DSE_19141_Hritik Bana_Project_Moneyball- Uncovering the Process.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DSE 309 Advanced Programming in Python: Final Project\n",
    "# Moneyball : Uncovering the Process\n",
    "## Name : Hritik Bana\n",
    "## Roll No. : 19141\n",
    "## Department : DSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing the required libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reading the MLB data\n",
    "df = pd.read_csv('baseball.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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>Team</th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ARI</td>\n",
       "      <td>NL</td>\n",
       "      <td>2012</td>\n",
       "      <td>734</td>\n",
       "      <td>688</td>\n",
       "      <td>81</td>\n",
       "      <td>0.328</td>\n",
       "      <td>0.418</td>\n",
       "      <td>0.259</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.317</td>\n",
       "      <td>0.415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ATL</td>\n",
       "      <td>NL</td>\n",
       "      <td>2012</td>\n",
       "      <td>700</td>\n",
       "      <td>600</td>\n",
       "      <td>94</td>\n",
       "      <td>0.320</td>\n",
       "      <td>0.389</td>\n",
       "      <td>0.247</td>\n",
       "      <td>1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.306</td>\n",
       "      <td>0.378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BAL</td>\n",
       "      <td>AL</td>\n",
       "      <td>2012</td>\n",
       "      <td>712</td>\n",
       "      <td>705</td>\n",
       "      <td>93</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.417</td>\n",
       "      <td>0.247</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.315</td>\n",
       "      <td>0.403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BOS</td>\n",
       "      <td>AL</td>\n",
       "      <td>2012</td>\n",
       "      <td>734</td>\n",
       "      <td>806</td>\n",
       "      <td>69</td>\n",
       "      <td>0.315</td>\n",
       "      <td>0.415</td>\n",
       "      <td>0.260</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.331</td>\n",
       "      <td>0.428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>CHC</td>\n",
       "      <td>NL</td>\n",
       "      <td>2012</td>\n",
       "      <td>613</td>\n",
       "      <td>759</td>\n",
       "      <td>61</td>\n",
       "      <td>0.302</td>\n",
       "      <td>0.378</td>\n",
       "      <td>0.240</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.424</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Team League  Year   RS   RA   W    OBP    SLG     BA  Playoffs  RankSeason  \\\n",
       "0  ARI     NL  2012  734  688  81  0.328  0.418  0.259         0         NaN   \n",
       "1  ATL     NL  2012  700  600  94  0.320  0.389  0.247         1         4.0   \n",
       "2  BAL     AL  2012  712  705  93  0.311  0.417  0.247         1         5.0   \n",
       "3  BOS     AL  2012  734  806  69  0.315  0.415  0.260         0         NaN   \n",
       "4  CHC     NL  2012  613  759  61  0.302  0.378  0.240         0         NaN   \n",
       "\n",
       "   RankPlayoffs    G   OOBP   OSLG  \n",
       "0           NaN  162  0.317  0.415  \n",
       "1           5.0  162  0.306  0.378  \n",
       "2           4.0  162  0.315  0.403  \n",
       "3           NaN  162  0.331  0.428  \n",
       "4           NaN  162  0.335  0.424  "
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1232, 15)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
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       "      <th>RankPlayoffs</th>\n",
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       "      <th>count</th>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>244.000000</td>\n",
       "      <td>244.000000</td>\n",
       "      <td>1232.000000</td>\n",
       "      <td>420.000000</td>\n",
       "      <td>420.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1988.957792</td>\n",
       "      <td>715.081981</td>\n",
       "      <td>715.081981</td>\n",
       "      <td>80.904221</td>\n",
       "      <td>0.326331</td>\n",
       "      <td>0.397342</td>\n",
       "      <td>0.259273</td>\n",
       "      <td>0.198052</td>\n",
       "      <td>3.122951</td>\n",
       "      <td>2.717213</td>\n",
       "      <td>161.918831</td>\n",
       "      <td>0.332264</td>\n",
       "      <td>0.419743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>14.819625</td>\n",
       "      <td>91.534294</td>\n",
       "      <td>93.079933</td>\n",
       "      <td>11.458139</td>\n",
       "      <td>0.015013</td>\n",
       "      <td>0.033267</td>\n",
       "      <td>0.012907</td>\n",
       "      <td>0.398693</td>\n",
       "      <td>1.738349</td>\n",
       "      <td>1.095234</td>\n",
       "      <td>0.624365</td>\n",
       "      <td>0.015295</td>\n",
       "      <td>0.026510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1962.000000</td>\n",
       "      <td>463.000000</td>\n",
       "      <td>472.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>0.277000</td>\n",
       "      <td>0.301000</td>\n",
       "      <td>0.214000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>158.000000</td>\n",
       "      <td>0.294000</td>\n",
       "      <td>0.346000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1976.750000</td>\n",
       "      <td>652.000000</td>\n",
       "      <td>649.750000</td>\n",
       "      <td>73.000000</td>\n",
       "      <td>0.317000</td>\n",
       "      <td>0.375000</td>\n",
       "      <td>0.251000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>162.000000</td>\n",
       "      <td>0.321000</td>\n",
       "      <td>0.401000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1989.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>709.000000</td>\n",
       "      <td>81.000000</td>\n",
       "      <td>0.326000</td>\n",
       "      <td>0.396000</td>\n",
       "      <td>0.260000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>162.000000</td>\n",
       "      <td>0.331000</td>\n",
       "      <td>0.419000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2002.000000</td>\n",
       "      <td>775.000000</td>\n",
       "      <td>774.250000</td>\n",
       "      <td>89.000000</td>\n",
       "      <td>0.337000</td>\n",
       "      <td>0.421000</td>\n",
       "      <td>0.268000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>162.000000</td>\n",
       "      <td>0.343000</td>\n",
       "      <td>0.438000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2012.000000</td>\n",
       "      <td>1009.000000</td>\n",
       "      <td>1103.000000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>0.373000</td>\n",
       "      <td>0.491000</td>\n",
       "      <td>0.294000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>165.000000</td>\n",
       "      <td>0.384000</td>\n",
       "      <td>0.499000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "              Year           RS           RA            W          OBP  \\\n",
       "count  1232.000000  1232.000000  1232.000000  1232.000000  1232.000000   \n",
       "mean   1988.957792   715.081981   715.081981    80.904221     0.326331   \n",
