Final
## 4 0 2 2 3 1 0 0 2 17 -14 2020-03-01 Final
## 5 2 1 3 4 1 0 2 2 13 -20 2020-03-01 Final
## 6 0 5 5 2 0 1 1 2 11 2 2020-03-01 Final
## VISITOR_TEAM_ID SEASON PTS_home FG_PCT_home FT_PCT_home FG3_PCT_home AST_home
## 1 1610612749 2019 85 0.354 0.9 0.229 22
## 2 1610612749 2019 85 0.354 0.9 0.229 22
## 3 1610612749 2019 85 0.354 0.9 0.229 22
## 4 1610612749 2019 85 0.354 0.9 0.229 22
## 5 1610612749 2019 85 0.354 0.9 0.229 22
## 6 1610612749 2019 85 0.354 0.9 0.229 22
## REB_home PTS_away FG_PCT_away FT_PCT_away FG3_PCT_away AST_away REB_away
## 1 47 93 0.402 0.762 0.226 20 61
## 2 47 93 0.402 0.762 0.226 20 61
## 3 47 93 0.402 0.762 0.226 20 61
## 4 47 93 0.402 0.762 0.226 20 61
## 5 47 93 0.402 0.762 0.226 20 61
## 6 47 93 0.402 0.762 0.226 20 61
## HOME_TEAM_WINS
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0The “games_details.csv” dataset is not tidy because “COMMENT” is not really a variable.
According to Tidy Principle,
Each variable should form a column, wheareas comment is not a variable
Comment is absent in almost all the rows, for it to be considered as part of a table
To tidy this problem, droping “COMMENT” column from the joined “nba_games_dataset” dataset.
nba_games_dataset <- nba_games_dataset %>% subset( select= -c(COMMENT) )
head(nba_games_dataset)## GAME_ID HOME_TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID PLAYER_NAME
## 1 21900895 1610612766 CHA Charlotte 1628970 Miles Bridges
## 2 21900895 1610612766 CHA Charlotte 1629023 P.J. Washington
## 3 21900895 1610612766 CHA Charlotte 202687 Bismack Biyombo
## 4 21900895 1610612766 CHA Charlotte 1628984 Devonte' Graham
## 5 21900895 1610612766 CHA Charlotte 1626179 Terry Rozier
## 6 21900895 1610612766 CHA Charlotte 1628998 Cody Martin
## START_POSITION MIN FGM FGA FG_PCT FG3M FG3A FG3_PCT FTM FTA FT_PCT OREB
## 1 F 35:15 3 13 0.231 1 7 0.143 0 0 0 1
## 2 F 31:52 5 14 0.357 1 8 0.125 1 1 1 1
## 3 C 22:07 2 8 0.250 0 0 0.000 4 4 1 4
## 4 G 32:21 7 18 0.389 3 8 0.375 0 1 0 0
## 5 G 36:05 6 18 0.333 0 3 0.000 1 1 1 2
## 6 29:08 4 8 0.500 2 5 0.400 1 1 1 0
## DREB REB AST STL BLK TO PF PTS PLUS_MINUS GAME_DATE_EST GAME_STATUS_TEXT
## 1 3 4 2 2 2 2 2 7 -4 2020-03-01 Final
## 2 5 6 3 0 2 2 3 12 -13 2020-03-01 Final
## 3 5 9 2 0 2 1 3 8 -15 2020-03-01 Final
## 4 2 2 3 1 0 0 2 17 -14 2020-03-01 Final
## 5 1 3 4 1 0 2 2 13 -20 2020-03-01 Final
## 6 5 5 2 0 1 1 2 11 2 2020-03-01 Final
## VISITOR_TEAM_ID SEASON PTS_home FG_PCT_home FT_PCT_home FG3_PCT_home AST_home
## 1 1610612749 2019 85 0.354 0.9 0.229 22
## 2 1610612749 2019 85 0.354 0.9 0.229 22
## 3 1610612749 2019 85 0.354 0.9 0.229 22
## 4 1610612749 2019 85 0.354 0.9 0.229 22
## 5 1610612749 2019 85 0.354 0.9 0.229 22
## 6 1610612749 2019 85 0.354 0.9 0.229 22
## REB_home PTS_away FG_PCT_away FT_PCT_away FG3_PCT_away AST_away REB_away
## 1 47 93 0.402 0.762 0.226 20 61
## 2 47 93 0.402 0.762 0.226 20 61
## 3 47 93 0.402 0.762 0.226 20 61
## 4 47 93 0.402 0.762 0.226 20 61
## 5 47 93 0.402 0.762 0.226 20 61
## 6 47 93 0.402 0.762 0.226 20 61
## HOME_TEAM_WINS
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0“MIN” is the total time played by a player. Where the minutes are stored as hours, minutes and seconds concatenated by “:”
According to Tidy Principle,
- Each variable should form a column, whereas MIN contains multiples variables stored in one column.
To tidy this problem, dividing “MIN” column into “HOURS” and “MINUTES” COLUMNS using “:” as the separator.
