01EDA-TournamentModeling2003-2019.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tournament Modeling 2003-2019\n",
    "This notebook is where the modeling will take place. The first stage in the modeling will be using end of season metrics from the 2003-2014 seasons to predict "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.7/site-packages/lightgbm/__init__.py:48: UserWarning: Starting from version 2.2.1, the library file in distribution wheels for macOS is built by the Apple Clang (Xcode_8.3.3) compiler.\n",
      "This means that in case of installing LightGBM from PyPI via the ``pip install lightgbm`` command, you don't need to install the gcc compiler anymore.\n",
      "Instead of that, you need to install the OpenMP library, which is required for running LightGBM on the system with the Apple Clang compiler.\n",
      "You can install the OpenMP library by the following command: ``brew install libomp``.\n",
      "  \"You can install the OpenMP library by the following command: ``brew install libomp``.\", UserWarning)\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "import sys\n",
    "import os\n",
    "import json\n",
    "import pickle\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import cross_val_score, GridSearchCV\n",
    "from sklearn.linear_model import LogisticRegression, SGDClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.metrics import accuracy_score, roc_auc_score\n",
    "from lightgbm import LGBMClassifier\n",
    "from xgboost import XGBClassifier\n",
    "sys.path.append(\"/Users/atticussoane/Desktop/atticus_tools/\")\n",
    "from recursive_selection import FeatureSelector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "if not os.path.exists(\"./models/\"):\n",
    "    os.makedirs(\"./models/\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Season</th>\n",
       "      <th>DayNum</th>\n",
       "      <th>WTeamID</th>\n",
       "      <th>WScore</th>\n",
       "      <th>LTeamID</th>\n",
       "      <th>LScore</th>\n",
       "      <th>WseedN</th>\n",
       "      <th>WDRB_DIF</th>\n",
       "      <th>WORB_DIF</th>\n",
       "      <th>WPPG</th>\n",
       "      <th>WPPP</th>\n",
       "      <th>WTRB_DIF</th>\n",
       "      <th>Wast_TO</th>\n",
       "      <th>We_fg</th>\n",
       "      <th>Wfg</th>\n",
       "      <th>Wfree_throw_pct</th>\n",
       "      <th>Wopp_PPG</th>\n",
       "      <th>Wopp_PPP</th>\n",
       "      <th>Wopp_ast_TO</th>\n",
       "      <th>Wopp_efg</th>\n",
       "      <th>Wopp_fg</th>\n",
       "      <th>Wopp_three_point_pct</th>\n",
       "      <th>Wopp_trueshooting</th>\n",
       "      <th>Wthree_point_pct</th>\n",
       "      <th>Wtotal_point_differential</th>\n",
       "      <th>Wtrue_shooting</th>\n",
       "      <th>Wacc</th>\n",
       "      <th>Wbig_east</th>\n",
       "      <th>Wbig_ten</th>\n",
       "      <th>Wbig_twelve</th>\n",
       "      <th>Wsec</th>\n",
       "      <th>Wpac12</th>\n",
       "      <th>WMOR</th>\n",
       "      <th>WAP_top10</th>\n",
       "      <th>WAP_top25</th>\n",
       "      <th>LseedN</th>\n",
       "      <th>LDRB_DIF</th>\n",
       "      <th>LORB_DIF</th>\n",
       "      <th>LPPG</th>\n",
       "      <th>LPPP</th>\n",
       "      <th>LTRB_DIF</th>\n",
       "      <th>Last_TO</th>\n",
       "      <th>Le_fg</th>\n",
       "      <th>Lfg</th>\n",
       "      <th>Lfree_throw_pct</th>\n",
       "      <th>Lopp_PPG</th>\n",
       "      <th>Lopp_PPP</th>\n",
       "      <th>Lopp_ast_TO</th>\n",
       "      <th>Lopp_efg</th>\n",
       "      <th>Lopp_fg</th>\n",
       "      <th>Lopp_three_point_pct</th>\n",
       "      <th>Lopp_trueshooting</th>\n",
       "      <th>Lthree_point_pct</th>\n",
       "      <th>Ltotal_point_differential</th>\n",
       "      <th>Ltrue_shooting</th>\n",
       "      <th>Lacc</th>\n",
       "      <th>Lbig_east</th>\n",
       "      <th>Lbig_ten</th>\n",
       "      <th>Lbig_twelve</th>\n",
       "      <th>Lsec</th>\n",
       "      <th>Lpac12</th>\n",
       "      <th>LMOR</th>\n",
       "      <th>LAP_top10</th>\n",
       "      <th>LAP_top25</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2003</td>\n",
       "      <td>134</td>\n",
       "      <td>1421</td>\n",
       "      <td>92</td>\n",
       "      <td>1411</td>\n",
       "      <td>84</td>\n",
       "      <td>16</td>\n",
       "      <td>10</td>\n",
       "      <td>-42</td>\n",
       "      <td>71.206897</td>\n",
       "      <td>0.866162</td>\n",
       "      <td>-32</td>\n",
       "      <td>0.804255</td>\n",
       "      <td>0.486339</td>\n",
       "      <td>0.429265</td>\n",
       "      <td>0.762768</td>\n",
       "      <td>78.448276</td>\n",
       "      <td>0.937078</td>\n",
       "      <td>1.236559</td>\n",
       "      <td>0.518382</td>\n",
       "      <td>0.455882</td>\n",
       "      <td>0.367110</td>\n",
       "      <td>0.553323</td>\n",
       "      <td>0.360153</td>\n",
       "      <td>-210</td>\n",
       "      <td>0.539424</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>277.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>58</td>\n",
       "      <td>37</td>\n",
       "      <td>72.800000</td>\n",
       "      <td>0.878704</td>\n",
       "      <td>95</td>\n",
       "      <td>0.932166</td>\n",
       "      <td>0.501206</td>\n",
       "      <td>0.447527</td>\n",
       "      <td>0.619952</td>\n",
       "      <td>70.833333</td>\n",
       "      <td>0.853660</td>\n",
       "      <td>0.960465</td>\n",
       "      <td>0.487307</td>\n",
       "      <td>0.424945</td>\n",
       "      <td>0.325180</td>\n",
       "      <td>0.515957</td>\n",
       "      <td>0.320721</td>\n",
       "      <td>59</td>\n",
       "      <td>0.538334</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>293.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1112</td>\n",
       "      <td>80</td>\n",
       "      <td>1436</td>\n",
       "      <td>51</td>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>58</td>\n",
       "      <td>85.214286</td>\n",
       "      <td>0.931304</td>\n",
       "      <td>180</td>\n",
       "      <td>1.193237</td>\n",
       "      <td>0.514946</td>\n",
       "      <td>0.461413</td>\n",
       "      <td>0.701429</td>\n",
       "      <td>70.250000</td>\n",
       "      <td>0.786410</td>\n",
       "      <td>0.917373</td>\n",
       "      <td>0.456378</td>\n",
       "      <td>0.407510</td>\n",
       "      <td>0.316637</td>\n",
       "      <td>0.484664</td>\n",
       "      <td>0.350534</td>\n",
       "      <td>419</td>\n",
       "      <td>0.555400</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>112</td>\n",
       "      <td>98</td>\n",
       "      <td>67.793103</td>\n",
       "      <td>0.863235</td>\n",
       "      <td>210</td>\n",
       "      <td>1.009804</td>\n",
       "      <td>0.491667</td>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.657848</td>\n",
       "      <td>63.137931</td>\n",
       "      <td>0.841808</td>\n",
       "      <td>1.021220</td>\n",
       "      <td>0.477458</td>\n",
       "      <td>0.413275</td>\n",
       "      <td>0.329582</td>\n",
       "      <td>0.509154</td>\n",
       "      <td>0.340757</td>\n",
       "      <td>135</td>\n",
       "      <td>0.525815</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1113</td>\n",
       "      <td>84</td>\n",
       "      <td>1272</td>\n",
       "      <td>71</td>\n",
       "      <td>10</td>\n",
       "      <td>80</td>\n",
       "      <td>78</td>\n",
       "      <td>75.965517</td>\n",
       "      <td>0.921603</td>\n",
       "      <td>158</td>\n",
       "      <td>1.110837</td>\n",
       "      <td>0.513333</td>\n",
       "      <td>0.478182</td>\n",
       "      <td>0.669737</td>\n",
       "      <td>69.172414</td>\n",
       "      <td>0.862499</td>\n",
       "      <td>0.906667</td>\n",
       "      <td>0.494424</td>\n",
       "      <td>0.445477</td>\n",
       "      <td>0.342733</td>\n",
       "      <td>0.534705</td>\n",
       "      <td>0.317808</td>\n",
       "      <td>197</td>\n",
       "      <td>0.555080</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>69</td>\n",
       "      <td>50</td>\n",
       "      <td>74.517241</td>\n",
       "      <td>0.888511</td>\n",
       "      <td>119</td>\n",
       "      <td>1.205000</td>\n",
       "      <td>0.496264</td>\n",
       "      <td>0.437931</td>\n",
       "      <td>0.653614</td>\n",
       "      <td>65.827586</td>\n",
       "      <td>0.802290</td>\n",
       "      <td>0.883295</td>\n",
       "      <td>0.453218</td>\n",
       "      <td>0.402265</td>\n",
       "      <td>0.322034</td>\n",
       "      <td>0.491392</td>\n",
       "      <td>0.348797</td>\n",
       "      <td>252</td>\n",
       "      <td>0.531700</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1141</td>\n",
       "      <td>79</td>\n",
       "      <td>1166</td>\n",
       "      <td>73</td>\n",
       "      <td>11</td>\n",
       "      <td>127</td>\n",
       "      <td>-48</td>\n",
       "      <td>79.344828</td>\n",
       "      <td>0.967538</td>\n",
       "      <td>79</td>\n",
       "      <td>0.856333</td>\n",
       "      <td>0.570026</td>\n",
       "      <td>0.505236</td>\n",
       "      <td>0.765753</td>\n",
       "      <td>73.241379</td>\n",
       "      <td>0.875414</td>\n",
       "      <td>0.733906</td>\n",
       "      <td>0.497619</td>\n",
       "      <td>0.454762</td>\n",
       "      <td>0.357320</td>\n",
       "      <td>0.541759</td>\n",
       "      <td>0.380769</td>\n",
       "      <td>177</td>\n",
       "      <td>0.622161</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>60</td>\n",
       "      <td>-6</td>\n",
       "      <td>79.242424</td>\n",
       "      <td>0.995114</td>\n",
       "      <td>54</td>\n",
       "      <td>1.258503</td>\n",
       "      <td>0.568829</td>\n",
       "      <td>0.499473</td>\n",
       "      <td>0.692890</td>\n",
       "      <td>64.333333</td>\n",
       "      <td>0.806783</td>\n",
       "      <td>0.724689</td>\n",
       "      <td>0.475630</td>\n",
       "      <td>0.431544</td>\n",
       "      <td>0.341102</td>\n",
       "      <td>0.513189</td>\n",
       "      <td>0.389053</td>\n",
       "      <td>492</td>\n",
       "      <td>0.597895</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1143</td>\n",
       "      <td>76</td>\n",
       "      <td>1301</td>\n",
       "      <td>74</td>\n",
       "      <td>8</td>\n",
       "      <td>40</td>\n",
       "      <td>2</td>\n",
       "      <td>74.482759</td>\n",
       "      <td>0.914077</td>\n",
       "      <td>42</td>\n",
       "      <td>1.128954</td>\n",
       "      <td>0.520258</td>\n",
       "      <td>0.465649</td>\n",
       "      <td>0.685512</td>\n",
       "      <td>69.758621</td>\n",
       "      <td>0.856971</td>\n",
       "      <td>1.073903</td>\n",
       "      <td>0.492082</td>\n",
       "      <td>0.431672</td>\n",
       "      <td>0.331190</td>\n",
       "      <td>0.524735</td>\n",
       "      <td>0.376518</td>\n",
       "      <td>137</td>\n",
       "      <td>0.553267</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>43.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>18</td>\n",
       "      <td>-24</td>\n",
       "      <td>72.400000</td>\n",
       "      <td>0.945927</td>\n",
       "      <td>-6</td>\n",
       "      <td>1.032864</td>\n",
       "      <td>0.530937</td>\n",
       "      <td>0.456250</td>\n",
       "      <td>0.770358</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>0.882032</td>\n",
       "      <td>0.858770</td>\n",
       "      <td>0.494981</td>\n",
       "      <td>0.441029</td>\n",
       "      <td>0.337255</td>\n",
       "      <td>0.544337</td>\n",
       "      <td>0.354074</td>\n",
       "      <td>132</td>\n",
       "      <td>0.580699</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Season  DayNum  WTeamID  WScore  LTeamID  LScore  WseedN  WDRB_DIF  \\\n",
       "0    2003     134     1421      92     1411      84      16        10   \n",
       "1    2003     136     1112      80     1436      51       1       122   \n",
       "2    2003     136     1113      84     1272      71      10        80   \n",
       "3    2003     136     1141      79     1166      73      11       127   \n",
       "4    2003     136     1143      76     1301      74       8        40   \n",
       "\n",
       "   WORB_DIF       WPPG      WPPP  WTRB_DIF   Wast_TO     We_fg       Wfg  \\\n",
       "0       -42  71.206897  0.866162       -32  0.804255  0.486339  0.429265   \n",
       "1        58  85.214286  0.931304       180  1.193237  0.514946  0.461413   \n",
       "2        78  75.965517  0.921603       158  1.110837  0.513333  0.478182   \n",
       "3       -48  79.344828  0.967538        79  0.856333  0.570026  0.505236   \n",
       "4         2  74.482759  0.914077        42  1.128954  0.520258  0.465649   \n",
       "\n",
       "   Wfree_throw_pct   Wopp_PPG  Wopp_PPP  Wopp_ast_TO  Wopp_efg   Wopp_fg  \\\n",
       "0         0.762768  78.448276  0.937078     1.236559  0.518382  0.455882   \n",
       "1         0.701429  70.250000  0.786410     0.917373  0.456378  0.407510   \n",
       "2         0.669737  69.172414  0.862499     0.906667  0.494424  0.445477   \n",
       "3         0.765753  73.241379  0.875414     0.733906  0.497619  0.454762   \n",
       "4         0.685512  69.758621  0.856971     1.073903  0.492082  0.431672   \n",
       "\n",
       "   Wopp_three_point_pct  Wopp_trueshooting  Wthree_point_pct  \\\n",
       "0              0.367110           0.553323          0.360153   \n",
       "1              0.316637           0.484664          0.350534   \n",
       "2              0.342733           0.534705          0.317808   \n",
       "3              0.357320           0.541759          0.380769   \n",
       "4              0.331190           0.524735          0.376518   \n",
       "\n",
       "   Wtotal_point_differential  Wtrue_shooting  Wacc  Wbig_east  Wbig_ten  \\\n",
       "0                       -210        0.539424     0          0         0   \n",
       "1                        419        0.555400     0          0         0   \n",
       "2                        197        0.555080     0          0         0   \n",
       "3                        177        0.622161     0          0         0   \n",
       "4                        137        0.553267     0          0         0   \n",
       "\n",
       "   Wbig_twelve  Wsec  Wpac12   WMOR  WAP_top10  WAP_top25  LseedN  LDRB_DIF  \\\n",
       "0            0     0       0  277.0          0          0      16        58   \n",
       "1            0     0       1    4.0          1          0      16       112   \n",