       "std      14.819625    91.534294    93.079933    11.458139     0.015013   \n",
       "min    1962.000000   463.000000   472.000000    40.000000     0.277000   \n",
       "25%    1976.750000   652.000000   649.750000    73.000000     0.317000   \n",
       "50%    1989.000000   711.000000   709.000000    81.000000     0.326000   \n",
       "75%    2002.000000   775.000000   774.250000    89.000000     0.337000   \n",
       "max    2012.000000  1009.000000  1103.000000   116.000000     0.373000   \n",
       "\n",
       "               SLG           BA     Playoffs  RankSeason  RankPlayoffs  \\\n",
       "count  1232.000000  1232.000000  1232.000000  244.000000    244.000000   \n",
       "mean      0.397342     0.259273     0.198052    3.122951      2.717213   \n",
       "std       0.033267     0.012907     0.398693    1.738349      1.095234   \n",
       "min       0.301000     0.214000     0.000000    1.000000      1.000000   \n",
       "25%       0.375000     0.251000     0.000000    2.000000      2.000000   \n",
       "50%       0.396000     0.260000     0.000000    3.000000      3.000000   \n",
       "75%       0.421000     0.268000     0.000000    4.000000      4.000000   \n",
       "max       0.491000     0.294000     1.000000    8.000000      5.000000   \n",
       "\n",
       "                 G        OOBP        OSLG  \n",
       "count  1232.000000  420.000000  420.000000  \n",
       "mean    161.918831    0.332264    0.419743  \n",
       "std       0.624365    0.015295    0.026510  \n",
       "min     158.000000    0.294000    0.346000  \n",
       "25%     162.000000    0.321000    0.401000  \n",
       "50%     162.000000    0.331000    0.419000  \n",
       "75%     162.000000    0.343000    0.438000  \n",
       "max     165.000000    0.384000    0.499000  "
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1232 entries, 0 to 1231\n",
      "Data columns (total 15 columns):\n",
      " #   Column        Non-Null Count  Dtype  \n",
      "---  ------        --------------  -----  \n",
      " 0   Team          1232 non-null   object \n",
      " 1   League        1232 non-null   object \n",
      " 2   Year          1232 non-null   int64  \n",
      " 3   RS            1232 non-null   int64  \n",
      " 4   RA            1232 non-null   int64  \n",
      " 5   W             1232 non-null   int64  \n",
      " 6   OBP           1232 non-null   float64\n",
      " 7   SLG           1232 non-null   float64\n",
      " 8   BA            1232 non-null   float64\n",
      " 9   Playoffs      1232 non-null   int64  \n",
      " 10  RankSeason    244 non-null    float64\n",
      " 11  RankPlayoffs  244 non-null    float64\n",
      " 12  G             1232 non-null   int64  \n",
      " 13  OOBP          420 non-null    float64\n",
      " 14  OSLG          420 non-null    float64\n",
      "dtypes: float64(7), int64(6), object(2)\n",
      "memory usage: 144.5+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are some null values in OOBP and OSLG, which we may have to take care of later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2012, 2012, 2012, ..., 1962, 1962, 1962], dtype=int64)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.Year.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this dataset contains data till 2012 but the moneyball analysis that was performed by Billy Beane and Paul DePodesta of the Oakland A's for the first time was before the 2002 season. So we will keep the data till 2001 only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "full_df = df  # saving the original data for all the seasons in 'full df'. We will need it for verification later\n",
    "df = df[df['Year'] <= 2001]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(902, 15)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>OSLG</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>ANA</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>691</td>\n",
       "      <td>730</td>\n",
       "      <td>75</td>\n",
       "      <td>0.327</td>\n",
       "      <td>0.405</td>\n",
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       "      <td>0.412</td>\n",
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       "      <td>ARI</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
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       "      <td>677</td>\n",
       "      <td>92</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.442</td>\n",
       "      <td>0.267</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>332</th>\n",
       "      <td>ATL</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>729</td>\n",
       "      <td>643</td>\n",
       "      <td>88</td>\n",
       "      <td>0.324</td>\n",
       "      <td>0.412</td>\n",
       "      <td>0.260</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>333</th>\n",
       "      <td>BAL</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>687</td>\n",
       "      <td>829</td>\n",
       "      <td>63</td>\n",
       "      <td>0.319</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.248</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.337</td>\n",
       "      <td>0.439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>334</th>\n",
       "      <td>BOS</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>772</td>\n",
       "      <td>745</td>\n",
       "      <td>82</td>\n",
       "      <td>0.334</td>\n",
       "      <td>0.439</td>\n",
       "      <td>0.266</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.393</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Team League  Year   RS   RA   W    OBP    SLG     BA  Playoffs  \\\n",
       "330  ANA     AL  2001  691  730  75  0.327  0.405  0.261         0   \n",
       "331  ARI     NL  2001  818  677  92  0.341  0.442  0.267         1   \n",
       "332  ATL     NL  2001  729  643  88  0.324  0.412  0.260         1   \n",
       "333  BAL     AL  2001  687  829  63  0.319  0.380  0.248         0   \n",
       "334  BOS     AL  2001  772  745  82  0.334  0.439  0.266         0   \n",
       "\n",
       "     RankSeason  RankPlayoffs    G   OOBP   OSLG  \n",
       "330         NaN           NaN  162  0.331  0.412  \n",
       "331         5.0           1.0  162  0.311  0.404  \n",
       "332         7.0           3.0  162  0.314  0.384  \n",
       "333         NaN           NaN  162  0.337  0.439  \n",
       "334         NaN           NaN  161  0.329  0.393  "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Team</th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1227</th>\n",
       "      <td>PHI</td>\n",
       "      <td>NL</td>\n",
       "      <td>1962</td>\n",
       "      <td>705</td>\n",
       "      <td>759</td>\n",
       "      <td>81</td>\n",
       "      <td>0.330</td>\n",
       "      <td>0.390</td>\n",
       "      <td>0.260</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1228</th>\n",
       "      <td>PIT</td>\n",
       "      <td>NL</td>\n",
       "      <td>1962</td>\n",
       "      <td>706</td>\n",
       "      <td>626</td>\n",
       "      <td>93</td>\n",
       "      <td>0.321</td>\n",
       "      <td>0.394</td>\n",
       "      <td>0.268</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1229</th>\n",
