t-test+Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis test + Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2 sample t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "from sklearn.cluster import KMeans\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "NBA_4th = pd.read_csv(\"data/NBA_4th_comp.csv\")\n",
    "first_3 = pd.read_csv(\"data/first_3_comp.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['index', 'TEAM', 'MATCH UP', 'GAME DATE', 'W/L', 'MIN', 'PTS', 'FGM',\n",
       "       'FGA', 'FG%', '3PM', '3PA', '3P%', 'FTM', 'FTA', 'FT%', 'OREB', 'DREB',\n",
       "       'REB', 'AST', 'TOV', 'STL', 'BLK', 'PF', '+/-', 'COURT', 'Opponent',\n",
       "       'OppPTS', 'OppFGM', 'OppFGA', 'OppFG%', 'Opp3PM', 'Opp3PA', 'Opp3P%',\n",
       "       'OppFTM', 'OppFTA', 'OppFT%', 'OppOREB', 'OppDREB', 'OppREB', 'OppAST',\n",
       "       'OppTOV', 'OppSTL', 'OppBLK', 'OppPF', 'Pos', 'OppPos', 'Pace',\n",
       "       'OFFRTG', 'DEFRTG', 'Margin', 'formatted_date', 'week_of_season',\n",
       "       'PTS/Q'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_3.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p value for Pace: 2.5703488123523338e-115 and the statistic: -23.573392663179916\n",
      "p value for OFFRTG: 0.6731949813303986 and the statistic: 0.42179752362989176\n",
      "p value for DEFRTG: 0.6731949813303812 and the statistic: 0.4217975236299151\n",
      "p value for 3P%: 0.0 and the statistic: 85.97462692789428\n",
      "p value for AST: 0.0 and the statistic: -132.1146149441038\n",
      "p value for FT%: 0.0 and the statistic: 126.24337384047551\n"
     ]
    }
   ],
   "source": [
    "# H0: first 3 quarter = 4th quarter\n",
    "\n",
    "columns = ['Pace','OFFRTG','DEFRTG',\"3P%\",\"AST\",'FT%']\n",
    "for col in columns:\n",
    "    t_stat, p_val = stats.ttest_ind(NBA_4th[col], first_3[col])\n",
    "    print(\"p value for %s: \" % (col) + str(p_val) +\" and the statistic: \" + str(t_stat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Reject H0 at the 95% confidence interval for Pace, AST, 3P%, 'PTS', 'FT%\n",
    "- Can´t reject H0 for DEFRTG and OFFRTG"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KMeans Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DEFRTG</th>\n",
       "      <th>OFFRTG</th>\n",
       "      <th>DEFRTG_4th</th>\n",
       "      <th>OFFRTG_4th</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TEAM</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ATL</th>\n",
       "      <td>116.624969</td>\n",
       "      <td>117.035673</td>\n",
       "      <td>114.161390</td>\n",
       "      <td>110.332808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BKN</th>\n",
       "      <td>113.515708</td>\n",
       "      <td>114.937408</td>\n",
       "      <td>111.305306</td>\n",
       "      <td>110.241938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BOS</th>\n",
       "      <td>107.380896</td>\n",
       "      <td>110.668632</td>\n",
       "      <td>112.215981</td>\n",
       "      <td>112.872153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHA</th>\n",
       "      <td>113.948561</td>\n",
       "      <td>113.462007</td>\n",
       "      <td>108.893058</td>\n",
       "      <td>114.119936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHI</th>\n",
       "      <td>112.702629</td>\n",
       "      <td>112.956782</td>\n",
       "      <td>114.976167</td>\n",
       "      <td>118.701130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CLE</th>\n",
       "      <td>110.760205</td>\n",
       "      <td>110.264056</td>\n",
       "      <td>114.277824</td>\n",
       "      <td>112.744565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DAL</th>\n",
       "      <td>110.038357</td>\n",
       "      <td>112.475246</td>\n",
       "      <td>107.110677</td>\n",
       "      <td>108.509729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DEN</th>\n",
       "      <td>111.465458</td>\n",
       "      <td>114.395260</td>\n",
       "      <td>116.466644</td>\n",
       "      <td>108.150348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DET</th>\n",
       "      <td>112.895421</td>\n",
       "      <td>109.874105</td>\n",
       "      <td>110.798256</td>\n",
       "      <td>105.087445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GSW</th>\n",
       "      <td>108.409172</td>\n",
       "      <td>112.724828</td>\n",
       "      <td>106.972879</td>\n",
       "      <td>111.355693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HOU</th>\n",
       "      <td>115.061222</td>\n",
       "      <td>109.716574</td>\n",
       "      <td>116.952996</td>\n",
