chapter_03.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Chapter 03"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Setup Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as ss\n",
    "from numpy.random import beta, binomial\n",
    "\n",
    "pd.set_option('display.max_columns', 50)\n",
    "pd.set_option('display.max_rows', 100)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Section 3.1\n",
    "\n",
    "Setup [Lahman baseball dataset](http://www.seanlahman.com/baseball-archive/statistics/). We downloaded the CSV files locally and will load those -- Python doesn't have an equivalent to R's `Lahman` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# read into dataframes\n",
    "Batting = pd.read_csv('data/Batting.csv', index_col=['playerID', 'yearID'])\n",
    "Pitching = pd.read_csv('data/Pitching.csv', index_col=['playerID', 'yearID'])\n",
    "Master = pd.read_csv('data/Master.csv', index_col='playerID')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>H</th>\n",
       "      <th>AB</th>\n",
       "      <th>average</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>playerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>aaronha01</th>\n",
       "      <td>3771</td>\n",
       "      <td>12364</td>\n",
       "      <td>0.304998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aaronto01</th>\n",
       "      <td>216</td>\n",
       "      <td>944</td>\n",
       "      <td>0.228814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abadan01</th>\n",
       "      <td>2</td>\n",
       "      <td>21</td>\n",
       "      <td>0.095238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abadijo01</th>\n",
       "      <td>11</td>\n",
       "      <td>49</td>\n",
       "      <td>0.224490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abbated01</th>\n",
       "      <td>772</td>\n",
       "      <td>3044</td>\n",
       "      <td>0.253614</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              H     AB   average\n",
       "playerID                        \n",
       "aaronha01  3771  12364  0.304998\n",
       "aaronto01   216    944  0.228814\n",
       "abadan01      2     21  0.095238\n",
       "abadijo01    11     49  0.224490\n",
       "abbated01   772   3044  0.253614"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "career = (Batting\n",
    "          .query(\"AB > 0\")\n",
    "          .join(Pitching, how='left', rsuffix='_')\n",
    "          .query(\"teamID_ != teamID_\")  # IS NULL hack for `query` method -> only Batters\n",
    "          .groupby(level=0)  # group by index -> playerID\n",
    "          .agg({'H': np.sum, 'AB': np.sum})\n",
    "          .assign(average = lambda x: x['H'] / x['AB'])\n",
    "         )\n",
    "\n",
    "career.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>H</th>\n",
       "      <th>AB</th>\n",
       "      <th>average</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>playerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>aaronha01</th>\n",
       "      <td>Hank Aaron</td>\n",
       "      <td>3771</td>\n",
       "      <td>12364</td>\n",
       "      <td>0.304998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aaronto01</th>\n",
       "      <td>Tommie Aaron</td>\n",
       "      <td>216</td>\n",
       "      <td>944</td>\n",
       "      <td>0.228814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abadan01</th>\n",
       "      <td>Andy Abad</td>\n",
       "      <td>2</td>\n",
       "      <td>21</td>\n",
       "      <td>0.095238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abadijo01</th>\n",
       "      <td>John Abadie</td>\n",
       "      <td>11</td>\n",
       "      <td>49</td>\n",
       "      <td>0.224490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abbated01</th>\n",
       "      <td>Ed Abbaticchio</td>\n",
       "      <td>772</td>\n",
       "      <td>3044</td>\n",
       "      <td>0.253614</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     name     H     AB   average\n",
       "playerID                                        \n",
       "aaronha01      Hank Aaron  3771  12364  0.304998\n",
       "aaronto01    Tommie Aaron   216    944  0.228814\n",
       "abadan01        Andy Abad     2     21  0.095238\n",
       "abadijo01     John Abadie    11     49  0.224490\n",
       "abbated01  Ed Abbaticchio   772   3044  0.253614"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pull in name\n",
    "career = (career\n",
    "          .join(Master)\n",