       "      <td>SFG</td>\n",
       "      <td>NL</td>\n",
       "      <td>1962</td>\n",
       "      <td>878</td>\n",
       "      <td>690</td>\n",
       "      <td>103</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.441</td>\n",
       "      <td>0.278</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>165</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1230</th>\n",
       "      <td>STL</td>\n",
       "      <td>NL</td>\n",
       "      <td>1962</td>\n",
       "      <td>774</td>\n",
       "      <td>664</td>\n",
       "      <td>84</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.394</td>\n",
       "      <td>0.271</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>163</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1231</th>\n",
       "      <td>WSA</td>\n",
       "      <td>AL</td>\n",
       "      <td>1962</td>\n",
       "      <td>599</td>\n",
       "      <td>716</td>\n",
       "      <td>60</td>\n",
       "      <td>0.308</td>\n",
       "      <td>0.373</td>\n",
       "      <td>0.250</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Team League  Year   RS   RA    W    OBP    SLG     BA  Playoffs  \\\n",
       "1227  PHI     NL  1962  705  759   81  0.330  0.390  0.260         0   \n",
       "1228  PIT     NL  1962  706  626   93  0.321  0.394  0.268         0   \n",
       "1229  SFG     NL  1962  878  690  103  0.341  0.441  0.278         1   \n",
       "1230  STL     NL  1962  774  664   84  0.335  0.394  0.271         0   \n",
       "1231  WSA     AL  1962  599  716   60  0.308  0.373  0.250         0   \n",
       "\n",
       "      RankSeason  RankPlayoffs    G  OOBP  OSLG  \n",
       "1227         NaN           NaN  161   NaN   NaN  \n",
       "1228         NaN           NaN  161   NaN   NaN  \n",
       "1229         1.0           2.0  165   NaN   NaN  \n",
       "1230         NaN           NaN  163   NaN   NaN  \n",
       "1231         NaN           NaN  162   NaN   NaN  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reset the index to start it from 0\n",
    "df = df.reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>Team</th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>330</td>\n",
       "      <td>ANA</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>691</td>\n",
       "      <td>730</td>\n",
       "      <td>75</td>\n",
       "      <td>0.327</td>\n",
       "      <td>0.405</td>\n",
       "      <td>0.261</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.331</td>\n",
       "      <td>0.412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>331</td>\n",
       "      <td>ARI</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>818</td>\n",
       "      <td>677</td>\n",
       "      <td>92</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.442</td>\n",
       "      <td>0.267</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>332</td>\n",
       "      <td>ATL</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>729</td>\n",
       "      <td>643</td>\n",
       "      <td>88</td>\n",
       "      <td>0.324</td>\n",
       "      <td>0.412</td>\n",
       "      <td>0.260</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>333</td>\n",
       "      <td>BAL</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>687</td>\n",
       "      <td>829</td>\n",
       "      <td>63</td>\n",
       "      <td>0.319</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.248</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.337</td>\n",
       "      <td>0.439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>334</td>\n",
       "      <td>BOS</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>772</td>\n",
       "      <td>745</td>\n",
       "      <td>82</td>\n",
       "      <td>0.334</td>\n",
       "      <td>0.439</td>\n",
       "      <td>0.266</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.393</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index Team League  Year   RS   RA   W    OBP    SLG     BA  Playoffs  \\\n",
       "0    330  ANA     AL  2001  691  730  75  0.327  0.405  0.261         0   \n",
       "1    331  ARI     NL  2001  818  677  92  0.341  0.442  0.267         1   \n",
       "2    332  ATL     NL  2001  729  643  88  0.324  0.412  0.260         1   \n",
       "3    333  BAL     AL  2001  687  829  63  0.319  0.380  0.248         0   \n",
       "4    334  BOS     AL  2001  772  745  82  0.334  0.439  0.266         0   \n",
       "\n",
       "   RankSeason  RankPlayoffs    G   OOBP   OSLG  \n",
       "0         NaN           NaN  162  0.331  0.412  \n",
       "1         5.0           1.0  162  0.311  0.404  \n",
       "2         7.0           3.0  162  0.314  0.384  \n",
       "3         NaN           NaN  162  0.337  0.439  \n",
       "4         NaN           NaN  161  0.329  0.393  "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step for the Oakland A's for deciding their strategy was to decide, what target is it they want to achieve, and how can their new techniques of Data Science and ML can help them do it ? \n",
    "Data Science and ML requires large amount of data for accurate predictions, for instance, it can't say if the result of a coin toss will be a head or a tail, but it can say that for a large number of tosses, the number of heads and tails would be nearly equal. Similarly, the ultimate prize of a league or competition is for the winner, but in order to win, a team has to perform well in the playoffs, in which there are typically very small number of matches for each team. But if we look at the league stage of a regular season, there are 162 games, and the target for all the teams is to win more games and qualify for the playoffs, and it provides a comparatively better sample for answering some questions related to that, for example, how many games are needed to qualify for the playoffs, let's see if the past data could help. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use scatter plot of teams with their matches won, with different color codes for depicting the teams which have qualified and the teams that did not. Since this is a panel data, so there will be multiple points for each team corresponding to different seasons. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating a series containing color codes corresponding to each entry of the dataframe\n",
    "color = df['Playoffs'].apply(lambda x: 'green' if x == 0 else 'coral')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (12, 8))\n",
    "plt.scatter(df[df['Playoffs'] == 0]['W'], df[df['Playoffs'] == 0]['Team'], c = 'green', label = 'not qualified')\n",
    "plt.scatter(df[df['Playoffs'] == 1]['W'], df[df['Playoffs'] == 1]['Team'], c = 'coral', label = 'qualified')\n",
    "plt.xlabel('Matches won')\n",
    "plt.ylabel('Teams')\n",
    "plt.legend()\n",
    "plt.savefig('Win for qualification.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this table we try to predict on average how many league games are needed to be won to qualify for playoffs with a probability of 90% or above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For qualifying with probability 90%, wins needed are: 90.0\n",
      "For qualifying with probability 91%, wins needed are: 90.0\n",
      "For qualifying with probability 92%, wins needed are: 90.0\n",