       "2            0     0       1   22.0          0          0       7        69   \n",
       "3            0     0       0   50.0          0          0       6        60   \n",
       "4            0     0       1   43.0          0          0       9        18   \n",
       "\n",
       "   LORB_DIF       LPPG      LPPP  LTRB_DIF   Last_TO     Le_fg       Lfg  \\\n",
       "0        37  72.800000  0.878704        95  0.932166  0.501206  0.447527   \n",
       "1        98  67.793103  0.863235       210  1.009804  0.491667  0.444444   \n",
       "2        50  74.517241  0.888511       119  1.205000  0.496264  0.437931   \n",
       "3        -6  79.242424  0.995114        54  1.258503  0.568829  0.499473   \n",
       "4       -24  72.400000  0.945927        -6  1.032864  0.530937  0.456250   \n",
       "\n",
       "   Lfree_throw_pct   Lopp_PPG  Lopp_PPP  Lopp_ast_TO  Lopp_efg   Lopp_fg  \\\n",
       "0         0.619952  70.833333  0.853660     0.960465  0.487307  0.424945   \n",
       "1         0.657848  63.137931  0.841808     1.021220  0.477458  0.413275   \n",
       "2         0.653614  65.827586  0.802290     0.883295  0.453218  0.402265   \n",
       "3         0.692890  64.333333  0.806783     0.724689  0.475630  0.431544   \n",
       "4         0.770358  68.000000  0.882032     0.858770  0.494981  0.441029   \n",
       "\n",
       "   Lopp_three_point_pct  Lopp_trueshooting  Lthree_point_pct  \\\n",
       "0              0.325180           0.515957          0.320721   \n",
       "1              0.329582           0.509154          0.340757   \n",
       "2              0.322034           0.491392          0.348797   \n",
       "3              0.341102           0.513189          0.389053   \n",
       "4              0.337255           0.544337          0.354074   \n",
       "\n",
       "   Ltotal_point_differential  Ltrue_shooting  Lacc  Lbig_east  Lbig_ten  \\\n",
       "0                         59        0.538334     0          0         0   \n",
       "1                        135        0.525815     0          0         0   \n",
       "2                        252        0.531700     0          0         0   \n",
       "3                        492        0.597895     0          0         0   \n",
       "4                        132        0.580699     1          0         0   \n",
       "\n",
       "   Lbig_twelve  Lsec  Lpac12   LMOR  LAP_top10  LAP_top25  \n",
       "0            0     0       0  293.0          0          0  \n",
       "1            0     0       0  187.0          0          0  \n",
       "2            0     0       0   23.0          0          1  \n",
       "3            0     0       0   33.0          0          1  \n",
       "4            0     0       0   31.0          0          0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.set_option('max.columns', 100)\n",
    "tourney_df = pd.read_csv(\"./engineered_data/tournament_modeling2003-2019.csv.gz\", compression = \"gzip\")\n",
    "tourney_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Right off the bat there is a problem with the way the data is structured. The dataframe is split into winning and losing teams, so creating a binary win/lose variable with the current set up would result in all 1s. Obviously this is not what we want, so there are two solutions that I see:\n",
    "\n",
    "$\\cdot$ Split the dataframe into two halves (alternating rows) and flip the winning and losing team stats, instead calling them team1 and team2. This will create a perfectly balanced target binary class.\n",
    "\n",
    "$\\cdot$ Leave the dataframe how it is, and instead create a binary feature of whether not a higher seeded team beat a lower seeded team; making a model that predicts upsets. \n",
    "\n",
    "The upset model is not the name of the game (although I'm going to do that anyway). The contest is about predicting win probabilities, so I will start with that method. I'm going to split the DataFrame perfectly in half. My concern with using a random split (like KFold splitter something of that nature) is that since we are using past seasons to model future seasons, there is a possibility that an entire season may end up with only one target class. The safest course is to create two perfectly balanced target classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1115\n"
     ]
    }
   ],
   "source": [
    "print(len(tourney_df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def all_even(n):\n",
    "    even_indices = []\n",
    "    i = 0\n",
    "    while 2 * i < n:\n",
    "        even_indices.append(2 * i)\n",
    "        i += 1\n",
    "    return(even_indices)\n",
    "\n",
    "even_indices = all_even(1115)\n",
    "even_df = tourney_df.iloc[even_indices].reset_index(drop = True)\n",
    "odd_df = tourney_df.drop(even_indices, axis = 0).reset_index(drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(558, 557)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(even_df), len(odd_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>Season</th>\n",
       "      <th>DayNum</th>\n",
       "      <th>WTeamID</th>\n",
       "      <th>WScore</th>\n",
       "      <th>LTeamID</th>\n",
       "      <th>LScore</th>\n",
       "      <th>WseedN</th>\n",
       "      <th>WDRB_DIF</th>\n",
       "      <th>WORB_DIF</th>\n",
       "      <th>WPPG</th>\n",
       "      <th>WPPP</th>\n",
       "      <th>WTRB_DIF</th>\n",
       "      <th>Wast_TO</th>\n",
       "      <th>We_fg</th>\n",
       "      <th>Wfg</th>\n",
       "      <th>Wfree_throw_pct</th>\n",
       "      <th>Wopp_PPG</th>\n",
       "      <th>Wopp_PPP</th>\n",
       "      <th>Wopp_ast_TO</th>\n",
       "      <th>Wopp_efg</th>\n",
       "      <th>Wopp_fg</th>\n",
       "      <th>Wopp_three_point_pct</th>\n",
       "      <th>Wopp_trueshooting</th>\n",
       "      <th>Wthree_point_pct</th>\n",
       "      <th>Wtotal_point_differential</th>\n",
       "      <th>Wtrue_shooting</th>\n",
       "      <th>Wacc</th>\n",
       "      <th>Wbig_east</th>\n",
       "      <th>Wbig_ten</th>\n",
       "      <th>Wbig_twelve</th>\n",
       "      <th>Wsec</th>\n",
       "      <th>Wpac12</th>\n",
       "      <th>WMOR</th>\n",
       "      <th>WAP_top10</th>\n",
       "      <th>WAP_top25</th>\n",
       "      <th>LseedN</th>\n",
       "      <th>LDRB_DIF</th>\n",
       "      <th>LORB_DIF</th>\n",
       "      <th>LPPG</th>\n",
       "      <th>LPPP</th>\n",
       "      <th>LTRB_DIF</th>\n",
       "      <th>Last_TO</th>\n",
       "      <th>Le_fg</th>\n",
       "      <th>Lfg</th>\n",
       "      <th>Lfree_throw_pct</th>\n",
       "      <th>Lopp_PPG</th>\n",
       "      <th>Lopp_PPP</th>\n",
       "      <th>Lopp_ast_TO</th>\n",
       "      <th>Lopp_efg</th>\n",
       "      <th>Lopp_fg</th>\n",
       "      <th>Lopp_three_point_pct</th>\n",
       "      <th>Lopp_trueshooting</th>\n",
       "      <th>Lthree_point_pct</th>\n",
       "      <th>Ltotal_point_differential</th>\n",
       "      <th>Ltrue_shooting</th>\n",
       "      <th>Lacc</th>\n",
       "      <th>Lbig_east</th>\n",
       "      <th>Lbig_ten</th>\n",
       "      <th>Lbig_twelve</th>\n",
       "      <th>Lsec</th>\n",
       "      <th>Lpac12</th>\n",
       "      <th>LMOR</th>\n",
       "      <th>LAP_top10</th>\n",
       "      <th>LAP_top25</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2003</td>\n",
       "      <td>134</td>\n",
       "      <td>1421</td>\n",
       "      <td>92</td>\n",
       "      <td>1411</td>\n",
       "      <td>84</td>\n",
       "      <td>16</td>\n",
       "      <td>10</td>\n",
       "      <td>-42</td>\n",
       "      <td>71.206897</td>\n",
       "      <td>0.866162</td>\n",
       "      <td>-32</td>\n",
       "      <td>0.804255</td>\n",
       "      <td>0.486339</td>\n",
       "      <td>0.429265</td>\n",
       "      <td>0.762768</td>\n",
       "      <td>78.448276</td>\n",
       "      <td>0.937078</td>\n",
       "      <td>1.236559</td>\n",
       "      <td>0.518382</td>\n",
       "      <td>0.455882</td>\n",
       "      <td>0.367110</td>\n",
       "      <td>0.553323</td>\n",
       "      <td>0.360153</td>\n",
       "      <td>-210</td>\n",
       "      <td>0.539424</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>277.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>58</td>\n",
       "      <td>37</td>\n",
       "      <td>72.800000</td>\n",
       "      <td>0.878704</td>\n",
       "      <td>95</td>\n",
       "      <td>0.932166</td>\n",
       "      <td>0.501206</td>\n",
       "      <td>0.447527</td>\n",
       "      <td>0.619952</td>\n",
       "      <td>70.833333</td>\n",
       "      <td>0.853660</td>\n",
       "      <td>0.960465</td>\n",
       "      <td>0.487307</td>\n",
       "      <td>0.424945</td>\n",
       "      <td>0.325180</td>\n",
       "      <td>0.515957</td>\n",
       "      <td>0.320721</td>\n",
       "      <td>59</td>\n",
       "      <td>0.538334</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>293.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1113</td>\n",
       "      <td>84</td>\n",
       "      <td>1272</td>\n",
       "      <td>71</td>\n",
       "      <td>10</td>\n",
       "      <td>80</td>\n",
       "      <td>78</td>\n",
       "      <td>75.965517</td>\n",
       "      <td>0.921603</td>\n",
       "      <td>158</td>\n",
       "      <td>1.110837</td>\n",
       "      <td>0.513333</td>\n",
       "      <td>0.478182</td>\n",
       "      <td>0.669737</td>\n",
       "      <td>69.172414</td>\n",
       "      <td>0.862499</td>\n",
       "      <td>0.906667</td>\n",
       "      <td>0.494424</td>\n",
       "      <td>0.445477</td>\n",
       "      <td>0.342733</td>\n",
       "      <td>0.534705</td>\n",
       "      <td>0.317808</td>\n",
       "      <td>197</td>\n",
       "      <td>0.555080</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>69</td>\n",
       "      <td>50</td>\n",
       "      <td>74.517241</td>\n",
       "      <td>0.888511</td>\n",
       "      <td>119</td>\n",
       "      <td>1.205000</td>\n",
       "      <td>0.496264</td>\n",
       "      <td>0.437931</td>\n",
       "      <td>0.653614</td>\n",
       "      <td>65.827586</td>\n",
       "      <td>0.802290</td>\n",
       "      <td>0.883295</td>\n",
       "      <td>0.453218</td>\n",
       "      <td>0.402265</td>\n",
       "      <td>0.322034</td>\n",
       "      <td>0.491392</td>\n",
       "      <td>0.348797</td>\n",
       "      <td>252</td>\n",
       "      <td>0.531700</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1143</td>\n",
       "      <td>76</td>\n",
       "      <td>1301</td>\n",
       "      <td>74</td>\n",
       "      <td>8</td>\n",
       "      <td>40</td>\n",
       "      <td>2</td>\n",
       "      <td>74.482759</td>\n",
       "      <td>0.914077</td>\n",
       "      <td>42</td>\n",
       "      <td>1.128954</td>\n",
       "      <td>0.520258</td>\n",
       "      <td>0.465649</td>\n",
       "      <td>0.685512</td>\n",
       "      <td>69.758621</td>\n",
       "      <td>0.856971</td>\n",
       "      <td>1.073903</td>\n",
       "      <td>0.492082</td>\n",
       "      <td>0.431672</td>\n",
       "      <td>0.331190</td>\n",
       "      <td>0.524735</td>\n",
       "      <td>0.376518</td>\n",
       "      <td>137</td>\n",
       "      <td>0.553267</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>43.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>18</td>\n",
       "      <td>-24</td>\n",
       "      <td>72.400000</td>\n",
       "      <td>0.945927</td>\n",
       "      <td>-6</td>\n",
       "      <td>1.032864</td>\n",
       "      <td>0.530937</td>\n",
       "      <td>0.456250</td>\n",
       "      <td>0.770358</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>0.882032</td>\n",
       "      <td>0.858770</td>\n",
       "      <td>0.494981</td>\n",
       "      <td>0.441029</td>\n",
       "      <td>0.337255</td>\n",
       "      <td>0.544337</td>\n",
       "      <td>0.354074</td>\n",
       "      <td>132</td>\n",
       "      <td>0.580699</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1181</td>\n",
       "      <td>67</td>\n",
       "      <td>1161</td>\n",
       "      <td>57</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "      <td>47</td>\n",
       "      <td>81.966667</td>\n",
       "      <td>0.945231</td>\n",
       "      <td>61</td>\n",
       "      <td>0.985748</td>\n",
       "      <td>0.514365</td>\n",
       "      <td>0.453591</td>\n",
       "      <td>0.709026</td>\n",
       "      <td>70.400000</td>\n",
       "      <td>0.831509</td>\n",
       "      <td>0.691589</td>\n",
       "      <td>0.481633</td>\n",
       "      <td>0.438484</td>\n",
       "      <td>0.341014</td>\n",
       "      <td>0.526694</td>\n",
       "      <td>0.355987</td>\n",
       "      <td>347</td>\n",
       "      <td>0.563867</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>132</td>\n",
       "      <td>-36</td>\n",
       "      <td>74.000000</td>\n",
       "      <td>0.937769</td>\n",
       "      <td>96</td>\n",
       "      <td>0.960744</td>\n",
       "      <td>0.547025</td>\n",
       "      <td>0.506718</td>\n",
       "      <td>0.700549</td>\n",
       "      <td>72.666667</td>\n",
       "      <td>0.913740</td>\n",
       "      <td>1.081744</td>\n",
       "      <td>0.498550</td>\n",
       "      <td>0.449536</td>\n",
       "      <td>0.344898</td>\n",
       "      <td>0.539925</td>\n",
       "      <td>0.363112</td>\n",
       "      <td>40</td>\n",
       "      <td>0.589385</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>85.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2003</td>\n",
       "      <td>136</td>\n",
       "      <td>1228</td>\n",
       "      <td>65</td>\n",
       "      <td>1443</td>\n",
       "      <td>60</td>\n",
       "      <td>4</td>\n",
       "      <td>126</td>\n",
       "      <td>-42</td>\n",
       "      <td>75.433333</td>\n",
       "      <td>0.974960</td>\n",
       "      <td>84</td>\n",
       "      <td>1.387342</td>\n",
       "      <td>0.552270</td>\n",
       "      <td>0.485663</td>\n",
       "      <td>0.722513</td>\n",
       "      <td>61.400000</td>\n",
       "      <td>0.784738</td>\n",
       "      <td>0.743820</td>\n",
       "      <td>0.428792</td>\n",
       "      <td>0.376079</td>\n",
       "      <td>0.298429</td>\n",
       "      <td>0.484156</td>\n",
       "      <td>0.368595</td>\n",
       "      <td>421</td>\n",
       "      <td>0.587450</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>13</td>\n",
       "      <td>51</td>\n",
       "      <td>25</td>\n",
       "      <td>73.096774</td>\n",
       "      <td>0.909762</td>\n",
       "      <td>76</td>\n",
       "      <td>0.936170</td>\n",
       "      <td>0.528852</td>\n",