       "      <td>110.222191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IND</th>\n",
       "      <td>116.415883</td>\n",
       "      <td>113.338467</td>\n",
       "      <td>113.391555</td>\n",
       "      <td>112.778354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LAC</th>\n",
       "      <td>109.957685</td>\n",
       "      <td>107.669562</td>\n",
       "      <td>111.161375</td>\n",
       "      <td>114.433841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LAL</th>\n",
       "      <td>113.586920</td>\n",
       "      <td>111.051695</td>\n",
       "      <td>111.219826</td>\n",
       "      <td>111.334863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MEM</th>\n",
       "      <td>108.802726</td>\n",
       "      <td>112.750489</td>\n",
       "      <td>112.730440</td>\n",
       "      <td>115.299347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MIA</th>\n",
       "      <td>109.923000</td>\n",
       "      <td>114.092897</td>\n",
       "      <td>108.903138</td>\n",
       "      <td>113.749722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MIL</th>\n",
       "      <td>113.553476</td>\n",
       "      <td>114.185755</td>\n",
       "      <td>105.401196</td>\n",
       "      <td>115.939234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MIN</th>\n",
       "      <td>112.296966</td>\n",
       "      <td>113.428980</td>\n",
       "      <td>115.547031</td>\n",
       "      <td>111.025345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOP</th>\n",
       "      <td>111.739120</td>\n",
       "      <td>109.568484</td>\n",
       "      <td>116.245159</td>\n",
       "      <td>116.159558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NYK</th>\n",
       "      <td>110.565058</td>\n",
       "      <td>111.142655</td>\n",
       "      <td>111.123822</td>\n",
       "      <td>108.072345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OKC</th>\n",
       "      <td>109.672851</td>\n",
       "      <td>104.247655</td>\n",
       "      <td>110.449047</td>\n",
       "      <td>109.338482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ORL</th>\n",
       "      <td>109.389130</td>\n",
       "      <td>104.366686</td>\n",
       "      <td>114.399555</td>\n",
       "      <td>111.615125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PHI</th>\n",
       "      <td>110.935685</td>\n",
       "      <td>115.332392</td>\n",
       "      <td>108.171559</td>\n",
       "      <td>111.186858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PHX</th>\n",
       "      <td>108.336707</td>\n",
       "      <td>111.269656</td>\n",
       "      <td>109.045913</td>\n",
       "      <td>122.864011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POR</th>\n",
       "      <td>114.666109</td>\n",
       "      <td>112.293438</td>\n",
       "      <td>119.892411</td>\n",
       "      <td>105.059341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SAC</th>\n",
       "      <td>114.647440</td>\n",
       "      <td>111.433552</td>\n",
       "      <td>117.000698</td>\n",
       "      <td>109.504678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SAS</th>\n",
       "      <td>113.284729</td>\n",
       "      <td>112.288170</td>\n",
       "      <td>110.197431</td>\n",
       "      <td>110.058777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOR</th>\n",
       "      <td>111.430002</td>\n",
       "      <td>112.627522</td>\n",
       "      <td>111.314064</td>\n",
       "      <td>116.962493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UTA</th>\n",
       "      <td>111.562522</td>\n",
       "      <td>116.609463</td>\n",
       "      <td>112.138766</td>\n",
       "      <td>114.310280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WAS</th>\n",
       "      <td>114.864709</td>\n",
       "      <td>111.852230</td>\n",
       "      <td>115.062771</td>\n",
       "      <td>116.117834</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          DEFRTG      OFFRTG  DEFRTG_4th  OFFRTG_4th\n",
       "TEAM                                                \n",
       "ATL   116.624969  117.035673  114.161390  110.332808\n",
       "BKN   113.515708  114.937408  111.305306  110.241938\n",
       "BOS   107.380896  110.668632  112.215981  112.872153\n",
       "CHA   113.948561  113.462007  108.893058  114.119936\n",
       "CHI   112.702629  112.956782  114.976167  118.701130\n",
       "CLE   110.760205  110.264056  114.277824  112.744565\n",
       "DAL   110.038357  112.475246  107.110677  108.509729\n",
       "DEN   111.465458  114.395260  116.466644  108.150348\n",