      "For qualifying with probability 93%, wins needed are: 91.0\n",
      "For qualifying with probability 94%, wins needed are: 91.0\n",
      "For qualifying with probability 95%, wins needed are: 92.0\n",
      "For qualifying with probability 96%, wins needed are: 93.0\n",
      "For qualifying with probability 97%, wins needed are: 94.0\n",
      "For qualifying with probability 98%, wins needed are: 95.05999999999995\n",
      "For qualifying with probability 99%, wins needed are: 97.52999999999997\n",
      "For qualifying with probability 100%, wins needed are: 103.0\n"
     ]
    }
   ],
   "source": [
    "for i in range(90, 101):\n",
    "    print(f'For qualifying with probability {i}%, wins needed are:', df[df['Playoffs'] == 0].W.quantile(i/100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oakland A's sabermatrician Paul Depodesta predicted that if a team won at least 95 league games then it has very high chances of qualifying. From the above table we can see that he must have concluded this by also considering that there is still a 2% chance for a team to win at least 95 games and still not qualify, but that is significantly less. Therefore this target of winning at least 95 games was indeed a very rational one. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the target was set, win atleast 95 games. Baseball has many analogies to cricket. One of them is that, in a match, the team which scores more runs, wins. In short, the run difference (runs scored - runs conceded) for the winning team is larger. Can we use this fact to somehow model this situation for the run difference for each team in the entire tournament and see if this run difference has any effect on the number of games won?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adding a column containing run difference\n",
    "df['RD'] = df['RS'] - df['RA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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>index</th>\n",
       "      <th>Team</th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "      <th>RD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>330</td>\n",
       "      <td>ANA</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>691</td>\n",
       "      <td>730</td>\n",
       "      <td>75</td>\n",
       "      <td>0.327</td>\n",
       "      <td>0.405</td>\n",
       "      <td>0.261</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.331</td>\n",
       "      <td>0.412</td>\n",
       "      <td>-39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>331</td>\n",
       "      <td>ARI</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>818</td>\n",
       "      <td>677</td>\n",
       "      <td>92</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.442</td>\n",
       "      <td>0.267</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.404</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>332</td>\n",
       "      <td>ATL</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>729</td>\n",
       "      <td>643</td>\n",
       "      <td>88</td>\n",
       "      <td>0.324</td>\n",
       "      <td>0.412</td>\n",
       "      <td>0.260</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.384</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>333</td>\n",
       "      <td>BAL</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>687</td>\n",
       "      <td>829</td>\n",
       "      <td>63</td>\n",
       "      <td>0.319</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.248</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.337</td>\n",
       "      <td>0.439</td>\n",
       "      <td>-142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>334</td>\n",
       "      <td>BOS</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>772</td>\n",
       "      <td>745</td>\n",
       "      <td>82</td>\n",
       "      <td>0.334</td>\n",
       "      <td>0.439</td>\n",
       "      <td>0.266</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.393</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index Team League  Year   RS   RA   W    OBP    SLG     BA  Playoffs  \\\n",
       "0    330  ANA     AL  2001  691  730  75  0.327  0.405  0.261         0   \n",
       "1    331  ARI     NL  2001  818  677  92  0.341  0.442  0.267         1   \n",
       "2    332  ATL     NL  2001  729  643  88  0.324  0.412  0.260         1   \n",
       "3    333  BAL     AL  2001  687  829  63  0.319  0.380  0.248         0   \n",
       "4    334  BOS     AL  2001  772  745  82  0.334  0.439  0.266         0   \n",
       "\n",
       "   RankSeason  RankPlayoffs    G   OOBP   OSLG   RD  \n",
       "0         NaN           NaN  162  0.331  0.412  -39  \n",
       "1         5.0           1.0  162  0.311  0.404  141  \n",
       "2         7.0           3.0  162  0.314  0.384   86  \n",
       "3         NaN           NaN  162  0.337  0.439 -142  \n",
       "4         NaN           NaN  161  0.329  0.393   27  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "      <th>RD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>index</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-9.986709e-01</td>\n",
       "      <td>-0.484551</td>\n",
       "      <td>-0.480807</td>\n",
       "      <td>-0.004241</td>\n",
       "      <td>-0.470721</td>\n",
       "      <td>-0.518911</td>\n",
       "      <td>-0.433440</td>\n",
       "      <td>-0.111469</td>\n",
       "      <td>-0.405830</td>\n",
       "      <td>-0.422142</td>\n",
       "      <td>0.025756</td>\n",
       "      <td>0.385843</td>\n",
       "      <td>0.168670</td>\n",
       "      <td>-1.220787e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</th>\n",
       "      <td>-0.998671</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>0.485502</td>\n",
       "      <td>0.483072</td>\n",
       "      <td>0.002756</td>\n",
       "      <td>0.474799</td>\n",
       "      <td>0.517828</td>\n",
       "      <td>0.438729</td>\n",
       "      <td>0.113014</td>\n",
       "      <td>0.415645</td>\n",
       "      <td>0.426403</td>\n",
       "      <td>-0.027085</td>\n",
       "      <td>-0.335533</td>\n",
       "      <td>-0.122668</td>\n",
       "      <td>-4.316055e-19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RS</th>\n",
       "      <td>-0.484551</td>\n",
       "      <td>4.855023e-01</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.415014</td>\n",
       "      <td>0.507382</td>\n",
       "      <td>0.904909</td>\n",
       "      <td>0.926384</td>\n",
       "      <td>0.831625</td>\n",
       "      <td>0.371631</td>\n",
       "      <td>0.135743</td>\n",
       "      <td>0.323624</td>\n",
       "      <td>0.056206</td>\n",
       "      <td>0.091057</td>\n",
       "      <td>0.039787</td>\n",
       "      <td>5.375395e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RA</th>\n",
       "      <td>-0.480807</td>\n",
       "      <td>4.830717e-01</td>\n",
       "      <td>0.415014</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.507772</td>\n",
       "      <td>0.367105</td>\n",
       "      <td>0.459514</td>\n",
       "      <td>0.350411</td>\n",
       "      <td>-0.241213</td>\n",
       "      <td>0.539387</td>\n",
       "      <td>0.382416</td>\n",
       "      <td>-0.037402</td>\n",
