01_Initial_EDA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dddae623",
   "metadata": {},
   "source": [
    "# EDA\n",
    "\n",
    "A dataset gathered from a famous sports website will be used for this project."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "218f545f",
   "metadata": {},
   "source": [
    "# Loading dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0efddc31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Fecha   Local Score   Visit Score      Local i5      Visit i5  \\\n",
      "count  1.694700e+04  16947.000000  16947.000000  16947.000000  16947.000000   \n",
      "mean   2.018229e+07      4.594560      4.462855      2.725379      2.438898   \n",
      "std    2.213964e+04      3.175195      3.219344      2.519743      2.337956   \n",
      "min    2.015040e+07      0.000000      0.000000      0.000000      0.000000   \n",
      "25%    2.016082e+07      2.000000      2.000000      1.000000      1.000000   \n",
      "50%    2.018063e+07      4.000000      4.000000      2.000000      2.000000   \n",
      "75%    2.020083e+07      6.000000      6.000000      4.000000      4.000000   \n",
      "max    2.022072e+07     29.000000     24.000000     22.000000     19.000000   \n",
      "\n",
      "         Local Hits    Visit Hits  Local pitcher in  Local pitcher ERA  \\\n",
      "count  16947.000000  16947.000000      16947.000000       16947.000000   \n",
      "mean       8.420605      8.559037          5.326724           2.671682   \n",
      "std        3.357877      3.530094          1.565992           2.015127   \n",
      "min        0.000000      0.000000          0.000000           0.000000   \n",
      "25%        6.000000      6.000000          5.000000           1.000000   \n",
      "50%        8.000000      8.000000          5.200000           2.000000   \n",
      "75%       10.000000     11.000000          6.100000           4.000000   \n",
      "max       28.000000     27.000000          9.000000          12.000000   \n",
      "\n",
      "       Local pitcher Hit ERA  Local pitcher K ERA  Local pitcher BB ERA  \\\n",
      "count           16947.000000         16947.000000          16947.000000   \n",
      "mean                5.198206             4.987077              1.724966   \n",
      "std                 2.268624             2.619437              1.309415   \n",
      "min                 0.000000             0.000000              0.000000   \n",
      "25%                 4.000000             3.000000              1.000000   \n",
      "50%                 5.000000             5.000000              2.000000   \n",
      "75%                 7.000000             7.000000              3.000000   \n",
      "max                15.000000            20.000000              8.000000   \n",
      "\n",
      "       Visit pitcher in  Visit pitcher ERA  Visit pitcher Hit ERA  \\\n",
      "count      16947.000000       16947.000000           16947.000000   \n",
      "mean           5.141288           2.852245               5.264354   \n",
      "std            1.586304           2.081260               2.276757   \n",
      "min            0.000000           0.000000               0.000000   \n",
      "25%            4.100000           1.000000               4.000000   \n",
      "50%            5.100000           3.000000               5.000000   \n",
      "75%            6.000000           4.000000               7.000000   \n",
      "max            9.000000          12.000000              14.000000   \n",
      "\n",
      "       Visit pitcher K ERA  Visit pitcher BB ERA    Local Win?  \\\n",
      "count         16947.000000          16947.000000  16939.000000   \n",
      "mean              4.663185              1.809288      0.534506   \n",
      "std               2.558803              1.319841      0.498823   \n",
      "min               0.000000              0.000000      0.000000   \n",
      "25%               3.000000              1.000000      0.000000   \n",
      "50%               4.000000              2.000000      1.000000   \n",
      "75%               6.000000              3.000000      1.000000   \n",
      "max              17.000000              8.000000      1.000000   \n",
      "\n",
      "       L bullpen recieved  V bullpen recieved  \n",
      "count        16947.000000        16947.000000  \n",
      "mean             1.791172            1.742314  \n",
      "std              2.170421            2.083551  \n",
      "min             -1.000000           -2.000000  \n",
      "25%              0.000000            0.000000  \n",
      "50%              1.000000            1.000000  \n",
      "75%              3.000000            3.000000  \n",
      "max             18.000000           22.000000  \n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Fecha</th>\n",
       "      <th>Local</th>\n",
       "      <th>Visit</th>\n",
       "      <th>Local Score</th>\n",
       "      <th>Visit Score</th>\n",
       "      <th>Local i5</th>\n",
       "      <th>Visit i5</th>\n",
       "      <th>Local Hits</th>\n",
       "      <th>Visit Hits</th>\n",
       "      <th>Local pitcher</th>\n",
       "      <th>Local pitcher in</th>\n",
       "      <th>Local pitcher ERA</th>\n",
       "      <th>Local pitcher Hit ERA</th>\n",
       "      <th>Local pitcher K ERA</th>\n",
       "      <th>Local pitcher BB ERA</th>\n",
       "      <th>Visit pitcher</th>\n",
       "      <th>Visit pitcher in</th>\n",
       "      <th>Visit pitcher ERA</th>\n",
       "      <th>Visit pitcher Hit ERA</th>\n",
       "      <th>Visit pitcher K ERA</th>\n",
       "      <th>Visit pitcher BB ERA</th>\n",
       "      <th>Local Win?</th>\n",
       "      <th>L bullpen recieved</th>\n",
       "      <th>V bullpen recieved</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20150405</td>\n",
       "      <td>Cubs</td>\n",
       "      <td>Cardinals</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>J. Lester</td>\n",
       "      <td>4.1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>A. Wainwright</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Yankees</td>\n",
       "      <td>Blue</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>M. Tanaka</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>D. Hutchison</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Tigers</td>\n",
       "      <td>Twins</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>D. Price</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>P. Hughes</td>\n",
       "      <td>6.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Brewers</td>\n",
       "      <td>Rockies</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>K. Lohse</td>\n",
       "      <td>3.1</td>\n",
       "      <td>8.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>K. Kendrick</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Phillies</td>\n",
       "      <td>Red</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>C. Hamels</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>C. Buchholz</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16942</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Cubs</td>\n",
       "      <td>Mets</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>A. Sampson</td>\n",
       "      <td>5.1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>D. Peterson</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16943</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Rangers</td>\n",
       "      <td>Mariners</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>G. Otto</td>\n",
       "      <td>6.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>C. Flexen</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16944</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Rockies</td>\n",
       "      <td>Pirates</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>A. Gomber</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>B. Wilson</td>\n",
       "      <td>3.1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16945</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Giants</td>\n",