       "      <td>0.459896</td>\n",
       "      <td>0.662080</td>\n",
       "      <td>66.419355</td>\n",
       "      <td>0.829079</td>\n",
       "      <td>0.762295</td>\n",
       "      <td>0.475216</td>\n",
       "      <td>0.434006</td>\n",
       "      <td>0.296680</td>\n",
       "      <td>0.515916</td>\n",
       "      <td>0.366564</td>\n",
       "      <td>207</td>\n",
       "      <td>0.560680</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Season  DayNum  WTeamID  WScore  LTeamID  LScore  WseedN  WDRB_DIF  \\\n",
       "0    2003     134     1421      92     1411      84      16        10   \n",
       "1    2003     136     1113      84     1272      71      10        80   \n",
       "2    2003     136     1143      76     1301      74       8        40   \n",
       "3    2003     136     1181      67     1161      57       3        14   \n",
       "4    2003     136     1228      65     1443      60       4       126   \n",
       "\n",
       "   WORB_DIF       WPPG      WPPP  WTRB_DIF   Wast_TO     We_fg       Wfg  \\\n",
       "0       -42  71.206897  0.866162       -32  0.804255  0.486339  0.429265   \n",
       "1        78  75.965517  0.921603       158  1.110837  0.513333  0.478182   \n",
       "2         2  74.482759  0.914077        42  1.128954  0.520258  0.465649   \n",
       "3        47  81.966667  0.945231        61  0.985748  0.514365  0.453591   \n",
       "4       -42  75.433333  0.974960        84  1.387342  0.552270  0.485663   \n",
       "\n",
       "   Wfree_throw_pct   Wopp_PPG  Wopp_PPP  Wopp_ast_TO  Wopp_efg   Wopp_fg  \\\n",
       "0         0.762768  78.448276  0.937078     1.236559  0.518382  0.455882   \n",
       "1         0.669737  69.172414  0.862499     0.906667  0.494424  0.445477   \n",
       "2         0.685512  69.758621  0.856971     1.073903  0.492082  0.431672   \n",
       "3         0.709026  70.400000  0.831509     0.691589  0.481633  0.438484   \n",
       "4         0.722513  61.400000  0.784738     0.743820  0.428792  0.376079   \n",
       "\n",
       "   Wopp_three_point_pct  Wopp_trueshooting  Wthree_point_pct  \\\n",
       "0              0.367110           0.553323          0.360153   \n",
       "1              0.342733           0.534705          0.317808   \n",
       "2              0.331190           0.524735          0.376518   \n",
       "3              0.341014           0.526694          0.355987   \n",
       "4              0.298429           0.484156          0.368595   \n",
       "\n",
       "   Wtotal_point_differential  Wtrue_shooting  Wacc  Wbig_east  Wbig_ten  \\\n",
       "0                       -210        0.539424     0          0         0   \n",
       "1                        197        0.555080     0          0         0   \n",
       "2                        137        0.553267     0          0         0   \n",
       "3                        347        0.563867     1          0         0   \n",
       "4                        421        0.587450     0          0         1   \n",
       "\n",
       "   Wbig_twelve  Wsec  Wpac12   WMOR  WAP_top10  WAP_top25  LseedN  LDRB_DIF  \\\n",
       "0            0     0       0  277.0          0          0      16        58   \n",
       "1            0     0       1   22.0          0          0       7        69   \n",
       "2            0     0       1   43.0          0          0       9        18   \n",
       "3            0     0       0   10.0          1          0      14       132   \n",
       "4            0     0       0    5.0          0          1      13        51   \n",
       "\n",
       "   LORB_DIF       LPPG      LPPP  LTRB_DIF   Last_TO     Le_fg       Lfg  \\\n",
       "0        37  72.800000  0.878704        95  0.932166  0.501206  0.447527   \n",
       "1        50  74.517241  0.888511       119  1.205000  0.496264  0.437931   \n",
       "2       -24  72.400000  0.945927        -6  1.032864  0.530937  0.456250   \n",
       "3       -36  74.000000  0.937769        96  0.960744  0.547025  0.506718   \n",
       "4        25  73.096774  0.909762        76  0.936170  0.528852  0.459896   \n",
       "\n",
       "   Lfree_throw_pct   Lopp_PPG  Lopp_PPP  Lopp_ast_TO  Lopp_efg   Lopp_fg  \\\n",
       "0         0.619952  70.833333  0.853660     0.960465  0.487307  0.424945   \n",
       "1         0.653614  65.827586  0.802290     0.883295  0.453218  0.402265   \n",
       "2         0.770358  68.000000  0.882032     0.858770  0.494981  0.441029   \n",
       "3         0.700549  72.666667  0.913740     1.081744  0.498550  0.449536   \n",
       "4         0.662080  66.419355  0.829079     0.762295  0.475216  0.434006   \n",
       "\n",
       "   Lopp_three_point_pct  Lopp_trueshooting  Lthree_point_pct  \\\n",
       "0              0.325180           0.515957          0.320721   \n",
       "1              0.322034           0.491392          0.348797   \n",
       "2              0.337255           0.544337          0.354074   \n",
       "3              0.344898           0.539925          0.363112   \n",
       "4              0.296680           0.515916          0.366564   \n",
       "\n",
       "   Ltotal_point_differential  Ltrue_shooting  Lacc  Lbig_east  Lbig_ten  \\\n",
       "0                         59        0.538334     0          0         0   \n",
       "1                        252        0.531700     0          0         0   \n",
       "2                        132        0.580699     1          0         0   \n",
       "3                         40        0.589385     0          0         0   \n",
       "4                        207        0.560680     0          0         0   \n",
       "\n",
       "   Lbig_twelve  Lsec  Lpac12   LMOR  LAP_top10  LAP_top25  \n",
       "0            0     0       0  293.0          0          0  \n",
       "1            0     0       0   23.0          0          1  \n",
       "2            0     0       0   31.0          0          0  \n",
       "3            0     0       0   85.0          0          0  \n",
       "4            0     0       0   59.0          0          0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "even_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "even_columns = list(even_df.columns)\n",
    "for i in range(len(even_columns)):\n",
    "    if even_columns[i][0] == \"W\":\n",
    "        even_columns[i] = even_columns[i].replace(\"W\", \"team1_\", 1)\n",
    "    elif even_columns[i][0] == \"L\":\n",
    "        even_columns[i] = even_columns[i].replace(\"L\", \"team2_\", 1)\n",
    "\n",
    "odd_columns = list(odd_df.columns)\n",
    "for i in range(len(odd_columns)):\n",
    "    if odd_columns[i][0] == \"W\":\n",
    "        odd_columns[i] = odd_columns[i].replace(\"W\", \"team2_\", 1)\n",
    "    elif odd_columns[i][0] == \"L\":\n",
    "        odd_columns[i] = odd_columns[i].replace(\"L\", \"team1_\", 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "even_df.columns = even_columns\n",
    "odd_df.columns = odd_columns\n",
    "\n",
    "even_df = even_df.assign(team1_win = 1)\n",
    "odd_df = odd_df.assign(team1_win = 0)\n",
    "\n",
    "final_df = pd.concat([even_df, odd_df], axis = 0, sort = False)\n",
    "del even_df\n",
    "del odd_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_df = final_df.sort_values(by = [\"Season\"]).reset_index(drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_df.to_csv(\"./engineered_data/model_ready.csv.gz\", index = False, compression = \"gzip\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that a target variable has been prepared, it is time to begin training and model building. The process will be this: build as robust a model as possible on the 2003-2014 season, use it to predict to the 2015 season matchups, then incorporate the 2015 season in the training and use it to predict the 2016 matchups and so forth. "
   ]
  },
  {
   "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>Season</th>\n",
       "      <th>DayNum</th>\n",
       "      <th>team1_TeamID</th>\n",
       "      <th>team1_Score</th>\n",
       "      <th>team2_TeamID</th>\n",
       "      <th>team2_Score</th>\n",
       "      <th>team1_seedN</th>\n",
       "      <th>team1_DRB_DIF</th>\n",
       "      <th>team1_ORB_DIF</th>\n",
       "      <th>team1_PPG</th>\n",
       "      <th>team1_PPP</th>\n",
       "      <th>team1_TRB_DIF</th>\n",
       "      <th>team1_ast_TO</th>\n",
       "      <th>team1_e_fg</th>\n",
       "      <th>team1_fg</th>\n",
       "      <th>team1_free_throw_pct</th>\n",
       "      <th>team1_opp_PPG</th>\n",
       "      <th>team1_opp_PPP</th>\n",
       "      <th>team1_opp_ast_TO</th>\n",
       "      <th>team1_opp_efg</th>\n",
       "      <th>team1_opp_fg</th>\n",
       "      <th>team1_opp_three_point_pct</th>\n",
       "      <th>team1_opp_trueshooting</th>\n",
       "      <th>team1_three_point_pct</th>\n",
       "      <th>team1_total_point_differential</th>\n",
       "      <th>team1_true_shooting</th>\n",
       "      <th>team1_acc</th>\n",
       "      <th>team1_big_east</th>\n",
       "      <th>team1_big_ten</th>\n",
       "      <th>team1_big_twelve</th>\n",
       "      <th>team1_sec</th>\n",
       "      <th>team1_pac12</th>\n",
       "      <th>team1_MOR</th>\n",
       "      <th>team1_AP_top10</th>\n",
       "      <th>team1_AP_top25</th>\n",
       "      <th>team2_seedN</th>\n",
       "      <th>team2_DRB_DIF</th>\n",
       "      <th>team2_ORB_DIF</th>\n",
       "      <th>team2_PPG</th>\n",
       "      <th>team2_PPP</th>\n",
       "      <th>team2_TRB_DIF</th>\n",
       "      <th>team2_ast_TO</th>\n",
       "      <th>team2_e_fg</th>\n",
       "      <th>team2_fg</th>\n",
       "      <th>team2_free_throw_pct</th>\n",
       "      <th>team2_opp_PPG</th>\n",
       "      <th>team2_opp_PPP</th>\n",
       "      <th>team2_opp_ast_TO</th>\n",
       "      <th>team2_opp_efg</th>\n",
       "      <th>team2_opp_fg</th>\n",
       "      <th>team2_opp_three_point_pct</th>\n",
       "      <th>team2_opp_trueshooting</th>\n",
       "      <th>team2_three_point_pct</th>\n",
       "      <th>team2_total_point_differential</th>\n",
       "      <th>team2_true_shooting</th>\n",
       "      <th>team2_acc</th>\n",
       "      <th>team2_big_east</th>\n",
       "      <th>team2_big_ten</th>\n",
       "      <th>team2_big_twelve</th>\n",
       "      <th>team2_sec</th>\n",
       "      <th>team2_pac12</th>\n",
       "      <th>team2_MOR</th>\n",
       "      <th>team2_AP_top10</th>\n",
       "      <th>team2_AP_top25</th>\n",
       "      <th>team1_win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2003</td>\n",
       "      <td>134</td>\n",
       "      <td>1421</td>\n",
       "      <td>92</td>\n",
       "      <td>1411</td>\n",
       "      <td>84</td>\n",
       "      <td>16</td>\n",
       "      <td>10</td>\n",
       "      <td>-42</td>\n",
       "      <td>71.206897</td>\n",
       "      <td>0.866162</td>\n",
       "      <td>-32</td>\n",
       "      <td>0.804255</td>\n",
       "      <td>0.486339</td>\n",
       "      <td>0.429265</td>\n",
       "      <td>0.762768</td>\n",
       "      <td>78.448276</td>\n",
       "      <td>0.937078</td>\n",
       "      <td>1.236559</td>\n",
       "      <td>0.518382</td>\n",
       "      <td>0.455882</td>\n",
       "      <td>0.367110</td>\n",
       "      <td>0.553323</td>\n",
       "      <td>0.360153</td>\n",
       "      <td>-210</td>\n",
       "      <td>0.539424</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>277.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>58</td>\n",
       "      <td>37</td>\n",
       "      <td>72.800000</td>\n",
       "      <td>0.878704</td>\n",
       "      <td>95</td>\n",
       "      <td>0.932166</td>\n",
       "      <td>0.501206</td>\n",
       "      <td>0.447527</td>\n",
       "      <td>0.619952</td>\n",
       "      <td>70.833333</td>\n",
       "      <td>0.853660</td>\n",
       "      <td>0.960465</td>\n",
       "      <td>0.487307</td>\n",
       "      <td>0.424945</td>\n",
       "      <td>0.325180</td>\n",
       "      <td>0.515957</td>\n",
       "      <td>0.320721</td>\n",
       "      <td>59</td>\n",
       "      <td>0.538334</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>293.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2003</td>\n",
       "      <td>146</td>\n",
       "      <td>1328</td>\n",
       "      <td>47</td>\n",
       "      <td>1393</td>\n",
       "      <td>63</td>\n",
       "      <td>1</td>\n",
       "      <td>77</td>\n",
       "      <td>52</td>\n",
       "      <td>71.166667</td>\n",
       "      <td>0.930072</td>\n",
       "      <td>129</td>\n",
       "      <td>1.200565</td>\n",
       "      <td>0.512972</td>\n",
       "      <td>0.446934</td>\n",
       "      <td>0.707885</td>\n",
       "      <td>60.166667</td>\n",
       "      <td>0.799394</td>\n",
       "      <td>0.763990</td>\n",
       "      <td>0.446284</td>\n",
       "      <td>0.404747</td>\n",
       "      <td>0.326781</td>\n",
       "      <td>0.488641</td>\n",
       "      <td>0.393673</td>\n",
       "      <td>330</td>\n",
       "      <td>0.549827</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>134</td>\n",
       "      <td>-43</td>\n",
       "      <td>80.103448</td>\n",
       "      <td>0.929051</td>\n",
       "      <td>91</td>\n",
       "      <td>1.098734</td>\n",
       "      <td>0.512195</td>\n",
       "      <td>0.470067</td>\n",
       "      <td>0.693431</td>\n",
       "      <td>69.896552</td>\n",
       "      <td>0.799883</td>\n",
       "      <td>1.100239</td>\n",
       "      <td>0.443703</td>\n",
       "      <td>0.390075</td>\n",
       "      <td>0.306870</td>\n",
       "      <td>0.479169</td>\n",
       "      <td>0.330435</td>\n",
       "      <td>296</td>\n",
       "      <td>0.551677</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2003</td>\n",
       "      <td>144</td>\n",
       "      <td>1120</td>\n",
       "      <td>78</td>\n",
       "      <td>1393</td>\n",
       "      <td>79</td>\n",
       "      <td>10</td>\n",
       "      <td>59</td>\n",
       "      <td>-9</td>\n",
       "      <td>70.100000</td>\n",
       "      <td>0.884178</td>\n",
       "      <td>50</td>\n",
       "      <td>0.842767</td>\n",
       "      <td>0.521328</td>\n",
       "      <td>0.469835</td>\n",
       "      <td>0.662162</td>\n",
       "      <td>65.566667</td>\n",
       "      <td>0.822586</td>\n",
       "      <td>0.801688</td>\n",
       "      <td>0.481165</td>\n",
       "      <td>0.420247</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.512977</td>\n",
       "      <td>0.344898</td>\n",
       "      <td>136</td>\n",
       "      <td>0.552990</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>134</td>\n",
       "      <td>-43</td>\n",