nba_games_dataset <- nba_games_dataset %>% separate(MIN, into = c("HOURS", "MINUTES"), sep = ":")
head(nba_games_dataset)## GAME_ID HOME_TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID PLAYER_NAME
## 1 21900895 1610612766 CHA Charlotte 1628970 Miles Bridges
## 2 21900895 1610612766 CHA Charlotte 1629023 P.J. Washington
## 3 21900895 1610612766 CHA Charlotte 202687 Bismack Biyombo
## 4 21900895 1610612766 CHA Charlotte 1628984 Devonte' Graham
## 5 21900895 1610612766 CHA Charlotte 1626179 Terry Rozier
## 6 21900895 1610612766 CHA Charlotte 1628998 Cody Martin
## START_POSITION HOURS MINUTES FGM FGA FG_PCT FG3M FG3A FG3_PCT FTM FTA FT_PCT
## 1 F 35 15 3 13 0.231 1 7 0.143 0 0 0
## 2 F 31 52 5 14 0.357 1 8 0.125 1 1 1
## 3 C 22 07 2 8 0.250 0 0 0.000 4 4 1
## 4 G 32 21 7 18 0.389 3 8 0.375 0 1 0
## 5 G 36 05 6 18 0.333 0 3 0.000 1 1 1
## 6 29 08 4 8 0.500 2 5 0.400 1 1 1
## OREB DREB REB AST STL BLK TO PF PTS PLUS_MINUS GAME_DATE_EST GAME_STATUS_TEXT
## 1 1 3 4 2 2 2 2 2 7 -4 2020-03-01 Final
## 2 1 5 6 3 0 2 2 3 12 -13 2020-03-01 Final
## 3 4 5 9 2 0 2 1 3 8 -15 2020-03-01 Final
## 4 0 2 2 3 1 0 0 2 17 -14 2020-03-01 Final
## 5 2 1 3 4 1 0 2 2 13 -20 2020-03-01 Final
## 6 0 5 5 2 0 1 1 2 11 2 2020-03-01 Final
## VISITOR_TEAM_ID SEASON PTS_home FG_PCT_home FT_PCT_home FG3_PCT_home AST_home
## 1 1610612749 2019 85 0.354 0.9 0.229 22
## 2 1610612749 2019 85 0.354 0.9 0.229 22
## 3 1610612749 2019 85 0.354 0.9 0.229 22
## 4 1610612749 2019 85 0.354 0.9 0.229 22
## 5 1610612749 2019 85 0.354 0.9 0.229 22
## 6 1610612749 2019 85 0.354 0.9 0.229 22
## REB_home PTS_away FG_PCT_away FT_PCT_away FG3_PCT_away AST_away REB_away
## 1 47 93 0.402 0.762 0.226 20 61
## 2 47 93 0.402 0.762 0.226 20 61
## 3 47 93 0.402 0.762 0.226 20 61
## 4 47 93 0.402 0.762 0.226 20 61
## 5 47 93 0.402 0.762 0.226 20 61
## 6 47 93 0.402 0.762 0.226 20 61
## HOME_TEAM_WINS
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0Tidy & Manipulate Data II
Mutating a new variable called “Offensive_Rebound_To_Defensive_Rebound_Ratio” that measures offensive rebounds as a comparison to defensive rebounds. The value “0.00001” is added in the denominator so that ratio doesn’t turn to the infinity value.
#This disables the scientific notation
options(scipen = 999)
#Mutating the variable "Offensive_Rebound_To_Defensive_Rebound_Ratio"
nba_games_dataset <- nba_games_dataset %>% mutate(Offensive_Rebound_To_Defensive_Rebound_Ratio = round((OREB/(DREB+0.00001)),2))
head(nba_games_dataset)## GAME_ID HOME_TEAM_ID TEAM_ABBREVIATION TEAM_CITY PLAYER_ID PLAYER_NAME
## 1 21900895 1610612766 CHA Charlotte 1628970 Miles Bridges
## 2 21900895 1610612766 CHA Charlotte 1629023 P.J. Washington
## 3 21900895 1610612766 CHA Charlotte 202687 Bismack Biyombo
## 4 21900895 1610612766 CHA Charlotte 1628984 Devonte' Graham
## 5 21900895 1610612766 CHA Charlotte 1626179 Terry Rozier
## 6 21900895 1610612766 CHA Charlotte 1628998 Cody Martin
## START_POSITION HOURS MINUTES FGM FGA FG_PCT FG3M FG3A FG3_PCT FTM FTA FT_PCT
## 1 F 35 15 3 13 0.231 1 7 0.143 0 0 0
## 2 F 31 52 5 14 0.357 1 8 0.125 1 1 1
## 3 C 22 07 2 8 0.250 0 0 0.000 4 4 1
## 4 G 32 21 7 18 0.389 3 8 0.375 0 1 0
## 5 G 36 05 6 18 0.333 0 3 0.000 1 1 1
## 6 29 08 4 8 0.500 2 5 0.400 1 1 1
## OREB DREB REB AST STL BLK TO PF PTS PLUS_MINUS GAME_DATE_EST GAME_STATUS_TEXT
## 1 1 3 4 2 2 2 2 2 7 -4 2020-03-01 Final
## 2 1 5 6 3 0 2 2 3 12 -13 2020-03-01 Final
## 3 4 5 9 2 0 2 1 3 8 -15 2020-03-01 Final
## 4 0 2 2 3 1 0 0 2 17 -14 2020-03-01 Final
## 5 2 1 3 4 1 0 2 2 13 -20 2020-03-01 Final
## 6 0 5 5 2 0 1 1 2 11 2 2020-03-01 Final
## VISITOR_TEAM_ID SEASON PTS_home FG_PCT_home FT_PCT_home FG3_PCT_home AST_home
## 1 1610612749 2019 85 0.354 0.9 0.229 22
## 2 1610612749 2019 85 0.354 0.9 0.229 22
## 3 1610612749 2019 85 0.354 0.9 0.229 22
## 4 1610612749 2019 85 0.354 0.9 0.229 22
## 5 1610612749 2019 85 0.354 0.9 0.229 22
## 6 1610612749 2019 85 0.354 0.9 0.229 22
## REB_home PTS_away FG_PCT_away FT_PCT_away FG3_PCT_away AST_away REB_away
## 1 47 93 0.402 0.762 0.226 20 61
## 2 47 93 0.402 0.762 0.226 20 61
## 3 47 93 0.402 0.762 0.226 20 61
## 4 47 93 0.402 0.762 0.226 20 61
## 5 47 93 0.402 0.762 0.226 20 61
## 6 47 93 0.402 0.762 0.226 20 61
## HOME_TEAM_WINS Offensive_Rebound_To_Defensive_Rebound_Ratio
## 1 0 0.33
## 2 0 0.20
## 3 0 0.80
## 4 0 0.00
## 5 0 2.00
## 6 0 0.00Analysing Data.
Displaying the attributes in the data set to understand the data types in the merged data set
str(nba_games_dataset)## 'data.frame': 288643 obs. of 46 variables:
## $ GAME_ID : int 21900895 21900895 21900895 21900895 21900895 21900895 21900895 21900895 21900895 21900895 ...
## $ HOME_TEAM_ID : int 1610612766 1610612766 1610612766 1610612766 1610612766 1610612766 1610612766 1610612766 1610612766 1610612766 ...
