final.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data 550 Project 2\n",
    "### Names: Connor Fairbanks, Graham Kerford\n",
    "### Date: February 13, 2021"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Description of the Data\n",
    "\n",
    "The 'basketball players stats per season-49 leagues' dataset was used for this project. It comprises player data for 49 leagues from the year 1999 to present for each season. The dataset was downlaoded from [kaggle](https://www.kaggle.com/mirichoi0218/insurance/home) in January, 2020 and is available at: [https://www.kaggle.com/jacobbaruch/basketball-players-stats-per-season-49-leagues](https://www.kaggle.com/jacobbaruch/basketball-players-stats-per-season-49-leagues). In total ~11 thousand player's data was collected in 49 leagues. Due to the large amount of data available, the dataset used for this project was limited to players who played in more than 60 out of the possible 82 regular season games in only one league (the NBA). We omitted statistics from playoff games for this analysis. If a player played in more than 60 games in a season, it means they had close to a full season and did not miss an inordinate number of games due to injury. The dataset contains the following characteristics for each player:\n",
    "\n",
    "- `League`: The league that the players played in for the specified season, limited to the NBA for this analysis.\n",
    "\n",
    "- `Season`: Date of the NBA season (by year).\n",
    "\n",
    "- `Stage`: The period in the season during which the data was taken.\n",
    "\n",
    "- `Player`: The name of the player.\n",
    "\n",
    "- `Team`: The team the player played for during the season.\n",
    "\n",
    "- `GP`: Games played during the season. \n",
    "\n",
    "- `MIN`: Minutes played.\n",
    "\n",
    "- `FGM`: Field goals made.\n",
    "\n",
    "- `FGA`: Field goals attempts.\n",
    "\n",
    "- `3PM`: 3 pointers made.\n",
    "\n",
    "- `3PA`: 3 point attempts.\n",
    "\n",
    "- `FTM`: Free throws made.\n",
    "\n",
    "- `FTA`: Free throws attempts.\n",
    "\n",
    "- `TOV`: Turnovers\n",
    "\n",
    "- `PF`: Personal fouls\n",
    "\n",
    "- `ORB`: Offensive rebounds\n",
    "\n",
    "- `DRB`: Defensive rebounds\n",
    "\n",
    "- `REB`: Total rebounds\n",
    "\n",
    "- `AST`: Assists\n",
    "\n",
    "- `STL`: Steals\n",
    "\n",
    "- `BLK`: Blocks\n",
    "\n",
    "- `PTS`: Points\n",
    "\n",
    "- `Birth_year`: Year of birth\n",
    "\n",
    "- `Birth_month`: Month of birth\n",
    "\n",
    "- `Birth_date`: Birthdate\n",
    "\n",
    "- `height`: (feet - inches)\n",
    "\n",
    "- `height`: (cm)\n",
    "\n",
    "- `weight`: Weight in pounds\n",
    "\n",
    "- `weight_kg`: Weight in kilograms\n",
    "\n",
    "- `nationality`: Nationality of the player at birth\n",
    "\n",
    "- `high_school`: High school attended\n",
    "\n",
    "- `draft_round`: Draft hound\n",
    "\n",
    "- `draft_pick`: Draft pick\n",
    "\n",
    "- `draft_team`: Team drafted to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: 'dplyr'\n",
      "\n",
      "\n",
      "The following objects are masked from 'package:stats':\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "\n",
      "The following objects are masked from 'package:base':\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "\n",
      "-- \u001b[1mAttaching packages\u001b[22m --------------------------------------- tidyverse 1.3.0 --\n",
      "\n",
      "\u001b[32m<U+221A>\u001b[39m \u001b[34mtidyr  \u001b[39m 1.1.2     \u001b[32m<U+221A>\u001b[39m \u001b[34mstringr\u001b[39m 1.4.0\n",
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      "\u001b[32m<U+221A>\u001b[39m \u001b[34mpurrr  \u001b[39m 0.3.4     \n",
      "\n",
      "-- \u001b[1mConflicts\u001b[22m ------------------------------------------ tidyverse_conflicts() --\n",
      "\u001b[31mx\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31mx\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\n",
      "Warning message:\n",
      "\"package 'plotly' was built under R version 4.0.3\"\n",
      "\n",
      "Attaching package: 'plotly'\n",
      "\n",
      "\n",
      "The following object is masked from 'package:ggplot2':\n",
      "\n",
      "    last_plot\n",
      "\n",
      "\n",
      "The following object is masked from 'package:stats':\n",
      "\n",
      "    filter\n",
      "\n",
      "\n",
      "The following object is masked from 'package:graphics':\n",
      "\n",
      "    layout\n",
      "\n",
      "\n",
      "Warning message:\n",
      "\"package 'gapminder' was built under R version 4.0.3\"\n",
      "Warning message:\n",
      "\"package 'GGally' was built under R version 4.0.3\"\n",
      "Registered S3 method overwritten by 'GGally':\n",
      "  method from   \n",
      "  +.gg   ggplot2\n",
      "\n",
      "Warning message:\n",
      "\"package 'ggrepel' was built under R version 4.0.3\"\n"
     ]
    }
   ],
   "source": [
    "# Load necessary libraries\n",
    "library(dplyr) \n",
    "library(ggplot2)\n",
    "library(tibble)\n",
    "library(tidyverse)\n",
    "library(plotly)\n",
    "library(gapminder)\n",
    "library(GGally)\n",
    "library(ggrepel)\n",
    "\n",
    "# Set global theme\n",
    "my_theme <- theme_bw() +\n",
    "  theme(\n",
    "    text = element_text(size = 12),\n",
    "    panel.border = element_rect(colour = 'grey80'), \n",
    "    panel.grid.minor = element_blank(), \n",
    "    axis.title.x = element_text(margin = margin(t=10)),\n",
    "    axis.title.y = element_text(margin = margin(r=10))\n",
    "  )\n",
    "theme_set(my_theme)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read in the data: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "basketball_df <- read.csv('players_stats_by_season_full_details.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Filter the data to a more manageable size as mentioned in the description above: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "names(basketball_df)[1] <- 'League'\n",
    "NBA_data_filtered <- filter(basketball_df, Stage == 'Regular_Season' & League == 'NBA' & GP >60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploration of the data and initial thoughts:\n",
    "\n",
    "First we will look at some summary statistics and the types of data in each column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    League             Season             Stage              Player         \n",
       " Length:4245        Length:4245        Length:4245        Length:4245       \n",
       " Class :character   Class :character   Class :character   Class :character  \n",
       " Mode  :character   Mode  :character   Mode  :character   Mode  :character  \n",
       "                                                                            \n",
       "                                                                            \n",
       "                                                                            \n",
       "                                                                            \n",
       "     Team                 GP             MIN              FGM       \n",
       " Length:4245        Min.   :61.00   Min.   : 266.8   Min.   : 17.0  \n",
       " Class :character   1st Qu.:71.00   1st Qu.:1549.7   1st Qu.:198.0  \n",
       " Mode  :character   Median :76.00   Median :2029.0   Median :290.0  \n",
       "                    Mean   :75.08   Mean   :2016.8   Mean   :321.3  \n",
       "                    3rd Qu.:80.00   3rd Qu.:2485.6   3rd Qu.:419.0  \n",
       "                    Max.   :85.00   Max.   :3485.0   Max.   :978.0  \n",
       "                                                                    \n",
       "      FGA              X3PM             X3PA           FTM       \n",
       " Min.   :  49.0   Min.   :  0.00   Min.   :   0   Min.   :  6.0  \n",
       " 1st Qu.: 438.0   1st Qu.:  3.00   1st Qu.:  15   1st Qu.: 75.0  \n",
       " Median : 642.0   Median : 53.00   Median : 155   Median :127.0  \n",
       " Mean   : 701.2   Mean   : 61.55   Mean   : 170   Mean   :159.1  \n",
       " 3rd Qu.: 913.0   3rd Qu.:101.00   3rd Qu.: 274   3rd Qu.:208.0  \n",
       " Max.   :2173.0   Max.   :402.00   Max.   :1028   Max.   :756.0  \n",
       "                                                                 \n",
       "      FTA             TOV              PF             ORB        \n",
       " Min.   : 10.0   Min.   :  7.0   Min.   : 27.0   Min.   :  5.00  \n",
       " 1st Qu.:101.0   1st Qu.: 70.0   1st Qu.:132.0   1st Qu.: 39.00  \n",
       " Median :171.0   Median :104.0   Median :167.0   Median : 71.00  \n",
       " Mean   :208.1   Mean   :115.8   Mean   :168.8   Mean   : 91.99  \n",
       " 3rd Qu.:271.0   3rd Qu.:150.0   3rd Qu.:204.0   3rd Qu.:129.00  \n",
       " Max.   :972.0   Max.   :464.0   Max.   :371.0   Max.   :440.00  \n",
       "                                                                 \n",
       "      DRB             REB              AST             STL        \n",
       " Min.   : 17.0   Min.   :  22.0   Min.   :  8.0   Min.   :  4.00  \n",
       " 1st Qu.:165.0   1st Qu.: 216.0   1st Qu.: 81.0   1st Qu.: 40.00  \n",
       " Median :230.0   Median : 309.0   Median :140.0   Median : 58.00  \n",
       " Mean   :264.2   Mean   : 356.2   Mean   :188.2   Mean   : 63.76  \n",
       " 3rd Qu.:333.0   3rd Qu.: 457.0   3rd Qu.:249.0   3rd Qu.: 82.00  \n",
       " Max.   :894.0   Max.   :1247.0   Max.   :925.0   Max.   :225.00  \n",
       "                                                                  \n",
       "      BLK              PTS           birth_year   birth_month       \n",
       " Min.   :  0.00   Min.   :  59.0   Min.   :1961   Length:4245       \n",
       " 1st Qu.: 14.00   1st Qu.: 523.0   1st Qu.:1977   Class :character  \n",
       " Median : 27.00   Median : 775.0   Median :1983   Mode  :character  \n",
       " Mean   : 40.97   Mean   : 863.2   Mean   :1982                     \n",
       " 3rd Qu.: 53.00   3rd Qu.:1119.0   3rd Qu.:1988                     \n",
       " Max.   :307.00   Max.   :2832.0   Max.   :2000                     \n",
       "                                                                    \n",
       "  birth_date           height            height_cm        weight         \n",
       " Length:4245        Length:4245        Min.   :160.0   Length:4245       \n",
       " Class :character   Class :character   1st Qu.:196.0   Class :character  \n",
       " Mode  :character   Mode  :character   Median :201.0   Mode  :character  \n",
       "                                       Mean   :200.9                     \n",
       "                                       3rd Qu.:208.0                     \n",
       "                                       Max.   :229.0                     \n",
       "                                                                         \n",
       "   weight_kg     nationality        high_school         draft_round   \n",
       " Min.   : 61.0   Length:4245        Length:4245        Min.   :1.000  \n",
       " 1st Qu.: 91.0   Class :character   Class :character   1st Qu.:1.000  \n",
       " Median :100.0   Mode  :character   Mode  :character   Median :1.000  \n",
       " Mean   :100.8                                         Mean   :1.224  \n",
       " 3rd Qu.:109.0                                         3rd Qu.:1.000  \n",
       " Max.   :147.0                                         Max.   :7.000  \n",
       "                                                       NA's   :419    \n",
       "   draft_pick    draft_team       \n",
       " Min.   : 1.0   Length:4245       \n",
       " 1st Qu.: 5.0   Class :character  \n",
       " Median :11.0   Mode  :character  \n",
       " Mean   :12.4                     \n",