       "DET   112.895421  109.874105  110.798256  105.087445\n",
       "GSW   108.409172  112.724828  106.972879  111.355693\n",
       "HOU   115.061222  109.716574  116.952996  110.222191\n",
       "IND   116.415883  113.338467  113.391555  112.778354\n",
       "LAC   109.957685  107.669562  111.161375  114.433841\n",
       "LAL   113.586920  111.051695  111.219826  111.334863\n",
       "MEM   108.802726  112.750489  112.730440  115.299347\n",
       "MIA   109.923000  114.092897  108.903138  113.749722\n",
       "MIL   113.553476  114.185755  105.401196  115.939234\n",
       "MIN   112.296966  113.428980  115.547031  111.025345\n",
       "NOP   111.739120  109.568484  116.245159  116.159558\n",
       "NYK   110.565058  111.142655  111.123822  108.072345\n",
       "OKC   109.672851  104.247655  110.449047  109.338482\n",
       "ORL   109.389130  104.366686  114.399555  111.615125\n",
       "PHI   110.935685  115.332392  108.171559  111.186858\n",
       "PHX   108.336707  111.269656  109.045913  122.864011\n",
       "POR   114.666109  112.293438  119.892411  105.059341\n",
       "SAC   114.647440  111.433552  117.000698  109.504678\n",
       "SAS   113.284729  112.288170  110.197431  110.058777\n",
       "TOR   111.430002  112.627522  111.314064  116.962493\n",
       "UTA   111.562522  116.609463  112.138766  114.310280\n",
       "WAS   114.864709  111.852230  115.062771  116.117834"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teams_3rd = first_3.pivot_table(index = \"TEAM\", values = [\"DEFRTG\",\"OFFRTG\"], aggfunc = np.mean)\n",
    "teams_4th = NBA_4th.pivot_table(index = \"TEAM\", values = [\"DEFRTG\",\"OFFRTG\"], aggfunc = np.mean)\n",
    "teams_3rd[[\"DEFRTG_4th\",\"OFFRTG_4th\"]] = teams_4th[[\"DEFRTG\",\"OFFRTG\"]]\n",
    "teams_3rd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = teams_3rd.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=4, random_state=1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = KMeans(n_clusters = 4, random_state = 1)\n",
    "classifier.fit(samples)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f850b38c790>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Four clusters are a good fit\n",
    "\n",
    "num_clusters = list(range(1,9))\n",
    "inertias =  []\n",
    "\n",
    "for k in num_clusters:\n",
    "  model = KMeans(n_clusters=k)\n",
    "  model.fit(samples)\n",
    "  inertias.append(model.inertia_)\n",
    "  \n",
    "plt.plot(num_clusters, inertias, '-o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 0, 1, 3, 0, 1, 2, 0, 1, 2, 2, 0, 0, 3, 1, 1, 2, 3, 0, 0, 0,\n",
       "       1, 3, 2, 2, 1, 3, 1, 3], dtype=int32)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 5, 8, 12, 13, 19, 20, 21]\n"
     ]
    }
   ],
   "source": [
    "cluster_zero_indices = []\n",
    "cluster_one_indices = []\n",
    "cluster_two_indices = []\n",
    "cluster_three_indices = []\n",
    "for i in range(len(classifier.labels_)):\n",
    "    if classifier.labels_[i] == 0:\n",
    "        cluster_zero_indices.append(i)\n",
    "    elif classifier.labels_[i] == 1:\n",
    "        cluster_one_indices.append(i)\n",
    "    elif classifier.labels_[i] == 2:\n",
    "        cluster_two_indices.append(i)\n",
    "    elif classifier.labels_[i] == 3:\n",
    "        cluster_three_indices.append(i)        \n",
    "print(cluster_zero_indices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DEFRTG</th>\n",
       "      <th>OFFRTG</th>\n",
       "      <th>DEFRTG_4th</th>\n",
       "      <th>OFFRTG_4th</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TEAM</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>BOS</th>\n",
       "      <td>107.380896</td>\n",
       "      <td>110.668632</td>\n",
       "      <td>112.215981</td>\n",
       "      <td>112.872153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CLE</th>\n",
       "      <td>110.760205</td>\n",
       "      <td>110.264056</td>\n",
       "      <td>114.277824</td>\n",
       "      <td>112.744565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DET</th>\n",
       "      <td>112.895421</td>\n",
       "      <td>109.874105</td>\n",
       "      <td>110.798256</td>\n",
       "      <td>105.087445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LAC</th>\n",
       "      <td>109.957685</td>\n",
       "      <td>107.669562</td>\n",
       "      <td>111.161375</td>\n",
       "      <td>114.433841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LAL</th>\n",
       "      <td>113.586920</td>\n",
       "      <td>111.051695</td>\n",
       "      <td>111.219826</td>\n",
       "      <td>111.334863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NYK</th>\n",
