01-Regression/moneyball.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Moneyball: a linear regression example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## a linear regression example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The book (and later a movie) Moneyball by Michael Lewis tells the story of how the USA baseball team Oakland Athletics in 2002 leveraged the power of data instead of relying on experts.\n",
    "Better data and better analysis of the data lead to find and use market inefficiencies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The team was one of the poorest in a period when only rich teams could afford the all-star players (the imbalance in total salaries being something like 4 to 1).\n",
    "A new ownership in 1995 was improving the team’s wins but in 2001 the loss of 3 key players and budget cuts were bringing a new idea: take a quantitative approach and find undervalued players."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The traditional way to select players was through scouting but Oakland and his general manager Billy Bean (Brad Pitt in the movie…) selected the players based on their statistics without any prejudice. Specifically, his assistant – the Harvard graduate Paul DePodesta looked at the data to find which ones were the undervalued skills."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A huge repository for the USA baseball statistics (called Sabermetrics) is the Lahman’s Baseball Database. This database contains complete batting and pitching statistics from 1871 to present plus fielding statistics, standings, team stats, managerial records, post-season data and more."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read baseball data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "baseball = pd.read_csv(\"../datasets/baseball.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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>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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseball.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Team', 'League', 'Year', 'RS', 'RA', 'W', 'OBP', 'SLG', 'BA',\n",
       "       'Playoffs', 'RankSeason', 'RankPlayoffs', 'G', 'OOBP', 'OSLG'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseball.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The feature named ‘W’ is the wins in the season ‘Year’ and the feature ‘Playoffs’ is a boolean value (0 = didn’t make to the playoffs; 1 = did make)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Subset to only include moneyball years (until 2001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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>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",
       "      <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>331</th>\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>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": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moneyball = baseball[baseball.Year < 2002]\n",
    "moneyball.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Team</th>\n",
       "      <th>Year</th>\n",
       "      <th>W</th>\n",
       "      <th>Playoffs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>ANA</td>\n",
       "      <td>2001</td>\n",
       "      <td>75</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>331</th>\n",
       "      <td>ARI</td>\n",
       "      <td>2001</td>\n",
       "      <td>92</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>332</th>\n",
       "      <td>ATL</td>\n",
       "      <td>2001</td>\n",
       "      <td>88</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>333</th>\n",
       "      <td>BAL</td>\n",
       "      <td>2001</td>\n",
       "      <td>63</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>334</th>\n",
       "      <td>BOS</td>\n",
       "      <td>2001</td>\n",
       "      <td>82</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Team  Year   W  Playoffs\n",
       "330  ANA  2001  75         0\n",
       "331  ARI  2001  92         1\n",
       "332  ATL  2001  88         1\n",
       "333  BAL  2001  63         0\n",
       "334  BOS  2001  82         0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moneyball[['Team','Year','W','Playoffs']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The goal: make to the playoffs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step was to understand what was needed for the team to enter the playoffs and he judged from the past seasons that it takes 95 wins to be reasonably sure to make to the playoffs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![wins](../images/wins.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10d178400>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AAIAghAgASKsTJ6Txcb8EaoAQAQBpNTEhrV7tl0ANECIAAEAQQgQAAAhCiAAAAEEIEQAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d135470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_yticks=['NO', 'YES']\n",
    "plt.yticks(moneyball.Playoffs, my_yticks)\n",
    "plt.scatter(moneyball.W, moneyball.Playoffs)\n",
    "plt.axvline(x=95, color='r', linestyle='dashed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: you might ask why the goal is to make to the playoff and not directly to win the world series.  \n",
    "The reason is because the A's managers see their job as making sure the team makes it to the playoffs – after that all bets are off.  \n",
    "\n",
    "> “Over a long season the luck evens out, and the skill shines through. But in a series of three out of five, or even four out of seven, anything can happen.”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The goal: make 95 wins "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "95 Wins are necessary to be relatively sure to go to the playoffs.  \n",
    "But how many Runs are then needed?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Run Difference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To win games a team needs to score more “runs” than their opponent but how many? DePodesta used linear regression to find out. We can see how.\n",
    "\n",
    "The feature ‘RS’ is the number of runs scored and ‘RA’ is the number of runs allowed.\n",
    "We can add an additional feature which summarise both of them by calculating the difference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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",
       "      <th>RD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <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",
       "      <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>331</th>\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>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",
       "      <td>86</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",
       "      <td>-142</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",
       "      <td>27</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   RD  \n",
       "330         NaN           NaN  162  0.331  0.412  -39  \n",
       "331         5.0           1.0  162  0.311  0.404  141  \n",
       "332         7.0           3.0  162  0.314  0.384   86  \n",
       "333         NaN           NaN  162  0.337  0.439 -142  \n",
       "334         NaN           NaN  161  0.329  0.393   27  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moneyball = moneyball.assign(RD = moneyball.RS - moneyball.RA)\n",
    "moneyball.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wins are directly correlated with Runs scored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x110aa91d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k44T6+sb9cstTT/0UW7aE1/mllQmMu9kMspNWXm8/52Kknh51wEODupeWlmb+4R8+zWOP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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d135e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(moneyball.RD, moneyball.W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to formalise the relation between Wins and Runs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our output would be the number of wins W and we want to see how it depends on the runs difference RD:\n",
    "\n",
    "W = beta0 + beta1 * RD\n",
    "\n",
    "This is a linear regression and the beta parameters can be estimated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression model to predict wins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we use the sklearn library and its linear_model module "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "WinsModel = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input variable is the Runs Difference, and the output is the Wins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = moneyball[['RD']]  # input\n",