       " 3rd Qu.:19.0                     \n",
       " Max.   :30.0                     \n",
       " NA's   :419                      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(NBA_data_filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Next we will look at the first few rows of the table to get an idea of what it looks like. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 34</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>League</th><th scope=col>Season</th><th scope=col>Stage</th><th scope=col>Player</th><th scope=col>Team</th><th scope=col>GP</th><th scope=col>MIN</th><th scope=col>FGM</th><th scope=col>FGA</th><th scope=col>X3PM</th><th scope=col>...</th><th scope=col>birth_date</th><th scope=col>height</th><th scope=col>height_cm</th><th scope=col>weight</th><th scope=col>weight_kg</th><th scope=col>nationality</th><th scope=col>high_school</th><th scope=col>draft_round</th><th scope=col>draft_pick</th><th scope=col>draft_team</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>...</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>NBA</td><td>1999 - 2000</td><td>Regular_Season</td><td>Shaquille O'Neal</td><td>LAL</td><td>79</td><td>3163</td><td>956</td><td>1665</td><td>  0</td><td>...</td><td>Mar 6, 1972 </td><td>7-1</td><td>216</td><td>325</td><td>147</td><td>United States</td><td>Robert G. Cole High School </td><td>1</td><td> 1</td><td>Orlando Magic        </td></tr>\n",
       "\t<tr><th scope=row>2</th><td>NBA</td><td>1999 - 2000</td><td>Regular_Season</td><td>Vince Carter    </td><td>TOR</td><td>82</td><td>3126</td><td>788</td><td>1696</td><td> 95</td><td>...</td><td>Jan 26, 1977</td><td>6-6</td><td>198</td><td>220</td><td>100</td><td>United States</td><td>Mainland High School       </td><td>1</td><td> 5</td><td>Golden State Warriors</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>NBA</td><td>1999 - 2000</td><td>Regular_Season</td><td>Karl Malone     </td><td>UTA</td><td>82</td><td>2947</td><td>752</td><td>1476</td><td>  2</td><td>...</td><td>Jul 24, 1963</td><td>6-9</td><td>206</td><td>265</td><td>120</td><td>United States</td><td>Summerfield High School    </td><td>1</td><td>13</td><td>Utah Jazz            </td></tr>\n",
       "\t<tr><th scope=row>4</th><td>NBA</td><td>1999 - 2000</td><td>Regular_Season</td><td>Allen Iverson   </td><td>PHI</td><td>70</td><td>2853</td><td>729</td><td>1733</td><td> 89</td><td>...</td><td>Jun 7, 1975 </td><td>6-0</td><td>183</td><td>165</td><td> 75</td><td>United States</td><td>Bethel High School         </td><td>1</td><td> 1</td><td>Philadelphia Sixers  </td></tr>\n",
       "\t<tr><th scope=row>5</th><td>NBA</td><td>1999 - 2000</td><td>Regular_Season</td><td>Gary Payton     </td><td>SEA</td><td>82</td><td>3425</td><td>747</td><td>1666</td><td>177</td><td>...</td><td>Jul 23, 1968</td><td>6-4</td><td>193</td><td>180</td><td> 82</td><td>United States</td><td>Skyline High School        </td><td>1</td><td> 2</td><td>Seattle SuperSonics  </td></tr>\n",
       "\t<tr><th scope=row>6</th><td>NBA</td><td>1999 - 2000</td><td>Regular_Season</td><td>Jerry Stackhouse</td><td>DET</td><td>82</td><td>3148</td><td>619</td><td>1447</td><td> 83</td><td>...</td><td>Nov 5, 1974 </td><td>6-6</td><td>198</td><td>218</td><td> 99</td><td>United States</td><td>Oak Hill Academy           </td><td>1</td><td> 3</td><td>Philadelphia Sixers  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 34\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & League & Season & Stage & Player & Team & GP & MIN & FGM & FGA & X3PM & ... & birth\\_date & height & height\\_cm & weight & weight\\_kg & nationality & high\\_school & draft\\_round & draft\\_pick & draft\\_team\\\\\n",
       "  & <chr> & <chr> & <chr> & <chr> & <chr> & <int> & <dbl> & <int> & <int> & <int> & ... & <chr> & <chr> & <int> & <chr> & <int> & <chr> & <chr> & <int> & <int> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 & NBA & 1999 - 2000 & Regular\\_Season & Shaquille O'Neal & LAL & 79 & 3163 & 956 & 1665 &   0 & ... & Mar 6, 1972  & 7-1 & 216 & 325 & 147 & United States & Robert G. Cole High School  & 1 &  1 & Orlando Magic        \\\\\n",
       "\t2 & NBA & 1999 - 2000 & Regular\\_Season & Vince Carter     & TOR & 82 & 3126 & 788 & 1696 &  95 & ... & Jan 26, 1977 & 6-6 & 198 & 220 & 100 & United States & Mainland High School        & 1 &  5 & Golden State Warriors\\\\\n",
       "\t3 & NBA & 1999 - 2000 & Regular\\_Season & Karl Malone      & UTA & 82 & 2947 & 752 & 1476 &   2 & ... & Jul 24, 1963 & 6-9 & 206 & 265 & 120 & United States & Summerfield High School     & 1 & 13 & Utah Jazz            \\\\\n",
       "\t4 & NBA & 1999 - 2000 & Regular\\_Season & Allen Iverson    & PHI & 70 & 2853 & 729 & 1733 &  89 & ... & Jun 7, 1975  & 6-0 & 183 & 165 &  75 & United States & Bethel High School          & 1 &  1 & Philadelphia Sixers  \\\\\n",
       "\t5 & NBA & 1999 - 2000 & Regular\\_Season & Gary Payton      & SEA & 82 & 3425 & 747 & 1666 & 177 & ... & Jul 23, 1968 & 6-4 & 193 & 180 &  82 & United States & Skyline High School         & 1 &  2 & Seattle SuperSonics  \\\\\n",
       "\t6 & NBA & 1999 - 2000 & Regular\\_Season & Jerry Stackhouse & DET & 82 & 3148 & 619 & 1447 &  83 & ... & Nov 5, 1974  & 6-6 & 198 & 218 &  99 & United States & Oak Hill Academy            & 1 &  3 & Philadelphia Sixers  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 34\n",
       "\n",
       "| <!--/--> | League &lt;chr&gt; | Season &lt;chr&gt; | Stage &lt;chr&gt; | Player &lt;chr&gt; | Team &lt;chr&gt; | GP &lt;int&gt; | MIN &lt;dbl&gt; | FGM &lt;int&gt; | FGA &lt;int&gt; | X3PM &lt;int&gt; | ... ... | birth_date &lt;chr&gt; | height &lt;chr&gt; | height_cm &lt;int&gt; | weight &lt;chr&gt; | weight_kg &lt;int&gt; | nationality &lt;chr&gt; | high_school &lt;chr&gt; | draft_round &lt;int&gt; | draft_pick &lt;int&gt; | draft_team &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | NBA | 1999 - 2000 | Regular_Season | Shaquille O'Neal | LAL | 79 | 3163 | 956 | 1665 |   0 | ... | Mar 6, 1972  | 7-1 | 216 | 325 | 147 | United States | Robert G. Cole High School  | 1 |  1 | Orlando Magic         |\n",
       "| 2 | NBA | 1999 - 2000 | Regular_Season | Vince Carter     | TOR | 82 | 3126 | 788 | 1696 |  95 | ... | Jan 26, 1977 | 6-6 | 198 | 220 | 100 | United States | Mainland High School        | 1 |  5 | Golden State Warriors |\n",
       "| 3 | NBA | 1999 - 2000 | Regular_Season | Karl Malone      | UTA | 82 | 2947 | 752 | 1476 |   2 | ... | Jul 24, 1963 | 6-9 | 206 | 265 | 120 | United States | Summerfield High School     | 1 | 13 | Utah Jazz             |\n",
       "| 4 | NBA | 1999 - 2000 | Regular_Season | Allen Iverson    | PHI | 70 | 2853 | 729 | 1733 |  89 | ... | Jun 7, 1975  | 6-0 | 183 | 165 |  75 | United States | Bethel High School          | 1 |  1 | Philadelphia Sixers   |\n",
       "| 5 | NBA | 1999 - 2000 | Regular_Season | Gary Payton      | SEA | 82 | 3425 | 747 | 1666 | 177 | ... | Jul 23, 1968 | 6-4 | 193 | 180 |  82 | United States | Skyline High School         | 1 |  2 | Seattle SuperSonics   |\n",
       "| 6 | NBA | 1999 - 2000 | Regular_Season | Jerry Stackhouse | DET | 82 | 3148 | 619 | 1447 |  83 | ... | Nov 5, 1974  | 6-6 | 198 | 218 |  99 | United States | Oak Hill Academy            | 1 |  3 | Philadelphia Sixers   |\n",
       "\n"
      ],
      "text/plain": [
       "  League Season      Stage          Player           Team GP MIN  FGM FGA  X3PM\n",
       "1 NBA    1999 - 2000 Regular_Season Shaquille O'Neal LAL  79 3163 956 1665   0 \n",
       "2 NBA    1999 - 2000 Regular_Season Vince Carter     TOR  82 3126 788 1696  95 \n",
       "3 NBA    1999 - 2000 Regular_Season Karl Malone      UTA  82 2947 752 1476   2 \n",
       "4 NBA    1999 - 2000 Regular_Season Allen Iverson    PHI  70 2853 729 1733  89 \n",
       "5 NBA    1999 - 2000 Regular_Season Gary Payton      SEA  82 3425 747 1666 177 \n",
       "6 NBA    1999 - 2000 Regular_Season Jerry Stackhouse DET  82 3148 619 1447  83 \n",
       "  ... birth_date   height height_cm weight weight_kg nationality  \n",
       "1 ... Mar 6, 1972  7-1    216       325    147       United States\n",
       "2 ... Jan 26, 1977 6-6    198       220    100       United States\n",
       "3 ... Jul 24, 1963 6-9    206       265    120       United States\n",
       "4 ... Jun 7, 1975  6-0    183       165     75       United States\n",
       "5 ... Jul 23, 1968 6-4    193       180     82       United States\n",
       "6 ... Nov 5, 1974  6-6    198       218     99       United States\n",
       "  high_school                 draft_round draft_pick draft_team           \n",
       "1 Robert G. Cole High School  1            1         Orlando Magic        \n",
       "2 Mainland High School        1            5         Golden State Warriors\n",
       "3 Summerfield High School     1           13         Utah Jazz            \n",
       "4 Bethel High School          1            1         Philadelphia Sixers  \n",
       "5 Skyline High School         1            2         Seattle SuperSonics  \n",
       "6 Oak Hill Academy            1            3         Philadelphia Sixers  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(NBA_data_filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We will perform part of our analysis on the nationality of NBA players, so we will first explore what the unique values are in that column. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'United States'</li><li>'Germany'</li><li>'Netherlands'</li><li>'Serbia'</li><li>'Democratic Republic of the Congo'</li><li>'United States / Jamaica'</li><li>'Serbia / Greece'</li><li>'United States / Spain'</li><li>'Nigeria / England'</li><li>'Lithuania'</li><li>'Ukraine'</li><li>'United States / Germany'</li><li>'Germany / United States'</li><li>'Canada / Bahamas'</li><li>'Slovenia'</li><li>'Australia'</li><li>'Haiti'</li><li>'Saint Vincent and the Grenadines / United States'</li><li>'Canada / South Africa'</li><li>'Dominican Republic'</li><li>'Turkey'</li><li>'Canada'</li><li>'Finland'</li><li>'Spain'</li><li>'Russia'</li><li>'France'</li><li>'Mexico'</li><li>'China'</li><li>'Croatia'</li><li>'Brazil'</li><li>'Montenegro'</li><li>'Argentina'</li><li>'Georgia'</li><li>'United States / Norway'</li><li>'Senegal'</li><li>'Puerto Rico / United States'</li><li>'Czech Republic'</li><li>'United States / Qatar'</li><li>'Canada / Haiti'</li><li>'Netherlands / United States'</li><li>'England / United States'</li><li>'England / South Sudan'</li><li>'United States / Dominican Republic'</li><li>'Netherlands / South Sudan'</li><li>'Latvia'</li><li>'Italy'</li><li>'United States / Nigeria'</li><li>'Argentina / Italy'</li><li>'Switzerland'</li><li>'Dominican Republic / United States'</li><li>'England / Nigeria'</li><li>'United States / Philippines'</li><li>'France / United States'</li><li>'Cameroon'</li><li>'Poland'</li><li>'Israel'</li><li>'Sweden'</li><li>'United States / Lebanon'</li><li>'Republic of the Congo / Spain'</li><li>'Venezuela'</li><li>'Switzerland / Turkey'</li><li>'Switzerland / Montenegro'</li><li>'United States / Greece'</li><li>'United States / Puerto Rico'</li><li>'Italy / United States'</li><li>'Nigeria'</li><li>'Tanzania'</li><li>'United States / Australia'</li><li>'Bosnia and Herzegovina'</li><li>'Greece / Nigeria'</li><li>'New Zealand'</li><li>'Montenegro / Spain'</li><li>'Bosnia and Herzegovina / Croatia'</li><li>'United States / Turkey'</li><li>'New Zealand / Australia'</li><li>'North Macedonia'</li><li>'Canada / United States'</li><li>'Bahamas'</li><li>'United States / Lithuania'</li><li>'United States / Croatia'</li><li>'Tunisia'</li><li>'Austria'</li><li>'United States / Democratic Republic of the Congo'</li><li>'Belgium / France'</li><li>'South Sudan / Australia'</li><li>'North Macedonia / Turkey'</li><li>'Nigeria / United States'</li><li>'Mali'</li><li>'United States / Egypt'</li><li>'Saint Lucia / Canada'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'United States'\n",
