chapter_04.ipynb

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   "source": [
    "# Chapter 04\n",
    "### Setup Environment"
   ]
  },
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    "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\n",
    "\n",
    "# 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')\n",
    "\n",
    "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 = (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",
    "# priors estimated in chapter 3\n",
    "alpha0 = 75.88\n",
    "beta0 = 216.69\n",
    "\n",
    "eb_estimate_func = lambda x: (x['H'] + alpha0) / (x['AB'] + alpha0 + beta0)\n",
    "\n",
    "career_eb = career.assign(eb_estimate=eb_estimate_func)"
   ]
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   "source": [
    "## Section 4.2 - Posterior Distribution"
   ]
  },
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       "<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",
       "      <th>alpha1</th>\n",
       "      <th>beta1</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",
       "      <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",
       "      <td>3846.88</td>\n",
       "      <td>8809.69</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",
       "      <td>291.88</td>\n",
       "      <td>944.69</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",
       "      <td>77.88</td>\n",
       "      <td>235.69</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>0.254355</td>\n",
       "      <td>86.88</td>\n",
       "      <td>254.69</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",
       "      <td>847.88</td>\n",
       "      <td>2488.69</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     name     H     AB   average  eb_estimate   alpha1  \\\n",
       "playerID                                                                 \n",
       "aaronha01      Hank Aaron  3771  12364  0.304998     0.303943  3846.88   \n",
       "aaronto01    Tommie Aaron   216    944  0.228814     0.236040   291.88   \n",
       "abadan01        Andy Abad     2     21  0.095238     0.248366    77.88   \n",
       "abadijo01     John Abadie    11     49  0.224490     0.254355    86.88   \n",
       "abbated01  Ed Abbaticchio   772   3044  0.253614     0.254117   847.88   \n",
       "\n",
       "             beta1  \n",
       "playerID            \n",
       "aaronha01  8809.69  \n",
       "aaronto01   944.69  \n",
       "abadan01    235.69  \n",
       "abadijo01   254.69  \n",
       "abbated01  2488.69  "
      ]
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   "source": [
    "career_eb = career_eb.assign(alpha1 = lambda x: alpha0 + x['H'],\n",
    "                             beta1 = lambda x: beta0 + x['AB'] - x['H'])\n",
    "career_eb.head()"
   ]
  },
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   "source": [
    "### Figure 4.1"
   ]
  },
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   "cell_type": "markdown",
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    "editable": true
   },
   "source": [
    "#### Setup: Yankees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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     "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",
       "      <th>alpha1</th>\n",
       "      <th>beta1</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>brosisc01</th>\n",
       "      <td>Scott Brosius</td>\n",
       "      <td>1001</td>\n",
       "      <td>3889</td>\n",
       "      <td>0.257393</td>\n",
       "      <td>0.257530</td>\n",
       "      <td>1076.88</td>\n",
       "      <td>3104.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>jeterde01</th>\n",
       "      <td>Derek Jeter</td>\n",
       "      <td>3465</td>\n",
       "      <td>11195</td>\n",
       "      <td>0.309513</td>\n",
       "      <td>0.308236</td>\n",
       "      <td>3540.88</td>\n",
       "      <td>7946.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>knoblch01</th>\n",
       "      <td>Chuck Knoblauch</td>\n",
       "      <td>1839</td>\n",
       "      <td>6366</td>\n",
       "      <td>0.288878</td>\n",
       "      <td>0.287581</td>\n",
       "      <td>1914.88</td>\n",
       "      <td>4743.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>martiti02</th>\n",