       "      <td>Brewers</td>\n",
       "      <td>9.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>L. Webb</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>A. Ashby</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16946</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Padres</td>\n",
       "      <td>Diamondbacks</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>M. Clevinger</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>M. Kelly</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>16947 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Fecha     Local         Visit  Local Score  Visit Score  Local i5  \\\n",
       "0      20150405      Cubs     Cardinals          0.0          3.0       0.0   \n",
       "1      20150406   Yankees          Blue          1.0          6.0       0.0   \n",
       "2      20150406    Tigers         Twins          4.0          0.0       3.0   \n",
       "3      20150406   Brewers       Rockies          0.0         10.0       0.0   \n",
       "4      20150406  Phillies           Red          0.0          8.0       0.0   \n",
       "...         ...       ...           ...          ...          ...       ...   \n",
       "16942  20220717      Cubs          Mets          3.0          2.0       1.0   \n",
       "16943  20220717   Rangers      Mariners          2.0          6.0       1.0   \n",
       "16944  20220717   Rockies       Pirates          3.0          8.0       3.0   \n",
       "16945  20220717    Giants       Brewers          9.0          5.0       7.0   \n",
       "16946  20220717    Padres  Diamondbacks          1.0          3.0       0.0   \n",
       "\n",
       "       Visit i5  Local Hits  Visit Hits  Local pitcher  Local pitcher in  \\\n",
       "0           3.0         5.0        10.0     J. Lester                4.1   \n",
       "1           5.0         3.0         6.0     M. Tanaka                4.0   \n",
       "2           0.0        10.0         5.0      D. Price                8.2   \n",
       "3          10.0         8.0        16.0      K. Lohse                3.1   \n",
       "4           4.0         3.0         9.0     C. Hamels                5.0   \n",
       "...         ...         ...         ...            ...               ...   \n",
       "16942       2.0         7.0         9.0     A. Sampson               5.1   \n",
       "16943       3.0         7.0        10.0       G. Otto                6.0   \n",
       "16944       3.0         9.0        16.0      A. Gomber               5.0   \n",
       "16945       1.0        12.0         9.0       L. Webb                6.0   \n",
       "16946       0.0         6.0         6.0  M. Clevinger                6.0   \n",
       "\n",
       "       Local pitcher ERA  Local pitcher Hit ERA  Local pitcher K ERA  \\\n",
       "0                    3.0                    8.0                  6.0   \n",
       "1                    5.0                    5.0                  6.0   \n",
       "2                    0.0                    5.0                  5.0   \n",
       "3                    8.0                   10.0                  1.0   \n",
       "4                    4.0                    5.0                  6.0   \n",
       "...                  ...                    ...                  ...   \n",
       "16942                2.0                    6.0                  1.0   \n",
       "16943                3.0                    5.0                  4.0   \n",
       "16944                3.0                    7.0                  5.0   \n",
       "16945                2.0                    4.0                  5.0   \n",
       "16946                1.0                    4.0                  8.0   \n",
       "\n",
       "       Local pitcher BB ERA   Visit pitcher  Visit pitcher in  \\\n",
       "0                       2.0  A. Wainwright                6.0   \n",
       "1                       2.0   D. Hutchison                6.0   \n",
       "2                       0.0      P. Hughes                6.0   \n",
       "3                       0.0    K. Kendrick                7.0   \n",
       "4                       3.0    C. Buchholz                7.0   \n",
       "...                     ...             ...               ...   \n",
       "16942                   3.0     D. Peterson               5.0   \n",
       "16943                   1.0       C. Flexen               3.2   \n",
       "16944                   2.0       B. Wilson               3.1   \n",
       "16945                   2.0       A. Ashby                1.0   \n",
       "16946                   2.0       M. Kelly                6.0   \n",
       "\n",
       "       Visit pitcher ERA  Visit pitcher Hit ERA  Visit pitcher K ERA  \\\n",
       "0                    0.0                    5.0                  6.0   \n",
       "1                    1.0                    3.0                  3.0   \n",
       "2                    4.0                    8.0                  6.0   \n",
       "3                    0.0                    7.0                  6.0   \n",
       "4                    0.0                    3.0                  9.0   \n",
       "...                  ...                    ...                  ...   \n",
       "16942                1.0                    3.0                  8.0   \n",
       "16943                1.0                    4.0                  3.0   \n",
       "16944                2.0                    4.0                  3.0   \n",
       "16945                2.0                    3.0                  2.0   \n",
       "16946                1.0                    6.0                  5.0   \n",
       "\n",
       "       Visit pitcher BB ERA  Local Win?  L bullpen recieved  \\\n",
       "0                       0.0         0.0                 0.0   \n",
       "1                       2.0         0.0                 1.0   \n",
       "2                       1.0         1.0                 0.0   \n",
       "3                       0.0         0.0                 2.0   \n",
       "4                       1.0         0.0                 4.0   \n",
       "...                     ...         ...                 ...   \n",
       "16942                   3.0         1.0                 0.0   \n",
       "16943                   1.0         0.0                 3.0   \n",
       "16944                   0.0         0.0                 5.0   \n",
       "16945                   0.0         1.0                 3.0   \n",
       "16946                   0.0         0.0                 2.0   \n",
       "\n",
       "       V bullpen recieved  \n",
       "0                     0.0  \n",
       "1                     0.0  \n",
       "2                     0.0  \n",
       "3                     0.0  \n",
       "4                     0.0  \n",
       "...                   ...  \n",
       "16942                 2.0  \n",
       "16943                 1.0  \n",
       "16944                 1.0  \n",
       "16945                 7.0  \n",
       "16946                 0.0  \n",
       "\n",
       "[16947 rows x 24 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Importing pandas, numpy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "#Importing pathlib\n",
    "import pathlib\n",
    "pathlib.Path.cwd()\n",
    "#display all columns\n",
    "pd.pandas.set_option (\"display.max_columns\", None)\n",
    "\n",
    "#reading csv\n",
    "path = pathlib.Path.cwd() / 'sets' / 'mlb_dataset.csv'\n",
    "df = pd.read_csv(path, index_col = None)\n",
    "\n",
    "#Initial describe\n",
    "print(df.describe())\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0c73308",
   "metadata": {},
   "source": [
    "# Missing values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "50ee1330",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical Missing Features %\n",
      "('Local Win?', 0.05) % MISSING VALUES\n",
      "Categorical Missing Features %\n"
     ]
    }
   ],
   "source": [
    "dataset = df.copy()\n",
    "#Checking the % of NAN in file\n",
    "features_with_na = [features for features in dataset.columns if dataset[features].isnull().sum()>1]\n",