       "      <td>80.103448</td>\n",
       "      <td>0.929051</td>\n",
       "      <td>91</td>\n",
       "      <td>1.098734</td>\n",
       "      <td>0.512195</td>\n",
       "      <td>0.470067</td>\n",
       "      <td>0.693431</td>\n",
       "      <td>69.896552</td>\n",
       "      <td>0.799883</td>\n",
       "      <td>1.100239</td>\n",
       "      <td>0.443703</td>\n",
       "      <td>0.390075</td>\n",
       "      <td>0.306870</td>\n",
       "      <td>0.479169</td>\n",
       "      <td>0.330435</td>\n",
       "      <td>296</td>\n",
       "      <td>0.551677</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2003</td>\n",
       "      <td>144</td>\n",
       "      <td>1268</td>\n",
       "      <td>58</td>\n",
       "      <td>1277</td>\n",
       "      <td>60</td>\n",
       "      <td>6</td>\n",
       "      <td>88</td>\n",
       "      <td>-16</td>\n",
       "      <td>80.785714</td>\n",
       "      <td>0.929044</td>\n",
       "      <td>72</td>\n",
       "      <td>1.339241</td>\n",
       "      <td>0.517756</td>\n",
       "      <td>0.464487</td>\n",
       "      <td>0.703642</td>\n",
       "      <td>66.857143</td>\n",
       "      <td>0.759001</td>\n",
       "      <td>0.703704</td>\n",
       "      <td>0.432193</td>\n",
       "      <td>0.378538</td>\n",
       "      <td>0.312715</td>\n",
       "      <td>0.479165</td>\n",
       "      <td>0.397895</td>\n",
       "      <td>390</td>\n",
       "      <td>0.554477</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>125</td>\n",
       "      <td>42</td>\n",
       "      <td>67.225806</td>\n",
       "      <td>0.891803</td>\n",
       "      <td>167</td>\n",
       "      <td>0.935698</td>\n",
       "      <td>0.498737</td>\n",
       "      <td>0.450758</td>\n",
       "      <td>0.734694</td>\n",
       "      <td>60.967742</td>\n",
       "      <td>0.826801</td>\n",
       "      <td>0.781038</td>\n",
       "      <td>0.458013</td>\n",
       "      <td>0.400641</td>\n",
       "      <td>0.338374</td>\n",
       "      <td>0.512773</td>\n",
       "      <td>0.366265</td>\n",
       "      <td>194</td>\n",
       "      <td>0.552539</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2003</td>\n",
       "      <td>143</td>\n",
       "      <td>1458</td>\n",
       "      <td>57</td>\n",
       "      <td>1246</td>\n",
       "      <td>63</td>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>61</td>\n",
       "      <td>70.724138</td>\n",
       "      <td>0.969208</td>\n",
       "      <td>86</td>\n",
       "      <td>1.265574</td>\n",
       "      <td>0.522393</td>\n",
       "      <td>0.464491</td>\n",
       "      <td>0.741135</td>\n",
       "      <td>58.689655</td>\n",
       "      <td>0.825396</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>0.479612</td>\n",
       "      <td>0.430481</td>\n",
       "      <td>0.339492</td>\n",
       "      <td>0.513566</td>\n",
       "      <td>0.359127</td>\n",
       "      <td>349</td>\n",
       "      <td>0.566212</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>134</td>\n",
       "      <td>54</td>\n",
       "      <td>77.531250</td>\n",
       "      <td>0.949992</td>\n",
       "      <td>188</td>\n",
       "      <td>1.151111</td>\n",
       "      <td>0.537988</td>\n",
       "      <td>0.487426</td>\n",
       "      <td>0.706767</td>\n",
       "      <td>64.093750</td>\n",
       "      <td>0.799199</td>\n",
       "      <td>0.652751</td>\n",
       "      <td>0.464146</td>\n",
       "      <td>0.412325</td>\n",
       "      <td>0.328014</td>\n",
       "      <td>0.502864</td>\n",
       "      <td>0.355932</td>\n",
       "      <td>430</td>\n",
       "      <td>0.573880</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Season  DayNum  team1_TeamID  team1_Score  team2_TeamID  team2_Score  \\\n",
       "0    2003     134          1421           92          1411           84   \n",
       "1    2003     146          1328           47          1393           63   \n",
       "2    2003     144          1120           78          1393           79   \n",
       "3    2003     144          1268           58          1277           60   \n",
       "4    2003     143          1458           57          1246           63   \n",
       "\n",
       "   team1_seedN  team1_DRB_DIF  team1_ORB_DIF  team1_PPG  team1_PPP  \\\n",
       "0           16             10            -42  71.206897   0.866162   \n",
       "1            1             77             52  71.166667   0.930072   \n",
       "2           10             59             -9  70.100000   0.884178   \n",
       "3            6             88            -16  80.785714   0.929044   \n",
       "4            5             25             61  70.724138   0.969208   \n",
       "\n",
       "   team1_TRB_DIF  team1_ast_TO  team1_e_fg  team1_fg  team1_free_throw_pct  \\\n",
       "0            -32      0.804255    0.486339  0.429265              0.762768   \n",
       "1            129      1.200565    0.512972  0.446934              0.707885   \n",
       "2             50      0.842767    0.521328  0.469835              0.662162   \n",
       "3             72      1.339241    0.517756  0.464487              0.703642   \n",
       "4             86      1.265574    0.522393  0.464491              0.741135   \n",
       "\n",
       "   team1_opp_PPG  team1_opp_PPP  team1_opp_ast_TO  team1_opp_efg  \\\n",
       "0      78.448276       0.937078          1.236559       0.518382   \n",
       "1      60.166667       0.799394          0.763990       0.446284   \n",
       "2      65.566667       0.822586          0.801688       0.481165   \n",
       "3      66.857143       0.759001          0.703704       0.432193   \n",
       "4      58.689655       0.825396          0.800000       0.479612   \n",
       "\n",
       "   team1_opp_fg  team1_opp_three_point_pct  team1_opp_trueshooting  \\\n",
       "0      0.455882                   0.367110                0.553323   \n",
       "1      0.404747                   0.326781                0.488641   \n",
       "2      0.420247                   0.333333                0.512977   \n",
       "3      0.378538                   0.312715                0.479165   \n",
       "4      0.430481                   0.339492                0.513566   \n",
       "\n",
       "   team1_three_point_pct  team1_total_point_differential  team1_true_shooting  \\\n",
       "0               0.360153                            -210             0.539424   \n",
       "1               0.393673                             330             0.549827   \n",
       "2               0.344898                             136             0.552990   \n",
       "3               0.397895                             390             0.554477   \n",
       "4               0.359127                             349             0.566212   \n",
       "\n",
       "   team1_acc  team1_big_east  team1_big_ten  team1_big_twelve  team1_sec  \\\n",
       "0          0               0              0                 0          0   \n",
       "1          0               0              0                 1          0   \n",
       "2          0               0              0                 0          1   \n",
       "3          1               0              0                 0          0   \n",
       "4          0               0              1                 0          0   \n",
       "\n",
       "   team1_pac12  team1_MOR  team1_AP_top10  team1_AP_top25  team2_seedN  \\\n",
       "0            0      277.0               0               0           16   \n",
       "1            0        6.0               1               0            3   \n",
       "2            0       44.0               0               0            3   \n",
       "3            0        9.0               0               1            7   \n",
       "4            0       15.0               0               1            1   \n",
       "\n",
       "   team2_DRB_DIF  team2_ORB_DIF  team2_PPG  team2_PPP  team2_TRB_DIF  \\\n",
       "0             58             37  72.800000   0.878704             95   \n",
       "1            134            -43  80.103448   0.929051             91   \n",
       "2            134            -43  80.103448   0.929051             91   \n",
       "3            125             42  67.225806   0.891803            167   \n",
       "4            134             54  77.531250   0.949992            188   \n",
       "\n",
       "   team2_ast_TO  team2_e_fg  team2_fg  team2_free_throw_pct  team2_opp_PPG  \\\n",
       "0      0.932166    0.501206  0.447527              0.619952      70.833333   \n",
       "1      1.098734    0.512195  0.470067              0.693431      69.896552   \n",
       "2      1.098734    0.512195  0.470067              0.693431      69.896552   \n",
       "3      0.935698    0.498737  0.450758              0.734694      60.967742   \n",
       "4      1.151111    0.537988  0.487426              0.706767      64.093750   \n",
       "\n",
       "   team2_opp_PPP  team2_opp_ast_TO  team2_opp_efg  team2_opp_fg  \\\n",
       "0       0.853660          0.960465       0.487307      0.424945   \n",
       "1       0.799883          1.100239       0.443703      0.390075   \n",
       "2       0.799883          1.100239       0.443703      0.390075   \n",
       "3       0.826801          0.781038       0.458013      0.400641   \n",
       "4       0.799199          0.652751       0.464146      0.412325   \n",
       "\n",
       "   team2_opp_three_point_pct  team2_opp_trueshooting  team2_three_point_pct  \\\n",
       "0                   0.325180                0.515957               0.320721   \n",
       "1                   0.306870                0.479169               0.330435   \n",
       "2                   0.306870                0.479169               0.330435   \n",
       "3                   0.338374                0.512773               0.366265   \n",
       "4                   0.328014                0.502864               0.355932   \n",
       "\n",
       "   team2_total_point_differential  team2_true_shooting  team2_acc  \\\n",
       "0                              59             0.538334          0   \n",
       "1                             296             0.551677          0   \n",
       "2                             296             0.551677          0   \n",
       "3                             194             0.552539          0   \n",
       "4                             430             0.573880          0   \n",
       "\n",
       "   team2_big_east  team2_big_ten  team2_big_twelve  team2_sec  team2_pac12  \\\n",
       "0               0              0                 0          0            0   \n",
       "1               1              0                 0          0            0   \n",
       "2               1              0                 0          0            0   \n",
       "3               0              1                 0          0            0   \n",
       "4               0              0                 0          1            0   \n",
       "\n",
       "   team2_MOR  team2_AP_top10  team2_AP_top25  team1_win  \n",
       "0      293.0               0               0          1  \n",
       "1       21.0               0               1          0  \n",
       "2       21.0               0               1          0  \n",
       "3       16.0               0               0          0  \n",
       "4        1.0               1               0          0  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = final_df[final_df.Season < 2015]\n",
    "validation_data = final_df[final_df.Season >= 2015].reset_index(drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = train_data.drop(columns = [\"Season\", \"DayNum\", \"team1_TeamID\", \"team1_Score\", \"team2_TeamID\", \n",
    "                              \"team2_Score\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before deciding on which features to remove, I am going to train a baseline model to get a performance benchmark \n",
    "before moving forward with feature selection. I am going to do this both with and without scaled features, although I am confident that the scaled features will yield the superior model. Because there is a high dimensional feature space relative to the number of observations, I have elected to go with L1 regularization to start with to reduce the feature set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Baseline cross-validation ROC-AUC Score: 0.7943458251150559\n"
     ]
    }
   ],
   "source": [
    "Xtrain = X.drop(columns = [\"team1_win\"])\n",
    "y = X[\"team1_win\"]\n",
    "\n",
    "lr = LogisticRegression(max_iter = 1000, penalty = \"l1\", solver = \"liblinear\", C = 0.1)\n",
    "baseline_cv = cross_val_score(lr, Xtrain, y, scoring = \"roc_auc\", cv = 10).mean()\n",
    "print(\"Baseline cross-validation ROC-AUC Score: {}\".format(baseline_cv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>team1_seedN</th>\n",
       "      <th>team1_DRB_DIF</th>\n",
       "      <th>team1_ORB_DIF</th>\n",
       "      <th>team1_PPG</th>\n",
       "      <th>team1_PPP</th>\n",
       "      <th>team1_TRB_DIF</th>\n",
       "      <th>team1_ast_TO</th>\n",
       "      <th>team1_e_fg</th>\n",
       "      <th>team1_fg</th>\n",
       "      <th>team1_free_throw_pct</th>\n",
       "      <th>team1_opp_PPG</th>\n",
       "      <th>team1_opp_PPP</th>\n",
       "      <th>team1_opp_ast_TO</th>\n",
       "      <th>team1_opp_efg</th>\n",
       "      <th>team1_opp_fg</th>\n",
       "      <th>team1_opp_three_point_pct</th>\n",
       "      <th>team1_opp_trueshooting</th>\n",
       "      <th>team1_three_point_pct</th>\n",
       "      <th>team1_total_point_differential</th>\n",
       "      <th>team1_true_shooting</th>\n",
       "      <th>team1_acc</th>\n",
       "      <th>team1_big_east</th>\n",
       "      <th>team1_big_ten</th>\n",
       "      <th>team1_big_twelve</th>\n",
       "      <th>team1_sec</th>\n",
       "      <th>team1_pac12</th>\n",
       "      <th>team1_MOR</th>\n",
       "      <th>team1_AP_top10</th>\n",
       "      <th>team1_AP_top25</th>\n",
       "      <th>team2_seedN</th>\n",
       "      <th>team2_DRB_DIF</th>\n",
       "      <th>team2_ORB_DIF</th>\n",
       "      <th>team2_PPG</th>\n",
       "      <th>team2_PPP</th>\n",
       "      <th>team2_TRB_DIF</th>\n",
       "      <th>team2_ast_TO</th>\n",
       "      <th>team2_e_fg</th>\n",
       "      <th>team2_fg</th>\n",
       "      <th>team2_free_throw_pct</th>\n",
       "      <th>team2_opp_PPG</th>\n",
       "      <th>team2_opp_PPP</th>\n",
       "      <th>team2_opp_ast_TO</th>\n",
       "      <th>team2_opp_efg</th>\n",
       "      <th>team2_opp_fg</th>\n",
       "      <th>team2_opp_three_point_pct</th>\n",