       "      <td>0.909908</td>\n",
       "      <td>0.895110</td>\n",
       "      <td>-5.441052e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>W</th>\n",
       "      <td>-0.004241</td>\n",
       "      <td>2.755645e-03</td>\n",
       "      <td>0.507382</td>\n",
       "      <td>-0.507772</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.474080</td>\n",
       "      <td>0.405972</td>\n",
       "      <td>0.416391</td>\n",
       "      <td>0.588978</td>\n",
       "      <td>-0.747960</td>\n",
       "      <td>-0.235038</td>\n",
       "      <td>0.108128</td>\n",
       "      <td>-0.633657</td>\n",
       "      <td>-0.646920</td>\n",
       "      <td>9.385150e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OBP</th>\n",
       "      <td>-0.470721</td>\n",
       "      <td>4.747989e-01</td>\n",
       "      <td>0.904909</td>\n",
       "      <td>0.367105</td>\n",
       "      <td>0.474080</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.806154</td>\n",
       "      <td>0.854055</td>\n",
       "      <td>0.345530</td>\n",
       "      <td>0.146153</td>\n",
       "      <td>0.300446</td>\n",
       "      <td>-0.003827</td>\n",
       "      <td>0.052899</td>\n",
       "      <td>-0.008316</td>\n",
       "      <td>4.942505e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SLG</th>\n",
       "      <td>-0.518911</td>\n",
       "      <td>5.178276e-01</td>\n",
       "      <td>0.926384</td>\n",
       "      <td>0.459514</td>\n",
       "      <td>0.405972</td>\n",
       "      <td>0.806154</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.814068</td>\n",
       "      <td>0.300191</td>\n",
       "      <td>0.217315</td>\n",
       "      <td>0.341013</td>\n",
       "      <td>0.012873</td>\n",
       "      <td>0.101632</td>\n",
       "      <td>0.080376</td>\n",
       "      <td>4.284077e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>-0.433440</td>\n",
       "      <td>4.387291e-01</td>\n",
       "      <td>0.831625</td>\n",
       "      <td>0.350411</td>\n",
       "      <td>0.416391</td>\n",
       "      <td>0.854055</td>\n",
       "      <td>0.814068</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.278772</td>\n",
       "      <td>0.156881</td>\n",
       "      <td>0.229791</td>\n",
       "      <td>-0.001805</td>\n",
       "      <td>0.219021</td>\n",
       "      <td>0.231918</td>\n",
       "      <td>4.421417e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Playoffs</th>\n",
       "      <td>-0.111469</td>\n",
       "      <td>1.130136e-01</td>\n",
       "      <td>0.371631</td>\n",
       "      <td>-0.241213</td>\n",
       "      <td>0.588978</td>\n",
       "      <td>0.345530</td>\n",
       "      <td>0.300191</td>\n",
       "      <td>0.278772</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.009831</td>\n",
       "      <td>-0.495725</td>\n",
       "      <td>-0.510097</td>\n",
       "      <td>5.662745e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RankSeason</th>\n",
       "      <td>-0.405830</td>\n",
       "      <td>4.156449e-01</td>\n",
       "      <td>0.135743</td>\n",
       "      <td>0.539387</td>\n",
       "      <td>-0.747960</td>\n",
       "      <td>0.146153</td>\n",
       "      <td>0.217315</td>\n",
       "      <td>0.156881</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.352961</td>\n",
       "      <td>0.052870</td>\n",
       "      <td>0.141905</td>\n",
       "      <td>0.235886</td>\n",
       "      <td>-5.703690e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <td>-0.422142</td>\n",
       "      <td>4.264030e-01</td>\n",
       "      <td>0.323624</td>\n",
       "      <td>0.382416</td>\n",
       "      <td>-0.235038</td>\n",
       "      <td>0.300446</td>\n",
       "      <td>0.341013</td>\n",
       "      <td>0.229791</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.352961</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.012394</td>\n",
       "      <td>0.299376</td>\n",
       "      <td>0.318576</td>\n",
       "      <td>-7.677988e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.025756</td>\n",
       "      <td>-2.708490e-02</td>\n",
       "      <td>0.056206</td>\n",
       "      <td>-0.037402</td>\n",
       "      <td>0.108128</td>\n",
       "      <td>-0.003827</td>\n",
       "      <td>0.012873</td>\n",
       "      <td>-0.001805</td>\n",
       "      <td>0.009831</td>\n",
       "      <td>0.052870</td>\n",
       "      <td>0.012394</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.100545</td>\n",
       "      <td>-0.045432</td>\n",
       "      <td>8.649718e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OOBP</th>\n",
       "      <td>0.385843</td>\n",
       "      <td>-3.355334e-01</td>\n",
       "      <td>0.091057</td>\n",
       "      <td>0.909908</td>\n",
       "      <td>-0.633657</td>\n",
       "      <td>0.052899</td>\n",
       "      <td>0.101632</td>\n",
       "      <td>0.219021</td>\n",
       "      <td>-0.495725</td>\n",
       "      <td>0.141905</td>\n",
       "      <td>0.299376</td>\n",
       "      <td>-0.100545</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.796526</td>\n",
       "      <td>-6.040766e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OSLG</th>\n",
       "      <td>0.168670</td>\n",
       "      <td>-1.226680e-01</td>\n",
       "      <td>0.039787</td>\n",
       "      <td>0.895110</td>\n",
       "      <td>-0.646920</td>\n",
       "      <td>-0.008316</td>\n",
       "      <td>0.080376</td>\n",
       "      <td>0.231918</td>\n",
       "      <td>-0.510097</td>\n",
       "      <td>0.235886</td>\n",
       "      <td>0.318576</td>\n",
       "      <td>-0.045432</td>\n",
       "      <td>0.796526</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-6.302315e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RD</th>\n",
       "      <td>-0.001221</td>\n",
       "      <td>-4.316055e-19</td>\n",
       "      <td>0.537539</td>\n",
       "      <td>-0.544105</td>\n",
       "      <td>0.938515</td>\n",
       "      <td>0.494251</td>\n",
       "      <td>0.428408</td>\n",
       "      <td>0.442142</td>\n",
       "      <td>0.566274</td>\n",
       "      <td>-0.570369</td>\n",
       "      <td>-0.076780</td>\n",
       "      <td>0.086497</td>\n",
       "      <td>-0.604077</td>\n",
       "      <td>-0.630231</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 index          Year        RS        RA         W       OBP  \\\n",
       "index         1.000000 -9.986709e-01 -0.484551 -0.480807 -0.004241 -0.470721   \n",
       "Year         -0.998671  1.000000e+00  0.485502  0.483072  0.002756  0.474799   \n",
       "RS           -0.484551  4.855023e-01  1.000000  0.415014  0.507382  0.904909   \n",
       "RA           -0.480807  4.830717e-01  0.415014  1.000000 -0.507772  0.367105   \n",
       "W            -0.004241  2.755645e-03  0.507382 -0.507772  1.000000  0.474080   \n",
       "OBP          -0.470721  4.747989e-01  0.904909  0.367105  0.474080  1.000000   \n",
       "SLG          -0.518911  5.178276e-01  0.926384  0.459514  0.405972  0.806154   \n",
       "BA           -0.433440  4.387291e-01  0.831625  0.350411  0.416391  0.854055   \n",