    "\n",
    "numerical_features_na = [features for features in features_with_na if dataset[features].dtypes != \"O\"]\n",
    "categorical_features_na = [features for features in features_with_na if dataset[features].dtypes == \"O\"]\n",
    "\n",
    "\n",
    "#Print missin values numerical val\n",
    "print(\"Numerical Missing Features %\")\n",
    "for feature in numerical_features_na:\n",
    "    print((feature,np.round(dataset[feature].isnull().mean(),4)*100), \"% MISSING VALUES\")\n",
    "    \n",
    "    \n",
    "print(\"Categorical Missing Features %\")\n",
    "for feature in categorical_features_na:\n",
    "    print((feature,np.round(dataset[feature].isnull().mean(),4)*100), \"% MISSING VALUES\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f89b094",
   "metadata": {},
   "source": [
    "Since missing values are only present in the feature we are looking for, we will not do any missing value handle and just will drop NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9470721c",
   "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>Fecha</th>\n",
       "      <th>Local</th>\n",
       "      <th>Visit</th>\n",
       "      <th>Local Score</th>\n",
       "      <th>Visit Score</th>\n",
       "      <th>Local i5</th>\n",
       "      <th>Visit i5</th>\n",
       "      <th>Local Hits</th>\n",
       "      <th>Visit Hits</th>\n",
       "      <th>Local pitcher</th>\n",
       "      <th>Local pitcher in</th>\n",
       "      <th>Local pitcher ERA</th>\n",
       "      <th>Local pitcher Hit ERA</th>\n",
       "      <th>Local pitcher K ERA</th>\n",
       "      <th>Local pitcher BB ERA</th>\n",
       "      <th>Visit pitcher</th>\n",
       "      <th>Visit pitcher in</th>\n",
       "      <th>Visit pitcher ERA</th>\n",
       "      <th>Visit pitcher Hit ERA</th>\n",
       "      <th>Visit pitcher K ERA</th>\n",
       "      <th>Visit pitcher BB ERA</th>\n",
       "      <th>Local Win?</th>\n",
       "      <th>L bullpen recieved</th>\n",
       "      <th>V bullpen recieved</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20150405</td>\n",
       "      <td>Cubs</td>\n",
       "      <td>Cardinals</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>J. Lester</td>\n",
       "      <td>4.1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>A. Wainwright</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Yankees</td>\n",
       "      <td>Blue</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>M. Tanaka</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>D. Hutchison</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Tigers</td>\n",
       "      <td>Twins</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>D. Price</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>P. Hughes</td>\n",
       "      <td>6.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Brewers</td>\n",
       "      <td>Rockies</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>K. Lohse</td>\n",
       "      <td>3.1</td>\n",
       "      <td>8.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>K. Kendrick</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20150406</td>\n",
       "      <td>Phillies</td>\n",
       "      <td>Red</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>C. Hamels</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>C. Buchholz</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16934</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Cubs</td>\n",
       "      <td>Mets</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>A. Sampson</td>\n",
       "      <td>5.1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>D. Peterson</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16935</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Rangers</td>\n",
       "      <td>Mariners</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>G. Otto</td>\n",
       "      <td>6.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>C. Flexen</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16936</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Rockies</td>\n",
       "      <td>Pirates</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>A. Gomber</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>B. Wilson</td>\n",
       "      <td>3.1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16937</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Giants</td>\n",
       "      <td>Brewers</td>\n",
       "      <td>9.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>L. Webb</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>A. Ashby</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16938</th>\n",
       "      <td>20220717</td>\n",
       "      <td>Padres</td>\n",
       "      <td>Diamondbacks</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>M. Clevinger</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>M. Kelly</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>16939 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Fecha     Local         Visit  Local Score  Visit Score  Local i5  \\\n",
       "0      20150405      Cubs     Cardinals          0.0          3.0       0.0   \n",
       "1      20150406   Yankees          Blue          1.0          6.0       0.0   \n",
       "2      20150406    Tigers         Twins          4.0          0.0       3.0   \n",
       "3      20150406   Brewers       Rockies          0.0         10.0       0.0   \n",
       "4      20150406  Phillies           Red          0.0          8.0       0.0   \n",
       "...         ...       ...           ...          ...          ...       ...   \n",
       "16934  20220717      Cubs          Mets          3.0          2.0       1.0   \n",
       "16935  20220717   Rangers      Mariners          2.0          6.0       1.0   \n",
       "16936  20220717   Rockies       Pirates          3.0          8.0       3.0   \n",
       "16937  20220717    Giants       Brewers          9.0          5.0       7.0   \n",
       "16938  20220717    Padres  Diamondbacks          1.0          3.0       0.0   \n",
       "\n",
       "       Visit i5  Local Hits  Visit Hits  Local pitcher  Local pitcher in  \\\n",
       "0           3.0         5.0        10.0     J. Lester                4.1   \n",
       "1           5.0         3.0         6.0     M. Tanaka                4.0   \n",
       "2           0.0        10.0         5.0      D. Price                8.2   \n",
       "3          10.0         8.0        16.0      K. Lohse                3.1   \n",
       "4           4.0         3.0         9.0     C. Hamels                5.0   \n",
       "...         ...         ...         ...            ...               ...   \n",
       "16934       2.0         7.0         9.0     A. Sampson               5.1   \n",
       "16935       3.0         7.0        10.0       G. Otto                6.0   \n",
       "16936       3.0         9.0        16.0      A. Gomber               5.0   \n",
       "16937       1.0        12.0         9.0       L. Webb                6.0   \n",
       "16938       0.0         6.0         6.0  M. Clevinger                6.0   \n",
       "\n",
       "       Local pitcher ERA  Local pitcher Hit ERA  Local pitcher K ERA  \\\n",
       "0                    3.0                    8.0                  6.0   \n",
       "1                    5.0                    5.0                  6.0   \n",
       "2                    0.0                    5.0                  5.0   \n",
       "3                    8.0                   10.0                  1.0   \n",
       "4                    4.0                    5.0                  6.0   \n",
       "...                  ...                    ...                  ...   \n",
       "16934                2.0                    6.0                  1.0   \n",
       "16935                3.0                    5.0                  4.0   \n",
       "16936                3.0                    7.0                  5.0   \n",
       "16937                2.0                    4.0                  5.0   \n",