    "features.insert(0, 'intercept', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WinsModel.fit(features, moneyball.W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see the fitted beta parameters we can examine the following values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80.881374722838132"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WinsModel.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.10576562])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WinsModel.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore the prediction formula for the number of wins is:  \n",
    "Wins = 80.9042 + 0.1045 * RD  \n",
    "\n",
    "To get the number of Runs necessary we need to solve this simple equation:  \n",
    "95 = 80.9042 + 0.1045 * RD  \n",
    "RD = (95-80.9042)/0.1045 = 134.89"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "135 Runs are necessary for 95 wins.  \n",
    "We can verify it by predicting the wins for 135 Runs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 95.15973375])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WinsModel.predict([[1, 135]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The goal: score 135+ runs more than opponent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does a team increase the runs difference (RD)?  \n",
    "There are two ways: either scoring more runs (RS) or allowing less runs (RA).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The A’s started using a different method to select players,\n",
    " based on their statistics, not on their looks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most teams focused on Batting Average (BA): getting on base by hitting the ball."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The A’s discovered that BA was overvalued and two baseball statistics were significantly more important than anything else:  \n",
    "* On-Base Percentage (OBP)   \n",
    "Percentage of time a player gets on base (including walks)  \n",
    "* Slugging Percentage (SLG)  \n",
    "How far a player gets around the bases on his turn (measures\n",
    "power)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use linear regression to verify which baseball player features are more important tot predict runs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression model to predict runs scored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel = linear_model.LinearRegression()\n",
    "features = moneyball[['OBP', 'SLG', 'BA']]  # input\n",
    "features.insert(0, 'intercept', 1)\n",
    "RSmodel.fit(features, moneyball.RS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-788.45704708079347"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0.        ,  2917.42140821,  1637.92766577,  -368.96606009])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that now the beta parameters are 3, being 3 the input features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prediction formula for Scored Runs would be:  \n",
    "  RS = -788 + 2917 \\* OBP + 1638 \\* SLG -369 \\* BA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The score() function returns the R2 metric for the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.93020162587862809"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel.score(features, moneyball.RS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is very high, almost the maximum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And if we remove the BA feature?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel2 = linear_model.LinearRegression()\n",
    "features = moneyball[['OBP', 'SLG']]  # input\n",
    "features.insert(0, 'intercept', 1)\n",
    "RSmodel2.fit(features, moneyball.RS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.92958106080965974"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel2.score(features, moneyball.RS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is almost no difference in the R2 when removing the BA feature.  \n",
    "A sign that BA is not significant. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Batting Average (BA) is overvalued  \n",
    "On Base Percentage (OBP) and Slugging Percentage (SLG) are enough."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-804.62706106223959"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel2.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0.        ,  2737.76802227,  1584.90860546])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression model to predict runs allowed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predicting the Runs Allowed is more difficult because there are missing values in the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Team              0\n",
       "League            0\n",
       "Year              0\n",
       "RS                0\n",
       "RA                0\n",
       "W                 0\n",
       "OBP               0\n",
       "SLG               0\n",
       "BA                0\n",
       "Playoffs          0\n",
       "RankSeason      748\n",
       "RankPlayoffs    748\n",
       "G                 0\n",
       "OOBP            812\n",
       "OSLG            812\n",
       "RD                0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moneyball.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(902, 16)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moneyball.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Out of 902 rows, 812 misses the OOBP and OSLG features that would be critical for RA prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just for exercise, we can go on but results will not be significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are too many missing values to use the average values instead, better to ignore these rows altogether."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "moneyball = moneyball[np.isfinite(moneyball['OOBP'])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "moneyball = moneyball[np.isfinite(moneyball['OSLG'])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90, 16)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moneyball.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the data set is reduced to 90 rows ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RAmodel = linear_model.LinearRegression()\n",
    "features = moneyball[['OOBP', 'OSLG']]\n",
    "features.insert(0, 'intercept', 1)\n",
    "RAmodel.fit(features, moneyball.RA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-837.37788861333513"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RAmodel.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0.        ,  2913.59948582,  1514.28595842])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RAmodel.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9073132027228662"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RAmodel.score(features, moneyball.RA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2002 Prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know that the A's Team OBP in 2002 is 0.339 and the Team SLG is 0.430  \n",
    "How many Runs and Wins can we expect?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could just put these values in the formula above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "804.9853300000001"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RS = -804.63 + 2737.77*0.339 + 1584.91*0.43\n",
    "RS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can use the handy function predict():"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 804.98699884])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSmodel2.predict([[1, 0.339, 0.43]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We predict 805 Runs scored in 2002**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's predict also RA even if the model is very weak, just as example.  \n",
    "We know that Team OOBP in 2002 is 0.307 and Team OSLG is 0.373"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 621.92581602])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RAmodel.predict([[1, 0.307, 0.373]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Our 2002 prediction is 622 Runs Allowed.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In reality, Paul Podesta at the A's team used a similar but slightly different approach and predicted 650-670 Runs Allowed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally the number of wins:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 100.23648363])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WinsModel.predict([[1, (805-622)]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our prediction for A's team in 2002 is **100 wins in total**, that would be probably enough to access the playoff."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are 2002 final results:  \n",
    "- Actual runs score were 800 instead of 805  \n",
    "- Runs allowed were 653 instead of 622 (note the bigger difference)  \n",
    "- And wins were 103 instead of 100  \n",
    "  \n",
    "They made it to the playoffs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Models (even relatively simple models) allow managers to more accurately value players and minimise risk.  \n",
    "  \n",
    "Every major league baseball team now has a statistics group.  \n",
    "Analytics are used in other sports, too."
   ]
  }
 ],
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