       "Playoffs     -0.111469  1.130136e-01  0.371631 -0.241213  0.588978  0.345530   \n",
       "RankSeason   -0.405830  4.156449e-01  0.135743  0.539387 -0.747960  0.146153   \n",
       "RankPlayoffs -0.422142  4.264030e-01  0.323624  0.382416 -0.235038  0.300446   \n",
       "G             0.025756 -2.708490e-02  0.056206 -0.037402  0.108128 -0.003827   \n",
       "OOBP          0.385843 -3.355334e-01  0.091057  0.909908 -0.633657  0.052899   \n",
       "OSLG          0.168670 -1.226680e-01  0.039787  0.895110 -0.646920 -0.008316   \n",
       "RD           -0.001221 -4.316055e-19  0.537539 -0.544105  0.938515  0.494251   \n",
       "\n",
       "                   SLG        BA  Playoffs  RankSeason  RankPlayoffs  \\\n",
       "index        -0.518911 -0.433440 -0.111469   -0.405830     -0.422142   \n",
       "Year          0.517828  0.438729  0.113014    0.415645      0.426403   \n",
       "RS            0.926384  0.831625  0.371631    0.135743      0.323624   \n",
       "RA            0.459514  0.350411 -0.241213    0.539387      0.382416   \n",
       "W             0.405972  0.416391  0.588978   -0.747960     -0.235038   \n",
       "OBP           0.806154  0.854055  0.345530    0.146153      0.300446   \n",
       "SLG           1.000000  0.814068  0.300191    0.217315      0.341013   \n",
       "BA            0.814068  1.000000  0.278772    0.156881      0.229791   \n",
       "Playoffs      0.300191  0.278772  1.000000         NaN           NaN   \n",
       "RankSeason    0.217315  0.156881       NaN    1.000000      0.352961   \n",
       "RankPlayoffs  0.341013  0.229791       NaN    0.352961      1.000000   \n",
       "G             0.012873 -0.001805  0.009831    0.052870      0.012394   \n",
       "OOBP          0.101632  0.219021 -0.495725    0.141905      0.299376   \n",
       "OSLG          0.080376  0.231918 -0.510097    0.235886      0.318576   \n",
       "RD            0.428408  0.442142  0.566274   -0.570369     -0.076780   \n",
       "\n",
       "                     G      OOBP      OSLG            RD  \n",
       "index         0.025756  0.385843  0.168670 -1.220787e-03  \n",
       "Year         -0.027085 -0.335533 -0.122668 -4.316055e-19  \n",
       "RS            0.056206  0.091057  0.039787  5.375395e-01  \n",
       "RA           -0.037402  0.909908  0.895110 -5.441052e-01  \n",
       "W             0.108128 -0.633657 -0.646920  9.385150e-01  \n",
       "OBP          -0.003827  0.052899 -0.008316  4.942505e-01  \n",
       "SLG           0.012873  0.101632  0.080376  4.284077e-01  \n",
       "BA           -0.001805  0.219021  0.231918  4.421417e-01  \n",
       "Playoffs      0.009831 -0.495725 -0.510097  5.662745e-01  \n",
       "RankSeason    0.052870  0.141905  0.235886 -5.703690e-01  \n",
       "RankPlayoffs  0.012394  0.299376  0.318576 -7.677988e-02  \n",
       "G             1.000000 -0.100545 -0.045432  8.649718e-02  \n",
       "OOBP         -0.100545  1.000000  0.796526 -6.040766e-01  \n",
       "OSLG         -0.045432  0.796526  1.000000 -6.302315e-01  \n",
       "RD            0.086497 -0.604077 -0.630231  1.000000e+00  "
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(method = 'pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the very high correlation coefficient of RD (Run Difference) and W (wins), which is 0.9385, we can say that for teams with higher run difference, the number of wins is also larger."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can as well see this by a scatter plot between wins and run difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (12, 8))\n",
    "plt.scatter(df[df['Playoffs'] == 0]['RD'], df[df['Playoffs'] == 0]['W'], c = 'green', label = 'not qualified')\n",
    "plt.scatter(df[df['Playoffs'] == 1]['RD'], df[df['Playoffs'] == 1]['W'], c = 'coral', label = 'qualified')\n",
    "plt.xlabel('Run Difference')\n",
    "plt.ylabel('Wins')\n",
    "plt.legend()\n",
    "plt.savefig('Win vs Run Difference.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot establishes that having a higher run differential for the entire tournament means more wins."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to connect this with the earlier finding, we need to predict the run difference needed for winning 95 games. For this we will use a linear regression model, as the plot above also represents a linear relation between run difference and wins. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "run_difference_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(df['W']).reshape(-1, 1)    # reshaping the array because there is just one column\n",
    "y = np.array(df['RD']).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_difference_model.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8.32794581]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_difference_model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-673.57570548])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_difference_model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we have got the OLS regression equation,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{RD}$ = -673.5757054841915 + 8.32794581 * ${W}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On plugging in the target for wins i.e. ${W}$ = 95, we solve the equation to get the predicted Run difference, $\\hat{RD}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{RD}$ = -673.5757054841915 + 8.32794581 * 95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The run difference required to win 95 games is 117.57914646580844\n"
     ]
    }
   ],
   "source": [
    "required_rd = 8.32794581*95 - 673.5757054841915\n",
    "print(f'The run difference required to win 95 games is {required_rd}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now through this the strategy of the Oakland A's was to select a team that would score nearly 118 runs more than they concede. For this they needed to know, the players they have to target for signing to play for them. Jason Giambi was leaving the Oakland A's and now they had to bring in batters whose stats would ensure that the team achieved run difference of at least 118 runs, and one component was to figure out how to score more runs. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the question is what stats to select for this recruitment. Traditionally, the way a batter (analogous to batter in cricket (Sidenote : The terminology has changed from batsman to batter in cricket as well)) or pitcher (analogous to bowler in cricket) was judged was just by the conviction of the scouts, while they saw them play. The scouts themselves were retired baseball players and a lot of times they judged players just by their appearance. The only stats that were somewhat considered were superficial of the actual abilities of the players. This included the number of home runs, stolen bases and batting average. They were oblivious to the stats that spoke for the so called 'unfit' players. However it was Oakland A's Paul Depodesta and Billy Beane who argued that batting average is overvalued, while On-base percentage and Slugging percentage were more important indicators for the batting ability. \n",
    "Let's verify this claim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "run_scored_model = LinearRegression()\n",
    "X = df[['OBP', 'SLG', 'BA']]\n",