## $ TEAM_ABBREVIATION : chr "CHA" "CHA" "CHA" "CHA" ...
## $ TEAM_CITY : chr "Charlotte" "Charlotte" "Charlotte" "Charlotte" ...
## $ PLAYER_ID : int 1628970 1629023 202687 1628984 1626179 1628998 1629667 1626195 1628997 201587 ...
## $ PLAYER_NAME : chr "Miles Bridges" "P.J. Washington" "Bismack Biyombo" "Devonte' Graham" ...
## $ START_POSITION : chr "F" "F" "C" "G" ...
## $ HOURS : chr "35" "31" "22" "32" ...
## $ MINUTES : chr "15" "52" "07" "21" ...
## $ FGM : num 3 5 2 7 6 4 1 4 2 NA ...
## $ FGA : num 13 14 8 18 18 8 2 9 6 NA ...
## $ FG_PCT : num 0.231 0.357 0.25 0.389 0.333 0.5 0.5 0.444 0.333 NA ...
## $ FG3M : num 1 1 0 3 0 2 0 0 1 NA ...
## $ FG3A : num 7 8 0 8 3 5 1 1 2 NA ...
## $ FG3_PCT : num 0.143 0.125 0 0.375 0 0.4 0 0 0.5 NA ...
## $ FTM : num 0 1 4 0 1 1 0 2 0 NA ...
## $ FTA : num 0 1 4 1 1 1 0 2 0 NA ...
## $ FT_PCT : num 0 1 1 0 1 1 0 1 0 NA ...
## $ OREB : num 1 1 4 0 2 0 0 3 1 NA ...
## $ DREB : num 3 5 5 2 1 5 1 10 3 NA ...
## $ REB : num 4 6 9 2 3 5 1 13 4 NA ...
## $ AST : num 2 3 2 3 4 2 1 4 1 NA ...
## $ STL : num 2 0 0 1 1 0 0 2 1 NA ...
## $ BLK : num 2 2 2 0 0 1 1 0 0 NA ...
## $ TO : num 2 2 1 0 2 1 0 1 1 NA ...
## $ PF : num 2 3 3 2 2 2 1 0 3 NA ...
## $ PTS : num 7 12 8 17 13 11 2 10 5 NA ...
## $ PLUS_MINUS : num -4 -13 -15 -14 -20 2 0 11 13 NA ...
## $ GAME_DATE_EST : chr "2020-03-01" "2020-03-01" "2020-03-01" "2020-03-01" ...
## $ GAME_STATUS_TEXT : chr "Final" "Final" "Final" "Final" ...
## $ VISITOR_TEAM_ID : int 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 1610612749 ...
## $ SEASON : int 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 ...
## $ PTS_home : num 85 85 85 85 85 85 85 85 85 85 ...
## $ FG_PCT_home : num 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 ...
## $ FT_PCT_home : num 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 ...
## $ FG3_PCT_home : num 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 ...
## $ AST_home : num 22 22 22 22 22 22 22 22 22 22 ...
## $ REB_home : num 47 47 47 47 47 47 47 47 47 47 ...
## $ PTS_away : num 93 93 93 93 93 93 93 93 93 93 ...
## $ FG_PCT_away : num 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 ...
## $ FT_PCT_away : num 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 ...
## $ FG3_PCT_away : num 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 ...
## $ AST_away : num 20 20 20 20 20 20 20 20 20 20 ...
## $ REB_away : num 61 61 61 61 61 61 61 61 61 61 ...
## $ HOME_TEAM_WINS : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Offensive_Rebound_To_Defensive_Rebound_Ratio: num 0.33 0.2 0.8 0 2 0 0 0.3 0.33 NA ...GAME_ID, HOME_TEAM_ID,VISITOR_TEAM_ID, PLAYER_ID are not factors in the merged dataset, which needs to be converted into a factor because Identification numbers are factors.
Checking the Data Type
a <- nba_games_dataset$GAME_ID %>% class()
b <- nba_games_dataset$HOME_TEAM_ID %>% class()
c <- nba_games_dataset$VISITOR_TEAM_ID %>% class()
d <- nba_games_dataset$PLAYER_ID %>% class()
print(c(a,b,c,d))## [1] "integer" "integer" "integer" "integer"After Data Type Conversion
nba_games_dataset$GAME_ID <- nba_games_dataset$GAME_ID %>% as.factor()
nba_games_dataset$HOME_TEAM_ID <- nba_games_dataset$HOME_TEAM_ID %>% as.factor()
nba_games_dataset$VISITOR_TEAM_ID <- nba_games_dataset$VISITOR_TEAM_ID %>% as.factor()
nba_games_dataset$PLAYER_ID <- nba_games_dataset$PLAYER_ID %>% as.integer() %>% as.factor()
a <- nba_games_dataset$GAME_ID %>% class()
b <- nba_games_dataset$HOME_TEAM_ID %>% class()
c <- nba_games_dataset$VISITOR_TEAM_ID %>% class()
d <- nba_games_dataset$PLAYER_ID %>% class()
print(c(a,b,c,d))## [1] "factor" "factor" "factor" "factor"TEAM_CITY, TEAM_ABBREVIATION,PLAYER_NAME are all character variables. So no changes needs to be made.
#Checking the data type
nba_games_dataset$TEAM_CITY %>% class()## [1] "character"nba_games_dataset$TEAM_ABBREVIATION %>% class()## [1] "character"nba_games_dataset$PLAYER_NAME %>% class()## [1] "character"START_POSITION is a character variable in the merged dataset. In reality it is a ordered factor variable where positions are ranked by height. Guard(G)Forward(F)<Center(C). G is the smallest player on the team and C is the largest player on the team. Therefore START POSITION needs to be converted to a ordered factor variable.
Checking the class of START_POSITION
nba_games_dataset$START_POSITION %>% class()## [1] "character"Converting START_POSITION to an ordered factor variable and checking the levels of the factor variable.
nba_games_dataset$START_POSITION<-factor(nba_games_dataset$START_POSITION ,levels=c("G", "F", "C"),ordered=TRUE)
head(nba_games_dataset$START_POSITION)## [1] F F C G G <NA>
## Levels: G < F < C#Checking the levels of the factor variable
levels(nba_games_dataset$START_POSITION)## [1] "G" "F" "C"HOURS and MINUTES are all characters variables in the merged data set.