    "          .assign(name = lambda x: x['nameFirst'] + ' ' + x['nameLast'])\n",
    "          [['name', 'H', 'AB', 'average']]  # select only columns we want\n",
    "         )\n",
    "\n",
    "career.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 3.2\n",
    "### Step 1: Estimate a prior from all your data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 3.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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XGTMzy8ZFxszMsnGRMTOzbFrv3uVm1hBzS3ri6Yal00pZrrUm78mYmVk2LjJmZpaNi4yZ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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa2f860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# not sure if in the book this is `career` or `career_filtered` -- code not given\n",
    "career['average'].hist(bins=50)\n",
    "plt.xlim(0.15, 0.375)\n",
    "plt.xlabel('average')\n",
    "plt.ylabel('count');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Alpha = 75.88, Beta = 216.69\n"
     ]
    }
   ],
   "source": [
    "career_filtered = career.query(\"AB > 500\")\n",
    "\n",
    "# maximum likelihood estimation\n",
    "\n",
    "alpha0, beta0, loc0, scale0 = ss.beta.fit(career_filtered['average'], floc=0, fscale=1)\n",
    "print('Alpha = {:.2f}, Beta = {:.2f}'.format(alpha0, beta0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 3.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0X4CXUBsfbZuk/w0cHRE/Sst8jReKzO8Ar9ULd+58KXACtbHUzCrJxcQskdQN\n/Dbwxoh4WlIfMJfaSKurgH+iNlpvpENV10bEZXVWdSginkvrnAv8L2p3rXtU0rq0zjGjAH8QEd8b\nZzmzyvBhLrMXvBTYlwrJq6mN5Aq1Q10rGX43us3Au4fujS3pWGXuIZ8xVDiekNRB7Q6JRMR+4GC6\nlwTUhgEf8j3gI5Jmp3Uvk3RUS35Cs4J4z8TsBd8FPixpB7URcLcARMS+1HZiRNyZ2rZL+mPgHyXN\nojby8cXAz7MrjIj9kr5EbVTYfwbuysy+CPiSpOeB24Bfpva/oTY68N1pD+hfmPjtgc3ayqMGm5VE\nUkdEDKTpS6ndk+TjJccymxTvmZiV5z9Iuoza5/DnwAfKjWM2ed4zMTOz3NwBb2ZmubmYmJlZbi4m\nZmaWm4uJmZnl5mJiZma5uZiYmVlu/x/GrWxqz6DL4wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1062c2a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_fitted = beta(alpha0, beta0, size=len(career_filtered))\n",
    "\n",
    "# not sure if in the book this is `career` or `career_filtered` -- code not given\n",
    "# assume it's `career_filtered`, since that's what we're fitting MLE to\n",
    "career_filtered['average'].hist(bins=50, alpha=.5)\n",
    "plt.hist(random_fitted, histtype='step', bins=50, alpha=2)\n",
    "plt.xlim(0.15, 0.375)\n",
    "plt.xlabel('average')\n",
    "plt.ylabel('count');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems like a pretty good fit to me."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 3.3\n",
    "### Step 2: Use that distribution as a prior for each individual estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>H</th>\n",
       "      <th>AB</th>\n",
       "      <th>average</th>\n",
       "      <th>eb_estimate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>playerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>aaronha01</th>\n",
       "      <td>Hank Aaron</td>\n",
       "      <td>3771</td>\n",
       "      <td>12364</td>\n",
       "      <td>0.304998</td>\n",
       "      <td>0.303943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aaronto01</th>\n",
       "      <td>Tommie Aaron</td>\n",
       "      <td>216</td>\n",
       "      <td>944</td>\n",
       "      <td>0.228814</td>\n",
       "      <td>0.236040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abadan01</th>\n",
       "      <td>Andy Abad</td>\n",
       "      <td>2</td>\n",
       "      <td>21</td>\n",
       "      <td>0.095238</td>\n",
       "      <td>0.248366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abadijo01</th>\n",
       "      <td>John Abadie</td>\n",
       "      <td>11</td>\n",
       "      <td>49</td>\n",
       "      <td>0.224490</td>\n",
       "      <td>0.254356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>abbated01</th>\n",
       "      <td>Ed Abbaticchio</td>\n",
       "      <td>772</td>\n",
       "      <td>3044</td>\n",
       "      <td>0.253614</td>\n",
       "      <td>0.254117</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     name     H     AB   average  eb_estimate\n",
       "playerID                                                     \n",
       "aaronha01      Hank Aaron  3771  12364  0.304998     0.303943\n",
       "aaronto01    Tommie Aaron   216    944  0.228814     0.236040\n",
       "abadan01        Andy Abad     2     21  0.095238     0.248366\n",
       "abadijo01     John Abadie    11     49  0.224490     0.254356\n",