       "      <th>team2_opp_trueshooting</th>\n",
       "      <th>team2_three_point_pct</th>\n",
       "      <th>team2_total_point_differential</th>\n",
       "      <th>team2_true_shooting</th>\n",
       "      <th>team2_acc</th>\n",
       "      <th>team2_big_east</th>\n",
       "      <th>team2_big_ten</th>\n",
       "      <th>team2_big_twelve</th>\n",
       "      <th>team2_sec</th>\n",
       "      <th>team2_pac12</th>\n",
       "      <th>team2_MOR</th>\n",
       "      <th>team2_AP_top10</th>\n",
       "      <th>team2_AP_top25</th>\n",
       "      <th>team1_win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
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       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
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       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
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       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "      <td>780.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.952564</td>\n",
       "      <td>84.105128</td>\n",
       "      <td>23.535897</td>\n",
       "      <td>73.964807</td>\n",
       "      <td>0.936586</td>\n",
       "      <td>107.641026</td>\n",
       "      <td>1.144887</td>\n",
       "      <td>0.519432</td>\n",
       "      <td>0.460378</td>\n",
       "      <td>0.704889</td>\n",
       "      <td>64.764026</td>\n",
       "      <td>0.827074</td>\n",
       "      <td>0.850488</td>\n",
       "      <td>0.466079</td>\n",
       "      <td>0.412669</td>\n",
       "      <td>0.327972</td>\n",
       "      <td>0.506632</td>\n",
       "      <td>0.361990</td>\n",
       "      <td>292.346154</td>\n",
       "      <td>0.560311</td>\n",
       "      <td>0.096154</td>\n",
       "      <td>0.135897</td>\n",
       "      <td>0.110256</td>\n",
       "      <td>0.110256</td>\n",
       "      <td>0.069231</td>\n",
       "      <td>0.082051</td>\n",
       "      <td>42.361538</td>\n",
       "      <td>0.269231</td>\n",
       "      <td>0.264103</td>\n",
       "      <td>6.908974</td>\n",
       "      <td>86.979487</td>\n",
       "      <td>21.211538</td>\n",
       "      <td>73.925774</td>\n",
       "      <td>0.936239</td>\n",
       "      <td>108.191026</td>\n",
       "      <td>1.147209</td>\n",
       "      <td>0.519695</td>\n",
       "      <td>0.460766</td>\n",
       "      <td>0.704883</td>\n",
       "      <td>64.735759</td>\n",
       "      <td>0.826153</td>\n",
       "      <td>0.854495</td>\n",
       "      <td>0.465409</td>\n",
       "      <td>0.411587</td>\n",
       "      <td>0.329224</td>\n",
       "      <td>0.505615</td>\n",
       "      <td>0.360509</td>\n",
       "      <td>292.135897</td>\n",
       "      <td>0.560303</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.130769</td>\n",
       "      <td>0.103846</td>\n",
       "      <td>0.096154</td>\n",
       "      <td>0.108974</td>\n",
       "      <td>0.070513</td>\n",
       "      <td>42.062821</td>\n",
       "      <td>0.288462</td>\n",
       "      <td>0.257692</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.647973</td>\n",
       "      <td>76.011091</td>\n",
       "      <td>57.434050</td>\n",
       "      <td>5.043469</td>\n",
       "      <td>0.042773</td>\n",
       "      <td>106.233615</td>\n",
       "      <td>0.191859</td>\n",
       "      <td>0.024491</td>\n",
       "      <td>0.021491</td>\n",
       "      <td>0.035753</td>\n",
       "      <td>4.536315</td>\n",
       "      <td>0.039948</td>\n",
       "      <td>0.148068</td>\n",
       "      <td>0.023515</td>\n",
       "      <td>0.021809</td>\n",
       "      <td>0.021945</td>\n",
       "      <td>0.022445</td>\n",
       "      <td>0.026333</td>\n",
       "      <td>140.815981</td>\n",
       "      <td>0.023107</td>\n",
       "      <td>0.294991</td>\n",
       "      <td>0.342899</td>\n",
       "      <td>0.313410</td>\n",
       "      <td>0.313410</td>\n",
       "      <td>0.254009</td>\n",
       "      <td>0.274619</td>\n",
       "      <td>51.437114</td>\n",
       "      <td>0.443845</td>\n",
       "      <td>0.441137</td>\n",
       "      <td>4.725934</td>\n",
       "      <td>76.280020</td>\n",
       "      <td>57.328279</td>\n",
       "      <td>5.139738</td>\n",
       "      <td>0.043829</td>\n",
       "      <td>104.300190</td>\n",
       "      <td>0.188039</td>\n",
       "      <td>0.025605</td>\n",
       "      <td>0.022391</td>\n",
       "      <td>0.035990</td>\n",
       "      <td>4.327330</td>\n",
       "      <td>0.038141</td>\n",
       "      <td>0.143814</td>\n",
       "      <td>0.022806</td>\n",
       "      <td>0.020470</td>\n",
       "      <td>0.020921</td>\n",
       "      <td>0.022051</td>\n",
       "      <td>0.025877</td>\n",
       "      <td>143.287952</td>\n",
       "      <td>0.024015</td>\n",
       "      <td>0.300192</td>\n",
       "      <td>0.337364</td>\n",
       "      <td>0.305257</td>\n",
       "      <td>0.294991</td>\n",
       "      <td>0.311807</td>\n",
       "      <td>0.256174</td>\n",
       "      <td>52.105452</td>\n",
       "      <td>0.453338</td>\n",
       "      <td>0.437644</td>\n",
       "      <td>0.500321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-177.000000</td>\n",
       "      <td>-151.000000</td>\n",
       "      <td>58.812500</td>\n",
       "      <td>0.796848</td>\n",
       "      <td>-298.000000</td>\n",
       "      <td>0.527397</td>\n",
       "      <td>0.443312</td>\n",
       "      <td>0.396034</td>\n",
       "      <td>0.595561</td>\n",
       "      <td>50.428571</td>\n",
       "      <td>0.725203</td>\n",
       "      <td>0.506522</td>\n",
       "      <td>0.403670</td>\n",
       "      <td>0.359858</td>\n",
       "      <td>0.264559</td>\n",
       "      <td>0.447398</td>\n",
       "      <td>0.293151</td>\n",
       "      <td>-210.000000</td>\n",
       "      <td>0.492915</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-249.000000</td>\n",
       "      <td>-151.000000</td>\n",
       "      <td>58.812500</td>\n",
       "      <td>0.778533</td>\n",
       "      <td>-261.000000</td>\n",
       "      <td>0.596899</td>\n",
       "      <td>0.418934</td>\n",
       "      <td>0.384921</td>\n",
       "      <td>0.595561</td>\n",
       "      <td>52.878788</td>\n",
       "      <td>0.725203</td>\n",
       "      <td>0.545902</td>\n",
       "      <td>0.403670</td>\n",
       "      <td>0.359858</td>\n",
       "      <td>0.266284</td>\n",
       "      <td>0.447398</td>\n",
       "      <td>0.264901</td>\n",
       "      <td>-237.000000</td>\n",
       "      <td>0.460374</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>-15.000000</td>\n",
       "      <td>70.424242</td>\n",
       "      <td>0.910878</td>\n",
       "      <td>45.750000</td>\n",
       "      <td>1.029704</td>\n",
       "      <td>0.501713</td>\n",
       "      <td>0.445295</td>\n",
       "      <td>0.681324</td>\n",
       "      <td>61.606061</td>\n",
       "      <td>0.799732</td>\n",
       "      <td>0.741451</td>\n",
       "      <td>0.449898</td>\n",
       "      <td>0.397781</td>\n",
       "      <td>0.311902</td>\n",
       "      <td>0.490967</td>\n",
       "      <td>0.342358</td>\n",
       "      <td>202.000000</td>\n",
       "      <td>0.544425</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>40.750000</td>\n",
       "      <td>-17.250000</td>\n",
       "      <td>70.454545</td>\n",
       "      <td>0.906402</td>\n",
       "      <td>42.750000</td>\n",
       "      <td>1.015905</td>\n",
       "      <td>0.502765</td>\n",
       "      <td>0.445872</td>\n",
       "      <td>0.679449</td>\n",
       "      <td>61.582843</td>\n",
       "      <td>0.798645</td>\n",
       "      <td>0.746710</td>\n",
       "      <td>0.448663</td>\n",
       "      <td>0.397997</td>\n",
       "      <td>0.314465</td>\n",
       "      <td>0.489807</td>\n",
       "      <td>0.340426</td>\n",
       "      <td>193.750000</td>\n",
       "      <td>0.544334</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>85.000000</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>73.590909</td>\n",
       "      <td>0.935371</td>\n",
       "      <td>106.000000</td>\n",
       "      <td>1.133630</td>\n",
       "      <td>0.519445</td>\n",
       "      <td>0.459313</td>\n",
       "      <td>0.703772</td>\n",
       "      <td>64.794118</td>\n",
       "      <td>0.827639</td>\n",
       "      <td>0.843555</td>\n",
       "      <td>0.465393</td>\n",
       "      <td>0.412433</td>\n",
       "      <td>0.327731</td>\n",
       "      <td>0.506099</td>\n",
       "      <td>0.362009</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>0.558254</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>87.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>73.745977</td>\n",
       "      <td>0.934876</td>\n",
       "      <td>102.000000</td>\n",
       "      <td>1.134529</td>\n",
       "      <td>0.518653</td>\n",
       "      <td>0.460656</td>\n",
       "      <td>0.706360</td>\n",
       "      <td>64.769413</td>\n",
       "      <td>0.826955</td>\n",
       "      <td>0.843590</td>\n",
       "      <td>0.464826</td>\n",
       "      <td>0.410745</td>\n",
       "      <td>0.328947</td>\n",
       "      <td>0.505513</td>\n",
       "      <td>0.360225</td>\n",
       "      <td>293.000000</td>\n",
       "      <td>0.558087</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>23.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>11.000000</td>\n",
       "      <td>131.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>77.551915</td>\n",
       "      <td>0.963470</td>\n",
       "      <td>175.500000</td>\n",
       "      <td>1.268293</td>\n",
       "      <td>0.535238</td>\n",
       "      <td>0.475305</td>\n",
       "      <td>0.730711</td>\n",
       "      <td>67.477941</td>\n",
       "      <td>0.853433</td>\n",
       "      <td>0.937369</td>\n",
       "      <td>0.481241</td>\n",
       "      <td>0.428725</td>\n",
       "      <td>0.343158</td>\n",
       "      <td>0.521905</td>\n",
       "      <td>0.380741</td>\n",
       "      <td>371.000000</td>\n",
       "      <td>0.577188</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>134.000000</td>\n",
       "      <td>59.000000</td>\n",
       "      <td>77.401515</td>\n",
       "      <td>0.965846</td>\n",
       "      <td>181.250000</td>\n",
       "      <td>1.269608</td>\n",
       "      <td>0.536075</td>\n",
       "      <td>0.475329</td>\n",
       "      <td>0.729441</td>\n",
       "      <td>67.666667</td>\n",
       "      <td>0.850511</td>\n",
       "      <td>0.931312</td>\n",
       "      <td>0.481184</td>\n",
       "      <td>0.423809</td>\n",
       "      <td>0.342908</td>\n",
       "      <td>0.521076</td>\n",
       "      <td>0.378378</td>\n",
       "      <td>371.250000</td>\n",
       "      <td>0.575415</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>16.000000</td>\n",
       "      <td>273.000000</td>\n",
       "      <td>208.000000</td>\n",
       "      <td>89.387097</td>\n",
       "      <td>1.041700</td>\n",
       "      <td>387.000000</td>\n",
       "      <td>2.107438</td>\n",
       "      <td>0.590935</td>\n",
       "      <td>0.530651</td>\n",
       "      <td>0.824034</td>\n",
       "      <td>78.448276</td>\n",
       "      <td>0.958509</td>\n",
       "      <td>1.488235</td>\n",
       "      <td>0.543001</td>\n",
       "      <td>0.493129</td>\n",
       "      <td>0.407002</td>\n",
       "      <td>0.578435</td>\n",
       "      <td>0.437596</td>\n",
       "      <td>719.000000</td>\n",
       "      <td>0.624683</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>301.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>273.000000</td>\n",
       "      <td>208.000000</td>\n",
       "      <td>89.387097</td>\n",
       "      <td>1.084460</td>\n",
       "      <td>401.000000</td>\n",
       "      <td>1.783537</td>\n",
       "      <td>0.593055</td>\n",
       "      <td>0.526858</td>\n",
       "      <td>0.824034</td>\n",
       "      <td>78.413793</td>\n",
       "      <td>0.949599</td>\n",
       "      <td>1.488235</td>\n",
       "      <td>0.554993</td>\n",
       "      <td>0.489204</td>\n",
       "      <td>0.388778</td>\n",
       "      <td>0.605202</td>\n",
       "      <td>0.437596</td>\n",
       "      <td>719.000000</td>\n",
       "      <td>0.627222</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>293.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       team1_seedN  team1_DRB_DIF  team1_ORB_DIF   team1_PPG   team1_PPP  \\\n",
       "count   780.000000     780.000000     780.000000  780.000000  780.000000   \n",
       "mean      6.952564      84.105128      23.535897   73.964807    0.936586   \n",
       "std       4.647973      76.011091      57.434050    5.043469    0.042773   \n",
       "min       1.000000    -177.000000    -151.000000   58.812500    0.796848   \n",
       "25%       3.000000      38.000000     -15.000000   70.424242    0.910878   \n",
       "50%       6.000000      85.000000      24.000000   73.590909    0.935371   \n",
       "75%      11.000000     131.000000      61.000000   77.551915    0.963470   \n",
       "max      16.000000     273.000000     208.000000   89.387097    1.041700   \n",
       "\n",
       "       team1_TRB_DIF  team1_ast_TO  team1_e_fg    team1_fg  \\\n",
       "count     780.000000    780.000000  780.000000  780.000000   \n",
       "mean      107.641026      1.144887    0.519432    0.460378   \n",
       "std       106.233615      0.191859    0.024491    0.021491   \n",
       "min      -298.000000      0.527397    0.443312    0.396034   \n",
       "25%        45.750000      1.029704    0.501713    0.445295   \n",
       "50%       106.000000      1.133630    0.519445    0.459313   \n",
       "75%       175.500000      1.268293    0.535238    0.475305   \n",
       "max       387.000000      2.107438    0.590935    0.530651   \n",
       "\n",
       "       team1_free_throw_pct  team1_opp_PPG  team1_opp_PPP  team1_opp_ast_TO  \\\n",
       "count            780.000000     780.000000     780.000000        780.000000   \n",
       "mean               0.704889      64.764026       0.827074          0.850488   \n",
       "std                0.035753       4.536315       0.039948          0.148068   \n",
       "min                0.595561      50.428571       0.725203          0.506522   \n",
       "25%                0.681324      61.606061       0.799732          0.741451   \n",
       "50%                0.703772      64.794118       0.827639          0.843555   \n",
       "75%                0.730711      67.477941       0.853433          0.937369   \n",
       "max                0.824034      78.448276       0.958509          1.488235   \n",