#Checking the data type
nba_games_dataset$HOURS %>% class()## [1] "character"nba_games_dataset$MINUTES %>% class()## [1] "character"HOURS and MINUTES are all numeric variables, more specifically, Integer variables logically.
nba_games_dataset$HOURS<-nba_games_dataset$HOURS %>% as.numeric()
nba_games_dataset$MINUTES<-nba_games_dataset$MINUTES %>% as.numeric()
nba_games_dataset$HOURS %>% class()## [1] "numeric"nba_games_dataset$MINUTES %>% class()## [1] "numeric"FGM,FGA,FG3M,FTM,FTA,OREB,DREB,REB,AST,STL,BLK,TO, PF,PTS,PLUS_MINUS,PTS_home,AST_home,REB_home,PTS_away,AST_away,REB_away are double variables(i.e. numeric) in the merged dataset. Therefore no data type conversions needs to be made.
a <- nba_games_dataset$FGM %>% class()
b <- nba_games_dataset$FGA %>% class()
c <- nba_games_dataset$FG3M %>% class()
d <- nba_games_dataset$FTM %>% class()
e <- nba_games_dataset$FTA %>% class()
f <- nba_games_dataset$OREB %>% class()
g <- nba_games_dataset$DREB %>% class()
h <- nba_games_dataset$REB %>% class()
i <- nba_games_dataset$AST%>% class()
j <- nba_games_dataset$STL %>% class()
k <- nba_games_dataset$BLK %>% class()
l <- nba_games_dataset$TO%>% class()
m <- nba_games_dataset$PF %>% class()
n <- nba_games_dataset$PTS %>% class()
o <- nba_games_dataset$PLUS_MINUS %>% class()
p <- nba_games_dataset$PTS_home %>% class()
q <- nba_games_dataset$AST_home%>% class()
r <- nba_games_dataset$REB_home %>% class()
s <- nba_games_dataset$PTS_away %>% class()
t <- nba_games_dataset$AST_away%>% class()
u <- nba_games_dataset$REB_away %>% class()
print(c(a,b,c,d,e,f,g,h,i,j,l,m,n,o,p,q,r,s,t,u))## [1] "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## [8] "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## [15] "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"FG_PCT,FG3_PCT,FT_PCT,FT_PCT_home,FG3_PCT_home,FT_PCT_away,FG3_PCT_away are all double variables (i.e.) because they contain percentage value.Therefore, no data type conversion need to be made.
#assigning it to individualy to print the output in one chunck while kniting
a <- nba_games_dataset$FG_PCT %>% typeof()
b <- nba_games_dataset$FG3_PCT %>% typeof()
c <- nba_games_dataset$FT_PCT %>% typeof()
d <- nba_games_dataset$FT_PCT_home %>% typeof()
e <- nba_games_dataset$FG3_PCT_home %>% typeof()
f <- nba_games_dataset$FT_PCT_away %>% typeof()
g <- nba_games_dataset$FG3_PCT_away %>% typeof()
print(c(a,b,c,d,e,f,g))## [1] "double" "double" "double" "double" "double" "double" "double"SEASON is a numeric variable in the merged dataset. In reality is a factor variable.
nba_games_dataset$SEASON %>% class()## [1] "integer"Converting the SEASON variable to factor variable
nba_games_dataset$SEASON<-nba_games_dataset$SEASON %>% as.factor()
nba_games_dataset$SEASON %>% class() ## [1] "factor"GAME_STATUS_TEXT is a character variable in the merged dataset. However, it is a factor variable with “FINAL” being one of the states. The other states might include “HALF-TIME” and others
nba_games_dataset$GAME_STATUS_TEXT %>% class() ## [1] "character"Converting the GAME_STATUS_TEXT variable to factor variable
nba_games_dataset$GAME_STATUS_TEXT<-nba_games_dataset$GAME_STATUS_TEXT %>% as.factor()
nba_games_dataset$GAME_STATUS_TEXT %>% class() ## [1] "factor"HOME_TEAM_WINS is a numeric variable is the merged dataset. However it is encoded ordered factor where 0 means loss and 1 means WIN.
The hierarchy is LOSS<WIN
nba_games_dataset$HOME_TEAM_WINS %>% class()## [1] "integer"Changing it to the right hierarchy.
nba_games_dataset$HOME_TEAM_WINS <- factor(nba_games_dataset$HOME_TEAM_WINS,levels = c(0,1),labels = c("LOSS","WIN"),ordered = TRUE)
levels(nba_games_dataset$HOME_TEAM_WINS )## [1] "LOSS" "WIN"nba_games_dataset$HOME_TEAM_WINS %>% class()## [1] "ordered" "factor"GAME_DATE_EST is a date variable in the merged data set, so no conversion is needed in the data set.
nba_games_dataset$GAME_DATE_EST %>% class()## [1] "character"The mutated variable Offensive_Rebound_To_Defensive_Rebound_Ratio is a ratio, it must be in the data type must be “double” which it already is in the original dataset.
nba_games_dataset$Offensive_Rebound_To_Defensive_Rebound_Ratio %>% typeof()## [1] "double"Checking all the data types of the merged “nba_games_dataset” after data type conversion.
str(nba_games_dataset)## 'data.frame': 288643 obs. of 46 variables:
## $ GAME_ID : Factor w/ 23096 levels "10300001","10300002",..: 21754 21754 21754 21754 21754 21754 21754 21754 21754 21754 ...