       "abbated01  Ed Abbaticchio   772   3044  0.253614     0.254117"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eb_estimate_func = lambda x: (x['H'] + alpha0) / (x['AB'] + alpha0 + beta0)\n",
    "\n",
    "career_eb = career.assign(eb_estimate=eb_estimate_func)\n",
    "career_eb.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 3.4\n",
    "### Results\n",
    "\n",
    "**NOTE:** Our numbers will be slightly different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>H</th>\n",
       "      <th>AB</th>\n",
       "      <th>average</th>\n",
       "      <th>eb_estimate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>playerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cobbty01</th>\n",
       "      <td>Ty Cobb</td>\n",
       "      <td>3871</td>\n",
       "      <td>10598</td>\n",
       "      <td>0.365258</td>\n",
       "      <td>0.362413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hornsro01</th>\n",
       "      <td>Rogers Hornsby</td>\n",
       "      <td>2930</td>\n",
       "      <td>8173</td>\n",
       "      <td>0.358497</td>\n",
       "      <td>0.355071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>jacksjo01</th>\n",
       "      <td>Shoeless Joe Jackson</td>\n",
       "      <td>1772</td>\n",
       "      <td>4981</td>\n",
       "      <td>0.355752</td>\n",
       "      <td>0.350404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>odoulle01</th>\n",
       "      <td>Lefty O'Doul</td>\n",
       "      <td>1126</td>\n",
       "      <td>3192</td>\n",
       "      <td>0.352757</td>\n",
       "      <td>0.344915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delahed01</th>\n",
       "      <td>Ed Delahanty</td>\n",
       "      <td>2596</td>\n",
       "      <td>7505</td>\n",
       "      <td>0.345903</td>\n",
       "      <td>0.342656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaktr01</th>\n",
       "      <td>Tris Speaker</td>\n",
       "      <td>3321</td>\n",
       "      <td>9624</td>\n",
       "      <td>0.345075</td>\n",
       "      <td>0.342546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>willite01</th>\n",
       "      <td>Ted Williams</td>\n",
       "      <td>2461</td>\n",
       "      <td>7145</td>\n",
       "      <td>0.344437</td>\n",
       "      <td>0.341090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hamilbi01</th>\n",
       "      <td>Billy Hamilton</td>\n",
       "      <td>2158</td>\n",
       "      <td>6268</td>\n",
       "      <td>0.344288</td>\n",
       "      <td>0.340501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sislege01</th>\n",
       "      <td>George Sisler</td>\n",
       "      <td>1565</td>\n",
       "      <td>4528</td>\n",
       "      <td>0.345627</td>\n",
       "      <td>0.340391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ruthba01</th>\n",
       "      <td>Babe Ruth</td>\n",
       "      <td>1831</td>\n",
       "      <td>5314</td>\n",
       "      <td>0.344562</td>\n",
       "      <td>0.340115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           name     H     AB   average  eb_estimate\n",
       "playerID                                                           \n",
       "cobbty01                Ty Cobb  3871  10598  0.365258     0.362413\n",
       "hornsro01        Rogers Hornsby  2930   8173  0.358497     0.355071\n",
       "jacksjo01  Shoeless Joe Jackson  1772   4981  0.355752     0.350404\n",
       "odoulle01          Lefty O'Doul  1126   3192  0.352757     0.344915\n",
       "delahed01          Ed Delahanty  2596   7505  0.345903     0.342656\n",
       "speaktr01          Tris Speaker  3321   9624  0.345075     0.342546\n",
       "willite01          Ted Williams  2461   7145  0.344437     0.341090\n",
       "hamilbi01        Billy Hamilton  2158   6268  0.344288     0.340501\n",
       "sislege01         George Sisler  1565   4528  0.345627     0.340391\n",
       "ruthba01              Babe Ruth  1831   5314  0.344562     0.340115"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "career_eb.sort_values('eb_estimate', ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>H</th>\n",
       "      <th>AB</th>\n",
       "      <th>average</th>\n",
       "      <th>eb_estimate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>playerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bergebi01</th>\n",
       "      <td>Bill Bergen</td>\n",
       "      <td>516</td>\n",
       "      <td>3028</td>\n",
       "      <td>0.170410</td>\n",