       "      <td>Tino Martinez</td>\n",
       "      <td>1925</td>\n",
       "      <td>7111</td>\n",
       "      <td>0.270707</td>\n",
       "      <td>0.270259</td>\n",
       "      <td>2000.88</td>\n",
       "      <td>5402.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>posadjo01</th>\n",
       "      <td>Jorge Posada</td>\n",
       "      <td>1664</td>\n",
       "      <td>6092</td>\n",
       "      <td>0.273145</td>\n",
       "      <td>0.272513</td>\n",
       "      <td>1739.88</td>\n",
       "      <td>4644.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>strawda01</th>\n",
       "      <td>Darryl Strawberry</td>\n",
       "      <td>1401</td>\n",
       "      <td>5418</td>\n",
       "      <td>0.258583</td>\n",
       "      <td>0.258622</td>\n",
       "      <td>1476.88</td>\n",
       "      <td>4233.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>willibe02</th>\n",
       "      <td>Bernie Williams</td>\n",
       "      <td>2336</td>\n",
       "      <td>7869</td>\n",
       "      <td>0.296861</td>\n",
       "      <td>0.295517</td>\n",
       "      <td>2411.88</td>\n",
       "      <td>5749.69</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        name     H     AB   average  eb_estimate   alpha1  \\\n",
       "playerID                                                                    \n",
       "brosisc01      Scott Brosius  1001   3889  0.257393     0.257530  1076.88   \n",
       "jeterde01        Derek Jeter  3465  11195  0.309513     0.308236  3540.88   \n",
       "knoblch01    Chuck Knoblauch  1839   6366  0.288878     0.287581  1914.88   \n",
       "martiti02      Tino Martinez  1925   7111  0.270707     0.270259  2000.88   \n",
       "posadjo01       Jorge Posada  1664   6092  0.273145     0.272513  1739.88   \n",
       "strawda01  Darryl Strawberry  1401   5418  0.258583     0.258622  1476.88   \n",
       "willibe02    Bernie Williams  2336   7869  0.296861     0.295517  2411.88   \n",
       "\n",
       "             beta1  \n",
       "playerID            \n",
       "brosisc01  3104.69  \n",
       "jeterde01  7946.69  \n",
       "knoblch01  4743.69  \n",
       "martiti02  5402.69  \n",
       "posadjo01  4644.69  \n",
       "strawda01  4233.69  \n",
       "willibe02  5749.69  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drobs_fav_yankees = ['willibe02', 'strawda01','knoblch01',\n",
    "                     'jeterde01', 'posadjo01', 'martiti02',\n",
    "                     'brosisc01']\n",
    "\n",
    "yankee_1998_career = career_eb.loc[drobs_fav_yankees].sort_index()\n",
    "yankee_1998_career"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
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   "source": [
    "Python doesn't have an equivalent of R's `qbeta` function. We'll have to roll our own."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "source": [
    "# TODO: Change this to use np.beta\n",
    "def qbeta(alpha, beta):\n",
    "    \"\"\"\n",
    "    Generate the probability density function of the Beta\n",
    "    distribution for a given alpha and beta.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    alpha: float\n",
    "    beta: float\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    tuple: x, Beta pdf\n",
    "    \"\"\"\n",
    "    x = np.linspace(ss.beta.ppf(0.01, alpha, beta),\n",
    "                    ss.beta.ppf(0.99, alpha, beta), num=100)\n",
    "    return (x, ss.beta.pdf(x, alpha, beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    "It feels like there has to be a better way to do this. If you find one, let me know."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109028550>"
      ]
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IEBdCBIiroYHmH34gLDOzw/eNsbGYhw2TIN4Dqqq6M3EvCptobRyV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\nSsQVCoVCoQhSlIgrFAqFQhGk/H+4I/kr+QZbdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10affe048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 10))\n",
    "for id_, row in yankee_1998_career.iterrows():\n",
    "    plt.plot(*qbeta(row['alpha1'], row['beta1']), label=row['name'])\n",
    "\n",
    "plt.plot(*qbeta(alpha0, beta0), 'k--')\n",
    "plt.legend()\n",
    "plt.xlabel('Batting Average')\n",