## $ HOME_TEAM_ID : Factor w/ 30 levels "1610612737","1610612738",..: 30 30 30 30 30 30 30 30 30 30 ...
## $ TEAM_ABBREVIATION : chr "CHA" "CHA" "CHA" "CHA" ...
## $ TEAM_CITY : chr "Charlotte" "Charlotte" "Charlotte" "Charlotte" ...
## $ PLAYER_ID : Factor w/ 2236 levels "15","42","43",..: 1974 2023 1198 1987 1639 1999 2165 1654 1998 954 ...
## $ PLAYER_NAME : chr "Miles Bridges" "P.J. Washington" "Bismack Biyombo" "Devonte' Graham" ...
## $ START_POSITION : Ord.factor w/ 3 levels "G"<"F"<"C": 2 2 3 1 1 NA NA NA NA NA ...
## $ HOURS : num 35 31 22 32 36 29 9 20 23 NA ...
## $ MINUTES : num 15 52 7 21 5 8 21 21 30 NA ...
## $ FGM : num 3 5 2 7 6 4 1 4 2 NA ...
## $ FGA : num 13 14 8 18 18 8 2 9 6 NA ...
## $ FG_PCT : num 0.231 0.357 0.25 0.389 0.333 0.5 0.5 0.444 0.333 NA ...
## $ FG3M : num 1 1 0 3 0 2 0 0 1 NA ...
## $ FG3A : num 7 8 0 8 3 5 1 1 2 NA ...
## $ FG3_PCT : num 0.143 0.125 0 0.375 0 0.4 0 0 0.5 NA ...
## $ FTM : num 0 1 4 0 1 1 0 2 0 NA ...
## $ FTA : num 0 1 4 1 1 1 0 2 0 NA ...
## $ FT_PCT : num 0 1 1 0 1 1 0 1 0 NA ...
## $ OREB : num 1 1 4 0 2 0 0 3 1 NA ...
## $ DREB : num 3 5 5 2 1 5 1 10 3 NA ...
## $ REB : num 4 6 9 2 3 5 1 13 4 NA ...
## $ AST : num 2 3 2 3 4 2 1 4 1 NA ...
## $ STL : num 2 0 0 1 1 0 0 2 1 NA ...
## $ BLK : num 2 2 2 0 0 1 1 0 0 NA ...
## $ TO : num 2 2 1 0 2 1 0 1 1 NA ...
## $ PF : num 2 3 3 2 2 2 1 0 3 NA ...
## $ PTS : num 7 12 8 17 13 11 2 10 5 NA ...
## $ PLUS_MINUS : num -4 -13 -15 -14 -20 2 0 11 13 NA ...
## $ GAME_DATE_EST : chr "2020-03-01" "2020-03-01" "2020-03-01" "2020-03-01" ...
## $ GAME_STATUS_TEXT : Factor w/ 1 level "Final": 1 1 1 1 1 1 1 1 1 1 ...
## $ VISITOR_TEAM_ID : Factor w/ 30 levels "1610612737","1610612738",..: 13 13 13 13 13 13 13 13 13 13 ...
## $ SEASON : Factor w/ 17 levels "2003","2004",..: 17 17 17 17 17 17 17 17 17 17 ...
## $ PTS_home : num 85 85 85 85 85 85 85 85 85 85 ...
## $ FG_PCT_home : num 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 ...
## $ FT_PCT_home : num 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 ...
## $ FG3_PCT_home : num 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 ...
## $ AST_home : num 22 22 22 22 22 22 22 22 22 22 ...
## $ REB_home : num 47 47 47 47 47 47 47 47 47 47 ...
## $ PTS_away : num 93 93 93 93 93 93 93 93 93 93 ...
## $ FG_PCT_away : num 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 ...
## $ FT_PCT_away : num 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 ...
## $ FG3_PCT_away : num 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 ...
## $ AST_away : num 20 20 20 20 20 20 20 20 20 20 ...
## $ REB_away : num 61 61 61 61 61 61 61 61 61 61 ...
## $ HOME_TEAM_WINS : Ord.factor w/ 2 levels "LOSS"<"WIN": 1 1 1 1 1 1 1 1 1 1 ...
## $ Offensive_Rebound_To_Defensive_Rebound_Ratio: num 0.33 0.2 0.8 0 2 0 0 0.3 0.33 NA ...Missing Values
Scanning for any “NA” values in the data set as it can affect the results of analysis.
# creating a dataframe with the sum of na values in the data set
a<- data.frame(colSums(is.na (nba_games_dataset )))
a## colSums.is.na.nba_games_dataset..
## GAME_ID 0
## HOME_TEAM_ID 0
## TEAM_ABBREVIATION 0
## TEAM_CITY 0
## PLAYER_ID 0
## PLAYER_NAME 0
## START_POSITION 177959
## HOURS 46304
## MINUTES 58253
## FGM 46304
## FGA 46304
## FG_PCT 46304
## FG3M 46304
## FG3A 46304
## FG3_PCT 46304
## FTM 46304
## FTA 46304
## FT_PCT 46304
## OREB 46304
## DREB 46304
## REB 46304
## AST 46304
## STL 46304
## BLK 46304
## TO 46304
## PF 46304
## PTS 46304
## PLUS_MINUS 58253
## GAME_DATE_EST 0
## GAME_STATUS_TEXT 0
## VISITOR_TEAM_ID 0
## SEASON 0
## PTS_home 0
## FG_PCT_home 0
## FT_PCT_home 0
## FG3_PCT_home 0
## AST_home 0
## REB_home 0
## PTS_away 0
## FG_PCT_away 0
## FT_PCT_away 0
## FG3_PCT_away 0
## AST_away 0
## REB_away 0
## HOME_TEAM_WINS 0
## Offensive_Rebound_To_Defensive_Rebound_Ratio 46304From the output of the columns and their missing values are as follows:
START_POSITION - 177959, HOURS - 58906, MINUTES - 58906, SECONDS - 58906, FGM - 46304, FGA - 46304, FG_PCT - 46304, FG3M - 46304, FG3A - 46304, FG3_PCT - 46304, FTM - 46304, FTA - 46304, FT_PCT - 46304, OREB - 46304, DREB - 46304, REB - 46304, AST - 46304, STL - 46304, BLK - 46304, TO - 46304, PF - 46304, PTS - 46304, PLUS_MINUS - 58253.
As it is seen that major columns have a missing values of 46304 which would not add any value and if replaced by any other value it would give wrong results while analysis and hence omitting these rows.
# dropping all the rows with na values
nba_games_dataset<- nba_games_dataset %>% drop_na(FGM)
#Checking the dimensions after dropping the all the rows with NA values
dim(nba_games_dataset)## [1] 242339 46# checking the missing values
b<- data.frame( colSums(is.na(nba_games_dataset)))left with na values from
START_POSITION - 131655,
HOURS - 12602,
MINUTES - 12602,
SECONDS - 12602,
PLUS_MINUS - 11949,
As the time column was split into hour, minute, seconds all of the columns have the same number o missing values and since the hours played for each match are almost the same, replacing it with mean values of the columns.