       "      <td>0.178247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>oylerra01</th>\n",
       "      <td>Ray Oyler</td>\n",
       "      <td>221</td>\n",
       "      <td>1265</td>\n",
       "      <td>0.174704</td>\n",
       "      <td>0.190605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>humphjo01</th>\n",
       "      <td>John Humphries</td>\n",
       "      <td>52</td>\n",
       "      <td>364</td>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.194770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vukovjo01</th>\n",
       "      <td>John Vukovich</td>\n",
       "      <td>90</td>\n",
       "      <td>559</td>\n",
       "      <td>0.161002</td>\n",
       "      <td>0.194793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bakerge01</th>\n",
       "      <td>George Baker</td>\n",
       "      <td>74</td>\n",
       "      <td>474</td>\n",
       "      <td>0.156118</td>\n",
       "      <td>0.195520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gladmbu01</th>\n",
       "      <td>Buck Gladmon</td>\n",
       "      <td>56</td>\n",
       "      <td>380</td>\n",
       "      <td>0.147368</td>\n",
       "      <td>0.196084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>eastehe01</th>\n",
       "      <td>Henry Easterday</td>\n",
       "      <td>203</td>\n",
       "      <td>1129</td>\n",
       "      <td>0.179805</td>\n",
       "      <td>0.196178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>armbrch01</th>\n",
       "      <td>Charlie Armbruster</td>\n",
       "      <td>53</td>\n",
       "      <td>355</td>\n",
       "      <td>0.149296</td>\n",
       "      <td>0.199021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bastich01</th>\n",
       "      <td>Charlie Bastian</td>\n",
       "      <td>321</td>\n",
       "      <td>1700</td>\n",
       "      <td>0.188824</td>\n",
       "      <td>0.199180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>traffbi01</th>\n",
       "      <td>Bill Traffley</td>\n",
       "      <td>116</td>\n",
       "      <td>663</td>\n",
       "      <td>0.174962</td>\n",
       "      <td>0.200802</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         name    H    AB   average  eb_estimate\n",
       "playerID                                                       \n",
       "bergebi01         Bill Bergen  516  3028  0.170410     0.178247\n",
       "oylerra01           Ray Oyler  221  1265  0.174704     0.190605\n",
       "humphjo01      John Humphries   52   364  0.142857     0.194770\n",
       "vukovjo01       John Vukovich   90   559  0.161002     0.194793\n",
       "bakerge01        George Baker   74   474  0.156118     0.195520\n",
       "gladmbu01        Buck Gladmon   56   380  0.147368     0.196084\n",
       "eastehe01     Henry Easterday  203  1129  0.179805     0.196178\n",
       "armbrch01  Charlie Armbruster   53   355  0.149296     0.199021\n",
       "bastich01     Charlie Bastian  321  1700  0.188824     0.199180\n",
       "traffbi01       Bill Traffley  116   663  0.174962     0.200802"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "career_eb.sort_values('eb_estimate', ascending=True).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 3.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.15, 0.4)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HyPH2ktXTSW1+CV5vkN4eP6FQCDDW1w4j9Jc/f+a0ZakMV6nJptkYs3ykJ0Wk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\nREQk6f4bMZPJB4Z52MMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa94908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# what we would guess someone's batting average is with no evidence\n",
    "prior = alpha0 / (alpha0 + beta0)\n",
    "\n",
    "# use of `sharex` is a hack due to a known bug in pandas:\n",
    "# https://github.com/pandas-dev/pandas/issues/10611\n",
    "ax = career_eb.plot.scatter(x='average', y='eb_estimate', c='AB',\n",
    "                            colormap='Blues_r', figsize=(6,6), grid=True,\n",
    "                            sharex=False)\n",
    "\n",
    "plt.axhline(prior, color='r', linestyle=':')\n",
    "\n",
    "# draw a straight line where x = y\n",
    "lims = [\n",
    "    np.min([ax.get_xlim(), ax.get_ylim()]),\n",
    "    np.max([ax.get_xlim(), ax.get_ylim()])\n",
    "]\n",
    "\n",
    "plt.plot(lims, lims, 'r-', alpha=.7)\n",
    "\n",
    "# redo axes limits\n",
    "plt.xlim(-0.1, 1.1)\n",
    "plt.ylim(0.150, 0.400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I miss ggplot2."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}