    "y = df['RS']\n",
    "run_scored_model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2917.42140821, 1637.92766577, -368.96606009])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_scored_model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9302016258786281"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_scored_model.score(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The claim indeed is right, as the coefficient corresponding to 'BA' is highly negative, while that for 'OBP' and 'SLG' is highly positive. Let's see if removing 'BA' from the features affects adjusted R^2 value that is given by run_model.score(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "run_scored_model = LinearRegression()\n",
    "X = df[['OBP', 'SLG']]\n",
    "y = df['RS']\n",
    "run_scored_model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2737.76802227, 1584.90860546])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_scored_model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-804.6270610622403"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_scored_model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9295810608096599"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_scored_model.score(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a very slight drop in the R^2 value, so we can safely choose to ignore 'BA' to predict the runs scored. So we get the OLS regression equation,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{RS}$ = -804.6270610622403 + 2737.76802227 * $OBP$ + 1584.90860546 * ${SLG}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can similarly predict the runs allowed i.e. RA using Opposition On-base percentage (OOBP) and Opposition slugging percentage (OSLG). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "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>index</th>\n",
       "      <th>Team</th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "      <th>RD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>330</td>\n",
       "      <td>ANA</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>691</td>\n",
       "      <td>730</td>\n",
       "      <td>75</td>\n",
       "      <td>0.327</td>\n",
       "      <td>0.405</td>\n",
       "      <td>0.261</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.331</td>\n",
       "      <td>0.412</td>\n",
       "      <td>-39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>331</td>\n",
       "      <td>ARI</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>818</td>\n",
       "      <td>677</td>\n",
       "      <td>92</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.442</td>\n",
       "      <td>0.267</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.404</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>332</td>\n",
       "      <td>ATL</td>\n",
       "      <td>NL</td>\n",
       "      <td>2001</td>\n",
       "      <td>729</td>\n",
       "      <td>643</td>\n",
       "      <td>88</td>\n",
       "      <td>0.324</td>\n",
       "      <td>0.412</td>\n",
       "      <td>0.260</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.384</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>333</td>\n",
       "      <td>BAL</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>687</td>\n",
       "      <td>829</td>\n",
       "      <td>63</td>\n",
       "      <td>0.319</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.248</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>162</td>\n",
       "      <td>0.337</td>\n",
       "      <td>0.439</td>\n",
       "      <td>-142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>334</td>\n",
       "      <td>BOS</td>\n",
       "      <td>AL</td>\n",
       "      <td>2001</td>\n",
       "      <td>772</td>\n",
       "      <td>745</td>\n",
       "      <td>82</td>\n",
       "      <td>0.334</td>\n",
       "      <td>0.439</td>\n",
       "      <td>0.266</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.393</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index Team League  Year   RS   RA   W    OBP    SLG     BA  Playoffs  \\\n",
       "0    330  ANA     AL  2001  691  730  75  0.327  0.405  0.261         0   \n",
       "1    331  ARI     NL  2001  818  677  92  0.341  0.442  0.267         1   \n",
       "2    332  ATL     NL  2001  729  643  88  0.324  0.412  0.260         1   \n",
       "3    333  BAL     AL  2001  687  829  63  0.319  0.380  0.248         0   \n",
       "4    334  BOS     AL  2001  772  745  82  0.334  0.439  0.266         0   \n",
       "\n",
       "   RankSeason  RankPlayoffs    G   OOBP   OSLG   RD  \n",
       "0         NaN           NaN  162  0.331  0.412  -39  \n",
       "1         5.0           1.0  162  0.311  0.404  141  \n",
       "2         7.0           3.0  162  0.314  0.384   86  \n",
       "3         NaN           NaN  162  0.337  0.439 -142  \n",
       "4         NaN           NaN  161  0.329  0.393   27  "
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OOBP    812\n",
       "OSLG    812\n",
       "dtype: int64"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# As pointed out earlier, there are null values in OOBP and OSLG columns.\n",
    "df[['OOBP', 'OSLG']].isnull().sum()    # Counting the number of null values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity we drop the rows having null values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "ra_df = df.dropna(subset=['OOBP', 'OSLG'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90, 17)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ra_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Linear regression model to predict runs allowed from OOBP and OSLG.\n",
    "from sklearn.linear_model import LinearRegression\n",
    "run_allowed_model = LinearRegression()\n",
    "X = ra_df[['OOBP', 'OSLG']]\n",
    "y = ra_df['RA']\n",
    "run_allowed_model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-837.3778886133363"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_allowed_model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2913.59948582, 1514.28595842])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_allowed_model.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{RA}$ = -837.3778886133363 + 2913.59948582 * $OOBP$ + 1514.28595842 * $OSLG$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now considering that much focus was given to recruiting batters, if we assume that the OOBP and OSLG of Oakland A's will remain the same as it was in the previous year, we can predict how many runs will Oakland A's concede in the 2002 season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Int64Index([20], dtype='int64')"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# getting the index value for the Oakland A's 2001 season\n",
    "df[(df['Year'] == 2001) & (df['Team'] == 'OAK')].index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OOBP of Oakland A's in 2001 = 0.308\n",
      "OSLG of Oakland A's in 2001 = 0.38\n"
     ]
    }
   ],
   "source": [
    "OOBP_2001 = df[(df['Team'] == 'OAK') & (df['Year'] == 2001)].loc[20, 'OOBP']   # Putting 20 in loc since we know the index\n",
    "OSLG_2001 = df[(df['Team'] == 'OAK') & (df['Year'] == 2001)].loc[20, 'OSLG']   # from the previous cell\n",