# replacing the hour, minutes, column.
nba_games_dataset$HOURS[is.na(nba_games_dataset$HOURS)] <- mean(nba_games_dataset$HOURS, na.rm =TRUE)
nba_games_dataset$MINUTES[is.na(nba_games_dataset$MINUTES)] <- mean(nba_games_dataset$MINUTES, na.rm =TRUE)As the start position has many missing values and the guards(“G”) can play small Forward position which is “F”, and Center(“C”) players can also play in the power Forward position which is “F”, hence replacing the na values with “F”
# checking the levels of the column
levels(nba_games_dataset$START_POSITION)## [1] "G" "F" "C"# replacing
nba_games_dataset$START_POSITION[is.na(nba_games_dataset$START_POSITION)] <- "F"
# checking if it is factor
is.factor(nba_games_dataset$START_POSITION)## [1] TRUE# Checking if all the na values were replaced
sum(is.na(nba_games_dataset$START_POSITION))## [1] 0The column plus_minus is the performance of the players and is replaced with 0 as it can be considered as neutral because positive values indicate good performance and negative values indicate bad performance of a player.
# replacing
nba_games_dataset$PLUS_MINUS[is.na(nba_games_dataset$PLUS_MINUS)] <- 0
# checking if all the na values are replaced.
sum(is.na(nba_games_dataset))## [1] 0# checking if there are any missing values in the data set
bb<- data.frame( colSums(is.na(nba_games_dataset)))
sum(is.na(bb))## [1] 0From the last output it can be seen that the data set does not have any missing values
Tidying the character variables
The strip.white = True was used while reading the data set which removes any white space in the data set but the data set contains in the characters. This ensures that there are no white spaces in the character columns.
nba_games_dataset$TEAM_ABBREVIATION <- str_replace_all(nba_games_dataset$TEAM_ABBREVIATION, "[\r\n]" , "")
nba_games_dataset$TEAM_CITY <- str_replace_all(nba_games_dataset$TEAM_CITY, "[\r\n]" , "")
nba_games_dataset$PLAYER_NAME <- str_replace_all(nba_games_dataset$PLAYER_NAME, "[\r\n]" , "")
nba_games_dataset$GAME_DATE_EST <- str_replace_all(nba_games_dataset$GAME_DATE_EST, "[\r\n]" , "")Analysing Outliers
Scanning for outliers in all of the numeric columns.
# creating a data set with only the numerical columns called d
d<-data.frame(select_if(nba_games_dataset, is.numeric))
str(d)## 'data.frame': 242339 obs. of 34 variables:
## $ HOURS : num 35 31 22 32 36 29 9 20 23 22 ...
## $ MINUTES : num 15 52 7 21 5 8 21 21 30 59 ...
## $ FGM : num 3 5 2 7 6 4 1 4 2 4 ...
## $ FGA : num 13 14 8 18 18 8 2 9 6 8 ...
## $ FG_PCT : num 0.231 0.357 0.25 0.389 0.333 0.5 0.5 0.444 0.333 0.5 ...
## $ FG3M : num 1 1 0 3 0 2 0 0 1 1 ...
## $ FG3A : num 7 8 0 8 3 5 1 1 2 2 ...
## $ FG3_PCT : num 0.143 0.125 0 0.375 0 0.4 0 0 0.5 0.5 ...
## $ FTM : num 0 1 4 0 1 1 0 2 0 0 ...
## $ FTA : num 0 1 4 1 1 1 0 2 0 0 ...
## $ FT_PCT : num 0 1 1 0 1 1 0 1 0 0 ...
## $ OREB : num 1 1 4 0 2 0 0 3 1 3 ...
## $ DREB : num 3 5 5 2 1 5 1 10 3 3 ...
## $ REB : num 4 6 9 2 3 5 1 13 4 6 ...
## $ AST : num 2 3 2 3 4 2 1 4 1 1 ...
## $ STL : num 2 0 0 1 1 0 0 2 1 1 ...
## $ BLK : num 2 2 2 0 0 1 1 0 0 2 ...
## $ TO : num 2 2 1 0 2 1 0 1 1 2 ...
## $ PF : num 2 3 3 2 2 2 1 0 3 3 ...
## $ PTS : num 7 12 8 17 13 11 2 10 5 9 ...
## $ PLUS_MINUS : num -4 -13 -15 -14 -20 2 0 11 13 -9 ...
## $ PTS_home : num 85 85 85 85 85 85 85 85 85 91 ...
## $ FG_PCT_home : num 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.364 ...
## $ FT_PCT_home : num 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.4 ...
## $ FG3_PCT_home : num 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.229 0.31 ...
## $ AST_home : num 22 22 22 22 22 22 22 22 22 19 ...
## $ REB_home : num 47 47 47 47 47 47 47 47 47 57 ...
## $ PTS_away : num 93 93 93 93 93 93 93 93 93 111 ...
## $ FG_PCT_away : num 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.468 ...
## $ FT_PCT_away : num 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.762 0.632 ...
## $ FG3_PCT_away : num 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.275 ...
## $ AST_away : num 20 20 20 20 20 20 20 20 20 28 ...
## $ REB_away : num 61 61 61 61 61 61 61 61 61 56 ...
## $ Offensive_Rebound_To_Defensive_Rebound_Ratio: num 0.33 0.2 0.8 0 2 0 0 0.3 0.33 1 ...Plotting the box-plot to visualize the outliers.
#Plotting the boxplot
boxplot(d)
Since the box-plot does not detail display all the columns and the outliers clearly, it is nessary to plot individual box plot to identify any kind of outliers. Also plotted the histograms of the data set to better understand the outliers.
par(mfrow=c(3,2))
# plotting the histogram
for(i in colnames(nba_games_dataset[,c("HOURS","MINUTES","FGM","FGA","FG_PCT","FG3M","FG3A","FG3_PCT","FTM","FTA","FT_PCT","OREB","DREB","REB","AST","STL","BLK","TO","PF","PTS","PLUS_MINUS","PTS_home","FG_PCT_home","FT_PCT_home","FG3_PCT_home","AST_home","REB_home","PTS_away","FG_PCT_away","FT_PCT_away","FG3_PCT_away","AST_away","REB_away","Offensive_Rebound_To_Defensive_Rebound_Ratio")]))
{
hist(nba_games_dataset[,i],main = colnames(nba_games_dataset[i]))
boxplot(nba_games_dataset[i])
title(colnames(nba_games_dataset[i]))
}
From the box-plots and histograms it can be seen that all the numerical columns except PLUS_MINUS,PTS_HOme,FG_PCT_home,REB_home,PTS_away and FG_PCT_away are all skewed. Since PLUS_MINUS,PTS_HOme,FG_PCT_home,REB_home,PTS_away and FG_PCT_away is normally distributed, we could have used the z-score to only identify the ouliers. But insted have chosen “Capping” method, as it does not require for the columns to be normally distributed, allowing us to us this method for all the numerical columns regardless of the distribution of the data.