       "\n",
       "       team1_opp_efg  team1_opp_fg  team1_opp_three_point_pct  \\\n",
       "count     780.000000    780.000000                 780.000000   \n",
       "mean        0.466079      0.412669                   0.327972   \n",
       "std         0.023515      0.021809                   0.021945   \n",
       "min         0.403670      0.359858                   0.264559   \n",
       "25%         0.449898      0.397781                   0.311902   \n",
       "50%         0.465393      0.412433                   0.327731   \n",
       "75%         0.481241      0.428725                   0.343158   \n",
       "max         0.543001      0.493129                   0.407002   \n",
       "\n",
       "       team1_opp_trueshooting  team1_three_point_pct  \\\n",
       "count              780.000000             780.000000   \n",
       "mean                 0.506632               0.361990   \n",
       "std                  0.022445               0.026333   \n",
       "min                  0.447398               0.293151   \n",
       "25%                  0.490967               0.342358   \n",
       "50%                  0.506099               0.362009   \n",
       "75%                  0.521905               0.380741   \n",
       "max                  0.578435               0.437596   \n",
       "\n",
       "       team1_total_point_differential  team1_true_shooting   team1_acc  \\\n",
       "count                      780.000000           780.000000  780.000000   \n",
       "mean                       292.346154             0.560311    0.096154   \n",
       "std                        140.815981             0.023107    0.294991   \n",
       "min                       -210.000000             0.492915    0.000000   \n",
       "25%                        202.000000             0.544425    0.000000   \n",
       "50%                        296.000000             0.558254    0.000000   \n",
       "75%                        371.000000             0.577188    0.000000   \n",
       "max                        719.000000             0.624683    1.000000   \n",
       "\n",
       "       team1_big_east  team1_big_ten  team1_big_twelve   team1_sec  \\\n",
       "count      780.000000     780.000000        780.000000  780.000000   \n",
       "mean         0.135897       0.110256          0.110256    0.069231   \n",
       "std          0.342899       0.313410          0.313410    0.254009   \n",
       "min          0.000000       0.000000          0.000000    0.000000   \n",
       "25%          0.000000       0.000000          0.000000    0.000000   \n",
       "50%          0.000000       0.000000          0.000000    0.000000   \n",
       "75%          0.000000       0.000000          0.000000    0.000000   \n",
       "max          1.000000       1.000000          1.000000    1.000000   \n",
       "\n",
       "       team1_pac12   team1_MOR  team1_AP_top10  team1_AP_top25  team2_seedN  \\\n",
       "count   780.000000  780.000000      780.000000      780.000000   780.000000   \n",
       "mean      0.082051   42.361538        0.269231        0.264103     6.908974   \n",
       "std       0.274619   51.437114        0.443845        0.441137     4.725934   \n",
       "min       0.000000    1.000000        0.000000        0.000000     1.000000   \n",
       "25%       0.000000   10.000000        0.000000        0.000000     3.000000   \n",
       "50%       0.000000   23.000000        0.000000        0.000000     6.000000   \n",
       "75%       0.000000   50.000000        1.000000        1.000000    11.000000   \n",
       "max       1.000000  301.000000        1.000000        1.000000    16.000000   \n",
       "\n",
       "       team2_DRB_DIF  team2_ORB_DIF   team2_PPG   team2_PPP  team2_TRB_DIF  \\\n",
       "count     780.000000     780.000000  780.000000  780.000000     780.000000   \n",
       "mean       86.979487      21.211538   73.925774    0.936239     108.191026   \n",
       "std        76.280020      57.328279    5.139738    0.043829     104.300190   \n",
       "min      -249.000000    -151.000000   58.812500    0.778533    -261.000000   \n",
       "25%        40.750000     -17.250000   70.454545    0.906402      42.750000   \n",
       "50%        87.000000      19.000000   73.745977    0.934876     102.000000   \n",
       "75%       134.000000      59.000000   77.401515    0.965846     181.250000   \n",
       "max       273.000000     208.000000   89.387097    1.084460     401.000000   \n",
       "\n",
       "       team2_ast_TO  team2_e_fg    team2_fg  team2_free_throw_pct  \\\n",
       "count    780.000000  780.000000  780.000000            780.000000   \n",
       "mean       1.147209    0.519695    0.460766              0.704883   \n",
       "std        0.188039    0.025605    0.022391              0.035990   \n",
       "min        0.596899    0.418934    0.384921              0.595561   \n",
       "25%        1.015905    0.502765    0.445872              0.679449   \n",
       "50%        1.134529    0.518653    0.460656              0.706360   \n",
       "75%        1.269608    0.536075    0.475329              0.729441   \n",
       "max        1.783537    0.593055    0.526858              0.824034   \n",
       "\n",
       "       team2_opp_PPG  team2_opp_PPP  team2_opp_ast_TO  team2_opp_efg  \\\n",
       "count     780.000000     780.000000        780.000000     780.000000   \n",
       "mean       64.735759       0.826153          0.854495       0.465409   \n",
       "std         4.327330       0.038141          0.143814       0.022806   \n",
       "min        52.878788       0.725203          0.545902       0.403670   \n",
       "25%        61.582843       0.798645          0.746710       0.448663   \n",
       "50%        64.769413       0.826955          0.843590       0.464826   \n",
       "75%        67.666667       0.850511          0.931312       0.481184   \n",
       "max        78.413793       0.949599          1.488235       0.554993   \n",
       "\n",
       "       team2_opp_fg  team2_opp_three_point_pct  team2_opp_trueshooting  \\\n",
       "count    780.000000                 780.000000              780.000000   \n",
       "mean       0.411587                   0.329224                0.505615   \n",
       "std        0.020470                   0.020921                0.022051   \n",
       "min        0.359858                   0.266284                0.447398   \n",
       "25%        0.397997                   0.314465                0.489807   \n",
       "50%        0.410745                   0.328947                0.505513   \n",
       "75%        0.423809                   0.342908                0.521076   \n",
       "max        0.489204                   0.388778                0.605202   \n",
       "\n",
       "       team2_three_point_pct  team2_total_point_differential  \\\n",
       "count             780.000000                      780.000000   \n",
       "mean                0.360509                      292.135897   \n",
       "std                 0.025877                      143.287952   \n",
       "min                 0.264901                     -237.000000   \n",
       "25%                 0.340426                      193.750000   \n",
       "50%                 0.360225                      293.000000   \n",
       "75%                 0.378378                      371.250000   \n",
       "max                 0.437596                      719.000000   \n",
       "\n",
       "       team2_true_shooting   team2_acc  team2_big_east  team2_big_ten  \\\n",
       "count           780.000000  780.000000      780.000000     780.000000   \n",
       "mean              0.560303    0.100000        0.130769       0.103846   \n",
       "std               0.024015    0.300192        0.337364       0.305257   \n",
       "min               0.460374    0.000000        0.000000       0.000000   \n",
       "25%               0.544334    0.000000        0.000000       0.000000   \n",
       "50%               0.558087    0.000000        0.000000       0.000000   \n",
       "75%               0.575415    0.000000        0.000000       0.000000   \n",
       "max               0.627222    1.000000        1.000000       1.000000   \n",
       "\n",
       "       team2_big_twelve   team2_sec  team2_pac12   team2_MOR  team2_AP_top10  \\\n",
       "count        780.000000  780.000000   780.000000  780.000000      780.000000   \n",
       "mean           0.096154    0.108974     0.070513   42.062821        0.288462   \n",
       "std            0.294991    0.311807     0.256174   52.105452        0.453338   \n",
       "min            0.000000    0.000000     0.000000    1.000000        0.000000   \n",
       "25%            0.000000    0.000000     0.000000   10.000000        0.000000   \n",
       "50%            0.000000    0.000000     0.000000   23.500000        0.000000   \n",
       "75%            0.000000    0.000000     0.000000   50.000000        1.000000   \n",
       "max            1.000000    1.000000     1.000000  293.000000        1.000000   \n",
       "\n",
       "       team2_AP_top25   team1_win  \n",
       "count      780.000000  780.000000  \n",
       "mean         0.257692    0.500000  \n",
       "std          0.437644    0.500321  \n",
       "min          0.000000    0.000000  \n",
       "25%          0.000000    0.000000  \n",
       "50%          0.000000    0.500000  \n",
       "75%          1.000000    1.000000  \n",
       "max          1.000000    1.000000  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nothing looks out of the ordinary, every distribution falls within a reasonable range so I am not concerned about potential outliers. I am concerned about correlation and multicollinearity. Many of these features are highly related (indeed, several of these features are attempts to optimize each other) and I will need to remove some of the collinear features. I have an idea which ones I'd like to keep from my investigation in the previous notebook, but I will need to take a deeper look with the training set prepared. I also will likely scale the features, as some features like __point_differential__ have standard deviations thousands of times larger than some of the other features. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_corr = X.corr()\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (10, 10))\n",
    "sns.heatmap(X_corr, cbar = True, vmin = -1, vmax= 1, center = 0,\n",
    "            cmap=sns.diverging_palette(20, 220, n=200), ax = ax);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "team2_e_fg     team2_true_shooting       0.954824\n",
       "team2_opp_efg  team2_opp_trueshooting    0.951079\n",
       "               team2_opp_fg              0.949879\n",
       "team1_e_fg     team1_true_shooting       0.949395\n",
       "team1_opp_efg  team1_opp_trueshooting    0.949353\n",
       "               team1_opp_fg              0.948158\n",
       "team2_opp_fg   team2_opp_trueshooting    0.906947\n",
       "team1_opp_fg   team1_opp_trueshooting    0.906832\n",
       "team2_e_fg     team2_fg                  0.899743\n",
       "team1_e_fg     team1_fg                  0.883464\n",
       "team1_PPP      team1_true_shooting       0.881044\n",
       "team2_PPP      team2_true_shooting       0.877485\n",
       "team2_fg       team2_true_shooting       0.856970\n",
       "team1_DRB_DIF  team1_TRB_DIF             0.852304\n",
       "team2_DRB_DIF  team2_TRB_DIF             0.842798\n",
       "team1_PPP      team1_e_fg                0.841317\n",
       "team2_PPP      team2_e_fg                0.841066\n",
       "team1_fg       team1_true_shooting       0.838926\n",
       "team2_opp_PPP  team2_opp_trueshooting    0.835596\n",
       "               team2_opp_efg             0.830458\n",
       "team1_opp_PPP  team1_opp_trueshooting    0.823352\n",
       "               team1_opp_efg             0.809423\n",
       "team1_seedN    team1_MOR                 0.809261\n",
       "team2_seedN    team2_MOR                 0.800111\n",
       "team2_opp_PPP  team2_opp_fg              0.789692\n",
       "team1_opp_PPP  team1_opp_fg              0.774618\n",
       "dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_corr = X.corr().abs()\n",
    "all_correlated = X_corr.where(np.triu(np.ones(X_corr.shape), k = 1).astype(np.bool)).\\\n",
    "stack().sort_values(ascending = False)\n",
    "\n",
    "highly_correlated = all_correlated[all_correlated > 0.75]\n",
    "highly_correlated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "team2_seedN                     team1_win    0.414510\n",
       "team1_seedN                     team1_win    0.378406\n",
       "team2_total_point_differential  team1_win    0.377016\n",
       "team2_MOR                       team1_win    0.372733\n",
       "team2_AP_top10                  team1_win    0.325432\n",
       "team1_MOR                       team1_win    0.280732\n",
       "team1_AP_top10                  team1_win    0.277475\n",
       "team1_total_point_differential  team1_win    0.256637\n",
       "team2_opp_PPP                   team1_win    0.241520\n",
       "team2_opp_trueshooting          team1_win    0.216192\n",
       "team2_PPG                       team1_win    0.200518\n",
       "team2_ast_TO                    team1_win    0.198134\n",
       "team2_PPP                       team1_win    0.196631\n",
       "team2_opp_efg                   team1_win    0.184626\n",
       "team2_opp_fg                    team1_win    0.180588\n",
       "team2_fg                        team1_win    0.178654\n",
       "team2_TRB_DIF                   team1_win    0.176958\n",
       "team1_TRB_DIF                   team1_win    0.168629\n",
       "team1_opp_trueshooting          team1_win    0.167314\n",
       "team2_DRB_DIF                   team1_win    0.165220\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "team_one_correlation = []\n",
    "for i in all_correlated.index:\n",
    "    if \"team1_win\" in i:\n",
    "        team_one_correlation.append(i)\n",
    "\n",
    "team_one_correlation = all_correlated[team_one_correlation]\n",
    "team_one_correlation[:20]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly there is a lot going on here. I also now have an idea (at least linearly) of which features correlate strongly with the target. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>team1_seedN</th>\n",
       "      <th>team1_DRB_DIF</th>\n",
       "      <th>team1_ORB_DIF</th>\n",
       "      <th>team1_PPG</th>\n",
       "      <th>team1_PPP</th>\n",
       "      <th>team1_TRB_DIF</th>\n",
       "      <th>team1_ast_TO</th>\n",
       "      <th>team1_e_fg</th>\n",
       "      <th>team1_fg</th>\n",
       "      <th>team1_free_throw_pct</th>\n",
       "      <th>team1_opp_PPG</th>\n",
       "      <th>team1_opp_PPP</th>\n",