       "\\item 'Germany'\n",
       "\\item 'Netherlands'\n",
       "\\item 'Serbia'\n",
       "\\item 'Democratic Republic of the Congo'\n",
       "\\item 'United States / Jamaica'\n",
       "\\item 'Serbia / Greece'\n",
       "\\item 'United States / Spain'\n",
       "\\item 'Nigeria / England'\n",
       "\\item 'Lithuania'\n",
       "\\item 'Ukraine'\n",
       "\\item 'United States / Germany'\n",
       "\\item 'Germany / United States'\n",
       "\\item 'Canada / Bahamas'\n",
       "\\item 'Slovenia'\n",
       "\\item 'Australia'\n",
       "\\item 'Haiti'\n",
       "\\item 'Saint Vincent and the Grenadines / United States'\n",
       "\\item 'Canada / South Africa'\n",
       "\\item 'Dominican Republic'\n",
       "\\item 'Turkey'\n",
       "\\item 'Canada'\n",
       "\\item 'Finland'\n",
       "\\item 'Spain'\n",
       "\\item 'Russia'\n",
       "\\item 'France'\n",
       "\\item 'Mexico'\n",
       "\\item 'China'\n",
       "\\item 'Croatia'\n",
       "\\item 'Brazil'\n",
       "\\item 'Montenegro'\n",
       "\\item 'Argentina'\n",
       "\\item 'Georgia'\n",
       "\\item 'United States / Norway'\n",
       "\\item 'Senegal'\n",
       "\\item 'Puerto Rico / United States'\n",
       "\\item 'Czech Republic'\n",
       "\\item 'United States / Qatar'\n",
       "\\item 'Canada / Haiti'\n",
       "\\item 'Netherlands / United States'\n",
       "\\item 'England / United States'\n",
       "\\item 'England / South Sudan'\n",
       "\\item 'United States / Dominican Republic'\n",
       "\\item 'Netherlands / South Sudan'\n",
       "\\item 'Latvia'\n",
       "\\item 'Italy'\n",
       "\\item 'United States / Nigeria'\n",
       "\\item 'Argentina / Italy'\n",
       "\\item 'Switzerland'\n",
       "\\item 'Dominican Republic / United States'\n",
       "\\item 'England / Nigeria'\n",
       "\\item 'United States / Philippines'\n",
       "\\item 'France / United States'\n",
       "\\item 'Cameroon'\n",
       "\\item 'Poland'\n",
       "\\item 'Israel'\n",
       "\\item 'Sweden'\n",
       "\\item 'United States / Lebanon'\n",
       "\\item 'Republic of the Congo / Spain'\n",
       "\\item 'Venezuela'\n",
       "\\item 'Switzerland / Turkey'\n",
       "\\item 'Switzerland / Montenegro'\n",
       "\\item 'United States / Greece'\n",
       "\\item 'United States / Puerto Rico'\n",
       "\\item 'Italy / United States'\n",
       "\\item 'Nigeria'\n",
       "\\item 'Tanzania'\n",
       "\\item 'United States / Australia'\n",
       "\\item 'Bosnia and Herzegovina'\n",
       "\\item 'Greece / Nigeria'\n",
       "\\item 'New Zealand'\n",
       "\\item 'Montenegro / Spain'\n",
       "\\item 'Bosnia and Herzegovina / Croatia'\n",
       "\\item 'United States / Turkey'\n",
       "\\item 'New Zealand / Australia'\n",
       "\\item 'North Macedonia'\n",
       "\\item 'Canada / United States'\n",
       "\\item 'Bahamas'\n",
       "\\item 'United States / Lithuania'\n",
       "\\item 'United States / Croatia'\n",
       "\\item 'Tunisia'\n",
       "\\item 'Austria'\n",
       "\\item 'United States / Democratic Republic of the Congo'\n",
       "\\item 'Belgium / France'\n",
       "\\item 'South Sudan / Australia'\n",
       "\\item 'North Macedonia / Turkey'\n",
       "\\item 'Nigeria / United States'\n",
       "\\item 'Mali'\n",
       "\\item 'United States / Egypt'\n",
       "\\item 'Saint Lucia / Canada'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'United States'\n",
       "2. 'Germany'\n",
       "3. 'Netherlands'\n",
       "4. 'Serbia'\n",
       "5. 'Democratic Republic of the Congo'\n",
       "6. 'United States / Jamaica'\n",
       "7. 'Serbia / Greece'\n",
       "8. 'United States / Spain'\n",
       "9. 'Nigeria / England'\n",
       "10. 'Lithuania'\n",
       "11. 'Ukraine'\n",
       "12. 'United States / Germany'\n",
       "13. 'Germany / United States'\n",
       "14. 'Canada / Bahamas'\n",
       "15. 'Slovenia'\n",
       "16. 'Australia'\n",
       "17. 'Haiti'\n",
       "18. 'Saint Vincent and the Grenadines / United States'\n",
       "19. 'Canada / South Africa'\n",
       "20. 'Dominican Republic'\n",
       "21. 'Turkey'\n",
       "22. 'Canada'\n",
       "23. 'Finland'\n",
       "24. 'Spain'\n",
       "25. 'Russia'\n",
       "26. 'France'\n",
       "27. 'Mexico'\n",
       "28. 'China'\n",
       "29. 'Croatia'\n",
       "30. 'Brazil'\n",
       "31. 'Montenegro'\n",
       "32. 'Argentina'\n",
       "33. 'Georgia'\n",
       "34. 'United States / Norway'\n",
       "35. 'Senegal'\n",
       "36. 'Puerto Rico / United States'\n",
       "37. 'Czech Republic'\n",
       "38. 'United States / Qatar'\n",
       "39. 'Canada / Haiti'\n",
       "40. 'Netherlands / United States'\n",
       "41. 'England / United States'\n",
       "42. 'England / South Sudan'\n",
       "43. 'United States / Dominican Republic'\n",
       "44. 'Netherlands / South Sudan'\n",
       "45. 'Latvia'\n",
       "46. 'Italy'\n",
       "47. 'United States / Nigeria'\n",
       "48. 'Argentina / Italy'\n",
       "49. 'Switzerland'\n",
       "50. 'Dominican Republic / United States'\n",
       "51. 'England / Nigeria'\n",
       "52. 'United States / Philippines'\n",
       "53. 'France / United States'\n",
       "54. 'Cameroon'\n",
       "55. 'Poland'\n",
       "56. 'Israel'\n",
       "57. 'Sweden'\n",
       "58. 'United States / Lebanon'\n",
       "59. 'Republic of the Congo / Spain'\n",
       "60. 'Venezuela'\n",
       "61. 'Switzerland / Turkey'\n",
       "62. 'Switzerland / Montenegro'\n",
       "63. 'United States / Greece'\n",
       "64. 'United States / Puerto Rico'\n",
       "65. 'Italy / United States'\n",
       "66. 'Nigeria'\n",
       "67. 'Tanzania'\n",
       "68. 'United States / Australia'\n",
       "69. 'Bosnia and Herzegovina'\n",
       "70. 'Greece / Nigeria'\n",
       "71. 'New Zealand'\n",
       "72. 'Montenegro / Spain'\n",
       "73. 'Bosnia and Herzegovina / Croatia'\n",
       "74. 'United States / Turkey'\n",
       "75. 'New Zealand / Australia'\n",
       "76. 'North Macedonia'\n",
       "77. 'Canada / United States'\n",
       "78. 'Bahamas'\n",
       "79. 'United States / Lithuania'\n",
       "80. 'United States / Croatia'\n",
       "81. 'Tunisia'\n",
       "82. 'Austria'\n",
       "83. 'United States / Democratic Republic of the Congo'\n",
       "84. 'Belgium / France'\n",
       "85. 'South Sudan / Australia'\n",
       "86. 'North Macedonia / Turkey'\n",
       "87. 'Nigeria / United States'\n",
       "88. 'Mali'\n",
       "89. 'United States / Egypt'\n",
       "90. 'Saint Lucia / Canada'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"United States\"                                   \n",
       " [2] \"Germany\"                                         \n",
       " [3] \"Netherlands\"                                     \n",
       " [4] \"Serbia\"                                          \n",
       " [5] \"Democratic Republic of the Congo\"                \n",
       " [6] \"United States / Jamaica\"                         \n",
       " [7] \"Serbia / Greece\"                                 \n",
       " [8] \"United States / Spain\"                           \n",
       " [9] \"Nigeria / England\"                               \n",
       "[10] \"Lithuania\"                                       \n",
       "[11] \"Ukraine\"                                         \n",
       "[12] \"United States / Germany\"                         \n",
       "[13] \"Germany / United States\"                         \n",
       "[14] \"Canada / Bahamas\"                                \n",
       "[15] \"Slovenia\"                                        \n",
       "[16] \"Australia\"                                       \n",
       "[17] \"Haiti\"                                           \n",
       "[18] \"Saint Vincent and the Grenadines / United States\"\n",
       "[19] \"Canada / South Africa\"                           \n",
       "[20] \"Dominican Republic\"                              \n",
       "[21] \"Turkey\"                                          \n",
       "[22] \"Canada\"                                          \n",
       "[23] \"Finland\"                                         \n",
       "[24] \"Spain\"                                           \n",
       "[25] \"Russia\"                                          \n",
       "[26] \"France\"                                          \n",
       "[27] \"Mexico\"                                          \n",
       "[28] \"China\"                                           \n",
       "[29] \"Croatia\"                                         \n",
       "[30] \"Brazil\"                                          \n",
       "[31] \"Montenegro\"                                      \n",
       "[32] \"Argentina\"                                       \n",
       "[33] \"Georgia\"                                         \n",
       "[34] \"United States / Norway\"                          \n",
       "[35] \"Senegal\"                                         \n",
       "[36] \"Puerto Rico / United States\"                     \n",
       "[37] \"Czech Republic\"                                  \n",
       "[38] \"United States / Qatar\"                           \n",
       "[39] \"Canada / Haiti\"                                  \n",
       "[40] \"Netherlands / United States\"                     \n",
       "[41] \"England / United States\"                         \n",
       "[42] \"England / South Sudan\"                           \n",
       "[43] \"United States / Dominican Republic\"              \n",
       "[44] \"Netherlands / South Sudan\"                       \n",
       "[45] \"Latvia\"                                          \n",
       "[46] \"Italy\"                                           \n",
       "[47] \"United States / Nigeria\"                         \n",
       "[48] \"Argentina / Italy\"                               \n",
       "[49] \"Switzerland\"                                     \n",
       "[50] \"Dominican Republic / United States\"              \n",
       "[51] \"England / Nigeria\"                               \n",
       "[52] \"United States / Philippines\"                     \n",
       "[53] \"France / United States\"                          \n",
       "[54] \"Cameroon\"                                        \n",
       "[55] \"Poland\"                                          \n",
       "[56] \"Israel\"                                          \n",
       "[57] \"Sweden\"                                          \n",
       "[58] \"United States / Lebanon\"                         \n",
       "[59] \"Republic of the Congo / Spain\"                   \n",
       "[60] \"Venezuela\"                                       \n",
       "[61] \"Switzerland / Turkey\"                            \n",
       "[62] \"Switzerland / Montenegro\"                        \n",
       "[63] \"United States / Greece\"                          \n",
       "[64] \"United States / Puerto Rico\"                     \n",
       "[65] \"Italy / United States\"                           \n",
       "[66] \"Nigeria\"                                         \n",
       "[67] \"Tanzania\"                                        \n",
       "[68] \"United States / Australia\"                       \n",
       "[69] \"Bosnia and Herzegovina\"                          \n",
       "[70] \"Greece / Nigeria\"                                \n",
       "[71] \"New Zealand\"                                     \n",
       "[72] \"Montenegro / Spain\"                              \n",
       "[73] \"Bosnia and Herzegovina / Croatia\"                \n",