       "16938                1.0                    4.0                  8.0   \n",
       "\n",
       "       Local pitcher BB ERA   Visit pitcher  Visit pitcher in  \\\n",
       "0                       2.0  A. Wainwright                6.0   \n",
       "1                       2.0   D. Hutchison                6.0   \n",
       "2                       0.0      P. Hughes                6.0   \n",
       "3                       0.0    K. Kendrick                7.0   \n",
       "4                       3.0    C. Buchholz                7.0   \n",
       "...                     ...             ...               ...   \n",
       "16934                   3.0     D. Peterson               5.0   \n",
       "16935                   1.0       C. Flexen               3.2   \n",
       "16936                   2.0       B. Wilson               3.1   \n",
       "16937                   2.0       A. Ashby                1.0   \n",
       "16938                   2.0       M. Kelly                6.0   \n",
       "\n",
       "       Visit pitcher ERA  Visit pitcher Hit ERA  Visit pitcher K ERA  \\\n",
       "0                    0.0                    5.0                  6.0   \n",
       "1                    1.0                    3.0                  3.0   \n",
       "2                    4.0                    8.0                  6.0   \n",
       "3                    0.0                    7.0                  6.0   \n",
       "4                    0.0                    3.0                  9.0   \n",
       "...                  ...                    ...                  ...   \n",
       "16934                1.0                    3.0                  8.0   \n",
       "16935                1.0                    4.0                  3.0   \n",
       "16936                2.0                    4.0                  3.0   \n",
       "16937                2.0                    3.0                  2.0   \n",
       "16938                1.0                    6.0                  5.0   \n",
       "\n",
       "       Visit pitcher BB ERA  Local Win?  L bullpen recieved  \\\n",
       "0                       0.0         0.0                 0.0   \n",
       "1                       2.0         0.0                 1.0   \n",
       "2                       1.0         1.0                 0.0   \n",
       "3                       0.0         0.0                 2.0   \n",
       "4                       1.0         0.0                 4.0   \n",
       "...                     ...         ...                 ...   \n",
       "16934                   3.0         1.0                 0.0   \n",
       "16935                   1.0         0.0                 3.0   \n",
       "16936                   0.0         0.0                 5.0   \n",
       "16937                   0.0         1.0                 3.0   \n",
       "16938                   0.0         0.0                 2.0   \n",
       "\n",
       "       V bullpen recieved  \n",
       "0                     0.0  \n",
       "1                     0.0  \n",
       "2                     0.0  \n",
       "3                     0.0  \n",
       "4                     0.0  \n",
       "...                   ...  \n",
       "16934                 2.0  \n",
       "16935                 1.0  \n",
       "16936                 1.0  \n",
       "16937                 7.0  \n",
       "16938                 0.0  \n",
       "\n",
       "[16939 rows x 24 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df= df.reset_index(drop=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5ced053",
   "metadata": {},
   "source": [
    "# Temporal relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "be01323a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'% of games won by locals vs Season'}, xlabel='Year', ylabel='% of games won by locals'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import datetime\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "dft = df.copy()\n",
    "#Date to date format\n",
    "dft['Fecha'] =  pd.to_datetime(dft['Fecha'], format='%Y%m%d')\n",
    "dft\n",
    "\n",
    "#Creating a season (year column)\n",
    "dft['Season'] =  pd.DatetimeIndex(dft['Fecha']).year\n",
    "dft\n",
    "\n",
    "#Creating a pivot table to summarize each year local win %\n",
    "pivot = pd.pivot_table(dft, index = [\"Season\"], values= \"Local Win?\", aggfunc=[\"mean\"], fill_value= 0, margins=True, margins_name = \"Sum Total\" )\n",
    "pivot\n",
    "\n",
    "p1 = pivot.iloc[:-1,0:1]*100\n",
    "p1\n",
    "plt.style.use('seaborn-dark')\n",
    "a =p1.plot()\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"% of games won by locals\")\n",
    "plt.title(\"% of games won by locals vs Season\")\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2354e9e4",
   "metadata": {},
   "source": [
    "We can observe that % of local win has varied between 54.5% and 52% over the analyzed years"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "202622e7",
   "metadata": {},
   "source": [
    "# Numerical variables distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "6b7cbad3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mJgaLxYLFYiEiIoLq6moqKyt54okn3H0VCCIi3tHpgRAUFASAw+Fg7ty5zJs3j9zcXEwmk3t7bW0tDocDm83Waj+Hw9Gq/WrfG7Fa/fH1NXd2+TcVEhKo43fxGN6YQ2cxm326Vb0301PmAZpLe3jkPoRTp04xZ84ckpOTSUxMZPXq1e5tdXV1BAcHY7Vaqaura9Vus9latV/teyMOh9MTpd/UxYv1On4Xj+GNOXSWkJDAblXvzfSUeYDmclXv3rabbuv0zxDOnj3LjBkzWLhwIZMmTQJg0KBB7Nu3D4Dy8nJGjBhBdHQ0lZWVOJ1OamtrOXz4MFFRUQwbNoxdu3a5+w4fPryzSxQRkRvo9BXChg0buHTpEgUFBe7z/4sXL2bFihXk5+cTGRlJQkICZrOZlJQUkpOTMQyD9PR0/P39SUpKIiMjg6SkJPz8/MjLy+vsEkVE5AbaDISPP/6YZcuWYbVaWbZsGf3797/lAbOyssjKyrquffPmzde12e127HZ7q7aAgADWrl17y3FERKRztXnKaOXKlWRnZ7No0SLmz59PVVUVAJcuXfJKcSIi4j1trhDMZjODBw8GID8/n9WrVxMbG8u+ffv0W7yISA/TZiD4+/vz0ksvkZycTP/+/dmwYQMAU6dO9UpxIiLiPW2eMlqzZg2nT5/G4XB4qx4REekibQZCaGgomZmZlJSUtGrXlT8iIj1Pm6eMtmzZwtatWzl8+DDl5V98mUlzczNNTU0sWLDAKwWKiIh3tBkIjz32GKNHj2bjxo3Mnj0bAB8fH7761a96pTgREfGeNk8ZWSwWwsPD+e1vf8u5c+c4efIkx48f58CBA96qT0REvKRddyrPnTuXc+fO8fWvfx0Ak8nEyJEjPVqYiIh4V7sC4ezZs9d9sCwiIj1Lux5u169fP86cOePpWkREpAu1a4VQWVlJfHx8q6+y/OCDDzxWlIiIeF+7AuGvf/2rp+sQEZEu1q5AeOaZZ65ry8nJ6fRiRESk67QrECZMmACAYRj84x//4PPPP/doUSIi4n3tCoTY2Fj33+Pi4pgxY4bHChIRka7RrkD48gfINTU1nD171mMFiYhI12hXILz55pvuv1ssFlauXOmxgkREpGu0KxBycnL49NNP+de//kW/fv146KGHPF2XiIh4WbsCobCwkDfeeIPo6Gj++Mc/8uijjzJz5kxP1yYiIl7UrkB44403eOWVV/D19aWxsZEpU6YoEEREeph2PbrCMAx8fb/IDj8/P/z8/DxalIiIeF+7VgjDhw9n7ty5DB8+nMrKSmJiYjxdl4iIeNktA+HVV19l/vz5VFRUcOjQIUaNGsW0adO8UZuIiHhRm6eM1q1bR0VFBU1NTYwdO5aJEyeyd+9eXnjhhVse+MCBA6SkpABQVVVFbGwsKSkppKSk8Oc//xmA0tJSHn/8cex2Ozt37gTgypUrpKWlkZyczKxZszh//vydzlFERNqhzRVCeXk5paWlmEwmAMLDw/mv//ovpkyZwpw5c26636ZNm9i+fTsBAQEA/OMf/2D69Omt7nCuqamhsLCQsrIynE4nycnJjBkzhuLiYqKiokhLS+PNN9+koKCArKyszpiriIi0oc0VQmBgoDsMrvLz8yMoKKjNg0ZERLBu3Tr360OHDvHee+8xdepUFi1ahMPh4ODBg8TExGCxWLDZbERERFBdXU1lZaX7URlxcXHs2bOno3MTEZHb0OYK4b777uPYsWP07dvX3Xbs2LHrQuJaCQkJHD9+3P06OjqayZMnM2TIENavX88LL7zAwIEDsdls7j5BQUE4HA4cDoe7PSgoiNra2huOYbX64+trvvUMO0lISKCO38VjeGMOncVs9ulW9d5MT5kHaC7t0WYgPPXUU/z6179m9OjR9O3bl5MnT/LBBx+Qm5t7W4OMGzeO4OBg99+zs7MZMWIEdXV17j51dXXYbDasVqu7va6uzr3ftRwO523VcKcuXqzX8bt4jNs9/si88tvqv39B3G31b0tISKBX3nNP6ynzAM3lqt69bTfd1uYpowEDBlBUVMSgQYO4fPkygwcPpri4mEGDBt1WATNnzuTgwYMA7Nmzh8GDBxMdHU1lZSVOp5Pa2loOHz5MVFQUw4YNY9euXcAXn2EMHz78tsYSEZGOueVlpzabjYkTJ97RIMuXLyc7Oxs/Pz969epFdnY2VquVlJQUkpOTMQyD9PR0/P39SUpKIiMjg6SkJPz8/MjLy7ujsUVEpH3adWNaR4SHh1NaWgrA4MGDKSkpua6P3W7Hbre3agsICGDt2rWeKktERG6iXY+uEBGRnk+BICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcPBYIBw4cICUlBYCjR4+SlJREcnIyy5Yto6WlBYDS0lIef/xx7HY7O3fuBODKlSukpaWRnJzMrFmzOH/+vKdKFBGRL/FIIGzatImsrCycTicAOTk5zJs3j6KiIgzDYMeOHdTU1FBYWEhJSQkvvvgi+fn5NDQ0UFxcTFRUFEVFRUycOJGCggJPlCgiItfwSCBERESwbt069+uqqipGjRoFQFxcHLt37+bgwYPExMRgsViw2WxERERQXV1NZWUlsbGx7r579uzxRIkiInINX08cNCEhgePHj7tfG4aByWQCICgoiNraWhwOBzabzd0nKCgIh8PRqv1q3xuxWv3x9TV7ovwbCgkJ1PG7eIzudHyz2ccr77mn9ZR5gObSHh4JhGv5+Pz/hUhdXR3BwcFYrVbq6upatdtstlbtV/veiMPh9GzR17h4sV7H7+IxutPxQ0ICvfKee1pPmQdoLlf17m276TavXGU0aNAg9u3bB0B5eTkjRowgOjqayspKnE4ntbW1HD58mKioKIYNG8auXbvcfYcPH+6NEkVE7nleWSFkZGSwZMkS8vPziYyMJCEhAbPZTEpKCsnJyRiGQXp6Ov7+/iQlJZGRkUFSUhJ+fn7k5