    "print(f\"OOBP of Oakland A's in 2001 = {OOBP_2001}\")\n",
    "print(f\"OSLG of Oakland A's in 2001 = {OSLG_2001}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given this we predict that runs allowed by Oakland A's in 2002 season will be "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "635.4394172160479\n"
     ]
    }
   ],
   "source": [
    "print(run_allowed_model.predict(np.array([OOBP_2001, OSLG_2001]).reshape(1, -1))[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Given that they will allow nearly 636 runs in the season, in order to keep a run difference of 118 they need to score 754 runs in the season\n"
     ]
    }
   ],
   "source": [
    "print(f'Given that they will allow nearly 636 runs in the season, in order to keep a run difference of 118 they'\n",
    "      f' need to score {636 + 118} runs in the season') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was their player recruitment strategy, they looked for players who would bring the OBP and SLG to a level where the runs scored; as predicted by our OLS equation for RS, will be 754. Precisely, "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "754 = -804.6270610622403 + 2737.76802227 * $OBP$ + 1584.90860546 * ${SLG}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So they focussed on OBP and SLG while recruiting the players, and since they knew that all the other teams would just consider batting average, home runs and stolen bases for the recruitment, they were confident that they would get the players they want at a low price, which they eventually did!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have uncovered the strategy used by the Oakland A's, let's see if that worked by checking the data for 2002 that is stored in full_df."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "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>Team</th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>RS</th>\n",
       "      <th>RA</th>\n",
       "      <th>W</th>\n",
       "      <th>OBP</th>\n",
       "      <th>SLG</th>\n",
       "      <th>BA</th>\n",
       "      <th>Playoffs</th>\n",
       "      <th>RankSeason</th>\n",
       "      <th>RankPlayoffs</th>\n",
       "      <th>G</th>\n",
       "      <th>OOBP</th>\n",
       "      <th>OSLG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>320</th>\n",
       "      <td>OAK</td>\n",
       "      <td>AL</td>\n",
       "      <td>2002</td>\n",
       "      <td>800</td>\n",
       "      <td>654</td>\n",
       "      <td>103</td>\n",
       "      <td>0.339</td>\n",
       "      <td>0.432</td>\n",
       "      <td>0.261</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>162</td>\n",
       "      <td>0.315</td>\n",
       "      <td>0.384</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Team League  Year   RS   RA    W    OBP    SLG     BA  Playoffs  \\\n",
       "320  OAK     AL  2002  800  654  103  0.339  0.432  0.261         1   \n",
       "\n",
       "     RankSeason  RankPlayoffs    G   OOBP   OSLG  \n",
       "320         1.0           4.0  162  0.315  0.384  "
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Storing the statistics of Oakland A's for the 2002 season in Oak_2002\n",
    "Oak_2002 = full_df[(full_df['Year'] == 2002) & (full_df['Team'] == 'OAK')]\n",
    "Oak_2002"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In 2002, given the OOBP and OSLG our model predicts the runs allowed by Oakland A's is 661.8917574504227\n"
     ]
    }
   ],
   "source": [
    "print(f\"In 2002, given the OOBP and OSLG our model predicts the runs allowed by Oakland A's is {run_allowed_model.predict(np.array(Oak_2002.loc[320, ['OOBP', 'OSLG']]).reshape(1, -1))[0]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing it with the actual data, shows that actual runs allowed in 2002 was 654, which is very close to 661.8917574504227"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In 2002, given the OBP and SLG our model predicts the runs scored by Oakland A's is 808.1568160466265\n"
     ]
    }
   ],
   "source": [
    "print(f\"In 2002, given the OBP and SLG our model predicts the runs scored by Oakland A's is {run_scored_model.predict(np.array(Oak_2002.loc[320, ['OBP', 'SLG']]).reshape(1, -1))[0]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again a spot on prediction of 808.1568160466265 as compared to the actual runs scored in 2002, i.e. 800"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This brings the run difference to 808.1568160466265 - 661.8917574504227 = 146.26505859620386\n"
     ]
    }
   ],
   "source": [
    "print(f'This brings the run difference to 808.1568160466265 - 661.8917574504227 = {808.1568160466265 - 661.8917574504227}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is again close to the actual run difference of 800 - 654 = 146\n"
     ]
    }
   ],
   "source": [
    "print(f'This is again close to the actual run difference of 800 - 654 = {800 - 654}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, almost identical!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just one more thing remains: to check if this run difference predicts the correct wins. Earlier we regressed run difference on wins, as we wanted to know the predicted value of run difference for 95 wins, but now we will regress wins on run difference to see the predicted value of wins, given the run difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "wins_model = LinearRegression()\n",
    "X = np.array(df['RD']).reshape(-1, 1)\n",
    "y = df['W']\n",
    "wins_model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The predicted wins for a run difference of 146.26505859620386 is 96.35118968785162\n"
     ]
    }
   ],
   "source": [
    "print(f'The predicted wins for a run difference of {808.1568160466265 - 661.8917574504227} is {wins_model.predict(np.array([808.1568160466265 - 661.8917574504227]).reshape(1, -1))[0]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, Oakland A's won 103 games in the season."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oakland A's qualified for the playoffs with a league ranking of 1, but could not win. Billy Beane and Paul DePodesta believed that in a 162-game season, luck would be compensated for and it won't really affect the final outcome, while skills will be the ultimate factor. So they focussed on preparing a team that could qualify for playoffs, now what happens in playoffs can't be predicted. It provides a very small sample size and through the course of those knockout stages, that luck factor; just a single moment of brilliance can turn any game towards any team. So they believed that their method will work and take them to the playoffs, and it did.\n",
    "\n",
    "Well, not everyone enjoyed seeing Oakland A's spending less and winning more, especially the teams with very big payrolls, and the scouts whose traditional ways of recruitment were being challenged. They would rather vent their frustration by commenting that what the Oakland A's did, was just a fluke, and their method does not work. On hearing this, Paul DePodesta would say to himself :-"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## “I hope they continue to believe that our way doesn’t work. It buys us a few more years.”"
   ]
  }
 ],
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