       "[74] \"United States / Turkey\"                          \n",
       "[75] \"New Zealand / Australia\"                         \n",
       "[76] \"North Macedonia\"                                 \n",
       "[77] \"Canada / United States\"                          \n",
       "[78] \"Bahamas\"                                         \n",
       "[79] \"United States / Lithuania\"                       \n",
       "[80] \"United States / Croatia\"                         \n",
       "[81] \"Tunisia\"                                         \n",
       "[82] \"Austria\"                                         \n",
       "[83] \"United States / Democratic Republic of the Congo\"\n",
       "[84] \"Belgium / France\"                                \n",
       "[85] \"South Sudan / Australia\"                         \n",
       "[86] \"North Macedonia / Turkey\"                        \n",
       "[87] \"Nigeria / United States\"                         \n",
       "[88] \"Mali\"                                            \n",
       "[89] \"United States / Egypt\"                           \n",
       "[90] \"Saint Lucia / Canada\"                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "unique(NBA_data_filtered$nationality)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We can see that there are many nationalities that state two countries for one player (separated by a backslash). This will be an important aspect to keep in mind when we perform our analysis. We will treat any player that has any country other than \"United States\" included in their `nationality` as being an \"International\" player (even if one of their countries listed is the \"United States\"). \n",
    "\n",
    "Next we would like to see the range of heights present in this dataset (in the format of \"feet - inches\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'5-10'</li><li>'5-11'</li><li>'5-3'</li><li>'5-5'</li><li>'5-9'</li><li>'6-0'</li><li>'6-1'</li><li>'6-10'</li><li>'6-11'</li><li>'6-2'</li><li>'6-3'</li><li>'6-4'</li><li>'6-5'</li><li>'6-6'</li><li>'6-7'</li><li>'6-8'</li><li>'6-9'</li><li>'7-0'</li><li>'7-1'</li><li>'7-2'</li><li>'7-3'</li><li>'7-4'</li><li>'7-6'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item '5-10'\n",
       "\\item '5-11'\n",
       "\\item '5-3'\n",
       "\\item '5-5'\n",
       "\\item '5-9'\n",
       "\\item '6-0'\n",
       "\\item '6-1'\n",
       "\\item '6-10'\n",
       "\\item '6-11'\n",
       "\\item '6-2'\n",
       "\\item '6-3'\n",
       "\\item '6-4'\n",
       "\\item '6-5'\n",
       "\\item '6-6'\n",
       "\\item '6-7'\n",
       "\\item '6-8'\n",
       "\\item '6-9'\n",
       "\\item '7-0'\n",
       "\\item '7-1'\n",
       "\\item '7-2'\n",
       "\\item '7-3'\n",
       "\\item '7-4'\n",
       "\\item '7-6'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. '5-10'\n",
       "2. '5-11'\n",
       "3. '5-3'\n",
       "4. '5-5'\n",
       "5. '5-9'\n",
       "6. '6-0'\n",
       "7. '6-1'\n",
       "8. '6-10'\n",
       "9. '6-11'\n",
       "10. '6-2'\n",
       "11. '6-3'\n",
       "12. '6-4'\n",
       "13. '6-5'\n",
       "14. '6-6'\n",
       "15. '6-7'\n",
       "16. '6-8'\n",
       "17. '6-9'\n",
       "18. '7-0'\n",
       "19. '7-1'\n",
       "20. '7-2'\n",
       "21. '7-3'\n",
       "22. '7-4'\n",
       "23. '7-6'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"5-10\" \"5-11\" \"5-3\"  \"5-5\"  \"5-9\"  \"6-0\"  \"6-1\"  \"6-10\" \"6-11\" \"6-2\" \n",
       "[11] \"6-3\"  \"6-4\"  \"6-5\"  \"6-6\"  \"6-7\"  \"6-8\"  \"6-9\"  \"7-0\"  \"7-1\"  \"7-2\" \n",
       "[21] \"7-3\"  \"7-4\"  \"7-6\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sort(unique(NBA_data_filtered$height))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We can see from the list above that our heights range from 5 foot 3 inches to 7 foot 6 inches. We can see that this column is in the class 'character', so it can't be sorted perfectly in ascending order. We will need to wrangle this data to be in some sort of numerical format if we want to use it properly in our analysis. \n",
    "\n",
    "Out of curiosity, who in the NBA was 5 foot 3?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Muggsy Bogues'"
      ],
      "text/latex": [
       "'Muggsy Bogues'"
      ],
      "text/markdown": [
       "'Muggsy Bogues'"
      ],
      "text/plain": [
       "[1] \"Muggsy Bogues\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NBA_data_filtered$Player[NBA_data_filtered$height == '5-3']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's amazing that Muggsy Bogues was only 5 foot 3 inches tall and he is still being considered for the [NBA Hall of Fame](https://godeacs.com/news/2019/12/20/mens-basketball-bogues-and-duncan-on-2020-naismith-hall-of-fame-ballot.aspx#:~:text=Muggsy%20Bogues%20(Class%20of%201987,for%20the%20fourth%20consecutive%20year.)\n",
    "\n",
    "Now back to the data, we will also check for missing values in our data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>League</dt><dd>0</dd><dt>Season</dt><dd>0</dd><dt>Stage</dt><dd>0</dd><dt>Player</dt><dd>0</dd><dt>Team</dt><dd>0</dd><dt>GP</dt><dd>0</dd><dt>MIN</dt><dd>0</dd><dt>FGM</dt><dd>0</dd><dt>FGA</dt><dd>0</dd><dt>X3PM</dt><dd>0</dd><dt>X3PA</dt><dd>0</dd><dt>FTM</dt><dd>0</dd><dt>FTA</dt><dd>0</dd><dt>TOV</dt><dd>0</dd><dt>PF</dt><dd>0</dd><dt>ORB</dt><dd>0</dd><dt>DRB</dt><dd>0</dd><dt>REB</dt><dd>0</dd><dt>AST</dt><dd>0</dd><dt>STL</dt><dd>0</dd><dt>BLK</dt><dd>0</dd><dt>PTS</dt><dd>0</dd><dt>birth_year</dt><dd>0</dd><dt>birth_month</dt><dd>0</dd><dt>birth_date</dt><dd>0</dd><dt>height</dt><dd>0</dd><dt>height_cm</dt><dd>0</dd><dt>weight</dt><dd>0</dd><dt>weight_kg</dt><dd>0</dd><dt>nationality</dt><dd>0</dd><dt>high_school</dt><dd>0</dd><dt>draft_round</dt><dd>419</dd><dt>draft_pick</dt><dd>419</dd><dt>draft_team</dt><dd>0</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[League] 0\n",
       "\\item[Season] 0\n",
       "\\item[Stage] 0\n",
       "\\item[Player] 0\n",
       "\\item[Team] 0\n",
       "\\item[GP] 0\n",
       "\\item[MIN] 0\n",
       "\\item[FGM] 0\n",
       "\\item[FGA] 0\n",
       "\\item[X3PM] 0\n",
       "\\item[X3PA] 0\n",
       "\\item[FTM] 0\n",
       "\\item[FTA] 0\n",
       "\\item[TOV] 0\n",
       "\\item[PF] 0\n",
       "\\item[ORB] 0\n",
       "\\item[DRB] 0\n",
       "\\item[REB] 0\n",
       "\\item[AST] 0\n",
       "\\item[STL] 0\n",
       "\\item[BLK] 0\n",
       "\\item[PTS] 0\n",
       "\\item[birth\\textbackslash{}\\_year] 0\n",
       "\\item[birth\\textbackslash{}\\_month] 0\n",
       "\\item[birth\\textbackslash{}\\_date] 0\n",
       "\\item[height] 0\n",
       "\\item[height\\textbackslash{}\\_cm] 0\n",
       "\\item[weight] 0\n",
       "\\item[weight\\textbackslash{}\\_kg] 0\n",
       "\\item[nationality] 0\n",
       "\\item[high\\textbackslash{}\\_school] 0\n",
       "\\item[draft\\textbackslash{}\\_round] 419\n",
       "\\item[draft\\textbackslash{}\\_pick] 419\n",
       "\\item[draft\\textbackslash{}\\_team] 0\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "League\n",
       ":   0Season\n",
       ":   0Stage\n",
       ":   0Player\n",
       ":   0Team\n",
       ":   0GP\n",
       ":   0MIN\n",
       ":   0FGM\n",
       ":   0FGA\n",
       ":   0X3PM\n",
       ":   0X3PA\n",
       ":   0FTM\n",
       ":   0FTA\n",
       ":   0TOV\n",
       ":   0PF\n",
       ":   0ORB\n",
       ":   0DRB\n",
       ":   0REB\n",
       ":   0AST\n",
       ":   0STL\n",
       ":   0BLK\n",
       ":   0PTS\n",
       ":   0birth_year\n",
       ":   0birth_month\n",
       ":   0birth_date\n",
       ":   0height\n",
       ":   0height_cm\n",
       ":   0weight\n",
       ":   0weight_kg\n",
       ":   0nationality\n",
       ":   0high_school\n",
       ":   0draft_round\n",
       ":   419draft_pick\n",
       ":   419draft_team\n",
       ":   0\n",
       "\n"
      ],
      "text/plain": [
       "     League      Season       Stage      Player        Team          GP \n",
       "          0           0           0           0           0           0 \n",
       "        MIN         FGM         FGA        X3PM        X3PA         FTM \n",
       "          0           0           0           0           0           0 \n",
       "        FTA         TOV          PF         ORB         DRB         REB \n",
       "          0           0           0           0           0           0 \n",
       "        AST         STL         BLK         PTS  birth_year birth_month \n",
       "          0           0           0           0           0           0 \n",
       " birth_date      height   height_cm      weight   weight_kg nationality \n",
       "          0           0           0           0           0           0 \n",
       "high_school draft_round  draft_pick  draft_team \n",
       "          0         419         419           0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colSums(is.na(NBA_data_filtered))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We can see that there are only missing values in the `draft_round` and `draft_pick` columns. This makes sense because not all players make it into the NBA through the draft (for instance some players get signed after playing in other professional leagues overseas prior to the NBA).\n",
    "\n",
    "The last part of the initial data exploration will be to examine the correlation between the numerical categories in the dataset:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5dErophxbszrfomcQ+l13rNt/patNX3\nrmiwt4ACajufy/t6iBV5HORbMlRgGIYTE1dWVkrWfKrpGp11FCt/gfF43PmDz86s7kf9Z6CS\nX97ub+SlpaXylUsrvlj3bwXnm8gp5vEa220nl2uwh413oL4aKl7/oKRMyeIUhmE4v/JXVlbs\n31sln6k6etV4mSa98/0XK3kPmKbp/KBLLsM6Pz/vfmLjHy6fna+mPJr7oet6xXey98e8hd8k\n7oyl6/rS0pIzY7O+vl4SKEsaDeq7y/+7opHeAgqoeeKspnXqKw7AuHksy+RWcUTd4xuhjmI1\n9adiWvVoaNNAnMlk3GXKTz2udg1KP6+x3XZysD0MpAP11VD+WSgvU/HXrVvJqE8dvQqkTJPe\n+f6L+elAxcGVBj9cPjvvwX2xXT+qpbriZh/zxl/spk1U2xslK614KP+QNvu7q/xd0UhvAQXU\n+Ufqph8b9x/93lZXVz3CYjweb3CQxmcxx6bhtVpa9WjIY7BT13X7z03311/5PEu1Gny+xnbb\nyQH2MKgO1FFD+UxcxWLVjpHXdd0em/SowU+vgirTjHd+TcVWVlY8vliqXQm+wQ+Xz8578381\nCO+JP++PeeMvdtMmPPbG+vq6918pzvs5qBZtdb8r6ustoID6v8uWlpbsKxW6Py2GYZQceOe/\nNtM0nQ9wPB7f9NJ+m34j1FSsYn/cv+dSqZS9sHvdDZVcMjKVSrmvbONOCRXHRfL5fCaTKelS\nTa+x3XZyID0MqgP11VAyIVut2MrKivt1GYbh/o3rUYOfyoMqY2vGO7+mYvZxuu59lclkNr0A\nVN0frsbfOQ5npbTyb0V7JWGflVT7mDf+YjdtYtO9sbKykslk3K37+ZAG8t1Vx7uivt4CW51W\nvPijBQAAgC3K1zp2AAAAaH8EOwAAAEUQ7AAAABRBsAMAAFAEwQ4AAEARBDsAAABFEOwAAAAU\nQbADAABQBMEOAABAEQQ7AAAARRDsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAAABSxzeOx\nxcXF0PoBAAA6XF9fX6u7sOV5BTthFwMAgFAwnBQIpmIBAAAUQbADAABQBMEOAABAEQQ7AAAA\nRRDsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAAABRBsAMAAFAEwQ4AAEARBDsAAABFEOwA\nAAAUQbADAABQBMEOAABAEQQ7AABwEU3TNE1rvOTc3FwsFguuX9jctlZ3AAAAqGn//v2t7kLH\nIdgBAICLFIvFVncBdWIqFgAAFSwvL2uaNjU15WzJ5XKapi0vLztbJiYmnC2FQmFqasqeS52a\nmioUCk6xkgnWjY2NsbExTdNGR0ftVsqnX2dmZjRNi8ViMzMzTiUlNxCGYnVf/OIXPR4FAABt\nRUR0XXfuZjIZEclkMu4Czq9+XdfdeSAej1csls/nS0q6H7Vvp1Ip90N2iz7DhoPUEQhG7AAA\nUIRpmpZlra2t2Xenp6ed/0XE3m6apohYlmVZlpP5MplMOp2em5srr/P06dOWZRmGUSwW8/m8\nYRjlZfL5fD6fLxaL2WzWabHoCoiBv1JUQ7ADAEARu3fvFhF7pjWXy9nRzbKsXC4nIs8884xT\n5sSJEyIyMDBgP9G+ce7cufI67ZKHDh0SkUgkYt8ocejQoUgkIiL22J5lWU14cfCFYAcAgCJ6\ne3tF5MyZMyJy9uxZEbntttuc23Zus8uk02l58Vg655i5RCJRXqddMhqN2nedG24VN6IlCHYA\nAKjDNM1kMlkoFKanp1OpVCQSSaVS9txoIpEoORgO6iHYAQCgDnum1T4w7uabbxaRm2++2bIs\n+2RVe4uIxONxqXROQ3mFdsmNjQ37rnMD7YlgBwCAOuyZVvt6D9dee62IXHfddSIyODjo3BaR\nffv2iYizNMnCwoKmaWNjY+UV2iWPHDli33VuoD0R7AAAUIp93ms8HrcPfYtEIvaom2EY9ikO\nInLbbbfpuj44OGgfYLd3714RGR4eLq/NLplMJu2SyWSy1v5wVbEwEewAAFCKPRtrj7TZbr/9\ndhG54447nC2RSOTo0aN2BBQRwzBWVla6urrKa7NL2qucxOPx+fl5/z2ZnZ2t6xWgfprH6jKL\ni4t9fX1h9gYAALQ5TdN0XbeXrAsQqSMQjNgBAICq7BlYeyU8efGwvIrXokA72NbqDgAAgPaV\nyWQGBwd7enrcGw8ePFhrPd5XjOXqFEFhxA4AAFQ1MDAwOztrn34hIqZprq+vsyJx