eV5o0QRkXuexwIhPDyc0tJSAPr168fmzZuv62O327Hb7a3aAgICWLt2rafKEhGRm/DKCkGkpxqZV35b/fcviPNQJSJ3Tncqi4gIoEAQEREXBYKIiAAKBBERcVEgiIgIoEAQEREXBYKIiAAKBBERcVEgiIgIoEAQEREXBYKIiAAKBBERcVEgiIgIoEAQEREXBYKIiAAKBBERcVEgiIgIoEAQEREXBYKIiAAKBBERcVEgiIgIoEAQEREXBYKIiADg683BJk6ciM1mAyA8PJzZs2eTmZmJyWRiwIABLFu2DB8fH0pLSykpKcHX15fU1FTi4+O9WaaIyD3Ja4HgdDoBKCwsdLfNnj2befPm8Z//+Z8sXbqUHTt2MHToUAoLCykrK8PpdJKcnMyYMWOwWCzeKlVE5J7ktUCorq7m8uXLzJgxg6amJubPn09VVRWjRo0CIC4ujoqKCnx8fIiJicFisWCxWIiIiKC6upro6GhvlSoick/yWiDcd999zJw5k8mTJ3PkyBFmzZqFYRiYTCYAgoKCqK2txeFwuE8rXW13OBzXHc9q9cfX1+yt8gkJCdTxu3iM7n58b43Rmcxmn25X881oLrfmtUDo168f999/PyaTiX79+hESEkJVVZV7e11dHcHBwVitVurq6lq1fzkgrnI4nF6p+6qLF+t1/C4eo7sfvyNjjMwrv63++xfE3Vb/WwkJCfTK++INmssXeve+/t/Tq7x2ldHWrVt57rnnADhz5gwOh4MxY8awb98+AMrLyxkxYgTR0dFUVlbidDqpra3l8OHDREVFeatMEZF7ltdWCJMmTeKZZ54hKSkJk8nEypUrCQ0NZcmSJeTn5xMZGUlCQgJms5mUlBSSk5MxDIP09HT8/f29VaaIyD3La4FgsVjIy8u7rn3z5s3Xtdntdux2uzfKEhERF92YJiIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcFAgiIgIoEERExEWBICIigAJBRERcvPb4axG5+3T1N7LJ3UUrBBERARQIIiLiokAQERFAgSAiIi4KBBERARQIIiLiokAQERFA9yGIiIfpXofu464MhJaWFpYvX84///lPLBYLK1as4P777+/qskREerS78pTRO++8Q0NDA6+++ioLFizgueee6+qSRER6vLtyhVBZWUlsbCwAQ4cO5dChQ11ckYjcrXRKqvOYDMMwurqIay1evJhHHnmE7373uwCMHTuWd955B1/fuzK/RER6hLvylJHVaqWurs79uqWlRWEgIuJhd2UgDBs2jPLyL5aB//M//0NUVFQXVyQi0vPdlaeMrl5l9Omnn2IYBitXrqR///5dXZaISI92VwaCp/Sky1kbGxtZtGgRJ06coKGhgdTUVL7//e93dVkddu7cOR5//HH++Mc/duvw37hxI++++y6NjY0kJSUxefLkri6pQxobG8nMzOTEiRP4+PiQnZ3dLX8uBw4cYM2aNRQWFnL06FEyMzMxmUwMGDCAZcuW4eNzV54kuc6X5/HJJ5+QnZ2N2WzGYrGQm5tLr169OmWc7vFudJKedDnr9u3bCQkJoaioiE2bNpGdnd3VJXVYY2MjS5cu5b777uvqUu7Ivn37+OijjyguLqawsJDTp093dUkdtmvXLpqamigpKWHOnDk8//zzXV3Sbdu0aRNZWVk4nU4AcnJymDdvHkVFRRiGwY4dO7q4wva5dh7PPvssS5YsobCwkHHjxrFp06ZOG+ueCoSedDnr+PHj+c1vfuN+bTabu7CaO5Obm8uUKVP42te+1tWl3JEPPviAqKgo5syZw+zZsxk7dmxXl9Rh/fr1o7m5mZaWFhwOR7e8qCMiIoJ169a5X1dVVTFq1CgA4uLi2L17d1eVdluunUd+fj4PPfQQAM3Nzfj7+3faWN3vp3wHHA4HVqvV/dpsNtPU1NQt/2MPCgoCvpjT3LlzmTdvXtcW1EHbtm0jLCyM2NhY/vCHP3R1OXfkwoULnDx5kg0bNnD8+HFSU1N56623MJlMXV3abQsMDOTEiRM8+uijXLhwgQ0bNnR1SbctISGB48ePu18bhuH+WQQFBVFbW9tVpd2Wa+dx9RenDz/8kM2bN/PKK6902lj31Aqhp13OeurUKX72s5/x2GOPkZiY2NXldEhZWRm7d+8mJSWFTz75hIyMDGpqarq6rA4JCQnh4YcfxmKxEBkZib+/P+fPn+/qsjrkpZde4uGHH+btt9/mtddeIzMz033Korv68ucFdXV1BAcHd2E1d+bPf/4zy5Yt4w9/+ANhYWGddtx7KhB60uWsZ8+eZcaMGSxcuJBJkyZ1dTkd9sorr7B582YKCwt56KGHyM3NpXfv3l1dVocMHz6c999/H8MwOHPmDJcvXyYkJKSry+qQ4OBgbDYbAF/5yldoamqiubm5i6u6M4MGDWLfvn0AlJeXM2LEiC6uqGNee+019/8zffv27dRjd99fjztg3LhxVFRUMGXKFPflrN3Vhg0buHTpEgUFBRQUFABffPjU3T+Y7c7i4+PZv38/kyZNwjAMli5d2m0/2/nFL37BokWLSE5OprGxkfT0dAIDA7u6rDuSkZHBkiVLyM/PJzIykoSEhK4u6bY1Nzfz7LPP8vWvf520tDQARo4cydy5czvl+PfUZaciInJz99QpIxERuTkFgoiIAAoEERFxUSCIiAigQBARERcFgnRL+/btIz09vdOPm5mZ6b5XpS01NTUsX74cgP3791NdXX3TvmPGjLnjulJSUpg0aRIpKSnuP++99x7Hjx9n2LBh7ja73c4vfvEL/v3vf7v3PXDgAEOGDOHgwYN3XIf0bPfUfQginaV3797uQCgrK2PChAkMHDjQo2Pm5uZe98TR48eP8+CDD1JYWOhuy8vLY+vWrcycOROALVu2MH36dIqKioiOjvZojdK9KRCkR6moqOD555/H39+fkJAQVq5cidVqZcWKFRw8eJDGxkbS0tKIj49n6dKlnD59mgsXLhAXF3fT50FlZmZiGAanTp2ivr6e3Nxc/P39mT9/PkuXLuX999+nqqqKBx98kIqKCoqLi2lpaeH73/8+aWlpNDQ0sGDBAk6ePElISAhr167lypUrLF68mAsXLgCQlZXFN7/5TeLj44mMjCQyMpLFixff9vyv1hkREQF88YiGvXv38uabb5KYmMj58+c79VEH0rMoEKTHMAyDJUuWUFxcTJ8+fXj55ZdZv349w4YN48KFC2zdupWamho2b97MwIEDGTp0KJMnT8bpdLYZCAB9+/YlNzeXXbt2sXr1arKysgAYMmQIsbGxTJgwAX9/fzZt2sT27duxWCw899xz1NXVUV9fT3p6OuHh4e5nNr399tt8+9vfJjk5mSNHjvDMM89QXFzMqVOn2LZtG6GhodfVkJGRQUBAgPv173//ewD+9a9/kZKSwsWLF3E6nSQmJvKTn/wE+OKZN+PGjcPf359HH32UrVu38stf/rIT33XpSRQI0mNcuHABq9VKnz59gC9u6c/Pzyc0NJShQ4cCX5zqSU9Px+Fw8PHHH7N3716sVisNDQ1tHvvb3/42ADExMTd95MmxY8cYMGCA+/EhixYtAr54FlB4eDgAvXr14vLly3z66afs3buXv/zlLwBcunQJgNDQ0BuGAdz4lFF9fb37lNGVK1eYPXs2X/3qV90PbdyyZQtms5mZM2dy5coVTp8+zRNPPNFtvhhGvEuBID1GaGgoDoeDzz//nK997Wv8/e9/54EHHiAyMpK33noLgNraWubNm8d3v/tdbDYbv/vd7zh69CilpaW09RSXqqoqRowYwYcffsiAAQNabTOZTBiGQUREBJ999hkNDQ1YLBbmzp3L4sWLb/j468jISH784x+TmJjIuXPn2LJlC8Ad/UN93333sWbNGiZOnMiwYcMwmUw0NzdTWlrq7jN9+nR27tzZrb9dTzxHgSDdVkVFBY8//rj7dV5eHitWrCAtLQ2TycRXvvIVcnJyCA0NZc+ePSQlJdHc3MycOXP4xje+wfz586msrCQgIID777+fzz///KZjlZeXs2PHDlpaWsjJyWm17Vvf+hZr1qzh+eefZ9asWUybNg2TyUR8fLx7tXKt2bNns3jxYkpLS3E4HDz55JO3nO+1p4weffRR4uLiWvXp1asXTz/9NEuXLiU6OprHHnus1fbJkyfzyiuvKBDkhvRwO5FbyMzMZMKECdf94yvS0+hEooiIAFohiIiIi1YIIiICKBBERMRFgSAiIoACQUREXBQIIiICKBBERMTl/wH2FuoAbTaIBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bzUZAQECj9Ww2W6Pp15Ztir+/L97e5hZlNJu9CApq36J13eVeyHijts5rxNfjbjMZ/fts9Hxg/IxGz3e9Nrns9PTp00yZMgWr1Up8fDxvvPGGa151dTWBgYH4+/tTXV3daHpAQECj6deWbYrNZm9xvqCg9ly8WNPi9d2htTO25JLKO9XWr6kRv2d3m8no/xeNng+Mn9Fo+Tp2DLjlvFZ/D+HcuXNMmDCB1NRURo8eDUCPHj04cOAAAEVFRfTt25fIyEhKSkqw2+1UVVVRXl5OREQE0dHR7Nmzx7Vsnz59WjuiiIg0odWPENasWcOlS5fIyclxnf+fO3cuGRkZZGdnEx4eTlxcHGazmaSkJKxWKw6Hg5SUFHx9fUlMTCQtLY3ExER8fHxYvnx5a0cUEZEmtHohpKenk56eftP0DRs23DQtISGBhISERtPatWvHypUrWzuWiIj8AN2YJiIigApBREScVAgiIgKoEERExEmFICIigApBREScVAgiIgKoEERExEmFICIigApBREScVAgiIgKoEERExEmFICIigApBREScVAgiIgKoEERExKnZQvjiiy949tlnef755ykvL3dXJhER8YBmC2HJkiUsWrSIOXPmMGPGDEpLSwG4dOmSW8KJiIj7NPsRmmazmZ49ewKQnZ3NG2+8weDBgzlw4IA+5lJE5D7TbCH4+vqyfv16rFYrXbt2Zc2aNQA899xzbgknIiLu0+wpo2XLlvHNN99gs9nclUdERDyk2UIIDg5m1qxZFBQUNJq+fPnyNg0lIiLu1+wpo02bNrF582bKy8spKioCoL6+nqtXrzJz5ky3BBQREfdothBGjhzJgAEDePvtt0lOTgbAy8uLH/3oR24JJyIi7tPsKSOLxUJoaCi///3vOX/+PKdOnaKiooLDhw+7K5+IiLhJs0cI10ybNo3z58/zk5/8BACTycQTTzzRpsFERMS9bqsQzp07d9MbyyIicn+5rbGMunTpwpkzZ9o6i4iIeNBtHSGUlJQQGxtLSEiIa9rnn3/e7DqHDx9m2bJl5ObmUlpaSnJyMp07dwYgMTGRESNGUFhYSEFBAd7e3kyePJnY2FiuXLlCamoq58+fx8/Pj6ysrEb7FRGRtnFbhfB///d/d7TRtWvXsm3bNtq1awfAX//6V8aPH8+ECRNcy1RWVpKbm8uWLVuw2+1YrVYGDhxIfn4+ERERTJ06lR07dpCTk0N6evod7V9ERO7cbRXC7Nmzb5qWmZl5y+XDwsJYtWoVr776KgBHjx7lH//4Bzt37uTRRx9lzpw5HDlyhKioKCwWCxaLhbCwMMrKyigpKeHFF18EICYmhpycnJY8LxERuUO3VQgjRowAwOFw8Ne//pWzZ882u3xcXBwVFRWux5GRkYwZM4ZevXqxevVq3nrrLbp3705AQIBrGT8/P2w2GzabzTXdz8+PqqqqJvfh7++Lt7f5duLfxGz2IiiofYvWdZd7IeON2jqvEV+Pu81k9O+z0fOB8TMaPd/1bqsQBg8e7Po6Jiam0amf2zF06FACAwNdXy9atIi+fftSXV3tWqa6upqAgAD8/f1d06urq13r3chms99RhusFBbXn4sWaFq/vDvdCxhu1dV4jvh53m8no32ej5wPjZzRavo4dA24577auMvr8889d//77v/+bc+fO3VGAiRMncuTIEQD27dtHz549iYyMpKSkBLvdTlVVFeXl5URERBAdHc2ePXsAKCoqok+fPne0LxERaZnbOkLYsWOH62uLxcKSJUvuaCcLFy5k0aJF+Pj40KFDBxYtWoS/vz9JSUlYrVYcDgcpKSn4+vqSmJhIWloaiYmJ+Pj4aCA9ERE3ua1CyMzM5NixYxw/fpwuXbrws5/97AfXCQ0NpbCwEICePXs2eWNbQkICCQkJjaa1a9dOH74jIuIBt1UIubm5fPjhh0RGRvKHP/yB4cOHM3HixLbOJiIibnRbhfDhhx/y3nvv4e3tTV1dHePGjVMhiIjcZ27rTWWHw4G39/fd4ePjg4+PT5uGEhER97utI4Q+ffowbdo0+vTpQ0lJCVFRUW2dS0RE3OwHC2Hjxo3MmDGD4uJijh49Sr9+/fj1r3/tjmwiIuJGzZ4yWrVqFcXFxVy9epUhQ4YwatQo9u/fz1tvveWufCIi4ibNFkJRURFvvvmma5C60NBQ/vM//5Ndu3a5JZyIiLhPs6eM2rdvj8lkajTNx8cHPz+/Ng0lcr96YnnRHS1/cGZMGyURuVmzRwgPPfQQJ0+ebDTt5MmTN5WEiIjc+5o9QnjllVd46aWXGDBgAI888ginTp3i888/Jysry135RETETZo9QujWrRt5eXn06NGDy5cv07NnT/Lz8+nRo4e78omIiJv84GWnAQEBjBo1yg1RRETEk27rTmUREbn/qRBERARQIYiIiJMKQUREABWCiIg4qRBERAS4zeGvpe1pSAMR8TQdIYiICKBCEBERJxWCiIgAKgQREXFSIYiICKBCEBERJxWCiIgAKgQREXFSIYiICNCGhXD48GGSkpIAOHHiBImJiVitVhYsWEBDQwMAhYWFPPvssyQkJLB7924Arly5wtSpU7FarUyaNIlvv/22rSKKiMh12qQQ1q5dS3p6Ona7HYDMzEymT59OXl4eDoeDnTt3UllZSW5uLgUFBaxbt47s7Gxqa2vJz88nIiKCvLw8Ro0aRU5OTltEFBGRG7RJIYSFhbFq1SrX49LSUvr16wdATEwMe/fu5ciRI0RFRWGxWAgICCAsLIyysjJKSkoYPHiwa9l9+/a1RUQREblBmwxuFxcXR0VFheuxw+HAZDIB4OfnR1VVFTabjYCAANcyfn5+2Gy2RtOvLdsUf39fvL3NLcpnNnsRFNS+ResahRHzt3UmPWf3uxd+Voye0ej5rueW0U69vP55IFJdXU1gYCD+/v5UV1c3mh4QENBo+rVlm2Kz2VucJyioPRcv1rR4fSMwYv62zqTn7H73ws+K0TMaLV/HjgG3nOeWq4x69OjBgQMHACgqKqJv375ERkZSUlKC3W6nqqqK8vJyIiIiiI6OZs+ePa5l+/Tp446IIiIPPLccIaSlpTFv3jyys7MJDw8nLi4Os9lMUlISVqsVh8NBSkoKvr6+JCYmkpaWRmJiIj4+PixfvtwdEUVEHnhtVgihoaEUFhYC0KVLFzZs2HDTMgkJCSQkJDSa1q5dO1auXNlWsURE5BZ0Y5qIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiABuGv5aRNzjieVFd7T8wZkxbZRE7kU6QhAREUCFICIiTioEEREBVAgiIuKkQhAREUCFICIiTioEEREBVAgiIuKkQhAREUB3Kt823QEqIvc7HSGIiAigQhAREScVgoiIAG5+D2HUqFEEBAQAEBoaSnJyMrNmzcJkMtGtWzcWLFiAl5cXhYWFFBQU4O3tzeTJk4mNjXVnTBGRB5LbCsFutwOQm5vrmpacnMz06dN58sknmT9/Pjt37qR3797k5uayZcsW7HY7VquVgQMHYrFY3BVVROSB5LZCKCsr4/Lly0yYMIGrV68yY8YMSktL6devHwAxMTEUFxfj5eVFVFQUFosFi8VCWFgYZWVlREZGuiuqiMgDyW2F8NBDDzFx4kTGjBnDV199xaRJk3A4HJhMJgD8/PyoqqrCZrO5Titdm26z2dwVU0TkgeW2QujSpQuPPvooJpOJLl26EBQURGlpqWt+dXU1gYGB+Pv7U11d3Wj69QVxjb+/L97e5hZlMZu9CApq36J1b9e9vv2W0HO+/7bvjp+Vu2X0jEbPdz23FcLmzZs5duwYCxcu5MyZM9hsNgYOHMiBAwd48sknKSoqon///kRGRrJixQrsdju1tbWUl5cTERFx0/ZsNnuLswQFtefixZq7eTo/6F7ffkvoOd9/23fHz8rdMnpGo+Xr2PHmP7CvcVshjB49mtmzZ5OYmIjJZGLJkiUEBwczb948srOzCQ8PJy4uDrPZTFJSElarFYfDQUpKCr6+vu6KKSLywHJbIVgsFpYvX37T9A0bNtw0LSEhgYSEBHfEEhERJ92YJiIigApBREScVAgiIgKoEERExEmFICIigApBRESc9IlpIg8wfRKgXE9HCCIiAqgQRETESYUgIiKACkFERJxUCCIiAqgQRETESYUgIiKACkFERJxUCCIiAqgQRETESYUgIiLAAzqWUbd5H3k6goiI4egIQUREABWCiIg4PZCnjETEfTTE9r1DRwgiIgKoEERExEmFICIigApBREScVAgiIgKoEERExMmQl502NDSwcOFC/va3v2GxWMjIyODRRx/1dCwRMaA7HXlAl7XemiGPED755BNqa2vZuHEjM2fO5PXXX/d0JBGR+54hC6GkpITBgwcD0Lt3b44ePerhRCIi9z+Tw+FweDrEjebOncsvf/lLnnrqKQCGDBnCJ598gre3Ic9wiYjcFwx5hODv7091dbXrcUNDg8pARKSNGbIQoqOjKSr6fvyTv/zlL0RERHg4kYjI/c+Qp4yuXWV07NgxHA4HS5YsoWvXrp6OJSJyXzPkEYKXlxevvfYaBQUFbNy4sdXKoKGhgfnz5zN27FiSkpI4ceJEq2y3tdTV1ZGamorVamX06NHs3LnT05Fu6fz58zz11FOUl5d7OkqT3n77bcaOHcuzzz7Lpk2bPB2nkbq6OmbOnMm4ceOwWq2Gew0PHz5MUlISACdOnCAxMRGr1cqCBQtoaGjwcLrG+b788kusVitJSUlMnDiRc+fOeTjd967PeM327dsZO3ashxLdHkMWQlsx+uWs27ZtIygoiLy8PNauXcuiRYs8HalJdXV1zJ8/n4ceesjTUZp04MAB/vznP5Ofn09ubi7ffPONpyM1smfPHq5evUpBQQFTpkxhxYoVno7ksnbtWtLT07Hb7QBkZmYyffp08vLycDgcHv8j5cZ8ixcvZt68eeTm5jJ06FDWrl3r0Xxwc0b4vrg2b96MAU/INPJAFYLRL2cdNmwYv/vd71yPzWazB9PcWlZWFuPGjePHP/6xp6M06fPPPyciIoIpU6aQnJzMkCFDPB2pkS5dulBfX09DQwM2m81QF0yEhYWxatUq1+PS0lL69esHQExMDHv37vVUNODmfNnZ2fzsZz8DoL6+Hl9fX09Fc7kx44ULF1i2bBlz5szxYKrbY5z/iW5gs9nw9/d3PTabzVy9etUwP5B+fn7A9zmnTZvG9OnTPRuoCVu3biUkJITBgwfzzjvveDpOky5cuMCpU6dYs2YNFRUVTJ48mY8++giTyeTpaAC0b9+er7/+muHDh3PhwgXWrFnj6UgucXFxVFRUuB47HA7X6+bn50dVVZWnogE357v2R8mhQ4fYsGED7733nqeiuVyfsb6+nrlz5zJnzhxDlNUPeaCOEO6Fy1lPnz7N888/z8iRI4mPj/d0nJts2bKFvXv3kpSUxJdffklaWhqVlZWejtVIUFAQgwYNwmKxEB4ejq+vL99++62nY7msX7+eQYMG8fHHH/PBBx8wa9asRqcXjMTL65+/IqqrqwkMDPRgmqb9z//8DwsWLOCdd94hJCTE03EaKS0t5cSJEyxcuJAZM2Zw/PhxFi9e7OlYt2Ss34ZtLDo6mt27dzNixAhDXs567tw5JkyYwPz58xkwYICn4zTp+r/AkpKSWLhwIR07dvRgopv16dOH//qv/2L8+PGcPXuWy5cvExQU5OlYLoGBgfj4+ADw8MMPc/XqVerr6z2cqmk9evTgwIEDPPnkkxQVFdG/f39PR2rkgw8+YOPGjeTm5hrqe3xNZGQkO3bsAKCiooIZM2Ywd+5cD6e6tQeqEIYOHUpxcTHjxo1zXc5qJGvWrOHSpUvk5OSQk5MDfP8GlVHfvDWq2NhYDh48yOjRo3E4HMyfP99Q78e88MILzJkzB6vVSl1dHSkpKbRv397TsZqUlpbGvHnzyM7OJjw8nLi4OE9Hcqmvr2fx4sX85Cc/YerUqQA88cQTTJs2zcPJ7l2GvA9BRETc74F6D0FERG5NhSAiIoAKQUREnFQIIiICqBBERMRJhSCGdODAAVJSUlp9u7NmzXINrd6cyspKFi5cCMDBgwcpKyu75bIDBw6861xJSUmNBrmz2+08/fTTwPfj9Zw6dYqLFy+yffv2JtcdPXo0SUlJrn+ffvopFRUVREdHu6YlJCTwwgsv8N1337nWPXz4ML169eLIkSN3/Rzk3vdA3Ycgcrs6duzoKoQtW7YwYsQIunfv7pEs125kOnDgALt27WryDvasrKybRgWuqKjgscceIzc31zVt+fLlbN68mYkTJwKwadMmxo8fT15eHpGRkW34LOReoEKQe0pxcTErVqzA19eXoKAglixZgr+/PxkZGRw5coS6ujqmTp1KbGws8+fP55tvvuHChQvExMTccmyoWbNm4XA4OH36NDU1NWRlZeHr68uMGTOYP38+n332GaWlpTz22GMUFxeTn59PQ0MDzzzzDFOnTqW2tpaZM2dy6tQpgoKCWLlyJVeuXGHu3LlcuHABgPT0dB5//HFiY2MJDw8nPDz8tu9YvXZH+Jo1aygrK2Pjxo0tGkb52nMMCwsDvh+KYv/+/ezYsYP4+Hi+/fZbww39IO6lQpB7hsPhYN68eeTn59OpUyfeffddVq9eTXR0NBcuXGDz5s1UVlayYcMGunfvTu/evRkzZgx2u73ZQgB45JFHyMrKYs+ePbzxxhukp6cD0KtXLwYPHsyIESPw9fVl7dq1bNu2DYvFwuuvv051dTU1NTWkpKQQGhrqGuPp448/pn///litVr766itmz55Nfn4+p0+fZuvWrQQHB9+UIS0tjXbt2gE0+bkDycnJFBQUNFkG168L8OabbwJw/PhxkpKSuHjxIna7nfj4eH71q18B348BNHToUHx9fRk+fDibN2/mP/7jP27/GyL3HRWC3DMuXLiAv78/nTp1Ar4fpiA7O5vg4GB69+4NfH+qJyUlBZvNxhdffMH+/fvx9/entra22W1fG6MnKirqlkOanDx5km7durmGErk2nPHDDz9MaGgoAB06dODy5cscO3aM/fv387//+78AXLp0CYDg4OAmywAan/ax2+0MHz78tl6XG9e9pqamxnXK6MqVKyQnJ/OjH/3INaDjpk2bMJvNTJw4kStXrvDNN9/w4osvNhrQTh4sKgS5ZwQHB2Oz2Th79iw//vGP+dOf/kTnzp0JDw/no48+AqCqqorp06fz1FNPERAQwGuvvcaJEycoLCxs9sNJSktL6du3L4cOHaJbt26N5plMJhwOB2FhYfz973+ntrYWi8XCtGnTmDt3bpPDaoeHh/Pv//7vxMfHc/78edentt3NL1svL68Wf2LZQw89xLJlyxg1ahTR0dGYTCbq6+spLCx0LTN+/Hh2797NM8880+KMcm9TIYhhFRcX8+yzz7oeL1++nIyMDKZOnYrJZOLhhx8mMzOT4OBg9u3bR2JiIvX19UyZMoWf/vSnzJgxg5KSEtq1a8ejjz7K2bNnb7mvoqIidu7cSUNDA5mZmY3m/fznP2fZsmWsWLGCSZMm8etf/xqTyURsbKzraOVGycnJzJ07l8LCQmw2Gy+//PJdvx5hYWEcO3aM9evX88ILLzSad+Mpo+HDhxMTE9NomQ4dOvDqq68yf/58IiMjGTlyZKP5Y8aM4b333lMhPMA0uJ088GbNmsWIESNu+gUq8qDRyUIREQF0hCAiIk46QhAREUCFICIiTioEEREBVAgiIuKkQhAREUCFICIiTv8fPYSOl8QtZDQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9e/cmKyuL0NBQJk2axLvvvktGRgZz5851R0wREbmJW0YIQUFBrFmzxnX76NGjfPzxx4wcOZLZs2djs9k4fPgw4eHhWCwW/P39CQoKoqioiIKCAiIjIwGIiooiPz/fHRFFROQWbimEmJgYvL3/NfgICwtjxowZbN68mfbt27N27VpsNhv+/v6uZfz8/LDZbJWm+/n5UVpa6o6IIiJyixp3GR05coQFCxZgtVpZsGABnTp1qtOD9O3blxYtWrj+nZqaSo8ePbDb7a5l7HY7/v7+WK1W13S73e5a71ZWqy/e3uY65TGbvQgIaF6ndRuLez1/XVT3nBvra6lctaNcteOuXDUWQnp6OqmpqZjNZqZMmUJ6ejpdunTh4sWLt/2grk5iYiLz5s0jLCyM/Px8unTpQlhYGKtWrcLhcFBWVsaJEycIDQ2le/fu7N27l7CwMHJzc4mIiKj2Pm02R+2e6U0CAppz4cKlOq/fGNzr+euiuufcWF9L5aod5aqdH5KrdWv/286rsRDMZjNdunQBYOXKlbzyyitERkZy4MABVq9efdcBFi5cSGpqKj4+PrRq1YrU1FSsVisJCQnEx8djGAbJycn4+voSFxfHzJkziYuLw8fHhxUrVtz144iISN2ZDMMwbjczMTGRyMhI4uPjsVgsnsx1RyUldf9uwROt7+5rKtf2cpJN4RrP1T3npvgXnDspV+00xVw1jRBq/FJ5+fLlfPfdd9hstjo9sIiI3DtqLITAwEBSUlLIzs6uNF27cUREmp4av0N4++232bZtGydOnCA398Yuh+vXr3Pt2jWmTp3qkYAiIuIZNRbC4MGD6dWrF6+//jrjxo0DwMvLi3/7t3/zSDgREfGcGncZWSwW2rVrx6JFizh37hynTp3im2++4dChQ57KJyIiHnJX5zJKSkri3LlztG3bFgCTycRjjz3m1mAiIuJZd1UIZ8+erfLFsoiINC13dS6jjh07Ulxc7O4sIiLSgO5qhFBQUEB0dDQtW7Z0TfvrX//qtlAiIuJ5d1UIf/7zn92dQ0REGthdFcKsWbOqTFu8eHG9hxERkYZzV4XQv39/AAzD4PPPP+fMmTNuDSUiIp53V4VQcQUzuHEVs5svhSkiIk3DXRXCzV8gl5SUcPbsWbcFEhGRhnFXhfDuu++6/m2xWEhPT3dbIBERaRh3VQiLFy/m+PHjfPHFF3Ts2JGf/OQn7s4lIiIedleFkJmZya5duwgLC+ONN97g17/+NYmJie7OJiIiHnRXhbBr1y42b96Mt7c3V69eZcSIESoEEZEm5q4KwTAMvL1vLOrj44OPj49bQ4nUh9peNrS2lyUVaWruqhAiIiJISkoiIiKCgoICwsPD3Z1LREQ87I6F8NZbbzFlyhTy8vI4evQoPXv2ZNSoUZ7IJiIiHlTj2U7XrFlDXl4e165do0+fPgwZMoT9+/ezdu1aT+UTEREPqbEQcnNz+c///E+aNWsGQLt27Xj11VfZs2ePR8KJiIjn1FgIzZs3x2QyVZrm4+ODn5+fW0OJiIjn1VgIDzzwAF9//XWlaV9//XWVkhARkXtfjV8qT5s2jQkTJtCrVy/at2/PqVOn+Otf/8rSpUs9lU9ERDykxhFCSEgIW7ZsoXPnzly+fJkuXbqQlZVF586dPZVPREQ85I6Hnfr7+zNkyBAPRBERkYZU4whBRETuHyoEEREBVAgiIuKkQhAREUCFICIiTm4rhEOHDpGQkADAyZMniYuLIz4+ngULFlBeXg7A1q1beeaZZ4iNjeWjjz4C4MqVK0yaNIn4+HjGjh3L999/766IIiJyE7cUwoYNG5g7dy4OhwO4cQnOyZMns2XLFgzDYPfu3ZSUlJCZmUl2djYbN25k5cqVlJWVkZWVRWhoKFu2bGHIkCFkZGS4I6KIiNzCLYUQFBTEmjVrXLcLCwvp2bMnAFFRUezbt4/Dhw8THh6OxWLB39+foKAgioqKKCgoIDIy0rVsfn6+OyKKiMgt7uoCObUVExPDN99847ptGIbr/Ed+fn6UlpZis9nw9/d3LePn54fNZqs0vWLZ6litvnh7m+uUz2z2IiCgeZ3WbSzu9fx1Ud1zrs/Xsj63aWN9jylX7dxvudxSCLfy8vrXQMRut9OiRQusVit2u73SdH9//0rTK5atjs3mqHOegIDmXLhwqc7rNwb3ev66qO451+drWZ/btLG+x5Srdppirtat/W87zyNHGXXu3JkDBw4AN66x0KNHD8LCwigoKMDhcFBaWsqJEycIDQ2le/fu7N2717VsRESEJyKKiNz3PDJCmDlzJvPmzWPlypUEBwcTExOD2WwmISGB+Ph4DMMgOTkZX19f4uLimDlzJnFxcfj4+LBixQpPRBQRue+5rRDatWvH1q1bAejYsSObNm2qskxsbCyxsbGVpjVr1ozVq1e7K5aIiNyGfpgmIiKAh3YZNQWPrcht6AgiIm6lEYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcVIhiIgIoEIQEREn74YOINJYPLYit9brfDI1yg1JRBqGRggiIgKoEERExEmFICIigApBREScVAgiIgKoEERExEmFICIigApBREScVAgiIgKoEERExMmjp64YMmQI/v7+ALRr145x48aRkpKCyWQiJCSEBQsW4OXlxdatW8nOzsbb25vx48cTHR3tyZgiIvcljxWCw+EAIDMz0zVt3LhxTJ48mZ///OfMnz+f3bt3061bNzIzM9m+fTsOh4P4+Hh69+6NxWLxVFQRkfuSxwqhqKiIy5cvM2bMGK5du8aUKVMoLCykZ8+eAERFRZGXl4eXlxfh4eFYLBYsFgtBQUEUFRURFhbmqagiIvcljxXCAw88QGJiIsOGDeOrr75i7NixGIaByWQCwM/Pj9LSUmw2m2u3UsV0m81W5f6sVl+8vc11ymI2exEQ0LxuT6SRuNfz10V1z7mhX8vbPXZD57od5aqd+y2XxwqhY8eOPPTQQ5hMJjp27EhAQACFhYWu+Xa7nRYtWmC1WrHb7ZWm31wQFWw2R52zBAQ058KFS3VevzG41/PXRXXPuaFfy9s9dkPnuh3lqp2mmKt166qfpxU8dpTRtm3bWLJkCQDFxcXYbDZ69+7NgQMHAMjNzaVHjx6EhYVRUFCAw+GgtLSUEydOEBoa6qmYIiL3LY+NEJ599llmzZpFXFwcJpOJ9PR0AgMDmTdvHitXriQ4OJiYmBjMZjMJCQnEx8djGAbJycn4+vp6KqaIyH3LY4VgsVhYsWJFlembNm2qMi02NpbY2FhPxBL5QWp7lTVdYU0aM/0wTUREABWCiIg4qRBERARQIYiIiJMKQUREABWCiIg4qRBERATw8OmvG4uQee83dAQRkUZHIwQREQFUCCIi4qRCEBERQIUgIiJOKgQREQFUCCIi4qRCEBERQIUgIiJO9+UP00Qaii6oI42ZRggiIgKoEERExEmFICIigApBREScVAgiIgKoEERExEmFICIigApBREScVAgiIgLol8oiTYp+CS0/hEYIIiICqBBERMRJhSAiIoAKQUREnFQIIiIC6CgjkfuajkqSmzXKQigvL2fhwoX84x//wGKxkJaWxkMPPdTQsUREmrRGWQgffvghZWVlvPXWW3z22WcsWbKE1157raFjidz3ajuiAI0q7iWNshAKCgqIjIwEoFu3bhw9erSBE4lIXWm31L3DZBiG0dAhbjVnzhz+4z/+gyeffBKAPn368OGHH+Lt3Sj7S0SkSWiURxlZrVbsdrvrdnl5ucpARMTNGmUhdO/endzcG8PMzz77jNDQ0AZOJCLS9DXKXUYVRxkdP34cwzBIT0+nU6dODR1LRKRJa5SFUF/udPjqnj17WLt2Ld7e3gwdOpTY2FiP5Lp69SqzZ8/m22+/paysjPHjx/PLX/7SNf+//uu/2LZtGy1btgRg0aJFBAcHeyTbkCFD8Pf3B6Bdu3YsXrzYNa+htldOTg7vvPMOAA6Hg2PHjpGXl0eLFi2Ahtlehw4dYvny5WRmZnLy5ElSUlIwmUyEhISwYMECvLz+Nfj25GHUN+c6duwYqampmM1mLBYLS5cupVWrVpWWr+n1dleuwsJCxo0bR4cOHQCIi4ujf//+rmUbanslJydz9uxZAL799lt+9rOf8eqrr1Za3t