       "      <th>team1_opp_ast_TO</th>\n",
       "      <th>team1_opp_efg</th>\n",
       "      <th>team1_opp_fg</th>\n",
       "      <th>team1_opp_three_point_pct</th>\n",
       "      <th>team1_opp_trueshooting</th>\n",
       "      <th>team1_three_point_pct</th>\n",
       "      <th>team1_total_point_differential</th>\n",
       "      <th>team1_true_shooting</th>\n",
       "      <th>team1_acc</th>\n",
       "      <th>team1_big_east</th>\n",
       "      <th>team1_big_ten</th>\n",
       "      <th>team1_big_twelve</th>\n",
       "      <th>team1_sec</th>\n",
       "      <th>team1_pac12</th>\n",
       "      <th>team1_MOR</th>\n",
       "      <th>team1_AP_top10</th>\n",
       "      <th>team1_AP_top25</th>\n",
       "      <th>team2_seedN</th>\n",
       "      <th>team2_DRB_DIF</th>\n",
       "      <th>team2_ORB_DIF</th>\n",
       "      <th>team2_PPG</th>\n",
       "      <th>team2_PPP</th>\n",
       "      <th>team2_TRB_DIF</th>\n",
       "      <th>team2_ast_TO</th>\n",
       "      <th>team2_e_fg</th>\n",
       "      <th>team2_fg</th>\n",
       "      <th>team2_free_throw_pct</th>\n",
       "      <th>team2_opp_PPG</th>\n",
       "      <th>team2_opp_PPP</th>\n",
       "      <th>team2_opp_ast_TO</th>\n",
       "      <th>team2_opp_efg</th>\n",
       "      <th>team2_opp_fg</th>\n",
       "      <th>team2_opp_three_point_pct</th>\n",
       "      <th>team2_opp_trueshooting</th>\n",
       "      <th>team2_three_point_pct</th>\n",
       "      <th>team2_total_point_differential</th>\n",
       "      <th>team2_true_shooting</th>\n",
       "      <th>team2_acc</th>\n",
       "      <th>team2_big_east</th>\n",
       "      <th>team2_big_ten</th>\n",
       "      <th>team2_big_twelve</th>\n",
       "      <th>team2_sec</th>\n",
       "      <th>team2_pac12</th>\n",
       "      <th>team2_MOR</th>\n",
       "      <th>team2_AP_top10</th>\n",
       "      <th>team2_AP_top25</th>\n",
       "      <th>team1_win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16</td>\n",
       "      <td>10</td>\n",
       "      <td>-42</td>\n",
       "      <td>71.206897</td>\n",
       "      <td>0.866162</td>\n",
       "      <td>-32</td>\n",
       "      <td>0.804255</td>\n",
       "      <td>0.486339</td>\n",
       "      <td>0.429265</td>\n",
       "      <td>0.762768</td>\n",
       "      <td>78.448276</td>\n",
       "      <td>0.937078</td>\n",
       "      <td>1.236559</td>\n",
       "      <td>0.518382</td>\n",
       "      <td>0.455882</td>\n",
       "      <td>0.367110</td>\n",
       "      <td>0.553323</td>\n",
       "      <td>0.360153</td>\n",
       "      <td>-210</td>\n",
       "      <td>0.539424</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>277.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>58</td>\n",
       "      <td>37</td>\n",
       "      <td>72.800000</td>\n",
       "      <td>0.878704</td>\n",
       "      <td>95</td>\n",
       "      <td>0.932166</td>\n",
       "      <td>0.501206</td>\n",
       "      <td>0.447527</td>\n",
       "      <td>0.619952</td>\n",
       "      <td>70.833333</td>\n",
       "      <td>0.853660</td>\n",
       "      <td>0.960465</td>\n",
       "      <td>0.487307</td>\n",
       "      <td>0.424945</td>\n",
       "      <td>0.325180</td>\n",
       "      <td>0.515957</td>\n",
       "      <td>0.320721</td>\n",
       "      <td>59</td>\n",
       "      <td>0.538334</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>293.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>77</td>\n",
       "      <td>52</td>\n",
       "      <td>71.166667</td>\n",
       "      <td>0.930072</td>\n",
       "      <td>129</td>\n",
       "      <td>1.200565</td>\n",
       "      <td>0.512972</td>\n",
       "      <td>0.446934</td>\n",
       "      <td>0.707885</td>\n",
       "      <td>60.166667</td>\n",
       "      <td>0.799394</td>\n",
       "      <td>0.763990</td>\n",
       "      <td>0.446284</td>\n",
       "      <td>0.404747</td>\n",
       "      <td>0.326781</td>\n",
       "      <td>0.488641</td>\n",
       "      <td>0.393673</td>\n",
       "      <td>330</td>\n",
       "      <td>0.549827</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>134</td>\n",
       "      <td>-43</td>\n",
       "      <td>80.103448</td>\n",
       "      <td>0.929051</td>\n",
       "      <td>91</td>\n",
       "      <td>1.098734</td>\n",
       "      <td>0.512195</td>\n",
       "      <td>0.470067</td>\n",
       "      <td>0.693431</td>\n",
       "      <td>69.896552</td>\n",
       "      <td>0.799883</td>\n",
       "      <td>1.100239</td>\n",
       "      <td>0.443703</td>\n",
       "      <td>0.390075</td>\n",
       "      <td>0.306870</td>\n",
       "      <td>0.479169</td>\n",
       "      <td>0.330435</td>\n",
       "      <td>296</td>\n",
       "      <td>0.551677</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>59</td>\n",
       "      <td>-9</td>\n",
       "      <td>70.100000</td>\n",
       "      <td>0.884178</td>\n",
       "      <td>50</td>\n",
       "      <td>0.842767</td>\n",
       "      <td>0.521328</td>\n",
       "      <td>0.469835</td>\n",
       "      <td>0.662162</td>\n",
       "      <td>65.566667</td>\n",
       "      <td>0.822586</td>\n",
       "      <td>0.801688</td>\n",
       "      <td>0.481165</td>\n",
       "      <td>0.420247</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.512977</td>\n",
       "      <td>0.344898</td>\n",
       "      <td>136</td>\n",
       "      <td>0.552990</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>134</td>\n",
       "      <td>-43</td>\n",
       "      <td>80.103448</td>\n",
       "      <td>0.929051</td>\n",
       "      <td>91</td>\n",
       "      <td>1.098734</td>\n",
       "      <td>0.512195</td>\n",
       "      <td>0.470067</td>\n",
       "      <td>0.693431</td>\n",
       "      <td>69.896552</td>\n",
       "      <td>0.799883</td>\n",
       "      <td>1.100239</td>\n",
       "      <td>0.443703</td>\n",
       "      <td>0.390075</td>\n",
       "      <td>0.306870</td>\n",
       "      <td>0.479169</td>\n",
       "      <td>0.330435</td>\n",
       "      <td>296</td>\n",
       "      <td>0.551677</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>88</td>\n",
       "      <td>-16</td>\n",
       "      <td>80.785714</td>\n",
       "      <td>0.929044</td>\n",
       "      <td>72</td>\n",
       "      <td>1.339241</td>\n",
       "      <td>0.517756</td>\n",
       "      <td>0.464487</td>\n",
       "      <td>0.703642</td>\n",
       "      <td>66.857143</td>\n",
       "      <td>0.759001</td>\n",
       "      <td>0.703704</td>\n",
       "      <td>0.432193</td>\n",
       "      <td>0.378538</td>\n",
       "      <td>0.312715</td>\n",
       "      <td>0.479165</td>\n",
       "      <td>0.397895</td>\n",
       "      <td>390</td>\n",
       "      <td>0.554477</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>125</td>\n",
       "      <td>42</td>\n",
       "      <td>67.225806</td>\n",
       "      <td>0.891803</td>\n",
       "      <td>167</td>\n",
       "      <td>0.935698</td>\n",
       "      <td>0.498737</td>\n",
       "      <td>0.450758</td>\n",
       "      <td>0.734694</td>\n",
       "      <td>60.967742</td>\n",
       "      <td>0.826801</td>\n",
       "      <td>0.781038</td>\n",
       "      <td>0.458013</td>\n",
       "      <td>0.400641</td>\n",
       "      <td>0.338374</td>\n",
       "      <td>0.512773</td>\n",
       "      <td>0.366265</td>\n",
       "      <td>194</td>\n",
       "      <td>0.552539</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>61</td>\n",
       "      <td>70.724138</td>\n",
       "      <td>0.969208</td>\n",
       "      <td>86</td>\n",
       "      <td>1.265574</td>\n",
       "      <td>0.522393</td>\n",
       "      <td>0.464491</td>\n",
       "      <td>0.741135</td>\n",
       "      <td>58.689655</td>\n",
       "      <td>0.825396</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>0.479612</td>\n",
       "      <td>0.430481</td>\n",
       "      <td>0.339492</td>\n",
       "      <td>0.513566</td>\n",
       "      <td>0.359127</td>\n",
       "      <td>349</td>\n",
       "      <td>0.566212</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>134</td>\n",
       "      <td>54</td>\n",
       "      <td>77.531250</td>\n",
       "      <td>0.949992</td>\n",
       "      <td>188</td>\n",
       "      <td>1.151111</td>\n",
       "      <td>0.537988</td>\n",
       "      <td>0.487426</td>\n",
       "      <td>0.706767</td>\n",
       "      <td>64.093750</td>\n",
       "      <td>0.799199</td>\n",
       "      <td>0.652751</td>\n",
       "      <td>0.464146</td>\n",
       "      <td>0.412325</td>\n",
       "      <td>0.328014</td>\n",
       "      <td>0.502864</td>\n",
       "      <td>0.355932</td>\n",
       "      <td>430</td>\n",
       "      <td>0.573880</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   team1_seedN  team1_DRB_DIF  team1_ORB_DIF  team1_PPG  team1_PPP  \\\n",
       "0           16             10            -42  71.206897   0.866162   \n",
       "1            1             77             52  71.166667   0.930072   \n",
       "2           10             59             -9  70.100000   0.884178   \n",
       "3            6             88            -16  80.785714   0.929044   \n",
       "4            5             25             61  70.724138   0.969208   \n",
       "\n",
       "   team1_TRB_DIF  team1_ast_TO  team1_e_fg  team1_fg  team1_free_throw_pct  \\\n",
       "0            -32      0.804255    0.486339  0.429265              0.762768   \n",
       "1            129      1.200565    0.512972  0.446934              0.707885   \n",
       "2             50      0.842767    0.521328  0.469835              0.662162   \n",
       "3             72      1.339241    0.517756  0.464487              0.703642   \n",
       "4             86      1.265574    0.522393  0.464491              0.741135   \n",
       "\n",
       "   team1_opp_PPG  team1_opp_PPP  team1_opp_ast_TO  team1_opp_efg  \\\n",
       "0      78.448276       0.937078          1.236559       0.518382   \n",
       "1      60.166667       0.799394          0.763990       0.446284   \n",
       "2      65.566667       0.822586          0.801688       0.481165   \n",
       "3      66.857143       0.759001          0.703704       0.432193   \n",
       "4      58.689655       0.825396          0.800000       0.479612   \n",
       "\n",
       "   team1_opp_fg  team1_opp_three_point_pct  team1_opp_trueshooting  \\\n",
       "0      0.455882                   0.367110                0.553323   \n",
       "1      0.404747                   0.326781                0.488641   \n",
       "2      0.420247                   0.333333                0.512977   \n",
       "3      0.378538                   0.312715                0.479165   \n",
       "4      0.430481                   0.339492                0.513566   \n",
       "\n",
       "   team1_three_point_pct  team1_total_point_differential  team1_true_shooting  \\\n",
       "0               0.360153                            -210             0.539424   \n",
       "1               0.393673                             330             0.549827   \n",
       "2               0.344898                             136             0.552990   \n",
       "3               0.397895                             390             0.554477   \n",
       "4               0.359127                             349             0.566212   \n",
       "\n",
       "   team1_acc  team1_big_east  team1_big_ten  team1_big_twelve  team1_sec  \\\n",
       "0          0               0              0                 0          0   \n",
       "1          0               0              0                 1          0   \n",
       "2          0               0              0                 0          1   \n",
       "3          1               0              0                 0          0   \n",
       "4          0               0              1                 0          0   \n",
       "\n",
       "   team1_pac12  team1_MOR  team1_AP_top10  team1_AP_top25  team2_seedN  \\\n",
       "0            0      277.0               0               0           16   \n",
       "1            0        6.0               1               0            3   \n",
       "2            0       44.0               0               0            3   \n",
       "3            0        9.0               0               1            7   \n",
       "4            0       15.0               0               1            1   \n",
       "\n",
       "   team2_DRB_DIF  team2_ORB_DIF  team2_PPG  team2_PPP  team2_TRB_DIF  \\\n",
       "0             58             37  72.800000   0.878704             95   \n",
       "1            134            -43  80.103448   0.929051             91   \n",
       "2            134            -43  80.103448   0.929051             91   \n",
       "3            125             42  67.225806   0.891803            167   \n",
       "4            134             54  77.531250   0.949992            188   \n",
       "\n",
       "   team2_ast_TO  team2_e_fg  team2_fg  team2_free_throw_pct  team2_opp_PPG  \\\n",
       "0      0.932166    0.501206  0.447527              0.619952      70.833333   \n",
       "1      1.098734    0.512195  0.470067              0.693431      69.896552   \n",
       "2      1.098734    0.512195  0.470067              0.693431      69.896552   \n",
       "3      0.935698    0.498737  0.450758              0.734694      60.967742   \n",
       "4      1.151111    0.537988  0.487426              0.706767      64.093750   \n",
       "\n",
       "   team2_opp_PPP  team2_opp_ast_TO  team2_opp_efg  team2_opp_fg  \\\n",
       "0       0.853660          0.960465       0.487307      0.424945   \n",
       "1       0.799883          1.100239       0.443703      0.390075   \n",
       "2       0.799883          1.100239       0.443703      0.390075   \n",
       "3       0.826801          0.781038       0.458013      0.400641   \n",
       "4       0.799199          0.652751       0.464146      0.412325   \n",
       "\n",
       "   team2_opp_three_point_pct  team2_opp_trueshooting  team2_three_point_pct  \\\n",
       "0                   0.325180                0.515957               0.320721   \n",
       "1                   0.306870                0.479169               0.330435   \n",
       "2                   0.306870                0.479169               0.330435   \n",
       "3                   0.338374                0.512773               0.366265   \n",
       "4                   0.328014                0.502864               0.355932   \n",
       "\n",
       "   team2_total_point_differential  team2_true_shooting  team2_acc  \\\n",