2+IYOwAA\n0HqkjkAwYgcAAKAIgh0AAIAiCHYAAACKINgBAAAogmAHAACgCNaxAwAApX54500htHLZx86G\n0EpHYcQOAABAEQQ7AAAARRDsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAAABRBsAMAAFAE\nwQ4AAEARBDsAAABFEOwAAAAUQbADAKDpNE3TNK3Zz/UuOTc3F4vF6usDtoptre4AAAAIw/79\n+1vdBTQdwQ4AgLZWLBZb3QVsGUzFAgAQnpmZGU3TYrHYzMyMe3uhUJiamrLnUqempgqFgvNQ\nyQTrxsbG2NiYpmmjo6PLy8sVp1/LW3HK+J8R3vjXHz6a23jJx8/98ue+dvwfn3O2v+Tj517y\n8XMiYj/6aG7DLnzfuX+071744fM+m0DgNI+/AxYXF/v6+sLsDQAASrLjVCqVSiQSzsZMJjMw\nMGDfjsVilmU5D8Xj8cnJSfdz7d/XhUJhaGjIXdJmP+rRijvP+RkC/M7B3nd94et/9e0LzpYP\nvWnnA91REbFT3YfetPO3v/xN+6HP/nz3sbXvmn9/3r47edNPvvt1OzZtQkQu+9hZ5zapIxCM\n2AEAEJJ8Pp/P54vFYjabFZHp6Wl7u2VZlmVlMplisVgsFjOZTDqdnpubK6/h9OnTlmUZhlEs\nFvP5vGEYPltxwpzPid2//qcLf/XtC5M3/eQP3nHjU79wnYg4Mc72issu+cE7bvzsz3eLyFv/\nV+5tO17u3B09+49+9wiCRrADACAkhw4dikQiIqLruog4A28nTpwQEWf0zr5x7ty58hrskocO\nHRKRSCRi3/DZSk1On/++iNz12stFpPsnXvaDd9z4g3fc6C6gvzoiIj93xY/bd//vV73CfRet\nQrADACAk0Wi04vZ0Oi0vHkvnHDPnnk4tKenUU7HCaq3UxJ5XfcVll1YrEH3ZZe67HiURJoId\nAACAIgh2AAC0WDweF5FimWolNzY27LvOjcCNXLtDRDi/dcsh2AEA0GL79u0TEWdpkoWFBU3T\nxsbGqpU8cuSIfde5Ebi37Xi5iPz1P10QkbV//oGzxAnaHMEOAIAWu+2223RdHxwctA+w27t3\nr4gMDw9XK5lMJu2SyWSy1rZ8XlXs5698+S+++hW/eubrL/n4udeffFpeHMNDmyPYAQDQYpFI\n5OjRo6Zp2ncNw1hZWenq6qpW0l7lJB6Pz8/P+29ldnbWf+Hoyy57bNdPPvTTV9l3J2/6yd+5\n7lX+n45WYYFiAAC2ME3TdF23l6wL0A/vvCnYCitigeLAMWIHAMCWYc/A5nI5+659WJ69Xh0g\nItta3QEAAOBXJpMZHBzs6elxbzx48GCt9XhfMdbn1SnQhhixAwBgyxgYGJidnbUXPRER0zTX\n19cDWZEYamDEDgCAraS/v7+/v39ycrKRShiTUxUjdgAAAIog2AEAACiCYAcAAKAIgh0AAIAi\nCHYAAACK4KxYAABQyn1NCGwhBDsAALaGwrMb4TQUuTKa/875EBrafsWOEFrpKEzFAgAAKIJg\nBwAAoAiCHQAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgBAAAogmAHAACg\nCIIdAACAIgh2AIDOpWmapmn1PTo3NxeLxXwWBsKxrdUdAABgS9q/f3+ruwCUItgBAFBZsVhs\ndReA2jAVCwCATExMaJo2Nja2sbHhbHTPrtq319bWYrHY2NiYe3tJVTMzM5qmxWKxmZmZTdst\nFAqapo2OjnpsLBQKU1NTmqZtj171+Ec/euHC99yFn/na1/5gcnJ79Krt0asGh4Y+/hd/4Txk\nb/zGN74xODT0gQ9+0O++wFZGsAMAdLqJiYlEIiEiyWTy3nvvLRQK1UpOTU1ZltXV1eVR1eDg\noIhYljU4OLhptotEIplMJp1OLy8vOxv/7u/+TkRuv/12++7Q0NDIyIh9+zd+88HfHR93Sj71\n9NM/s/ctxvt+17578m8+9e73xN3ZTkQe/+hHT/7Np1772td69wRqINgBADpdPp/P5/PFYtEw\nDMuyTp48Wa3k9ddfXywWh4eHnVnakulap6psNisi09PTm7b+lre8RUQ+9rGPOVuefPJJEenp\n6RERy7Isy8pkMsViMb+x/kcfSf/x44+f/uz/tkv+8Z88LiJ/e+JEfmM9v7H+1NlFEXn3e+Lu\n+n+6pye/sf7OX/1VP7sCWx3BDgDQ6Q4dOhSJROwbInLq1KlqJfv7+31Wpeu6iFiWtWnrXV1d\nqVQqmUyura3ZWxKJhK7r3d3dInLixAkRGRgYsB96x9vfLiJfeurL9t3f//Dv5TfWr7nm6qee\nfvqvP/Wpxz/60fL63/bWt27aByhD8zgydHFxsa+vL8zeAAAQJvsIOfevQveWarcrPnfTAh7W\n1tauvvrqVCr14IMPLi8v79q1yzTN4eFhqXQMny2/sW7f+MAHP/jh33+04qPbo1e5S/oXuTKa\n/875Wp9Vh+1X7HBukzoCwYgdAAAt1tXVFY/HE4nExsaGfYDd7t27/Tzx8Y9+9MO//+h/fuc7\nsx//+P/+zNxXv/J0k3uKdkewAwB0OudMWPtGPB73LN4UdqNzc3P2YXm9vb3u7cVi0T7Gzvln\nP/obv/mgiPz+h3/vbW/9v264/vqXvuSl4fccbYVgBwDodEeOHBGRQqFg33BORw1Tb29vPB4f\nHBy0LMswDGf7vn37RMQ5u/YLX1zcHr2qZO2SZ772NRG5cOF7R/7wf4bYZbQjFigGAHS67du3\nO4ey6br+tre9zf9zY7GYfQJs4+LxeDqdFpE77rjD2Xjbbbfpuj44OGivomJzTnH9o4+k3/2e\n+M/sfUsgHYACGLEDAHS6Bx98MJVKiUgqlTp69Kh9WuumZmdng+2GM/167bXXOhsjkcjRo0dN\n07Tv/tZvPvDF+c85i9K94+1v/39/f8L9ULBdwpbDWbEAALSFXC7X09MTj8cnJycrFig8u1Fx\ne+A4K3brYsQOAIC2cOzYMWnRqRtQBsfYAQDQXNXWorMVi0WngGEYzoQsUAdG7AAAaDH7MhWp\nVGrcdR1YoA6M2AEA0FybXnwiqPNqAUbsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAAABTB\nWbEAAGwNkSujobXlviYEthCCHQAA9SucfzachiI7rvzWRkhtvSZ65bPf+W4IDV15xStDaKWj\nMBULAACgCIIdAACAIgh2AAAAiiDYAQAAKIJgBwAAoAiCHQAAgCIIdgAAAIog2AEAACiCYAcA\nAKAIgh0AAIAiCHYAAACKINgBAFSjVTI1NbW2tuZdxuEUKxQKc3NzExMTsVhM07SxsbG5ublW\nvCbAF61YLFZ7bHFxsa+vL8zeAADQOHcyK7G6utrV1eVdRkTsX45ra2v33XefZVklj+q6fuzY\nsUgkIiKF888G0GMfIjuu/NZGSG29Jnrls9/5bggNXXnFK53bpI5AMGIHAFBT8WKZTEZEpqam\nyh+ttuXw4cOWZZmmmc/n7e3r6+uGYViWdfLkyZa8KMAbI3YAANXYo3Hlv+AC2V4oFLZv3+5s\nZ8SuEYzYBY4ROwAAKkulUiKyvLzs3hiJRNyjekBb2dbqDgAA0HSFQuH48eMiYpqm/2cNDQ2d\nOnVq165d8Xh8375911xzzbXXXhuNRpvWTaBRBDsAgJoqnh5x8OBB/zVEo9Fjx46dPn36xIkT\ng4OD9sZ4PP7AAw90d3cH00sgUEzFAgDUp+u6aZqrq6u1jrdFIhFd1ycnJ1dXVzOZjGmaO3bs\n6OnpWVhYaFJXgUYwYgcAUFOwh8F1dXXZ66SISDKZfOSRR7LZbID1A4FgxA4AgMrsxYoLhUL5\nQ+WL2wHtgGAHAEBl9tJ3qVQql8vZWwqFwszMjLx4wizQbpiKBQCgsoGBgVOnTvLIQQMAACAA\nSURBVCWTyWQy6d6u6/rQ0FCregV4YMQOAICqJicnZ2dnDcOw7+q6nslkjh07xqInaE+M2AEA\nVFPraRPe5fv7+/v7+8fHxxvrFBAGRuwAAAAUQbADAABQBMEOAABAEQQ7AAAARRDsAAAAFEGw\nAwAAUATBDgAAQBEEOwAAAEUQ7AAAABTBlScAAKhfZMeVobX1mmh4bV15xStDawsBItgBAFTz\nw+Unw2nost6bz3/3u+G0teOVr5QPDIfTlrx3Sh69P4yGHngsjFY6CVOxAAAAiiDYAQAAKIJg\nBwAAoAiCHQAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgBAAAogmAHAACg\nCIIdACAkWiVTU1O5XK6kjHcNJRvHxsbs7cvLy83qOrBFEOwAAK00MjLS09NTdyYbGxtLJpMi\nsrS01NvbG2jXgK2HYAcACFXxYtlsVkTS6XQdVdmpTtf19fV1Uh0gBDsAQGvpui51BTsn1R09\nejQajTaha8DWQ7ADALSSZVkikslkanqWneoMw8hms6Q6wLGt1R0AAHSW8rMfTNMcGBjwX0Ms\nFrPj4B133BFkz4CtjxE7AECLXbhwoabylmXZE7h79+7d2NhoTqeALYlgBwAIVcnJE/Pz84lE\nYmZmxn8NmUwmm80ahiEi73vf+5rWU2DrIdgBAFppz549IjI9Pe3/Kfa87aFDh3RdT6fTU1NT\nzeocsNUQ7AAArWcfM1eTaDSaSqVEZGRkZGFhoQmdArYegh0AoGUKhYI9CWtHtFp1d3fPzs4K\nB9sBLyLYAQBC5b6e2Pbt2wcHB0XkrrvuqlbG+yJj/f39pmmKyJEjR5rdc6D9sdwJAKBldF3X\ndf3AgQNdXV11VzI8PLy2tpZMJq+//vqalk0B1EOwAwCEpFgsNlim2qPj4+Pj4+N1dgtQCFOx\nAAAAiiDYAQAAKIJgBwAAoAiCHQAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiNI+lIBcX\nF/v6+sLsDQAA6EykjkBw5QkAQEjOf+e7IbSy44pXyodGQ2hIROS3J7+18Ww4Tb0meuWnvvzV\ncNr6hTe94X995WshNPTzb/ypEFrpKEzFAgAAKIJgBwAAoAiCHQAAgCIIdgAAAIog2AEAACiC\nYAcAAKAIgh0AAIAiCHYAAACKINgBAAAogmAHAACgCIIdAACAIgh2AAApFApzc3MTExOxWEzT\ntLGxsbm5OXcBzZO7TCu6D+DfbWt1BwAALba2tnbfffdZluVsSSaTyWRS1/Vjx45FIpEW9g1A\nTRixA4BOd/jwYcuyTNPM5/PFYrFYLK6vrxuGYVnWyZMn7TJFl2pbALQcwQ4AOl06nRaR4eFh\nZ3AuGo0mEgkRGRwcbGXPANSIYAcAnS6VSonI8vKye2MkEmE0DthyOMYOADrd0NDQqVOndu3a\nFY/H9+3bd80111x77bXRaLTV/QJQM0bsAKDTRaPRY8eOZbNZERkcHNy7d+9VV101Ojqay+Va\n3TUAtSHYAQAkEonouj45Obm6uprJZEzT3LFjR09Pz8LCQqu7BqAGTMUCAP5DV1dXV1eXfTuZ\nTD7yyCP2SB6ALYEROwDodPbCwoVCofwh9+J2ANofwQ4AOl0mkxGRVCrlHFRXKBRmZmbkxRNm\nAWwVTMUCQKcbGBg4deqUfbUJ93Zd14eGhmqtrfyqYqyZAoSGETsAgExOTs7OzhqGYd/VdT2T\nyRw7doxFT4CthRE7AICISH9/f39///j4+KYlq43AMTIHtBwjdgAAAIog2AEAACiCYAcAAKAI\ngh0AAIAiCHYAAACKINgBAAAogmAHAACgCIIdAACAIgh2AAAAitA8FgpfXFzs6+sLszcAAKAz\nkToCwSXFAKCzvfeekBr6wPSX/uEbIbTz5te9Vj58XwgNiYj81h98a+N8OE29JrrjI6fPhdPW\ne952458tfDmEhn5lz5tCaKWjMBULAACgCIIdAACAIgh2AAAAiiDYAQAAKIJgBwAAoAiCHQAA\ngCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgBQPvSXlT+UKFQmJubm5iYiMVi\nmqaNjY3Nzc1VfG5FYb0CAKEi2AFAm1peXq54W0TW1taGhob279+fSCQsyxKRZDK5f//+WCxW\nKBTC7iiAtkGwA4A2debMGRFJpVLObcfhw4ctyzJNM5/PF4vFYrG4vr5uGIZlWSdPnrTLFF2q\nbQGgGIIdALSpkZEREbn33nud2450Oi0iw8PDkUjE3hKNRhOJhIgMDg6G3VEAbYNgBwDtyJ57\nNU0zEomYpikXz8baw3gl87ORSITROKDDEewAoB3Zc6+7d+92/nfPxg4NDem6vmvXrtHR0ZmZ\nmYWFhY2NjVZ1FUD7INgBQDuy5157e3ud/92zsdFo9NixY9lsVkQGBwf37t171VVXjY6O5nK5\nFvUXQFsg2AFA23HmWEtWJ3HPvUYiEV3XJycnV1dXM5mMaZo7duzo6elZWFhoQY8BtIdtre4A\nAKBUyTmw7u326J1bV1dXV1eXfTuZTD7yyCP2SB6ADsSIHQC0HXtpOmcpk2KxmM/nne3y4khe\nxSXrnDIAOhDBDgDaSy6Xs9eoc5YyERH73FjLsuyj6DKZjIikUinnoLpCoTAzMyMvnjALoDMx\nFQsA7eXs2bMism/fvpLt9rmxZ8+e7e7uHhgYOHXqVDKZTCaT7jK6rg8NDYXWVQDthhE7AGgv\n09PTuq53d3eXbO/t7dV1fXp62r47OTk5OztrGIZ9V9f1TCZz7NixaDQaancBtBNG7ACgvXic\n+lDyUH9/f39///j4+KZ1smox0CEYsQMAAFAEwQ4AAEARBDsAAABFEOwAAAAUQbADAABQBMEO\nAABAEQQ7AAAARRDsAAAAFEGwAwAAUITmsRz54uJiX19fmL0BAACdidQRCC4pBgBt57nnngun\nocsvv/xHZ0+F09a2m/YVH4iF0JD2aFYePxxCQyIi73zo2e98J5ymrrziCvnQr4fTlvz2H8rh\n94TR0EMfCaOVTsJULAAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgBAAAo\ngmAHAACgCIIdAACAIgh2AAAAiiDYAQAAKIJgBwCb06qYmJjI5XKbFrN5lJmamnLXAwD1IdgB\nQP0SiURPT0/jmWxkZKSnp2d5eTmQXgHoWAQ7APCreLF8Pp/JZETk0Ucf9Sjm8CiTzWZFJJ1O\nh/lyAKiHYAcAdYpEIgMDAxJEINN1PZB6AHS4ba3uAABsVYVC4eTJkyISj8cbrMqyLBGxx/8A\noG4EOwDwyzkBosQDDzywabGSqdjyMqZp2uN/AFA3pmIBoH6maa6urnZ3dzde1YULFxqvBECH\nY8QOAPxyRt2Wl5d37dplGMbw8LBHMT9V2RYWFvbu3btz504G7QA0ghE7AKhZb29vJpNJJpNj\nY2OBVLhnzx4RmZ6eDqQ2AB2LYAcA9RgYGIjH48lk0j7vIRABVgWgMxHsAKBODz30kIjEYrG1\ntbVG6ikUCjMzMyKSSqWC6RmATkWwA4A6dXV12QsLHz582L3d+5Ji5WW2b98+ODgoInfddVeY\n/QegHoIdANRP1/V4PJ5OpxuZRdV13T67tqurK8C+AehAnBULAJvzONF1cnJycnJy02J+qgKA\nBjFiBwAAoAiCHQAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgBAAAogmAH\nAACgCM1jDfTFxcW+vr4wewMAADoTqSMQXFIMAHz5/nU/Hk5DL/+7//MvX/tKOG392E+98YVT\nfxlOW5fs+yV57z1htPSBafkfiTAaEpH/kvruc8+F09QrL79cJh8Opy0ZfUT+8KEwGvr1w2G0\n0kmYigUAAFAEwQ4AAEARBDsAAABFEOwAAAAUQbADAABQBMEOAABAESx3AgAAECRN81onWNM0\n57ZHsfoQ7AAAAALjzm0VH3WHOe8IWAemYgEAAIIReFCrFcEOAAAgGK1NdcJULAAA6BDf2+k1\nSVrRT3yzNKh9b6dWvrF9EOwAbFXlB7Loun7PPff09/dHo1GPYrZUKqXrend3t0cx0zT37dvn\nlAGwtXz/dZe572ovqTn2lNRQXyVhYioWgDosyxocHLzqqquWl5c3LZxIJHp6enK5nEeZkZGR\nnp4eP7UBaEcvvawp/9oYwQ7A1lZ0WV9fN01TRMbGxgqFQrVixWIxn89nMhkRefTRRz2KZbNZ\nEUmn0yG+IACB0S67rBn/Wv2yvBDsAKgjGo0ODw+bpmlZ1unTpz1KRiKRgYEB2Sy06bq+aRkA\nbUt7yWXN+Nfql+WlreeJAaAOBw4cEJEzZ87YsayiQqFw8uRJEYnH4x5VWZYlIvbYHoCt57KO\nyzkd94IBKK+rq0tEksnk+Pi4s7HaKRQPPPCA+255MdM07bE9AFuOtq1dco6zvl2xWOTKEwAQ\nPNM0Dxw4YKdADxcuXAinPwACp227tCXtlsc195amrnVHsAPQEZxv0uXl5V27dhmGMTw87FHM\ntrCwsHfv3p07dzJoB2xJLQp2LUSwA6AaewWTVCpV8dHe3t5MJjM4OCgi7rnaivbs2SMi09PT\nBDtgK2qfqdjQdNwLBqA8+4yHG2+8sVqBgYGBU6dOJZPJ3bt3e5xgUVIhgK2n80bsWO4EgDo2\nNjampqYSiYSu6/39/R4lH3roIRGJxWJra2vVyhQKhZmZGak++AegzWmXbmvGv1a/LC9t3TkA\n2FTF0103jWJdXV3ZbDYWix0+fHhyctK7trvuuqvBTgJoiVadPNFCjNgBUEc8Hs9kMvl83s/V\nXXVdj8fj6XS62kyrruumaa6urm565iyANnXppU3518YYsQOwVflcMsCj2OTkpDNc19QFCAC0\nhNbeIawZCHYAAEBRnBULAACgCEbsAAAA1MBULAAAgCoIdgAAAGrQLiHYAQAAqOHSjlvWjWAH\nAADU1OZXiWiGjnvBAACgU3TeMXaax5qci4uLfX19YfYGAAB0pmakjmLil4Ot0Kal/rwZ1QaC\nETsAW9vzI/tDaOVSc/bfDrwhhIZE5KV/89WzX1sLp62bfqor/53z4bS1/YodxQffHkJD2sRf\n/GjxMyE0JCLb+m755saz4bS1M3ql/O67wmlLfvdP5L2DYTT0gUxTq2e5EwAAAFUQ7AAAABTB\ncicAAACKYMQOAABAEQQ7AAAARRDsAAAAFMExdgAAAIoIfcRO0zTndrWlgt1lPIrVh2AHAAAU\nFe6InaZddN2HkrtuwYY5N4IdAABQFNeKBQAAUET7HWPnMYwXCIIdAABQ1G+kLrr7B79dcw33\nfah0Sx2VXMzPcXh1I9gBaIqFhYVPfvKTyWRSRAzDuOWWW/r7+90FSg4fdqRSKV3Xu7u7PYqZ\nprlv3z6nDABUNvnwRXfrOJeipIb6KrmYz+Pw6nNJgHUBgG1sbGzv3r12qhORZDK5f//+0dHR\njY2NTZ+bSCR6enpyuZxHmZGRkZ6enuXl5WC6C0BVl17alH8NaOo8rBDsAARubGwsmUwahrGy\nslIsFovF4srKimEY6XT6yJEjJYWLF8vn85lMRkQeffRRj2LZbFZE0ul0aC8KwJZ0yaVN+dfG\nCHYAgrS8vGynuvHxcWeqtLu7e3x83DCMZDLpPcwWiUQGBgZks9Cm6/qmZQBALt3WlH8NqHYU\nSlAIdgCC9OlPf1pEhoaGyh+68847nQLVFAqFmZkZEYnH4x7FLMsSEXtsDwCqau8Ru2acIcvJ\nEwCClEgkRKTiaQ29vb12gQcffNDZWO2P1wceeMB9t7yYaZr22B4AVBXutGmxWKx2xquT4UrK\nBI5gB6C9mKZ54MCBrq4u72IXLlwIpz8AtrDQLynm51ITrGMHQFnOF9zy8vKuXbsMwxgeHvYo\nZltYWNi7d+/OnTsZtAPgpb1PdGgGjrEDEKRUKiUiFRcrsTfaBcr19vZmMplkMjk2NrZpK3v2\n7BGR6enphvoKQHntt9xJsxHsAATp1ltvFZFjx46VP2RvvPnmm6s9d2BgIB6PJ5NJ+9yITfks\nBqBztffJE81AsAMQpN7eXntZk7GxMWfcLpfL2YvbxeNxe7CtmoceekhEYrHY2tpatTLOmbPV\nBv8A4N913ogdx9gBCNihQ4fOnz+fTCadK0/Y4vH4+9//fu/ndnV1ZbPZWCx2+PDhyclJZ3vF\nk8juuuuuQDoMQFntPbrWDIzYAQhYNBqdnJycnZ01DMPeYhjG7Ozs5ORkNBrd9Om6rsfj8XQ6\nXW2mVdd10zRXV1c3PXMWQKdrvwWKm62tOwdg6+rv7+/v7x8fH69WwOOE/8nJSWe4rtnXVQSg\nsvaeNm0Ggh0AAFBU503FEuwAAICaipc0Jec092qvjSHYAQAARTEVCwAAoIZic6ZiGbEDAAAI\nHcfYAQAAKIKpWAAAADU0aSq2nRHsAACAmortvZhwM3TcCwYAAJ2i80bsNI9V3RcXF/v6+sLs\nDQAA6EzNSB0/PPfZYCu0XXbjW5tRbSAYsQPQBB+Mh9TQf0vL7/0/YTT0X/+njL87jIZEZOyP\nvv+Nr4fT1Mtfe03x1F+E05a27+0y9b4wWhp+v/ylGUZDIvJLI099/ZvhNHXDNTvlE1PhtCUH\nh+VjfxBGQ3fe19z6mYoFAABQQ5GzYgEAANTAWbEAAACK4KxYAAAARTBiBwAAoIjiJR2Xczru\nBQMAgE7ByRMAAABqCH8qVtO0/2i9ylLBfsrUjWAHAADUFHKw07SLrvtQctd/mUYQ7AAAgJo4\nKxYAAEARnBULAACgiFdEX+W+mz9/vtYatu/YUbKljkrCRLADOpf7AF6HaZoHDhzo6uryKGML\n/JhfAAjWc889d9H92k+SLa2hrkrCRLADcJGRkRERWV1ddbIdAGxRz3fe35+XtLoDAFqseLFM\nJiMiU1NTHmVsLeovAPj1wgvFZvxr9cvyQrADcJGBgQERSSaTre4IADTqhWKxGf9a/bK8MBUL\nAADU1N6Da01BsAPwHwqFwvHjx0XENE339vJTKJiKBdD+Qh5dKxaL1a4q4SxE7FEmEAQ7oNNV\nPO/14MGD4fcEAIIV/rRptaDm3t7UP4wJdgD+g67ruq4fOHAgGo26tzM+B2AravPj4ZqBYAd0\nOkIbAFV14HInBDsAAKCmNl+apBkIdgAAQE2dl+sIdgAAQFEcYwcAAKAIgh2ADuLntAlOrQCw\ndT3feXOxBDsAAKAmRuwAAAAUwXInAAAAimDEDgAAQBGdd4gdwQ4AACiKETsAAABFcOUJAAAA\nRTBiBwAAoAjOigUAAFBE583EiuaxrPzi4mJfX1+YvQEAAJ2pGanj0089E2yFtltveH0zqg0E\nI3ZAx/izVEgN/Urih+c+G05Tl934Vvnj8TBa+s9j8sSRMBoSkbsOPT/cH05Tl07Nyft+LZy2\n5P1/+m9f+WII7bz0jT/zw4GfDaEhEbls5gv/9Oz5cNp61ZU7nl79ZjhtXX/1zq9/ez2Ehq55\n9VVNrZ9j7AAAABTBtWIBAAAUwckTAAAAimAqFgAAQBEEOwAAAEUQ7AAAABTxwgut7kHoCHYA\nAEBNLT95QtM053a1lYPdZTyK+USwAwAAamrtVKymXXQZiJK7bg2GOTeCHQAAUBPH2AEAACii\n/YOdxzBefQh2AABATUN73+y++yef+1KtNbzrLW8u2VJHJd78HIfnH8EOaJmSA2ZLlHy8FxYW\nPvnJTyaTSRExDOOWW27p7//3y4kWCoXt27fH4/HJycnyekZHR9Pp9Pr6ejS4ngPAlvDHTy63\nvIZN+TwOz6dLGu4PgKYbGxvbu3evnepEJJlM7t+/f3R0dGNjQ0QikYhhGOl02r7rtrGxkU6n\nDcOIRsl1ADrO8y8Um/EvwB4GOw8rBDughYou1baIyNjYWDKZNAxjZWXFfmhlZcVOckeOHLHL\n3HHHHSLy+c9/vqQJe4v9KAB0mheKxWb8q9iW5hLyy3RjKhZoa8vLy3aqGx8fdzZ2d3fbd5PJ\n5J133tnb23vdddeJyIkTJ3Rddz/9xIkTImI/CgCdJsyTJ+obewv85AlG7IC29ulPf1pEhoaG\nyh+68847nQKRSCSVSpXMxjrzsJFIJKz+AkAbeb5YbMa/JvU2kJBHsAPaWiKREJHu7u7yh3p7\ne50CInLrrbfKxbOxzMMC6HAvvFBsxj+frReLRff8bMlJEuVlAnnJBDtAEXbOs+debczDAuhw\nLxSb8s+/ikdOy8XzttXK1IdgB6jDNE1nNtaeh02lUszDAuhYW2sqNhAEO6CtpVIpEcnlcuUP\n2RvtArbdu3fLizOw9v/2/CwAdKYwz4ptEwQ7oK3ZyezYsWPlD9kbb775ZmeLezbW/t/eAgCd\nqQODHcudAG2tt7fXMAx7aeKhoSH7LIpcLnfs2LFkMhmPx/fs2eMub5rmyMhIPB5Pp9Omabam\n0wDQHtp82rQZCHZAuzt06ND58+eTyaRz5QlbPB5///vfX1LYno3dtWuXcxsAOlagF4nYGpiK\nBdpdNBqdnJycnZ01DMPeYhjG7Ozs5ORk+YXCent7nTWKmYcF0OE68OQJRuyAtrDpWe79/f39\n/f3u609Uk81mA+oUAGxtwV7XdUsg2AEAADW1+YkOzUCwAwAAamrzadNmINgBAAA1MWIHAACg\nCEbsAAAAFPHCC63uQegIdgAAQE2M2AEAACiCY+wAAAAUwYgdAACAIjow2Gke690vLi729fWF\n2RsAANCZmpE6ho/PBVuhberu/mZUGwhG7IBW+tGv3RxOQ9v+9En5s1Q4bcmvJOQvPxJSW7/0\nHvnwfWE09Ft/IP8jEUZDIvJfUvInHwiprXe9V8zfCamtkf8ufzMdRkMH7vm3X3xjGA2JvPSv\nvvJPz54Pp61XXbnj//zj34fT1o//5LX/mlsOoaGXdTf3ktYdOGJHsAMAAGriWrEAAACKYMQO\nAABAEQQ7AAAARRDsAAAAFPF8x+U6gh0AAFAUI3YAAACKaJOzYjXNa9lgTdOc2x7FfCLYAQAA\nNbXDiJ07t1V81B3mvCOgHwQ7AACgph+1OtjZQc072wWLYAcAANT0o1YP2DU+tVorgh0AAFDT\n3LvvcN/dd/Svaq3h1L2/WLKljkrCRLADKvAYNrf//PIeVy/5E80pHP6fbgAAR3lKa1UlzXNJ\nqzsAKG55ebnibQAAAkewA6oqVlL+ULUttjNnzohIKpVybgMA1KO5tLAbBDuguUZGRkTk3nvv\ndW4DANRT7c/7kBHsgCay515N04xEIqZpCrOxAIBmItgBVWllaq3BnnvdvXu38z+zsQAA90l1\n7t8yjY/2EeyAJrLnXnt7e53/mY0FgE5THtfcW4KdwyXYAVVVO3PCJ2fWtWTAj9lYAECTEOyA\nZqk268psLACgSQh2QLNYliUi+XzeGfDL5/POdgAAAkewA5oil8tZlmWfD+tstM+NtSwrl8u1\nsG8AAFUR7ICmOHv2rIjs27evZLt9bqz9KAAAwSLYAU0xPT2t63p3d3fJ9t7eXl3Xp6enW9Ir\nAIDatrW6A0A7qukE2IqFs9lstfIeDwEA0AhG7AAAABRBsAMAAFAEwQ4AAEARBDsAAABFEOwA\nAAAUQbADAABQBMEOAABAEQQ7AAAARRDsAAAAFKF5rLC/uLjY19cXZm8AAEBnInUEgkuKAaW+\n3/1j4TT08ty//OjXbg6nrW1/+qT8RTqctuTt8Rc+G9Jl0y55a0zSRhgtxZPypx8MoyER+bX/\nJpPvDamt0Q+E2dbzZz4dQjuX7r71X//T60NoSERe9rfPfPvZ8+G09eordzz33HPhtHX55Zdf\n+KdvhtDQK161M4RWOgpTsQAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgBAAAogmAH\nAACgCIIdAACAIgh2AAAAiiDYAQAAKIJLimFr0DSt2kP29Y49CjhlYrHYvn37brzxxhtuuCEa\njboLbGxsPPXUU+fOnTt16tR0QH0GACBkBDt0EMuyLMsSEdM0h4eH3Q994hOfGBkZ+fc7b3hZ\n+H0DAKBxTMViKylWUv5QtS22eDxuxzs3y7Li8XgILwEAgOYh2KHj3H777ZZl5XI5Z0sul7Ms\n6/bbb29hrwAAaBzBDh2np6dHRFZWVpwt9m17OwAAWxfBDluJVqaOSrq7u3VdP3HihLPFvt3d\n3R1YRwEAaAWCHTqRruvpdHpjY0NENjY20um0aZqt7hQAAI0i2GErqXbmRK12794tIk899ZTz\n/5ve9KYA+wkAQEsQ7NCJrrnmGhH5zGc+4/x/3XXXtbZLAAA0jmCHThSJRAzDSCaThUIhmUwa\nhhGJRFrdKQAAGkWwQ4e65ZZbROTo0aPy4swsAABbHcEOHeqGG24QkUQiISK9vb2t7g4AAAEg\n2KFDRaNRXddFRNf1rq6uVncHAIAAcK1YbA01nQBbrXDJ9mw2W7HA97t/rMbeAQDQFhixAwAA\nUATBDgAAQBEEOwAAAEUQ7AAAABRBsAMAAFAEwQ4AAEARBDsAAABFEOwAAAAUQbADAABQhOax\noP/i4mJfX1+YvQEAAJ2J1BEILimGLeOFJ0+E0MolN9/+g6fPhNCQiLzk+t3F2ePhtKXtvzv3\njW+H01b3a1/9+Oe+FE5b73zLm//hW+shNPS611z1+dzXQ2hIRH6u+xqZeTSctmTgAfn4H4bU\n1jt+/VNf/moI7fzCm94gf/TfQ2hIROTdv/ODLy+E09RL3rTnzxf/Lpy2frnvuie+8HQIDd31\ns9eH0EpHYSoWAABAEQQ7AAAARRDsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAAABRBsAMA\nAFAEwQ4AAEARBDsAAABFEOwAAAAUQbBDzaampjRNm5iYcLaMjY1pmjY1NeVsWVhYGB0d1TRt\ndHR0bm7O/XStkqmpqbW1tfK2nALNezkAACiDYIea3X333bquJxIJO4rNvb2meQAAFeNJREFU\nzc0lk0ld1++++267wMLCwt69e9PptIik0+n9+/eXZLtyIyMjV199dUm2W15erngbAABURLBD\nzSKRyP333y8iTzzxRKFQeOyxx0Tk/vvvj0QidoHHH39cRFZWVorF4tLSkojYZdyKF8tkMiLi\nHvMTkTNnzohIKpVybgMAAA8EO9Sjv7/fMIxEInH8+HHLsuLxeH9/v/Po5ORksVjs7u4Wkd7e\nXhGxLMu7woGBARFJJpPujSMjIyJy7733OrcBAIAHgh3qNDw8LC/mrYceeqhaMXsK1R6Qq4n9\nRNM0I5GIaZoisvzM39fdWwAAOgHBDnXq6uqy85Zpml1dXRXLTExM7Nq1K5VK2QNy1RQKBXsS\n1q7QZs+97t692/n/C1/JBdd9AAAURLBD/ewJVo9p1p07d8bj8UQi4T6F1uY+JXb79u32yN/B\ngwedAvYWeybX/v89v3ekCS8CAAB1EOxQp5mZGcuyUqmUZVkzMzMVywwMDExOTs7PzycSiWpl\nRETXddM0V1dXo9GovcU5B7ZkuRNmYwEA8LCt1R3AlrS2tjY4OCgit956q4gMDg6+5S1vqTYh\nu2fPHruMe0K2WCx61F/tHNgvfCXX+/pr6+42AABqY8QO9Th8+LCImKbZ29trHxjnXqkkFotp\nmlYoFOqu357ezefzznoo+XxeRKwnWfQEAICqCHao2dzcXDqddlYkttcrTiaTzirE99xzj4ic\nPn3aKS8XnxjhLZfLWZZlnw/rbIxEIh/5r4f+6snP59a+GeBrAQBAJQQ71MZZkfjhhx+2g1ck\nEnn44YdF5LHHHrNH6W677TZd1+1xO03T9u/fr+u6+8QIb2fPnhWRffv2lWz/2Td2i8i53DPB\nvRoAAJRCsENt7BWJDcOwj5yz7dmzxzAMy7KOHz8uIpFI5OjRo84QnWmaR48edU6M2NT09LSu\n6/b6xm69r7/2F2/+uem/PRXE6wAAQEGcPIHaDA8P20sTlxgfHx8fH3fuRqPRaiW9T5sQkWw2\nW+2hT3zod3z3FACAjsOIHQAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAIAiCHYAAACKINgB\nAAAogmAHAACgCIIdAACAIjSPywAsLi729fWF2RsAANCZSB2B4JJiaMj3X3dZOA29/B9++PyZ\nT4fQ0KW7b/3XleUQGhKRl/X0vvDZqtdPC9Ylb4199RvfDqetN7z21X86/6Vw2vq1vW/+h2+t\nh9DQ615z1ee/+vUQGhKRn3vDNfLxPwynLXnHr4v1RyG1pb/7b7/81RDa+U9veoP8ySMhNCQi\n8q6H/+0rXwynqZe+8Wc+cfb/C6etgzf99J8vfiWEhn65740htNJRmIoFAABQBMEOAABAEQQ7\nAAAARRDsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAAABRBsAMAAFAEwQ4AAEARBDsAAABF\nEOy2vKmpKU3TJiYmnC1jY2Oapk1NTTlbFhYWRkdHNU0bHR2dm5tzP12rZGpqam1tzSkTi8Um\nJibm5uY2NjZKWn/2+eKpf3nhSOGFu9efb87rAwAAfhHstry7775b1/VEImFHsbm5uWQyqev6\n3XffbRdYWFjYu3dvOp0WkXQ6vX///pJsV25kZOTqq692sp1lWYlEYv/+/Z/4xCdKSn7yn4u/\nuP7Cw8+9cPJfigG/MAAAUCOC3ZYXiUTuv/9+EXniiScKhcJjjz0mIvfff38kErELPP744yKy\nsrJSLBaXlpZExC7jVrxYJpMREfeYn4jE43HLskqeeOKfi+/+Ca0pLwwAANSIYKeC/v5+wzAS\nicTx48cty4rH4/39/c6jk5OTxWKxu7tbRHp7e0WkPJ+VGBgYEJFkMuneePvtt1uWlcvlnC25\nXO7kvxQP/BjBDgCAtkCwU8Tw8LCIjIyMiMhDDz1Urdjy8rKI2ANyterp6RGRlZUVZ4t9+/WX\nEewAAGgLBDtFdHV1maYpIqZpdnV1VSwzMTGxa9euVCplD8hVUygU7ElYu0JHd3e3rusnTpxw\ntti330CwAwCgPRDs1GFPsHpMs+7cuTMejycSCfcptDb3KbHbt2+3R/4OHjxYUkzX9XQ6bZ8b\nu7GxkU6nj1zBWwgAgHbBb2VFzMzMWJaVSqUsy5qZmalYZmBgYHJycn5+PpFIVCsjIrqum6a5\nuroajUZLHtq9e7eIPPXUU87/b2S4DgCAtkGwU8Ha2trg4KCI3HrrrSIyODjoXoWuxJ49e+wy\n7o3uU2Kz2ezw8HDF+dxrrrlGRD7zmc84///0SwJ8HQAAoCEEOxUcPnxYREzT7O3ttQ+Mc69U\nEovFNE0rFAqNNxSJRAzDSCaThUIhmUwahvGKSxixAwCgXRDstry5ubl0Ou2sSGyvV5xMJp1V\niO+55x4ROX36tFNeyk6M8O+WW24RkaNHj8qLM7MAAKBNEOy2NmdF4ocffthekTgSiTz88MMi\n8thjj9mjdLfddpuu6/a4naZp+/fv13W9/MQIn2644QYRSSQS8uKqeAAAoE0Q7LY2e0ViwzDs\nI+dse/bsMQzDsqzjx4+LSCQSOXr0qDNEZ5rm0aNHy0+M8Ckajeq6LiK6rldbVwUAALTEtlZ3\nAA0ZHh62lyYuMT4+Pj4+7tyNRqPVShaLm1/jtaRMNpstKfC9a3gjAQDQeozYAQAAKIJgBwAA\noAiCHQAAgCIIdgAAAIog2AEAACiCYAcAAKAIgh0AAP9/e/cbG+d90AH8d2taNph0tNtMh7YQ\nMc1RRbqHYRpcJtGlDSAZPS7VttIA4sVUm4uqTAMCbN2FqtytG+CDaVXFcY72AkEyuk0lfkSk\nwOpsSMMmw1luCi/saYhkgxV3ay9SYaN/Zl487Djs+JI68VPnd5/Pi9Pd8+e+P/vVV7/fPc8D\nkVDsAAAiodgBAESi1OfBAwsLCyMjI0WOBgAYTFrHVeFJUDE6/HBBQfc/FJofKiir8uEXfum2\nAnKu/6svvvhr7yggKISw7c+/8OIv/1RBWUf+MWSfKCYrpO/973/+YjFR3/djt4Xph4pImng4\nPP5oEUEhhHsPhI9UCsr6YDN8+CIPG9wUH5r+ztKXC8h59fDbnht+TQFBIYTXLn372WefLSbr\nxhtv/Oq/P1VM1lt++OavPbVcQNCbb97gg8tZj6VYAIBIKHYAAJFQ7AAAIqHYAQBEQrEDAIiE\nYgcAEAnFDgAgEoodAEAkFDsAgEgodgAAkVDsAAAiodgVpLS+VUfOz883Go181/j4+PT09NLS\nUv/v3PzhAwDXAMVuazl06NDtt99+8ODB/GOWZZOTkzt37vzkJz+56sh2u33R9wDAwFLsCrVy\nMd29hw4dqtfr1Wp1cXEx39XpdObm5tI03bdv3/nz53u/6tSpUyGEqamp7nsAYMApdltFu92u\n1+uVSqVWqw0PD+cby+Xy6OhorVYLIZw4caL3+MnJyRDC/fff330PAAw4xW6ryGfdKpXK2l1J\nknQ6nYmJie6WfO211WqVy+VWqxWsxgIAil3B+lw5kWVZCCFJkoueWC6Xez/mLXD37t3dV6ux\nAIBit1Xkxa5XnxaYr73mLTB/tRoLACh2hepz5cTl6666rip8VmMBYMApdltFfn1rbzlbr/+t\nt+pqNRYABpxit1Xs3bs3hNBsNi95ZL5o2+l0urWv0+mEiy3mAgADRbHbKpIkqVarzWZz//79\nq24+3Gg0uh+XlpayLMuvh+1uzK+NzbJsvWdUAACDYNsrPQD+T36/unq9vnbeLk3TfK329OnT\nIYQ77rhj1QH5tbGnT5/u3gMPABg0Zuy2llqtdubMmVarlaZpvmVqampubm5mZiZvbEeOHEnT\ndG17S5IkTdMjR44UPWIAYMswY1eQy78ANkmSJEl6b0fca2ZmZr0T++wCAAaBGTsAgEgodgAA\nkVDsAAAiodgBAERCsQMAiIRiBwAQCcUOACASih0AQCQUOwCASJT6PBFhYWFhZGSkyNEAAINJ\n67gqPFKsIM/tfE0xQa9d/HZ44s+KyQr3/Hr4zGMFZb3rgRfe/fYCcq7/9JdeuPcnCwgKIVz/\n+D+9+Ku3F5O17S/mwqceLSYrvOfAyueeKCaq9M57wh8+UETS7zwW/vTBIoJCCPsfCR/7zYKy\n3v/HofG+grJ+6+Mvzf9tATnXjf7cc2+5oYCgEMJrv/p855tPF5P1g69/w7eeeaaYrNfddNOF\n5acKCCoP3VxAykCxFAsAEAnFDgAgEoodAEAkFDsAgEgodgAAkVDsAAAiodgBAERCsQMAiIRi\nBwAQCcUOACASg1vsSutbdeT8/Hyj0ch3jY+PT09PLy0t9R4wPj7eaDRmZ2eXl5dXnbu8vDw7\nO9toNO79t+c39+8BAAaeZ8VewqFDh+r1evdjlmVZloUQjh49et99963a2Gq1JiYmek8/duzY\n5ORkgeMFAAbX4M7Y5VYuprs3b3XVanVxcTHf1el05ubm0jTdt2/f+fPne7+qUqnk9a5XlmWV\nSqWIvwQAGHiDXuz6aLfb9Xq9UqnUarXh4eF8Y7lcHh0drdVqIYQTJ070Hj82NpZlWe8q7dLS\nUpZlY2NjRQ4bABhYlmLXderUqRDCRefbkiTpdDrlcrl3486dO0MIi4uL3Ra4uLjY3Q4AsNkG\nfcauz5UT+bpqkiQXPXFVqwshDA8Pp2l6/Pjx7pb8fbfnAQBsqkEvdn2s/cHcJa+fTdO02Wzm\n18YuLy83m81Wq1XQcAGAgTfoxa7PlRMbsHv37hDC2bNnu6+33nrrVRknAMAlDXqx62NqaiqE\n0G63u1su2f927NgRQjh58mT39ZZbbilgqAAAQbHrY+/evSGEZrN5+aeUy+VqtVqv1y9cuJDf\nJ2XtT/EAADaJYreuJEmq1Wqz2dy/f3/vvF273W40GuudtWfPnhDC4cOHw/dWZgEAiuF2J/3k\n96ur1+tr5+3SNM3XalfZtWtXCOHgwYNh/StqAQA2gxm7S6jVamfOnGm1Wmma5lumpqbm5uZm\nZmYueh+ToaGh/Mg0Tbdv317oWAGAwTa4M3aXfwFskiRJkqx6CGyfr5qZmVl7wHM7X/NyRwgA\n8LKYsQMAiIRiBwAQCcUOACASih0AQCQUOwCASCh2AACRUOwAACKh2AEAREKxAwCIRKnPAxgW\nFhZGRkaKHA0AMJi0jqticB8plnv+nrcVkHLDE19+/u5dBQSFEG44djZ85rFissK7HgiPf7yg\nrHvft/L+8QJySh+bWfmNuwsICiGU/uTYSxN3FpN13fRseOwDxWSFBz66MvvpYqJKd747fLRS\nRNIHmkX+A8NHCvmjQggfbIbffU9BWX/wqZfmTxSQc93ozz9/T1JAUAjhhifaX/n6N4rJeuub\n3vj1/3i6mKw3/dAbvvH0NwsIeuMbXl9AykCxFAsAEAnFDgAgEoodAEAkFDsAgEgodgAAkVDs\nAAAiodgBAERCsQMAiIRiBwAQCcUOACASih0AQCS2brEbHx9vNBqzs7PLy8urdi0vL8/OzjYa\njfHx/314aKlUKpVKve/n5+fXfmfvYQAAkdn2Sg9gXVmWZVkWQmi1WhMTE727jh07Njk52f/0\nRx555PDhw0NDQ5s4RACArWTrztjlKpVKXu96ZVlWqVT6n5hl2aOPPrpp4wIA2HK2erEbGxvL\nsmxpaam7ZWlpKcuysbGx/ifOzMzU6/XZ2dlNHiAAwFax1Yvdzp07QwiLi4vdLfn7fHsfaZpW\nKpW77rpr7U/0AACitNWL3fDwcJqmx48f727J3w8PD1/y3IcffjiEYEEWABgQW73YhRDSNG02\nm/nE2/LycrPZbLVal3Pi0NDQk08+aUEWABgQ10Cx2717dwjh7Nmz3ddbb731Ms+98847q9Wq\nBVkAYBBcA8Vux44dIYSTJ092X2+55ZbLP/3AgQMhhIceemhTBgcAsGVcA8WuXC5Xq9V6vX7h\nwoV6vV6tVsvl8uWfni/INpvNtbdNAQCIyTVQ7EIIe/bsCSEcPnw4fG9l9mXJF2S7j6kAAIjS\ntVHsdu3aFUI4ePBgCCFJkg18w4EDB9I0vcrDAgDYSq6NYjc0NJTXsjRNt2/fvrFvePDBB6/2\nuAAAtpCt+6zYlZWV3o8zMzN9Dljvfa/R0dH1dgEARODamLEDAOCSFDsAgEgodgAAkVDsAAAi\nodgBAERCsQMAiIRiBwAQCcUOACASih0AQCRKfR7GsLCwMDIyUuRoAIDBpHVcFVvykWKf+P2C\ngt77eysnP1NATmnPu4oJyrP+61+/UkzW9+9463+eKyjrB37krS9+8ckCgrbddtdLp/6ugKAQ\nwnW7f3Zl9tPFZJXufHf4yz8qJiv8ym+/ePrzxURt+4k7vvuFvykg6FXv+IXv/sPxAoJCCK/6\n6bEXvvT3xWRd//afWfncE8Vkld55z3cW2wUEvXpn8t3P/3UBQSGEV93xi2f+5WvFZP34j775\nW888U0zW62666dlnny0g6MYbbywgZaBYigUAiIRiBwAQCcUOACASih0AQCQUOwCASCh2AACR\nUOwAACKh2AEAREKxAwCIhGIHABAJxQ4AIBJXWuzm5+cbjUapVCqVSuPj49PT00tLS70HlC5m\nenr6/PnzVxgNAECvbVdy8qFDh+r1evdjlmVZloUQjh49et999/U5cXJyMoRw7ty57du3X8kA\nAADo2viMXd7qqtXq4uLiysrKyspKp9OZm5tL03Tfvn2rJuRW/r+jR4+GEKanp690+AAAfM8G\ni1273a7X65VKpVarDQ8P5xvL5fLo6GitVgshnDhxos/p+Xxe72wfAABXaINLsadOnQohVCqV\ntbuSJOl0OuVy+YrGBQDAy7TBYpf/li5Jkovu7d/qLly48Pjjj4cQWq3WxtIBAFjriopdr1Kp\ntGrLyspKn70hhLvvvntj6QAArPUK3McuTdNWq3Xu3LmhoaHi0wEAYrXBGbupqamDBw+22+3u\namz/+bnevQAAbIYNztjt3bs3hNBsNq/qYAAA2LgNztglSVKtVvP7lVQqle68Xbvd/uxnP3vV\nRgcAwGXb+JMn8vvV1ev1tfN2aZpOTU1d0bgAAHiZrujiiVqtdubMmVarlaZpvmVqampubm5m\nZqZ712IAAIpxRc+KDSEkSZIkycTExHoHuGwCAKAYr8DtTgAA2AyKHQBAJBQ7AIBIKHYAAJFQ\n7AAAIqHYAQBEQrEDAIiEYgcAEAnFDgAgEqU+T4ZYWFgYGRkpcjQAwGDSOq4KM3YAAJFQ7AAA\nIrGt/+6FhYVixgEAwBXq9xs7AACuIZZiAQAiodgBAERCsQMAiIRiBwAQCcUOACASih0AQCQU\nOwCASCh2AACRUOwAACKh2AEAREKxAwCIhGIHABAJxQ4AIBKKHQBAJBQ7AIBIKHYAAJFQ7AAA\nIqHYAQBEQrEDAIiEYgcAEAnFDgAgEoodAEAkFDsAgEgodgAAkVDsAAAiodgBAERCsQMAiIRi\nBwAQCcUOACASih0AQCQUOwCASCh2AACRUOwAACKh2AEAROJ/AMBLBBcp1LK7AAAAAElFTkSu\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numbers <- NBA_data_filtered %>% select_if(is.numeric) \n",
    "\n",
    "# Drop draft_pick and draft_round columns that contain NA values. \n",
    "numbers_na <- numbers %>% select(which(colSums(is.na(.)) == 0))\n",
    "\n",
    "corr_df <- ggcorr(numbers_na) + ggtitle('Correlation of Numerical Statistics') + theme(title = element_text(size=20))\n",
    "\n",
    "corr_df\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The correlation plot displays many potential relationships that we can explore in the future. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Wrangling and Visualizations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Research Question #1:\n",