It is seen from the box-plot, there are multiple columns with outliers, HOURS,FGM,FGA,FG3M,FG3A,,FG3_PCT,FTA,OREB,DREB.REB,AST,STL,BLK,TO,PF,PTS,PLUS_MINUS,PTS_home,FG_PCT_home,FT_PCT_home,FG3_PCT,AST_home,REB_home,PTS_away,FG_PCT_away,FT_PCT_away,FG3_PCT_away,AST_away and REB_away
Eliminating these outliers would not be right for analysis since these outliers do not present any meaningful information and would not affect the data analysis of the data. The advatange of “Capping” method is that it replaces the outliers with the best value near it which makes it an appropriate method for outlier detection of all numerical columns and imputations with appropriate values.
# Defining the function for the "capping" method
cap <-function(x){ quantiles <- quantile( x, c(.05,0.25,0.75,.95) )
x[ x < quantiles[2] -1.5*IQR(x) ] <- quantiles[1]
x[ x > quantiles[3] +1.5*IQR(x) ] <- quantiles[4]
x }
par(mfrow=c(3,2))
#Selecting the numerical columns
for (i in colnames(nba_games_dataset[,c("HOURS","MINUTES","FGM","FGA","FG_PCT","FG3M","FG3A","FG3_PCT","FTM","FTA","FT_PCT","OREB","DREB","REB","AST","STL","BLK","TO","PF","PTS","PLUS_MINUS","PTS_home","FG_PCT_home","FT_PCT_home","FG3_PCT_home","AST_home","REB_home","PTS_away","FG_PCT_away","FT_PCT_away","FG3_PCT_away","AST_away","REB_away","Offensive_Rebound_To_Defensive_Rebound_Ratio")]))
{
nba_games_dataset[,c("HOURS","MINUTES","FGM","FGA","FG_PCT","FG3M","FG3A","FG3_PCT","FTM","FTA","FT_PCT","OREB","DREB","REB","AST","STL","BLK","TO","PF","PTS","PLUS_MINUS","PTS_home","FG_PCT_home","FT_PCT_home","FG3_PCT_home","AST_home","REB_home","PTS_away","FG_PCT_away","FT_PCT_away","FG3_PCT_away","AST_away","REB_away","Offensive_Rebound_To_Defensive_Rebound_Ratio")] <- sapply( nba_games_dataset[,c("HOURS","MINUTES","FGM","FGA","FG_PCT","FG3M","FG3A","FG3_PCT","FTM","FTA","FT_PCT","OREB","DREB","REB","AST","STL","BLK","TO","PF","PTS","PLUS_MINUS","PTS_home","FG_PCT_home","FT_PCT_home","FG3_PCT_home","AST_home","REB_home","PTS_away","FG_PCT_away","FT_PCT_away","FG3_PCT_away","AST_away","REB_away","Offensive_Rebound_To_Defensive_Rebound_Ratio")], FUN = cap)
}
#Plot the histograms and box-plots
for(i in colnames(nba_games_dataset[,c("HOURS","MINUTES","FGM","FGA","FG_PCT","FG3M","FG3A","FG3_PCT","FTM","FTA","FT_PCT","OREB","DREB","REB","AST","STL","BLK","TO","PF","PTS","PLUS_MINUS","PTS_home","FG_PCT_home","FT_PCT_home","FG3_PCT_home","AST_home","REB_home","PTS_away","FG_PCT_away","FT_PCT_away","FG3_PCT_away","AST_away","REB_away","Offensive_Rebound_To_Defensive_Rebound_Ratio")]))
{
hist(nba_games_dataset[,i],main = colnames(nba_games_dataset[i]))
boxplot(nba_games_dataset[i])
title(colnames(nba_games_dataset[i]))
}
From the output of the box-plots above, it can be seen that there are no outliers remaining in almost all of the numerical columns, except for columns FG3M,FG3_PCT,STL and Offensive_Rebound_To_Defensive_Rebound Ratio.. It can be also seen that after the outliers are removed all the numerical columns except columns MINUTES,FGM,FGA,FG_PCT,FG3M,FG3A,FG3PCT,FTM,FTM,FTA,FT_PCT,OREB,DREB,AST,STL,TO,PF,PTS and Offensive_Rebound_To_Defensive_Rebound Ratio are not normally distributed.
Data Transforming
Applying Box-Cox transformation to the columns to reduce the skewness of the numerical columns.Box Cox Transformation is used instead it can be used to reduce both left and right skewness of the data.MINUTES, FGM, FGA,FG_PCT ,FG3M ,FG3A, FG3PCT, FTM, FTA, FT_PCT, OREB,DREB,AST,STL,TO,PF,PTS and Offensive_Rebound_To_Defensive_Rebound_Ratio which are not normally distributed.This is because most machine learning models, for example regression models, require the data to be normalized.
BoxCox transformation is applied to reduce the skewness of the columns that are normally distributed.