       "      <td>110.565058</td>\n",
       "      <td>111.142655</td>\n",
       "      <td>111.123822</td>\n",
       "      <td>108.072345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OKC</th>\n",
       "      <td>109.672851</td>\n",
       "      <td>104.247655</td>\n",
       "      <td>110.449047</td>\n",
       "      <td>109.338482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ORL</th>\n",
       "      <td>109.389130</td>\n",
       "      <td>104.366686</td>\n",
       "      <td>114.399555</td>\n",
       "      <td>111.615125</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          DEFRTG      OFFRTG  DEFRTG_4th  OFFRTG_4th\n",
       "TEAM                                                \n",
       "BOS   107.380896  110.668632  112.215981  112.872153\n",
       "CLE   110.760205  110.264056  114.277824  112.744565\n",
       "DET   112.895421  109.874105  110.798256  105.087445\n",
       "LAC   109.957685  107.669562  111.161375  114.433841\n",
       "LAL   113.586920  111.051695  111.219826  111.334863\n",
       "NYK   110.565058  111.142655  111.123822  108.072345\n",
       "OKC   109.672851  104.247655  110.449047  109.338482\n",
       "ORL   109.389130  104.366686  114.399555  111.615125"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The worst group: bad defense and/or bad offense\n",
    "\n",
    "cluster_zero_df = teams_3rd.iloc[cluster_zero_indices]\n",
    "cluster_zero_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DEFRTG</th>\n",
       "      <th>OFFRTG</th>\n",
       "      <th>DEFRTG_4th</th>\n",
       "      <th>OFFRTG_4th</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TEAM</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>BKN</th>\n",
       "      <td>113.515708</td>\n",
       "      <td>114.937408</td>\n",
       "      <td>111.305306</td>\n",
       "      <td>110.241938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHA</th>\n",
       "      <td>113.948561</td>\n",
       "      <td>113.462007</td>\n",
       "      <td>108.893058</td>\n",
       "      <td>114.119936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DAL</th>\n",
       "      <td>110.038357</td>\n",
       "      <td>112.475246</td>\n",
       "      <td>107.110677</td>\n",
       "      <td>108.509729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GSW</th>\n",
       "      <td>108.409172</td>\n",
       "      <td>112.724828</td>\n",
       "      <td>106.972879</td>\n",
       "      <td>111.355693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MIA</th>\n",
       "      <td>109.923000</td>\n",
       "      <td>114.092897</td>\n",
       "      <td>108.903138</td>\n",
       "      <td>113.749722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MIL</th>\n",
       "      <td>113.553476</td>\n",
       "      <td>114.185755</td>\n",
       "      <td>105.401196</td>\n",
       "      <td>115.939234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PHI</th>\n",
       "      <td>110.935685</td>\n",
       "      <td>115.332392</td>\n",
       "      <td>108.171559</td>\n",
       "      <td>111.186858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SAS</th>\n",
       "      <td>113.284729</td>\n",
       "      <td>112.288170</td>\n",
       "      <td>110.197431</td>\n",
       "      <td>110.058777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UTA</th>\n",
       "      <td>111.562522</td>\n",
       "      <td>116.609463</td>\n",
       "      <td>112.138766</td>\n",
       "      <td>114.310280</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          DEFRTG      OFFRTG  DEFRTG_4th  OFFRTG_4th\n",
       "TEAM                                                \n",
       "BKN   113.515708  114.937408  111.305306  110.241938\n",
       "CHA   113.948561  113.462007  108.893058  114.119936\n",
       "DAL   110.038357  112.475246  107.110677  108.509729\n",
       "GSW   108.409172  112.724828  106.972879  111.355693\n",
       "MIA   109.923000  114.092897  108.903138  113.749722\n",
       "MIL   113.553476  114.185755  105.401196  115.939234\n",
       "PHI   110.935685  115.332392  108.171559  111.186858\n",
       "SAS   113.284729  112.288170  110.197431  110.058777\n",
       "UTA   111.562522  116.609463  112.138766  114.310280"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Good teams in the first 3 quarters, but declined in the 4th quarter\n",
    "\n",
    "cluster_one_df = teams_3rd.iloc[cluster_one_indices]\n",
    "cluster_one_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DEFRTG</th>\n",
       "      <th>OFFRTG</th>\n",
       "      <th>DEFRTG_4th</th>\n",