    "\n",
    "What has happened to the rate of 3-point shooting in the NBA over time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make new data frame to alter for this plot \n",
    "df_threes <- NBA_data_filtered \n",
    "# Group dataframe by season and average ration of 3 pointers attempted out of total shots attempted\n",
    "df_3_ratio <- df_threes %>% group_by(Season) %>% mutate(X3PM_FGM_ratio = mean(X3PA/FGA))\n",
    "# Condense df\n",
    "df_3_ratio <- df_3_ratio %>% distinct(Season, X3PM_FGM_ratio)\n",
    "\n",
    "# Create new columns with the Stephen Curry MVP season rows to be highlighted as the only TRUE values. \n",
    "df_3_ratio$highlight <- FALSE\n",
    "df_3_ratio$highlight[df_3_ratio$Season == '2014 - 2015' | df_3_ratio$Season == '2015 - 2016'] <- TRUE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xGEBRA7XlTiJ4KwAGLHi0r8RBAWQOx4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\nhAUAwYCwACAYEBYABMP/A8ML0ipK2LXhAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set size of plot\n",
    "options(repr.plot.width=10, repr.plot.height=10)\n",
    "# Create plot with label of highlighted bars. \n",
    "ggplot(df_3_ratio) + aes(x= Season, y= X3PM_FGM_ratio, fill= highlight) + \n",
    "    geom_col(show.legend=FALSE) +  \n",
    "    theme(axis.text.x = element_text(angle=-70, hjust=-0.2, size=12), axis.text.y= element_text(size = 12),\n",
    "     panel.grid.major = element_blank(), plot.title= element_text(size=18), axis.title.x= element_text(size=14),\n",
    "     axis.title.y= element_text(size=14), legend.title= element_text(size=14), legend.text = element_text(size = 12))+\n",
    "    labs(x= \"Year of Season\", y=\"Percentage of Shots that were 3-Pointers\", title= \"The Rise of the 3-Pointer in the NBA\") + \n",
    "    scale_y_continuous(labels = scales::percent) + scale_fill_manual(values= c(\"blue3\", \"gold\"))+\n",
    "    annotate('text', label = 'S. Curry MVP', x = 16.3, y = 0.295, size=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot above that the rate of 3-point shot attempts has been steadily increasing over time. Part of this increase has been contributed to the increase in the use of [analytics in the NBA](https://www.theatlantic.com/entertainment/archive/2015/06/nba-data-analytics/396776/), but there is also evidence that the influence of a specific player has played a role. Stephen Curry of the Golden State Warriors is known as the most prolific 3-point shooter of all time, and we can see from the graph that as his influence in the NBA grew, there was a jump in the percentage of 3 point shot attempts throughout the league. Stephen Curry first named an \"All-Star\" in the 2013-2014 season, and he was named the NBA's most valuable player in the next two seasons. Although there is a general upward trend with time, these three seasons are where we see the most dramatic increases in 3-point attempts. Perhaps this is partially due to the popularity and success of Stephen Curry and his 3-point loving Golden State Warriors (that is why the plot is made in the Warriors team colors)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Research Question #2: \n",
    "\n",
    "The NBA is popular in the United States, but they have been making efforts to become a worldwide league and spread the brand, and the game of basketball around the world. \n",
    "\n",
    "Have the NBA's efforts to globalize been successful? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Note: \n",
    "For this plot, we removed the 2011-2012 and the 2019-2020 seasons. These were both shortened seasons (2011-2012 due to the NBA lockout, and 2019-2020 due to the coronavirus pandemic). Our data is filtered by the number of players that played in more than 60 games in each season, and in a shortened season (less than the regular 82 games), there are less players that make it to the 60-game benchmark. To accurately compare from year to year, we decided to remove the years with shortened seasons from this plot.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    " \n",
    "# Make new data frame with two seasons that had a shortened amount of games removed (NBA lockout year and pandemic year). \n",
    "df_country <- NBA_data_filtered %>% filter(NBA_data_filtered$Season != '2011 - 2012' & NBA_data_filtered$Season != '2019 - 2020')\n",
    "# alter nationality column to be either 'United States' or 'International'\n",
    "df_int <- df_country %>% mutate(nationality = ifelse(nationality != 'United States', 'International', nationality))\n",
    "# Find out how many international and US players there are in each season. \n",
    "df_int_count <- df_int %>% group_by(Season) %>% count(nationality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A5nvHqlEDkKC0PhNcWeKUSOwsJAmLXV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\nGBQWgGBQWACC8X/v0sVtNMqe9gAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set variables for making the ticks marks on the x axis once every 10 years. \n",
    "end <- length(df_int_count$Season)\n",
    "var <- df_int_count$Season\n",
    "interval <- var[seq(1, end, by=10)]\n",
    "\n",
    "# Create the plot\n",
    "ggplot(df_int_count) + aes(x= Season, y= n, color= nationality) + geom_point(size=3) +\n",
    "scale_x_discrete(breaks= interval, labels= interval) + \n",
    "theme(axis.text.x = element_text(angle=-60, hjust=-0.1, size=12), axis.text.y= element_text(size = 12),\n",
    "     panel.grid.major = element_blank(), plot.title= element_text(size=18), axis.title.x= element_text(size=14),\n",
    "     axis.title.y= element_text(size=14), legend.title= element_text(size=14), legend.text = element_text(size = 12))+\n",
    "labs(x= \"Year of Season\", y=\"Number of Players\", title= \"International Influence of the NBA\", color= \"Player Nationality\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We can see from this plot that although there are many more American players than international players in the NBA, the number of international players is steadily increasing. It does appear that the NBA's efforts to globalize are starting to pay off. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Follow-up Question #1 (Not Answered in this Project):\n",
    "\n",
    "With the increase in the number of international players, perhaps there are more international fans of the NBA. To determine if this is the case, we could pose the question:\n",
    "\n",
    "How have the NBA's international viewing ratings been affected by the increasing number of international players?\n",
    "\n",
    "In order to answer this question, we would need the TV ratings data from multiple countries around the world to analyze NBA viewing rates in each country. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Research Question #3:\n",
    "\n",
    "How does age affect scoring ability of NBA players?\n",
    "\n",
    "To determine the variation in a players' scoring ability with age, a new column was created by subtracting the `Season` by the `birth_year` for each player. The new column called `year` was also added. The data was then filtered and grouped by age to include only numeric columns and to represent the mean value for each player statistic for each age group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`summarise()` ungrouping output (override with `.groups` argument)\n",
      "\n",
      "Warning message:\n",
      "\"`funs()` is deprecated as of dplyr 0.8.0.\n",
      "Please use a list of either functions or lambdas: \n",
      "\n",
      "  # Simple named list: \n",
      "  list(mean = mean, median = median)\n",
      "\n",
      "  # Auto named with `tibble::lst()`: \n",
      "  tibble::lst(mean, median)\n",
      "\n",
      "  # Using lambdas\n",
      "  list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))\n",
      "\u001b[90mThis warning is displayed once every 8 hours.\u001b[39m\n",
      "\u001b[90mCall `lifecycle::last_warnings()` to see where this warning was generated.\u001b[39m\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 6 × 19</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>age</th><th scope=col>year</th><th scope=col>GP</th><th scope=col>MIN</th><th scope=col>FGM</th><th scope=col>FGA</th><th scope=col>X3PM</th><th scope=col>X3PA</th><th scope=col>FTM</th><th scope=col>FTA</th><th scope=col>TOV</th><th scope=col>PF</th><th scope=col>ORB</th><th scope=col>DRB</th><th scope=col>REB</th><th scope=col>AST</th><th scope=col>STL</th><th scope=col>BLK</th><th scope=col>PTS</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>20</td><td>2011.6</td><td>75.0</td><td>1836.6</td><td>277.8</td><td>635.0</td><td>47.2</td><td>143.9</td><td>139.4</td><td>193.3</td><td>115.0</td><td>160.0</td><td> 90.3</td><td>233.9</td><td>324.2</td><td>129.8</td><td>51.4</td><td>48.6</td><td>742.2</td></tr>\n",
       "\t<tr><td>21</td><td>2011.2</td><td>75.7</td><td>1945.2</td><td>308.3</td><td>679.2</td><td>47.9</td><td>142.0</td><td>155.0</td><td>212.7</td><td>124.0</td><td>174.6</td><td>102.1</td><td>259.7</td><td>361.8</td><td>162.1</td><td>63.9</td><td>48.5</td><td>819.4</td></tr>\n",
       "\t<tr><td>22</td><td>2011.0</td><td>74.8</td><td>1934.0</td><td>316.4</td><td>688.8</td><td>49.2</td><td>142.5</td><td>158.4</td><td>213.8</td><td>120.2</td><td>172.2</td><td> 99.3</td><td>257.7</td><td>357.0</td><td>166.5</td><td>61.6</td><td>45.4</td><td>840.3</td></tr>\n",
       "\t<tr><td>23</td><td>2010.2</td><td>75.0</td><td>1993.4</td><td>328.0</td><td>714.7</td><td>52.2</td><td>150.1</td><td>164.9</td><td>220.9</td><td>123.8</td><td>172.6</td><td> 99.6</td><td>268.2</td><td>367.8</td><td>186.9</td><td>66.1</td><td>43.0</td><td>873.1</td></tr>\n",
       "\t<tr><td>24</td><td>2010.1</td><td>75.5</td><td>1976.8</td><td>324.8</td><td>704.5</td><td>55.4</td><td>156.4</td><td>161.3</td><td>214.6</td><td>117.6</td><td>171.0</td><td> 95.3</td><td>256.8</td><td>352.2</td><td>178.8</td><td>65.1</td><td>41.9</td><td>866.3</td></tr>\n",
       "\t<tr><td>25</td><td>2010.3</td><td>75.0</td><td>2031.4</td><td>335.8</td><td>727.7</td><td>60.9</td><td>169.9</td><td>169.2</td><td>222.7</td><td>118.7</td><td>171.7</td><td> 96.9</td><td>266.0</td><td>362.9</td><td>182.6</td><td>65.5</td><td>42.1</td><td>901.7</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 19\n",
       "\\begin{tabular}{lllllllllllllllllll}\n",
       " age & year & GP & MIN & FGM & FGA & X3PM & X3PA & FTM & FTA & TOV & PF & ORB & DRB & REB & AST & STL & BLK & PTS\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 20 & 2011.6 & 75.0 & 1836.6 & 277.8 & 635.0 & 47.2 & 143.9 & 139.4 & 193.3 & 115.0 & 160.0 &  90.3 & 233.9 & 324.2 & 129.8 & 51.4 & 48.6 & 742.2\\\\\n",
       "\t 21 & 2011.2 & 75.7 & 1945.2 & 308.3 & 679.2 & 47.9 & 142.0 & 155.0 & 212.7 & 124.0 & 174.6 & 102.1 & 259.7 & 361.8 & 162.1 & 63.9 & 48.5 & 819.4\\\\\n",
       "\t 22 & 2011.0 & 74.8 & 1934.0 & 316.4 & 688.8 & 49.2 & 142.5 & 158.4 & 213.8 & 120.2 & 172.2 &  99.3 & 257.7 & 357.0 & 166.5 & 61.6 & 45.4 & 840.3\\\\\n",
       "\t 23 & 2010.2 & 75.0 & 1993.4 & 328.0 & 714.7 & 52.2 & 150.1 & 164.9 & 220.9 & 123.8 & 172.6 &  99.6 & 268.2 & 367.8 & 186.9 & 66.1 & 43.0 & 873.1\\\\\n",
       "\t 24 & 2010.1 & 75.5 & 1976.8 & 324.8 & 704.5 & 55.4 & 156.4 & 161.3 & 214.6 & 117.6 & 171.0 &  95.3 & 256.8 & 352.2 & 178.8 & 65.1 & 41.9 & 866.3\\\\\n",
       "\t 25 & 2010.3 & 75.0 & 2031.4 & 335.8 & 727.7 & 60.9 & 169.9 & 169.2 & 222.7 & 118.7 & 171.7 &  96.9 & 266.0 & 362.9 & 182.6 & 65.5 & 42.1 & 901.7\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 19\n",
       "\n",
       "| age &lt;dbl&gt; | year &lt;dbl&gt; | GP &lt;dbl&gt; | MIN &lt;dbl&gt; | FGM &lt;dbl&gt; | FGA &lt;dbl&gt; | X3PM &lt;dbl&gt; | X3PA &lt;dbl&gt; | FTM &lt;dbl&gt; | FTA &lt;dbl&gt; | TOV &lt;dbl&gt; | PF &lt;dbl&gt; | ORB &lt;dbl&gt; | DRB &lt;dbl&gt; | REB &lt;dbl&gt; | AST &lt;dbl&gt; | STL &lt;dbl&gt; | BLK &lt;dbl&gt; | PTS &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 20 | 2011.6 | 75.0 | 1836.6 | 277.8 | 635.0 | 47.2 | 143.9 | 139.4 | 193.3 | 115.0 | 160.0 |  90.3 | 233.9 | 324.2 | 129.8 | 51.4 | 48.6 | 742.2 |\n",