par(mfrow=c(3,2))
hist(nba_games_dataset$MINUTES,main = "Before Box-Cox Transformation: Histogram of MINUTES")
nba_games_dataset$MINUTES<-BoxCox(nba_games_dataset$MINUTES,lambda = "auto")
hist(nba_games_dataset$MINUTES,main = "After Box Cox Transformation Histogram of MINUTES")
hist(nba_games_dataset$FGM,main = "Before Box Cox Transformation: Histogram of FGM" )
nba_games_dataset$FGM<-BoxCox(nba_games_dataset$FGM,lambda = "auto")
hist(nba_games_dataset$FGM,main = "After Box Cox Transformation: Histogram of FGM")
hist(nba_games_dataset$FGA,main = "Before Box Cox Transformation: Histogram of FGA")
nba_games_dataset$FGA<-BoxCox(nba_games_dataset$FGA,lambda = "auto")
hist(nba_games_dataset$FGA,main = "After Box Cox Transformation: Histogram of FGA")
hist(nba_games_dataset$FG_PCT,main = "Before Box Cox Transformation: Histogram of FG_PCT")
nba_games_dataset$FG_PCT<-BoxCox(nba_games_dataset$FG_PCT,lambda = "auto")
hist(nba_games_dataset$FG_PCT, main = "After Box Cox Transformation: Histogram of FG_PCT")
hist(nba_games_dataset$FG3M, main = "Before Box Cox Transformation: Histogram of FG3M")
nba_games_dataset$FG3M<-BoxCox(nba_games_dataset$FG3M,lambda = "auto")
hist(nba_games_dataset$FG3M,main="After Box Cox Transformation: Histogram of FG3M")
hist(nba_games_dataset$FG3A,main="Before Box Cox Transformation: Histogram of FG3A")
nba_games_dataset$FG3A<-BoxCox(nba_games_dataset$FG3A,lambda = "auto")
hist(nba_games_dataset$FG3A, main="After Box Cox Transformation: Histogram of FG3A")
hist(nba_games_dataset$FG3_PCT, main="Before Box Cox Transformation: Histogram of FG3_PCT")
nba_games_dataset$FG3_PCT<-BoxCox(nba_games_dataset$FG3_PCT,lambda = "auto")
hist(nba_games_dataset$FG3_PCT, main="After Box Cox Transformation: Histogram of FG3_PCT")
hist(nba_games_dataset$FTM, main="Before Box Cox Transformation: Histogram of FTM")
nba_games_dataset$FTM<-BoxCox(nba_games_dataset$FTM,lambda = "auto")
hist(nba_games_dataset$FTM, main="After Box Cox Transformation: Histogram of FTM")
hist(nba_games_dataset$FTA, main="Before Box Cox Transformation: Histogram of FTA")
nba_games_dataset$FTA<-BoxCox(nba_games_dataset$FTA,lambda = "auto")
hist(nba_games_dataset$FTA, main="After Box Cox Transformation: Histogram of FTA")
hist(nba_games_dataset$FT_PCT, main="Before Box Cox Transformation: Histogram of FT_PCT")
nba_games_dataset$FT_PCT<-BoxCox(nba_games_dataset$FT_PCT,lambda = "auto")
hist(nba_games_dataset$FT_PCT, main="After Box Cox Transformation: Histogram of FT_PCT")
hist(nba_games_dataset$OREB, main="Before Box Cox Transformation: Histogram of OREB")
nba_games_dataset$OREB<-BoxCox(nba_games_dataset$OREB,lambda = "auto")
hist(nba_games_dataset$OREB,main="After Box Cox Transformation: Histogram of OREB")
hist(nba_games_dataset$DREB, main="Before Box Cox Transformation: Histogram of DREB")
nba_games_dataset$DREB<-BoxCox(nba_games_dataset$DREB,lambda = "auto")
hist(nba_games_dataset$DREB, main="After Box Cox Transformation: Histogram of DREB")
hist(nba_games_dataset$AST, main="Before Box Cox Transformation: Histogram of AST")
nba_games_dataset$AST<-BoxCox(nba_games_dataset$AST,lambda = "auto")
hist(nba_games_dataset$AST, main="After Box Cox Transformation: Histogram of AST")
hist(nba_games_dataset$STL, main="Before Box Cox Transformation: Histogram of STL")
nba_games_dataset$STL<-BoxCox(nba_games_dataset$STL,lambda = "auto")
hist(nba_games_dataset$STL, main="After Box Cox Transformation: Histogram of STL")
hist(nba_games_dataset$TO, main="Before Box Cox Transformation: Histogram of TO")
nba_games_dataset$TO<-BoxCox(nba_games_dataset$TO,lambda = "auto")
hist(nba_games_dataset$TO, main="After Box Cox Transformation of TO")
hist(nba_games_dataset$PF, main="After Box Cox Transformation: Histogram of PF")
nba_games_dataset$PF<-BoxCox(nba_games_dataset$PF,lambda = "auto")
hist(nba_games_dataset$PF, main="After Box Cox Transformation of PF")
hist(nba_games_dataset$PTS, main="Before Box Cox Transformation: Histogram of PTS")
nba_games_dataset$PTS<-BoxCox(nba_games_dataset$PTS,lambda = "auto")
hist(nba_games_dataset$PTS, main="After Box Cox Transformation of PTS")
hist(nba_games_dataset$Offensive_Rebound_To_Defensive_Rebound_Ratio, main="Before Box Cox Transformation: Histogram of Offensive_Rebound_To_Defensive_Rebound_Ratio")
nba_games_dataset$Offensive_Rebound_To_Defensive_Rebound_Ratio<-BoxCox(nba_games_dataset$Offensive_Rebound_To_Defensive_Rebound_Ratio,
lambda = "auto")
hist(nba_games_dataset$Offensive_Rebound_To_Defensive_Rebound_Ratio,main="After Box Cox Transformation of Offensive_Rebound_To_Defensive_Rebound_Ratio")
From the comparison of histograms before and after Box-Cox transformation, it can be seen that the skewness of the numerical columns have decreased all across the numerical columns.
Conclusion
The final “nba_games_dataset” is clean data set with no missing values.
- Almost all of the outliers were removed and replaced by the capping method.
- Finally, transformation is applied to reduce the skewness, of all numerical variables which were not normally distributed.
- In short, the data was cleaned in order to ensure the data set does not have any discrepancies relating to the NBA games 2019-2020 data set.
References
En.wikipedia.org. 2020. Rules Of Basketball. [online] Available at: https://en.wikipedia.org/wiki/Rules_of_basketball [Accessed 14 October 2020].
Kaggle.com. n.d. NBA Games Data. [online] Available at: https://www.kaggle.com/nathanlauga/nba-games?select=games.csv [Accessed 13 October 2020].
Kaggle.com. n.d. NBA Games Data. [online] Available at: https://www.kaggle.com/nathanlauga/nba-games?select=games_details.csv [Accessed 13 October 2020].
Ladd, T., 2020. NBA Official Basketball Rules And Regulations For Beginners. [online] Sportsierra. Available at: https://sportsierra.com/nba-official-basketball-rules-and-regulations/#:~:text=%20NBA%20basketball%20rules%20%201%20Regulation%20NBA,4%20Fighting%20and%20flagrant%20fouls.%20%20More%20 [Accessed 14 October 2020].