3bq7rPhocffthz7y+jCfvggw+MmTNnGoZhGH//+9+NcePGueaVlZUZv/rVr4wLFy4YDofDeOaZZ4wzZ854JNe2bduMtLQ0wzAM4/vvvzeefPLJSvOnTp1qHDlyxCNZbnblyhVj8ODB1c5ryO11s4ULFxrZ2dmVpnl6e61fv94YMGCAMWzYMMMwDOPFF1809u/fbxiGYcybN8/485//XGn5mt6H7sw1cuRI4/PPPzcMwzCysrKM9PT0SsvX9Hq7M9fWrVuNjRs33nb5htpeFS5cuGAMGjTIKC4urjTdE9urus8GT76/GuV3CPWlpsNXT5w4QVBQEA8++CAWi4WIiAg+/fRTj+Tq168fv/vd71y3zWZzpfmFhYWsX7+euLg4Xn/9dY9kAigqKuLy5cuMGTOG0aNH89lnn7nmNeT2qnDkyBG++OILhg8fXmm6p7dXUFAQa9asqfT4PXv2BCAqKop9+/ZVWt5Th1HfmmvlypX85Cc/AeD69ev4+vpWWr6m19uduY4ePcrHH3/MyJEjmT17NjabrdLyDbW9KqxZs4ZRo0bxox/9qNJ0T2yv6j4bPPn+atKFYLPZsFqtrttms5lr16655lUM/QD8/PyqvDHdxc/PD6vVis1mIykpicmTJ1ea//TTT7Nw4ULefPNNCgoK+OijjzyS64EHHiAxMZGNGzeyaNEipk2b1ii2V4XXX3+diRMnVpnu6e0VExNT6ag3wzAwmUzAje1SWlpaafma3ofuzFXxgXbw4EE2bdrE888/X2n5ml5vd+YKCwtjxowZbN68mfbt27N27dpKyzfU9gI4d+4c+fn5PPPMM1WW98T2qu6zwZPvryZdCDUdvnrrPLvdXukDz91Onz7N6NGjGTx4MAMHDnRNNwyD5557jpYtW2KxWHjyySf5/PPPPZKpY8eODBo0CJPJRMeOHQkICKCkpARo+O118eJFvvzySx5//PFK0xtye1W4eX+u3W53fbdRoSEPo37vvfdYsGAB69evd33HUqGm19ud+vbtS9euXV3/vvX1asjt9f777zNgwIAqo3bw3Pa69bPBk++vJl0INR2+2qlTJ06ePMmFCxcoKyvj008/JTw83CO5zp49y5gxY5g+fTrPPvtspXk2m40BAwZgt9sxDIMDBw64/udxt23btrFkyRIAiouLsdlstG7dGmjY7QXwySef8Itf/KLK9IbcXhU6d+7MgQMHAMjNzaVHjx6V5jfUYdT/8z//w6ZNm8jMzKR9+/ZV5tf0ertTYmIihw8fBiA/P58uXbpUmt+Qh53n5+cTFVX9L6U9sb2q+2zw5PurSf/aq2/fvuTl5TFixAjX4as7d+7k0qVLDB8+nJSUFBITEzEMg6FDh9KmTRuP5Fq3bh0XL14kIyODjIwMAIYNG8bly5cZPnw4ycnJjB49GovFQq9evVy/2Ha3Z599llmzZhEXF4fJZCI9PZ0//elPDb69AP75z3/Srl071+2bX8eG2l4VZs6cybx581i5ciXBwcHExMQAMGPGDCZPnlzt+9Ddrl+/zssvv0zbtm2ZNGkSAI899hhJSUmuXNW93p74S3zhwoWkpqbi4+NDq1atSE1NBRp2e1X45z//WaU8Pbm9qvtsmDNnDmlpaR55fzXpw05FROTuNeldRiIicvdUCCIiAqgQRETESYUgIiKACkFERJxUCNLoHThwgOTk5Hq/35SUFNfx2zUpKSlh4cKFwI3fQxQVFd122d69e//gXAkJCZw4cQK48UOkUaNGsX79+krL5OTk0KdPHxISElz/VRy+mZCQwLPPPktCQgIjR45k4MCB7N27t9L6gwcPZtGiRT84qzQtTfp3CCL1oXXr1q5C2L59O/379+fRRx91++PabDbGjh3LgAEDGDlyZJX5AwYMYNq0adWuu3TpUtcp47/88kuSkpJcv88oKCggNDSU/fv3VzntgdzfVAhyz8rLy2PVqlX4+voSEBBAeno6VquVtLQ0Dh8+zNWrV5k0aRLR0dHMnz+f7777jvPnzxMVFVXl/FEVUlJSMAyD06dPc+nSJZYuXYqvry9Tpkxh/vz5/OUvf6GwsJCHH36YvLw8srKyKC8v55e//CWTJk2irKyMqVOncurUKQICAli9ejVXrlxhzpw5nD9/HoC5c+fyyCOPEB0dTXBwMMHBwcyZM6dSjtLSUlJSUoiPj+c3v/nND9pOp06dqnS6g7fffpuYmBjatm3LH//4R0aNGvWD7l+aDhWC3JMMw2DevHlkZWXRpk0b3nzzTV577TW6d+/O+fPn2bZtGyUlJWzatIlHH32Ubt26MWzYMBwOR42FANC+fXuWLl3K3r17eeWVV5g7dy4AXbt2JTIykv79++Pr68uGDRvYsWMHFouFJUuWYLfbuXTpEsnJybRr146EhASOHTvGBx98wOOPP058fDxfffUVs2bNIisri9OnT5OTk0NgYGCVDNOnT6dVq1YUFxffNueuXbs4dOiQ6/bQoUMZMmQIcOPX097e3pw6dYpu3bq5zttvs9koKCggLS2NkJAQJkyYoEIQFxWC3JPOnz+P1Wp1nT7jscceY+XKlQQGBtKtWzfgxq6e5ORkbDYbR44cYf/+/VitVsrKymq874oT6IWHh9/2NABff/01ISEhPPDAAwDMnj0bgAcffNB1io1WrVpx+fJljh8/zv79+/nTn/4E3DhRH0BgYGC1ZQAwdepUnnjiCYYOHUr37t1dpz++2d3sMsrOzmbXrl20bdsWgB07dlBeXs6LL74I3Ph+JD8/n169etW4TeT+oC+V5Z4UGBiIzWbjzJkzAPztb3+jQ4cOBAcHc+TIEeDGbpfExERycnLw9/dnxYoVjBkzhitXrlDTGVsKCwuBG6eNDgkJqTTPZDJhGAZBQUF8+eWXrnJJSkqiuLjYdZrimwUHB/P888+TmZnJqlWrXGe3vfkslrcKCQnBarWydOlSZsyYwblz52qxdf5lxIgRtG3b1nXlr23btrFu3To2btzIxo0bmTt3Lps3b67TfUvToxGC3BPy8vIqnaN+xYoVpKWlMWnSJEwmEw8++CCLFy8mMDCQ/Px84uLiuH79OhMnTuTHP/4xU6ZMoaCggGbNmvHQQw+5iqQ6ubm57N69m/Ly8iqXSPzZz37G8uXLWbVqFWPHjmXUqFGYTCaio6Nve7K/cePGMWfOHLZu3YrNZuOll1666+fdrVs3YmNjmTp1Km+88UalErl1l5HVauW1116rch9z5sxh0KBBREdHYxhGpZKLiYlh8eLFnD592jWKkPuXTm4ncpOUlBT69+9/21MgizRl2mUkIiKARggiIuKkEYKIiAAqBBERcVIhiIgIoEIQEREnFYKIiAAqBBERcfp/4BvZleWR5rEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Wxq5duygpKSE2NpZevXqRnp5OeHg406dP58033yQ1NZVFixbV0dsVEZHqqPLIwWKx0KFDBx588EHWrFlDSkoK27Ztu+kP65CQEFJSUpyPjx8/zvvvv09cXBwLFizAbrdz7NgxOnXqhNVqJTAwkJCQEPLy8sjJyaF3794AREZGkp2dXQdvU0REaqLKIwc/Pz/+67/+i9jYWNq1a8f69esBiIuLq/JJo6Ki+Pbbb52PIyIiGDNmDA899BDr1q1j7dq1PPjggwQGBjrH+Pv7Y7fbsdvtzuX+/v4UFxdX+BoBAX74+Fiq9y5vYLF4ExTUrFbb1peb5XF3Zk+bH3BPJk/cN6rS2PKCMrvLrWaushxWrVrFhg0bsNvttGzZstYvMmDAAOdpqAEDBpCUlETXrl1xOBzOMQ6Hg8DAQAICApzLHQ5Hpaev7PaSWucJCmpGUdGlWm9fH26Wx92ZPW1+wD2ZPHHfqEpjywvK7C6VZW7VKrCC0WZVnlZq0aIF8+bNY8eOHS7LV69eXYOIMHnyZI4dOwZAdnY2HTp0ICIigpycHEpKSiguLiY/P5/w8HA6d+5MZmYmAFlZWXTp0qVGryUiIreuyiOH1157jZ07d5Kfn09WVhYAP/74I1evXmX27NnVfpGlS5eSlJSEr68vwcHBJCUlERAQgM1mIzY2FsMwSEhIwM/Pj5iYGBITE4mJicHX17fGRSQiIreuynIYPnw4PXv2ZMOGDUydOhUAb29v/uVf/uWmT9ymTRsyMjIA6NChg+noAyA6Opro6GiXZU2bNuWVV16p9hsQEZG6V2U5WK1W2rRpw7Jlyzh+/DglJdfO83/77bd069bNLQFFaqvb6qwajT8yO7Kekog0PlWWQ7kZM2Zw7tw5WrduDYCXl5fKQUTkNlatcjh79myFp4VEROT2VK17K7Vt25YzZ87UdxYREfEQ1TpyyMnJoV+/fi7fdfjggw/qLZSIiDSsapXD22+/Xd85RETEg1SrHObPn29atmLFijoPIyIinqFa5TBo0CAADMPgxIkTfP/99/UaSkREGla1yqH8Lqlw7U6p1996W0REbj/VKofrP3wuLCzk7Nmz9RZIREQaXrXK4c0333T+3Wq1kpycXG+BRESk4VWrHFasWMHJkyc5deoUbdu25ac//Wl95xIRkQZUrXJIS0tj3759RERE8Pvf/55f/OIXTJ48ub6ziYhIA6lWOezbt49t27bh4+PDDz/8wNixY1UOIiK3sWrdPsMwDHx8rvWIr68vvr6+9RpKREQaVrWOHLp06cKMGTPo0qULOTk5dOrUqb5ziYhIA7ppObz66qvMmjWLQ4cOcfz4cbp37864cePckU1ERBpIlaeVUlJSOHToEFevXqVv376MGDGCjz76iLVr17orn4iINIAqyyErK4vf/va3NG3aFLj2qz9feuklDh486JZwIiLSMKosh2bNmuHl5eWyzNfXF39//3oNJSIiDavKcmjSpAnffPONy7JvvvnGVBgiInJ7qfID6Tlz5vDrX/+anj17cu+99/Ldd9/xwQcfsHLlSnfl8xg1/WX1IiKNWZVHDmFhYWzfvp327dtz+fJlOnToQHp6Ou3bt3dXPhERaQA3vZQ1MDCQESNGuCGKiIh4imp9Q1pERO4sKgcRETFROYiIiInKQURETFQOIiJionIQERETlYOIiJioHERExKTeyuHo0aPYbDYAvv76a2JiYoiNjWXJkiWUlZUBkJGRwciRI4mOjua9994D4MqVK0yfPp3Y2FimTJnC+fPn6yuiiIhUol7KYdOmTSxatIiSkhIAVqxYwcyZM9m+fTuGYXDgwAEKCwtJS0tjx44dbN68mTVr1lBaWkp6ejrh4eFs376dESNGkJqaWh8RRUSkCvVSDiEhIaSkpDgf5+bm0r17dwAiIyP58MMPOXbsGJ06dcJqtRIYGEhISAh5eXnk5OTQu3dv59js7Oz6iCgiIlWo1u+QrqmoqCi+/fZb52PDMJy3+fb396e4uBi73U5gYKBzjL+/P3a73WV5+diKBAT44eNjqVU+i8WboKBmtdq2vtwsj7sze9r8QP1nCgpq5pH7RlUaW15QZne51cz1Ug438vb+/wMUh8NB8+bNCQgIwOFwuCwPDAx0WV4+tiJ2e0mt8wQFNaOo6FKtt68PN8vj7syeNj9Q/5mKii555L5RlcaWF5TZXSrL3KpVYAWjzdxytVL79u05fPgwcO1Xj3bt2pWIiAhycnIoKSmhuLiY/Px8wsPD6dy5M5mZmc6xXbp0cUdEERG5jluOHBITE1m8eDFr1qwhNDSUqKgoLBYLNpuN2NhYDMMgISEBPz8/YmJiSExMJCYmBl9fX1avXu2OiCIicp16K4c2bdqQkZEBQNu2bdm6datpTHR0NNHR0S7LmjZtyiuvvFJfsUQqVZvf9ndkdmQ9JBFpePoSnIiImKgcRETEROUgIiImKgcRETFROYiIiInKQURETFQOIiJionIQERETlYOIiJioHERExETlICIiJioHERExUTmIiIiJykFERExUDiIiYqJyEBERE5WDiIiYqBxERMRE5SAiIiYqBxERMVE5iIiIicpBRERMVA4iImKichAREROfhg4gcifptjqrRuOPzI6spyQiVdORg4iImKgcRETEROUgIiImKgcRETFROYiIiInKQURETNx6KeuIESMIDAwEoE2bNkydOpV58+bh5eVFWFgYS5Yswdvbm4yMDHbs2IGPjw/x8fH069fPnTFFRO54biuHkpISANLS0pzLpk6dysyZM+nRowfPPvssBw4coGPHjqSlpbFr1y5KSkqIjY2lV69eWK1Wd0UVEbnjua0c8vLyuHz5MpMmTeLq1avMmjWL3NxcunfvDkBkZCSHDh3C29ubTp06YbVasVqthISEkJeXR0REhLuiiojc8dxWDk2aNGHy5MmMGTOGf/zjH0yZMgXDMPDy8gLA39+f4uJi7Ha789RT+XK73e6umCIighvLoW3bttx33314eXnRtm1bgoKCyM3Nda53OBw0b96cgIAAHA6Hy/Lry6JcQIAfPj6WWmWxWLwJCmpWq23ry83yuDuzp80P3JmZPG2/qAvK7B63mtlt5bBz505OnjzJ0qVLOXPmDHa7nV69enH48GF69OhBVlYWDz/8MBEREbz88suUlJRQWlpKfn4+4eHhpuez20tqnSUoqBlFRZdu5e3UuZvlcXdmT5sfuDMzedp+UReU2T0qy9yqlfkf2xVxWzmMHj2a+fPnExMTg5eXF8nJybRo0YLFixezZs0aQkNDiYqKwmKxYLPZiI2NxTAMEhIS8PPzq9MsYYv/XKfPJyJyu3FbOVitVlavXm1avnXrVtOy6OhooqOj3RFLREQqoC/BiYiIicpBRERMVA4iImKichAREROVg4iImKgcRETExK13ZRWRmum2OqtG44/MjqynJHKn0ZGDiIiYqBxERMRE5SAiIiYqBxERMVE5iIiIicpBRERMVA4iImKichAREROVg4iImKgcRETEROUgIiImKgcRETFROYiIiInuyipyB9NdX6UyOnIQERETlYOIiJioHERExETlICIiJioHERExUTmIiIiJykFERExUDiIiYqIvwYlItdX0S3OgL841VjpyEBERE5WDiIiYeORppbKyMpYuXcp///d/Y7VaWb58Offdd19DxxIRN9D9njyDR5bDu+++S2lpKa+++iqffvopzz//POvWrWvoWCLigVQm9cMjTyvl5OTQu3dvADp27Mjx48cbOJGIyJ3FyzAMo6FD3GjhwoU8/vjj9OnTB4C+ffvy7rvv4uPjkQc6IiK3HY88cggICMDhcDgfl5WVqRhERNzII8uhc+fOZGVdO4/46aefEh4e3sCJRETuLB55Wqn8aqWTJ09iGAbJycm0a9euoWOJiNwxPLIc6srNLok9ePAga9euxcfHh1GjRhEdHd2AaeGHH35gwYIFnD59mtLSUuLj43n00Ued6//whz+wc+dOWrZsCcCyZcsIDQ1tqLhOI0aMIDAwEIA2bdqwYsUK5zpPm2OA3bt386c//QmAkpISPv/8cw4dOkTz5s0Bz5vno0ePsmrVKtLS0vj666+ZN28eXl5ehIWFsWTJEry9//8EgKdcBn595s8//5ykpCQsFgtWq5WVK1cSHBzsMr6qfcjdeXNzc5k6dSo/+clPAIiJiWHQoEHOsZ44xwkJCZw9exaA06dP87Of/YyXXnrJZXyN59i4jf3lL38xEhMTDcMwjL///e/G1KlTnetKS0uNxx57zCgqKjJKSkqMkSNHGt9//31DRTUMwzB27txpLF++3DAMwzh//rzRp08fl/WzZ882PvvsswZIVrkrV64Yw4cPr3CdJ87xjZYuXWrs2LHDZZknzfPGjRuNIUOGGGPGjDEMwzCeeuop46OPPjIMwzAWL15svP322y7jq9rn3eXGzHFxccaJEycMwzCM9PR0Izk52WV8VfuQO9yYNyMjw9i8eXOl4z1xjssVFRUZw4YNM86cOeOyvDZz7JGfOdSVqi6Jzc/PJyQkhLvuugur1UqXLl345JNPGioqAAMHDuTpp592PrZYLC7rc3Nz2bhxIzExMWzYsMHd8SqUl5fH5cuXmTRpEuPHj+fTTz91rvPEOb7eZ599xqlTp3jyySddlnvSPIeEhJCSkuJ8nJubS/fu3QGIjIzkww8/dBnvCZeB35h5zZo1/PSnPwXgxx9/xM/Pz2V8VfuQO9yY9/jx47z//vvExcWxYMEC7Ha7y3hPnONyKSkpjBs3jrvvvttleW3m+LYuB7vdTkBAgPOxxWLh6tWrznXlh1gA/v7+pp3A3fz9/QkICMButzNjxgxmzpzpsn7w4MEsXbqUP/7xj+Tk5PDee+81TNDrNGnShMmTJ7N582aWLVvGnDlzPHqOr7dhwwamTZtmWu5J8xwVFeVypZ5hGHh5eQHX5rO4uNhlfFX7vLvcmLn8B9Xf/vY3tm7dyoQJE1zGV7UPNUTeiIgInnnmGbZt28a9997L2rVrXcZ74hwDnDt3juzsbEaOHGkaX5s5vq3LoapLYm9c53A4XH6QNZSCggLGjx/P8OHDGTp0qHO5YRj88pe/pGXLllitVvr06cOJEycaMOk1bdu2ZdiwYXh5edG2bVuCgoIoLCwEPHeOAS5evMiXX37Jww8/7LLcU+e53PWfLzgcDufnJOU89TLw/fv3s2TJEjZu3Oj8LKdcVftQQxgwYAAPPfSQ8+83/vf31Dn+85//zJAhQ0xnHKB2c3xbl0NVl8S2a9eOr7/+mqKiIkpLS/nkk0/o1KlTQ0UF4OzZs0yaNIm5c+cyevRol3V2u50hQ4bgcDgwDIPDhw87d+CGtHPnTp5//nkAzpw5g91up1WrVoBnznG5I0eO8Mgjj5iWe+o8l2vfvj2HDx8GICsri65du7qs98TLwF9//XW2bt1KWloa9957r2l9VftQQ5g8eTLHjh0DIDs7mw4dOris98Q5hmtZIyMrvjVIbea44euuHg0YMIBDhw4xduxY5yWxb7zxBpcuXeLJJ59k3rx5TJ48GcMwGDVqFPfcc0+D5l2/fj0XL14kNTWV1NRUAMaMGcPly5d58sknSUhIYPz48VitVnr27On8BnlDGj16NPPnzycmJgYvLy+Sk5N56623PHaOy3311Ve0adPG+fj6/cIT57lcYmIiixcvZs2aNYSGhhIVFQXAM888w8yZMyvc5xvSjz/+yG9+8xtat27N9OnTAejWrRszZsxwZq5oH2rIf4kvXbqUpKQkfH19CQ4OJikpCfDcOS731Vdfmcr3Vub4tr6UVUREaue2Pq0kIiK1o3IQERETlYOIiJioHERExETlICIiJioHaTTi4uLIzs52WbZ8+XJee+01EhISKC0trXC73bt3c+DAAQC2bt1ardcqLCxk6dKlwLXvROTl5VU6tlevXtV6zqrYbDby8/OBa19uGzduHBs3bnQZs3v3bvr27YvNZnP+Kb/M0mazMXr0aGw2G3FxcQwdOpTMzEyX7YcPH86yZctuOavcIWpz0yeRhrBnzx7nDc8MwzBKSkqM/v37Gw6Ho9rP8cgjj9T4dRMTE43MzMw6fc4bjRs3zjh16pRRXFxsjB071ti6datpzK5du4wXX3yxyu3L5efnG4MHD3Y+/uSTT4w5c+YYAwcONIqLi285r9z+busvwcntZeDAgbz88stcvnyZpk2bcuDAAXr16kWzZs3o378/b731FpmZmWzatAkfHx/+/d//nRdeeIG1a9cSHBxMUVER//znP1m6dKnzqABg3rx5GIZBQUEBly5dYuXKlfj5+TFr1iyeffZZ/vrXv5Kbm8v999/PoUOHSE9Pp6ysjEcffZTp06dTWlrK7Nmz+e677wgKCuKVV17hypUrLFy4kAsXLgCwaNEiHnjgAfr160doaCihoaEsXLjQ5f0VFxczb948YmNjeeKJJ25prr777juXW2u89tprREVF0bp1a/bs2cO4ceNu6fnl9qdykEbDz8+PRx99lHfeeYdhw4axe/du080J9+3bx4QJExg8eDB79uxxudFffHw8W7dudSmGcvfeey8rV64kMzOTF198kUWLFgHw0EMP0bt3bwYNGoSfnx+bNm1i7969WK1Wnn/+eRwOB5cuXSIhIYE2bdpgs9n4/PPP+ctf/sLDDz9MbGws//jHP5g/fz7p6ekUFBSwe/duWrRoYcowd+5cgoODOXPmTKVzsG/fPo4ePep8PGrUKEaMGAFc+/a0j48P3333HR07dnTer99ut5OTk8Py5csJCwvj17/+tcpBbkrlII3KmDFjeOGFF+jRowcXL1403fdm/vz5bNiwgfT0dEJDQ3nssceq9bzlN+Dr1KlTpbdD+OabbwgLC6NJkyYALFiwAIC77rrLeSuO4OBgLl++zMmTJ/noo4946623gGs3+gNo0aJFhcUAMHv2bH7+858zatQoOnfu7Lw19/WGDBnCnDlzKtx+5cqVtGvXjh07drBv3z5at24NwN69eykrK+Opp54Crn2ekp2dTc+ePW8+MXLH0gfS0qg88MADOBwOtmzZwqhRo0zrX331VaZPn+784Pmdd95xWW9UcreY3Nxc4NptpcPCwlzWeXl5YRgGISEhfPnll84PvmfMmMGZM2ect9C+XmhoKBMmTCAtLY2XX37ZeYfd6++qeqOwsDACAgJYuXIlzzzzDOfOnat0bFXGjh1L69atnb8JbOfOnaxfv57NmzezefNmFi1axLZt22r13HLnUDlIozNq1Chee+01Bg8ebFoXERHBxIkTGT9+PIWFhfTt29dlfbt27Sr8l3dWVhbjx4/nd7/7HYmJiS7rfvazn7Fq1SouXLjAlClTGDduHE8++STt27ev9EaCU6dO5a233sJms/GrX/3KVDhV6dixI9HR0cyePZuysjKXdfv27XO5Wik+Pr7C51i4cCFvvvkmH3/8MYZhuLx+VFQUOTk5FBQUVDuT3Hl04z25482bN49BgwZVertjkTuRjhxERMRERw4iImKiIwcRETFROYiIiInKQURETFQOIiJionIQERETlYOIiJj8H8rG7wmE3Il1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Defining numerical features\n",
    "numerical_features = [features for features in dft.columns if dft[features].dtypes != \"O\"]\n",
    "#Defining discrete  features\n",
    "con_features = [feature for feature in numerical_features if feature != \"Season\" and feature != \"Fecha\" and feature != \"Local Win?\"]\n",
    "\n",
    "\n",
    "#Plot features distribution\n",
    "for feature in con_features:\n",
    "    \n",
    "    data = dataset.copy()\n",
    "        \n",
    "    #We will show each feature frequency distribution\n",
    "    plt.style.use('seaborn-dark')\n",
    "    dft[feature].hist(bins=25)\n",
    "    \n",
    "    plt.xlabel(feature)\n",
    "    plt.ylabel(\"Count?\")\n",
    "    plt.title(feature)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7dfcf54",
   "metadata": {},
   "source": [
    "We can observe most of the features follow a normal distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbe80834",
   "metadata": {},
   "source": [
    "# Distribution vs dependent variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "3cb9ff12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Showing boxplots of each feature vs the dependent variable (Local Win)\n",
    "for feature in con_features:\n",
    "    \n",
    "    dft\n",
    "        \n",
    "   \n",
    "\n",
    "\n",
    "    #Plotting, ponle en hue una vaiable para que te ponga varias boxplots en comparacion\n",
    "    a = sns.boxplot(x=\"Local Win?\", y= feature , data= dft)\n",
    "    plt.show()\n",
    "\n",
    "    #mov legend\n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1edec09",
   "metadata": {},
   "source": [
    "This quick boxplot review shows which variables affect the most a game win, being the largest different between 0 and 1 medians the ones that affects the most"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bbef0f9",
   "metadata": {},
   "source": [
    "# Correlation Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "f2d9a5cd",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Local Win?               1.000000\n",
      "Visit Score              0.573974\n",
      "Local Score              0.533262\n",
      "Local pitcher ERA        0.448253\n",
      "Visit Hits               0.447803\n",
      "Visit pitcher ERA        0.447646\n",
      "L bullpen recieved       0.435192\n",
      "Visit i5                 0.422709\n",
      "Local i5                 0.419665\n",
      "Local Hits               0.368031\n",
      "V bullpen recieved       0.365516\n",
      "Visit pitcher in         0.283692\n",
      "Local pitcher in         0.270676\n",
      "Visit pitcher Hit ERA    0.250301\n",
      "Local pitcher Hit ERA    0.240719\n",
      "Visit pitcher K ERA      0.191727\n",
      "Local pitcher K ERA      0.185379\n",
      "Visit pitcher BB ERA     0.098122\n",
      "Local pitcher BB ERA     0.095752\n",
      "Season                   0.004471\n",
      "Name: Local Win?, dtype: float64\n",
      "Correlation Matrix Heatmap\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation Matrix method\n"
     ]
    }
   ],
   "source": [
    "#Defining correlation function \n",
    "def cor(x_train,val):\n",
    "    \n",
    "    #Creating correlation matrix\n",
    "    corr_matrix = x_train.corr()\n",
    "    \n",
    "    sort = ((corr_matrix[\"Local Win?\"].sort_values(ascending=False)))\n",
    "    sort = abs(sort)\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    #Sorting the list\n",
    "    sort = sort.sort_values(ascending=False)\n",
    "    sort\n",
    "    #Priinting entire list\n",
    "    print(sort)\n",
    "\n",
    "    sort= sort.iloc[:].index.values\n",
    "    selected = list(sort)\n",
    "    \n",
    "    \n",
    "    \n",
    "    #Printing correlation matrix heatmap\n",
    "    \n",
    "    # import modules\n",
    "\n",
    "    sns.set_style(\"whitegrid\")\n",
    "    #Selecting top variables in a list\n",
    "    selected = selected[:val]\n",
    "    #Selecting top variables in original correlation matrix\n",
    "    cor_matrix_sel = corr_matrix.loc[selected,selected]\n",
    "    \n",
    "   \n",
    "    \n",
    "\n",
    "    # plotting correlation heatmap for top 10 features\n",
    "    print(\"Correlation Matrix Heatmap\")\n",
    "    dataplot = sns.heatmap(cor_matrix_sel, cmap=\"viridis\", annot=False)\n",
    "\n",
    "    # displaying heatmap\n",
    "    plt.show()\n",
    "    return selected\n",
    "\n",
    "cor_list =cor(dft,10)\n",
    "print(\"Correlation Matrix method\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cfa12ac",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "999e3578",
   "metadata": {},
   "source": [
    "The principal features that correlate with a team local win are the visit and local score, this features are related to the offensive power of teams.\n",
    "Opener pitchers perfomance as well as bullpen performance are also important.\n",
    "\n",
    "Generating some kind of data from previous games that describe possible offensive power as well as pitcher perfomance will be ideal for Local Win predictor.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c4b0d764",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
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