       "| 21 | 2011.2 | 75.7 | 1945.2 | 308.3 | 679.2 | 47.9 | 142.0 | 155.0 | 212.7 | 124.0 | 174.6 | 102.1 | 259.7 | 361.8 | 162.1 | 63.9 | 48.5 | 819.4 |\n",
       "| 22 | 2011.0 | 74.8 | 1934.0 | 316.4 | 688.8 | 49.2 | 142.5 | 158.4 | 213.8 | 120.2 | 172.2 |  99.3 | 257.7 | 357.0 | 166.5 | 61.6 | 45.4 | 840.3 |\n",
       "| 23 | 2010.2 | 75.0 | 1993.4 | 328.0 | 714.7 | 52.2 | 150.1 | 164.9 | 220.9 | 123.8 | 172.6 |  99.6 | 268.2 | 367.8 | 186.9 | 66.1 | 43.0 | 873.1 |\n",
       "| 24 | 2010.1 | 75.5 | 1976.8 | 324.8 | 704.5 | 55.4 | 156.4 | 161.3 | 214.6 | 117.6 | 171.0 |  95.3 | 256.8 | 352.2 | 178.8 | 65.1 | 41.9 | 866.3 |\n",
       "| 25 | 2010.3 | 75.0 | 2031.4 | 335.8 | 727.7 | 60.9 | 169.9 | 169.2 | 222.7 | 118.7 | 171.7 |  96.9 | 266.0 | 362.9 | 182.6 | 65.5 | 42.1 | 901.7 |\n",
       "\n"
      ],
      "text/plain": [
       "  age year   GP   MIN    FGM   FGA   X3PM X3PA  FTM   FTA   TOV   PF    ORB  \n",
       "1 20  2011.6 75.0 1836.6 277.8 635.0 47.2 143.9 139.4 193.3 115.0 160.0  90.3\n",
       "2 21  2011.2 75.7 1945.2 308.3 679.2 47.9 142.0 155.0 212.7 124.0 174.6 102.1\n",
       "3 22  2011.0 74.8 1934.0 316.4 688.8 49.2 142.5 158.4 213.8 120.2 172.2  99.3\n",
       "4 23  2010.2 75.0 1993.4 328.0 714.7 52.2 150.1 164.9 220.9 123.8 172.6  99.6\n",
       "5 24  2010.1 75.5 1976.8 324.8 704.5 55.4 156.4 161.3 214.6 117.6 171.0  95.3\n",
       "6 25  2010.3 75.0 2031.4 335.8 727.7 60.9 169.9 169.2 222.7 118.7 171.7  96.9\n",
       "  DRB   REB   AST   STL  BLK  PTS  \n",
       "1 233.9 324.2 129.8 51.4 48.6 742.2\n",
       "2 259.7 361.8 162.1 63.9 48.5 819.4\n",
       "3 257.7 357.0 166.5 61.6 45.4 840.3\n",
       "4 268.2 367.8 186.9 66.1 43.0 873.1\n",
       "5 256.8 352.2 178.8 65.1 41.9 866.3\n",
       "6 266.0 362.9 182.6 65.5 42.1 901.7"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "year <- list()\n",
    "age <- list()\n",
    "for(i in 1:nrow(NBA_data_filtered)){\n",
    "    current_year <- as.numeric(substring(NBA_data_filtered[i,2], 8,11))\n",
    "    age[i] <- current_year - NBA_data_filtered$birth_year[i]\n",
    "    year[i] <- current_year\n",
    "}\n",
    "\n",
    "NBA_data_temp <-add_column(NBA_data_filtered,age = as.numeric(age),.after=22)\n",
    "NBA_data_temp <-add_column(NBA_data_temp,year = as.numeric(year),.after=1)\n",
    "\n",
    "# Select only numerical columns and group by age and find mean of each stat\n",
    "NBA_grouped_age <- subset(NBA_data_temp,select=c(2,7:24)) %>% group_by(age) %>% summarize(across(everything(), mean)) %>% mutate_at(vars(-age), funs(round(., 1)))\n",
    "head(NBA_grouped_age)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fsCWFdUZq4Blge1PNg5atkXwLqiMnMNsDyo5cHOUcu+ANYVlZlrgOVBLQ92jlr2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\njf4/tfltBdHrbZQAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Create plot\n",
    "ggplot(NBA_grouped_age) + aes(x = age, y = PTS) + \n",
    "geom_col(fill = 'darkorange',alpha = 0.3) +\n",
    "scale_x_continuous(name=\"Age\") +\n",
    "scale_y_continuous(name=\"Average Total Points\") +\n",
    "ggtitle('Total Points Scored by NBA Players Each\\nSeason According to Age')+\n",
    "theme(axis.text=element_text(size=12),\n",
    "        axis.title=element_text(size=20,face=\"bold\"),\n",
    "        plot.title = element_text(size=25),\n",
    "        legend.position = \"none\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By modeling the total points scored based on the age of the player, we can observe that most players score an average of 750 points in their first season in the NBA, increasing to a peak of 900 points per season by the age of 25. At this point, a player's scoring rate plateaus until they turn 29, then it starts rapidly decreasing at a rate of 25 points per season each year. The data for players over 35 years old is highly variable as only a limited number of players remain in the NBA until the age of 35 and continue to play more than 60 games per season."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wanted to dig deeper into the breakdown of the type of points that are scored in the NBA. \n",
    "\n",
    "#### Research Question # 4:\n",
    "\n",
    "How are total points distributed by 2-pointers vs. 3-pointers in the NBA?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`summarise()` ungrouping output (override with `.groups` argument)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Group by year and find mean of numerical stats\n",
    "NBA_grouped_year <- subset(NBA_data_temp,select=c(2,7:24,29)) %>% group_by(year) %>% summarize(across(everything(), mean)) %>% mutate_at(vars(-year), funs(round(., 1)))\n",
    "# Add column showing points scored from 3 pointers (multiply 3 pointers made by 2 points for each shot)\n",
    "NBA_grouped_year <-add_column(NBA_grouped_year,X3PM_corrected = NBA_grouped_year$X3PM*3)\n",
    "# Add column showing points scored from 2 pointers\n",
    "NBA_grouped_year <-add_column(NBA_grouped_year,X2P_corrected = NBA_grouped_year$PTS - NBA_grouped_year$X3PM*3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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j37WzR5e/giWEjWnLPuBMvE1M3hjWAhXdODxTtCGxM3hz+ChXTNClbsmd+kiZvD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\nIFgAkkGwACSDYAFIBsECkIz/Dzqfw/QoOjirAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create plot\n",
    "\n",
    "ggplot(NBA_grouped_year, aes(x = year)) + \n",
    "    geom_area(aes(y = X3PM_corrected), fill = 'lightblue', color ='blue', size = 1,alpha = 0.5)  +\n",
    "    geom_area(aes(y = X2P_corrected), fill = 'orangered', color ='orangered', size = 1,alpha = 0.15)  +\n",
    "    geom_area(aes(y = PTS), fill = 'lightgrey', color ='black', size = 1,alpha = 0.15)  +\n",
    "    scale_x_continuous(name=\"Year\") +\n",
    "    scale_y_continuous(name=\"Points\") +\n",
    "    ggtitle('Average Yearly Points per Player in the NBA')+\n",
    "    theme(axis.text=element_text(size=12),\n",
    "        axis.title=element_text(size=20,face=\"bold\"),\n",
    "        plot.title = element_text(size=25),\n",
    "        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),\n",
    "        legend.position=\"bottom\",legend.text = element_text(colour=\"blue\", size=10, \n",
    "                                     face=\"bold\")\n",
    ")+\n",
    "annotate('text', label = 'NBA lockout', x = 2013, y = 550, size=5)+\n",
    "annotate('text', label = 'Total pts', x = 2021, y = 830, size=5) +\n",
    "annotate('text', label = '2 pts', x = 2020.7, y = 555, size=5) +\n",
    "annotate('text', label = '3 pts', x = 2020.7, y = 280, size=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the data is grouped by year, the plot above displays the overall total points, the total points from 3 pointers and the total points from 2 pointers over time. What we observed is that from the years 2000-2020. The total number of points scored from 2 pointers is significantly larger than that from 3 pointers, with 2 pointers scoring 750 points and 3 pointers totaling 130 points each year. However, by the year 2020, the number of points from 3 pointers has increased to 280 points, while points from 2 pointers has decreased to 550 points. This change in the distribution of points is fairly consistent, suggesting that within the next 16 years, assuming the trend stays consistent that the number of points from 3 pointers could overtake the number of points scored from 2 pointers. \n",
    "\n",
    "##### Note: \n",
    "We also see a dip in total points in the 2011-2012 season due to the NBA lockout causing there to be 66 games instead of the regular 82 games played that season. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Now we will look at this same points breakdown by age of players instead of year of the season. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perform same data wrangling as done for the previous chart, except grouping by age instead of year. \n",
    "NBA_grouped_age <-add_column(NBA_grouped_age,X3PM_corrected = NBA_grouped_age$X3PM*3)\n",
    "NBA_grouped_age <-add_column(NBA_grouped_age,X2P_corrected = NBA_grouped_age$PTS - NBA_grouped_age$X3PM*3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R2cMKEECJb8fQvxxff1l1r0v9uLv1xT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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create plot of points breakdown (3 pointers vs. 2 pointers) by age\n",
    "\n",
    "ggplot(NBA_grouped_age) + aes(x = age, y = PTS) + \n",
    " geom_area(aes(y = X3PM_corrected), fill = 'lightblue', color ='blue', size = 1,alpha = 0.5)  +\n",
    "    geom_area(aes(y = X2P_corrected), fill = 'orangered', color ='orangered', size = 1,alpha = 0.15)  +\n",
    "    geom_area(aes(y = PTS), fill = 'lightgrey', color ='black', size = 1,alpha = 0.15)  +\n",
    "    scale_x_continuous(name=\"Age\") +\n",
    "    scale_y_continuous(name=\"Points\") +\n",
    "    ggtitle('Average Yearly Points per Player in the NBA by Age')+\n",
    "    theme(axis.text=element_text(size=12),\n",
    "        axis.title=element_text(size=20,face=\"bold\"),\n",
    "        plot.title = element_text(size=25),\n",
    "        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),\n",
    "        legend.position=\"bottom\",legend.text = element_text(colour=\"blue\", size=10, \n",
    "                                     face=\"bold\")\n",
    ")+\n",
    "annotate('text', label = 'Total pts', x = 18.5, y = 745, size=5) +\n",
    "annotate('text', label = '2 pts', x = 19 , y = 600, size=5) +\n",
    "annotate('text', label = '3 pts', x = 19 , y = 145, size=5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As seen above, when we compared the distribution of points of two and three pointers made by players with their age, we observe that players quickly maximize their scoring ability for two pointer and plateau by the age of 23. In contrast, the players reach their maximum 3-point scoring rate when they're 29, and the rate decreases significantly more slowly than that of two pointers. This is expected as 3 pointers require technical ability that would develop over time while 2 pointers require more speed and agility. Therefore, as 3 pointers are increasingly becoming the dominate method for scoring points, it would suggest a change in demographic or strategy within the league, allowing for more older players to have a significant impact on scoring.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Follow-Up Question #2 (Not Answered in this Project):\n",
    "\n",
    "Why does the 3-point scoring rate increase sharply at ages 40 and 42?\n",
    "\n",
    "To answer this question, we would need to determine how many players there are at those specific ages and determine who those individual players are. It is possible that if there are very few players at those ages, a single player who makes a large amount of three pointers would skew the data as seen above. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Summary\n",
    "\n",
    "We have learned from an exploratory analysis of this NBA data that the three pointer is becoming more important. If this trend continues, it may allow older players to continue to score at high rates as they age. We also learned that the NBA is seeing an increase in the number of international players, which suggests that the globalization efforts of the NBA are proving effective.   "
   ]
  }
 ],
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   "file_extension": ".r",
   "mimetype": "text/x-r-source",
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