       "0                              59             0.538334          0   \n",
       "1                             296             0.551677          0   \n",
       "2                             296             0.551677          0   \n",
       "3                             194             0.552539          0   \n",
       "4                             430             0.573880          0   \n",
       "\n",
       "   team2_big_east  team2_big_ten  team2_big_twelve  team2_sec  team2_pac12  \\\n",
       "0               0              0                 0          0            0   \n",
       "1               1              0                 0          0            0   \n",
       "2               1              0                 0          0            0   \n",
       "3               0              1                 0          0            0   \n",
       "4               0              0                 0          1            0   \n",
       "\n",
       "   team2_MOR  team2_AP_top10  team2_AP_top25  team1_win  \n",
       "0      293.0               0               0          1  \n",
       "1       21.0               0               1          0  \n",
       "2       21.0               0               1          0  \n",
       "3       16.0               0               0          0  \n",
       "4        1.0               1               0          0  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "binary_features = [\"team1_acc\", \"team1_big_east\", \"team1_big_twelve\", \"team1_sec\", \"team1_pac12\",\n",
    "                  \"team1_AP_top10\", \"team1_AP_top25\", \"team2_acc\", \"team2_big_east\", \"team2_big_ten\", \n",
    "                  \"team2_big_twelve\", \"team2_sec\", \"team2_pac12\", \"team2_AP_top10\", \"team2_AP_top25\",\n",
    "                  \"team1_win\"]\n",
    "\n",
    "#fit and save standard scaler on training data (will use later on validation data)\n",
    "to_scale = X.drop(columns = binary_features)\n",
    "ss = StandardScaler()\n",
    "ss.fit(to_scale)\n",
    "\n",
    "pickle.dump(ss, open(\"./models/standard_scaler.pk\", \"wb\"))\n",
    "\n",
    "#transform training data\n",
    "to_scale_cols = list(to_scale.columns)\n",
    "npX = ss.transform(to_scale)\n",
    "scaled_X = pd.DataFrame(npX)\n",
    "scaled_X.columns = to_scale_cols\n",
    "scaled_X = pd.concat([scaled_X, X[binary_features]], axis = 1)\n",
    "#save scaled training data\n",
    "scaled_X.to_csv(\"./engineered_data/scaled_training_data.csv.gz\", index = False, compression = \"gzip\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "xtrain = scaled_X.drop(columns = [\"team1_win\"])\n",
    "y = scaled_X[\"team1_win\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithms = {\"RandomForestClassifier\" : [RandomForestClassifier(), {\"n_estimators\" : 100, \"max_depth\" : 8}],\n",
    "             \"LGBMClassifier\" : [LGBMClassifier(), {\"max_depth\" : 7, \"num_leaves\" : 49}],\n",
    "             \"XGBClassifier\" : [XGBClassifier(), {\"max_depth\" : 8}]}\n",
    "\n",
    "all_results = []\n",
    "for key in algorithms:\n",
    "    results_dict = {}\n",
    "    results_dict[\"algorithm\"] = key\n",
    "    selector = FeatureSelector(xtrain, y, algorithm = algorithms[key][0], metric = \"roc\", \n",
    "                              params = algorithms[key][1])\n",
    "    selector.recursive_selection()\n",
    "    results_dict[\"best_eval\"] = selector.best_eval\n",
    "    results_dict[\"best_subset\"] = list(selector.best_subset)\n",
    "    all_results.append(results_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('team1_seedN', 3),\n",
       " ('team1_total_point_differential', 3),\n",
       " ('team2_TRB_DIF', 3),\n",
       " ('team2_total_point_differential', 3),\n",
       " ('team2_MOR', 3),\n",
       " ('team1_MOR', 2),\n",
       " ('team2_seedN', 2),\n",
       " ('team1_ast_TO', 2),\n",
       " ('team1_opp_PPP', 2),\n",
       " ('team1_opp_three_point_pct', 2),\n",
       " ('team1_true_shooting', 2),\n",
       " ('team2_PPG', 2),\n",
       " ('team2_free_throw_pct', 2),\n",
       " ('team2_opp_three_point_pct', 2),\n",
       " ('team1_PPG', 1),\n",
       " ('team2_opp_ast_TO', 1),\n",
       " ('team2_true_shooting', 1),\n",
       " ('team1_PPP', 1),\n",
       " ('team1_TRB_DIF', 1),\n",
       " ('team1_opp_PPG', 1),\n",
       " ('team1_opp_fg', 1),\n",
       " ('team1_three_point_pct', 1),\n",
       " ('team2_DRB_DIF', 1),\n",
       " ('team2_PPP', 1),\n",
       " ('team2_opp_PPG', 1),\n",
       " ('team2_three_point_pct', 1),\n",
       " ('team1_big_east', 1),\n",
       " ('team1_big_twelve', 1),\n",
       " ('team1_pac12', 1),\n",
       " ('team2_sec', 1),\n",
       " ('team2_AP_top10', 1)]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "features = []\n",
    "for algo in all_results:\n",
    "    features += algo[\"best_subset\"]\n",
    "    \n",
    "count = Counter(features)\n",
    "count.most_common()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5 features were considered important by all three models. I will try these 11 features with our baseline model and see if there is improvement, and if there is we will move forward with parameter tuning with these 5 features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "top_5 = count.most_common()[:5]\n",
    "top_features = [i[0] for i in top_5]\n",
    "\n",
    "reduced_X = xtrain[top_features]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Baseline cross-validation ROC-AUC Score: 0.802432610124918\n"
     ]
    }
   ],
   "source": [
    "lr = LogisticRegression(max_iter = 1000, penalty = \"l1\", solver = \"liblinear\", C = 0.1)\n",
    "baseline_cv = cross_val_score(lr, reduced_X, y, scoring = \"roc_auc\", cv = 10).mean()\n",
    "print(\"Baseline cross-validation ROC-AUC Score: {}\".format(baseline_cv))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There was slight improvement from the full feature set and we were able using only five features, which is fantastic for model complexity and also understanding of important metrics. Now, with these 5 features selected, I will begin parameter tuning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression\n",
    "Logistic regression was chosen as the baseline linear performance model, and it's outperformed all three of the tree based models that were used in feature selection, so we will start with Logistic Regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the first round of parameter tuning, I am going to stick with the L1 regularization and use parameters compatible with L1 regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C': 0.1,\n",
       " 'class_weight': None,\n",
       " 'dual': False,\n",
       " 'fit_intercept': True,\n",
       " 'intercept_scaling': 1,\n",
       " 'l1_ratio': None,\n",
       " 'max_iter': 1000,\n",
       " 'multi_class': 'warn',\n",
       " 'n_jobs': None,\n",
       " 'penalty': 'l1',\n",
       " 'random_state': None,\n",
       " 'solver': 'liblinear',\n",
       " 'tol': 0.0001,\n",
       " 'verbose': 0,\n",
       " 'warm_start': False}"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.get_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best score: 0.8026298487836948\n",
      "\n",
      "Best parameters: {'C': 0.1, 'fit_intercept': True, 'solver': 'saga'}\n"
     ]
    }
   ],
   "source": [
    "l1parameter_grid = {\"C\" : [0.01, 0.1, 1.0],\n",
    "                 \"solver\" : [\"liblinear\", \"saga\"],\n",
    "                 \"fit_intercept\" : [True, False]}\n",
    "\n",
    "grid_search = GridSearchCV(LogisticRegression(penalty = \"l1\"), param_grid = l1parameter_grid, scoring = \"roc_auc\",\n",
    "                          n_jobs = -1, cv = 10)\n",
    "grid_search.fit(reduced_X, y)\n",
    "print('Best score: {}'.format(grid_search.best_score_))\n",
    "print()\n",
    "print('Best parameters: {}'.format(grid_search.best_params_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best score: 0.8012491781722552\n",
      "\n",
      "Best parameters: {'C': 0.01, 'fit_intercept': True, 'solver': 'newton-cg'}\n"
     ]
    }
   ],
   "source": [
    "l2parameter_grid = {\"C\" : [0.01, 0.1, 1.0, 10],\n",
    "                   \"solver\" : [\"newton-cg\", \"lbfgs\", \"sag\", \"saga\", \"liblinear\"],\n",
    "                   \"fit_intercept\" : [True, False]}\n",
    "\n",
    "grid_searchl2 = GridSearchCV(LogisticRegression(penalty = \"l2\"), param_grid = l2parameter_grid,\n",
    "                            scoring = \"roc_auc\", n_jobs = -1, cv = 10)\n",
    "grid_searchl2.fit(reduced_X, y)\n",
    "print('Best score: {}'.format(grid_searchl2.best_score_))\n",
    "print()\n",
    "print('Best parameters: {}'.format(grid_searchl2.best_params_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best score: 0.8040762656147271\n",
      "\n",
      "Best parameters: {'C': 0.01, 'fit_intercept': False, 'l1_ratio': 0.5}\n"
     ]
    }
   ],
   "source": [
    "elasticnet_grid = {\"C\" : [0.01, 0.1, 1.0, 10],\n",
    "                  \"fit_intercept\" : [True, False],\n",
    "                  \"l1_ratio\" : [0.1, 0.25, 0.5, 0.75]}\n",
    "\n",
    "grid_searchEN = GridSearchCV(LogisticRegression(penalty = \"elasticnet\", solver = \"saga\"),\n",
    "                            param_grid = elasticnet_grid, scoring = \"roc_auc\", n_jobs = -1, cv = 10)\n",
    "grid_searchEN.fit(reduced_X, y)\n",
    "print('Best score: {}'.format(grid_searchEN.best_score_))\n",
    "print()\n",
    "print('Best parameters: {}'.format(grid_searchEN.best_params_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the best parameter set and feature set avaiable, now I will test the model on the held-out validation data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=0.01, class_weight=None, dual=False, fit_intercept=False,\n",
       "                   intercept_scaling=1, l1_ratio=0.5, max_iter=100,\n",
       "                   multi_class='warn', n_jobs=None, penalty='elasticnet',\n",
       "                   random_state=None, solver='saga', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression(solver = \"saga\", penalty = \"elasticnet\", C = 0.01, fit_intercept = False,\n",
    "                       l1_ratio = 0.5)\n",
    "\n",
    "lr.fit(reduced_X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.35932129,  0.01613482,  0.        , -0.26189463,  0.25310965]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#peak at coefficients\n",
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "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>team1_seedN</th>\n",
       "      <th>team1_total_point_differential</th>\n",
       "      <th>team2_TRB_DIF</th>\n",
       "      <th>team2_total_point_differential</th>\n",
       "      <th>team2_MOR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.947783</td>\n",
       "      <td>-3.569683</td>\n",
       "      <td>-0.126553</td>\n",
       "      <td>-1.628089</td>\n",
       "      <td>4.819039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.281501</td>\n",
       "      <td>0.267569</td>\n",
       "      <td>-0.164928</td>\n",
       "      <td>0.026985</td>\n",
       "      <td>-0.404494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.656069</td>\n",
       "      <td>-1.110999</td>\n",
       "      <td>-0.164928</td>\n",
       "      <td>0.026985</td>\n",
       "      <td>-0.404494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.205073</td>\n",
       "      <td>0.693931</td>\n",
       "      <td>0.564205</td>\n",
       "      <td>-0.685325</td>\n",
       "      <td>-0.500515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.420359</td>\n",
       "      <td>0.402584</td>\n",
       "      <td>0.765676</td>\n",
       "      <td>0.962765</td>\n",
       "      <td>-0.788577</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   team1_seedN  team1_total_point_differential  team2_TRB_DIF  \\\n",
       "0     1.947783                       -3.569683      -0.126553   \n",
       "1    -1.281501                        0.267569      -0.164928   \n",
       "2     0.656069                       -1.110999      -0.164928   \n",
       "3    -0.205073                        0.693931       0.564205   \n",
       "4    -0.420359                        0.402584       0.765676   \n",
       "\n",
       "   team2_total_point_differential  team2_MOR  \n",
       "0                       -1.628089   4.819039  \n",
       "1                        0.026985  -0.404494  \n",
       "2                        0.026985  -0.404494  \n",
       "3                       -0.685325  -0.500515  \n",
       "4                        0.962765  -0.788577  "
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reduced_X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The LogisticRegression model is not using total rebound differential... good to know."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump(lr, open(\"./models/log_reg_pre2015.pk\", \"wb\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "validation2015 = validation_data[validation_data.Season == 2015].reset_index(drop = True).\\\n",
    "drop(columns = [\"Season\", \"DayNum\", \"team1_TeamID\", \"team1_Score\", \"team2_TeamID\", \n",
    "                              \"team2_Score\"])\n",
    "\n",
    "validation2015_target = validation2015[\"team1_win\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "ss = pickle.load(open(\"./models/standard_scaler.pk\", \"rb\"))\n",
    "\n",
    "#fit and save standard scaler on training data (will use later on validation data)\n",
    "to_scale = validation2015.drop(columns = binary_features)\n",
    "to_scale_cols = list(to_scale.columns)\n",
    "npX = ss.transform(to_scale)\n",
    "\n",
    "valid2015_scaled = pd.DataFrame(npX)\n",
    "valid2015_scaled.columns = to_scale_cols\n",
    "valid2015_scaled = pd.concat([valid2015_scaled, validation2015[binary_features]], axis = 1)\n",
    "#save scaled training data\n",
    "scaled_X.to_csv(\"./engineered_data/scaled_validation2015_data.csv.gz\", index = False, compression = \"gzip\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "valid2015_target = valid2015_scaled[\"team1_win\"]\n",
    "valid2015_scaled = valid2015_scaled.drop(columns = [\"team1_win\"])\n",
    "\n",
    "test2015 = valid2015_scaled[top_features]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The accuracy on the validation set was 0.7761194029850746\n",
      "\n",
      "The ROC area under the curve was 0.7762923351158645\n"
     ]
    }
   ],
   "source": [
    "_2015preds = lr.predict(test2015)\n",
    "print(\"The accuracy on the validation set was {}\".format(accuracy_score(valid2015_target, _2015preds)))\n",
    "print()\n",
    "print(\"The ROC area under the curve was {}\".format(roc_auc_score(valid2015_target, _2015preds)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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