       "      <th>OFFRTG_4th</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TEAM</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ATL</th>\n",
       "      <td>116.624969</td>\n",
       "      <td>117.035673</td>\n",
       "      <td>114.161390</td>\n",
       "      <td>110.332808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DEN</th>\n",
       "      <td>111.465458</td>\n",
       "      <td>114.395260</td>\n",
       "      <td>116.466644</td>\n",
       "      <td>108.150348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HOU</th>\n",
       "      <td>115.061222</td>\n",
       "      <td>109.716574</td>\n",
       "      <td>116.952996</td>\n",
       "      <td>110.222191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IND</th>\n",
       "      <td>116.415883</td>\n",
       "      <td>113.338467</td>\n",
       "      <td>113.391555</td>\n",
       "      <td>112.778354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MIN</th>\n",
       "      <td>112.296966</td>\n",
       "      <td>113.428980</td>\n",
       "      <td>115.547031</td>\n",
       "      <td>111.025345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POR</th>\n",
       "      <td>114.666109</td>\n",
       "      <td>112.293438</td>\n",
       "      <td>119.892411</td>\n",
       "      <td>105.059341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SAC</th>\n",
       "      <td>114.647440</td>\n",
       "      <td>111.433552</td>\n",
       "      <td>117.000698</td>\n",
       "      <td>109.504678</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          DEFRTG      OFFRTG  DEFRTG_4th  OFFRTG_4th\n",
       "TEAM                                                \n",
       "ATL   116.624969  117.035673  114.161390  110.332808\n",
       "DEN   111.465458  114.395260  116.466644  108.150348\n",
       "HOU   115.061222  109.716574  116.952996  110.222191\n",
       "IND   116.415883  113.338467  113.391555  112.778354\n",
       "MIN   112.296966  113.428980  115.547031  111.025345\n",
       "POR   114.666109  112.293438  119.892411  105.059341\n",
       "SAC   114.647440  111.433552  117.000698  109.504678"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Teams with bad offense in the 4th\n",
    "\n",
    "cluster_two_df = teams_3rd.iloc[cluster_two_indices]\n",
    "cluster_two_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DEFRTG</th>\n",
       "      <th>OFFRTG</th>\n",
       "      <th>DEFRTG_4th</th>\n",
       "      <th>OFFRTG_4th</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TEAM</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CHI</th>\n",
       "      <td>112.702629</td>\n",
       "      <td>112.956782</td>\n",
       "      <td>114.976167</td>\n",
       "      <td>118.701130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MEM</th>\n",
       "      <td>108.802726</td>\n",
       "      <td>112.750489</td>\n",
       "      <td>112.730440</td>\n",
       "      <td>115.299347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOP</th>\n",
       "      <td>111.739120</td>\n",
       "      <td>109.568484</td>\n",
       "      <td>116.245159</td>\n",
       "      <td>116.159558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PHX</th>\n",
       "      <td>108.336707</td>\n",
       "      <td>111.269656</td>\n",
       "      <td>109.045913</td>\n",
       "      <td>122.864011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOR</th>\n",
       "      <td>111.430002</td>\n",
       "      <td>112.627522</td>\n",
       "      <td>111.314064</td>\n",
       "      <td>116.962493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WAS</th>\n",
       "      <td>114.864709</td>\n",
       "      <td>111.852230</td>\n",
       "      <td>115.062771</td>\n",
       "      <td>116.117834</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          DEFRTG      OFFRTG  DEFRTG_4th  OFFRTG_4th\n",
       "TEAM                                                \n",
       "CHI   112.702629  112.956782  114.976167  118.701130\n",
       "MEM   108.802726  112.750489  112.730440  115.299347\n",
       "NOP   111.739120  109.568484  116.245159  116.159558\n",
       "PHX   108.336707  111.269656  109.045913  122.864011\n",
       "TOR   111.430002  112.627522  111.314064  116.962493\n",
       "WAS   114.864709  111.852230  115.062771  116.117834"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Elite group: good in the first 3 and in the 4th improved their defense and/or offense\n",
    "\n",
    "cluster_three_df = teams_3rd.iloc[cluster_three_indices]\n",
    "cluster_three_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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