    "plt.ylabel('density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Section 4.3 - Credible Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def qbeta(alpha, beta_, q=50., size=10000):\n",
    "    return np.percentile(beta(alpha, beta_, size=size), q=q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### TODO: Figure 4.2\n",
    "### TODO: Figure 4.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>name</th>\n",
       "      <th>H</th>\n",
       "      <th>AB</th>\n",
       "      <th>average</th>\n",
       "      <th>eb_estimate</th>\n",
       "      <th>alpha1</th>\n",
       "      <th>beta1</th>\n",
       "      <th>low</th>\n",
       "      <th>high</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>brosisc01</th>\n",
       "      <td>Scott Brosius</td>\n",
       "      <td>1001</td>\n",
       "      <td>3889</td>\n",
       "      <td>0.257393</td>\n",
       "      <td>0.257530</td>\n",
       "      <td>1076.88</td>\n",
       "      <td>3104.69</td>\n",
       "      <td>0.244244</td>\n",
       "      <td>0.270904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>jeterde01</th>\n",
       "      <td>Derek Jeter</td>\n",
       "      <td>3465</td>\n",
       "      <td>11195</td>\n",
       "      <td>0.309513</td>\n",
       "      <td>0.308236</td>\n",
       "      <td>3540.88</td>\n",
       "      <td>7946.69</td>\n",
       "      <td>0.299789</td>\n",
       "      <td>0.316680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>knoblch01</th>\n",
       "      <td>Chuck Knoblauch</td>\n",
       "      <td>1839</td>\n",
       "      <td>6366</td>\n",
       "      <td>0.288878</td>\n",
       "      <td>0.287581</td>\n",
       "      <td>1914.88</td>\n",
       "      <td>4743.69</td>\n",
       "      <td>0.276539</td>\n",
       "      <td>0.298585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>martiti02</th>\n",
       "      <td>Tino Martinez</td>\n",
       "      <td>1925</td>\n",
       "      <td>7111</td>\n",
       "      <td>0.270707</td>\n",
       "      <td>0.270259</td>\n",
       "      <td>2000.88</td>\n",
       "      <td>5402.69</td>\n",
       "      <td>0.260127</td>\n",
       "      <td>0.280295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>posadjo01</th>\n",
       "      <td>Jorge Posada</td>\n",
       "      <td>1664</td>\n",
       "      <td>6092</td>\n",
       "      <td>0.273145</td>\n",
       "      <td>0.272513</td>\n",
       "      <td>1739.88</td>\n",
       "      <td>4644.69</td>\n",
       "      <td>0.261575</td>\n",
       "      <td>0.283693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>strawda01</th>\n",
       "      <td>Darryl Strawberry</td>\n",
       "      <td>1401</td>\n",
       "      <td>5418</td>\n",
       "      <td>0.258583</td>\n",
       "      <td>0.258622</td>\n",
       "      <td>1476.88</td>\n",
       "      <td>4233.69</td>\n",
       "      <td>0.247376</td>\n",
       "      <td>0.270415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>willibe02</th>\n",
       "      <td>Bernie Williams</td>\n",
       "      <td>2336</td>\n",
       "      <td>7869</td>\n",
       "      <td>0.296861</td>\n",
       "      <td>0.295517</td>\n",
       "      <td>2411.88</td>\n",
       "      <td>5749.69</td>\n",
       "      <td>0.285621</td>\n",
       "      <td>0.305538</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        name     H     AB   average  eb_estimate   alpha1  \\\n",
       "playerID                                                                    \n",
       "brosisc01      Scott Brosius  1001   3889  0.257393     0.257530  1076.88   \n",
       "jeterde01        Derek Jeter  3465  11195  0.309513     0.308236  3540.88   \n",
       "knoblch01    Chuck Knoblauch  1839   6366  0.288878     0.287581  1914.88   \n",
       "martiti02      Tino Martinez  1925   7111  0.270707     0.270259  2000.88   \n",
       "posadjo01       Jorge Posada  1664   6092  0.273145     0.272513  1739.88   \n",
       "strawda01  Darryl Strawberry  1401   5418  0.258583     0.258622  1476.88   \n",
       "willibe02    Bernie Williams  2336   7869  0.296861     0.295517  2411.88   \n",
       "\n",
       "             beta1       low      high  \n",
       "playerID                                \n",
       "brosisc01  3104.69  0.244244  0.270904  \n",
       "jeterde01  7946.69  0.299789  0.316680  \n",
       "knoblch01  4743.69  0.276539  0.298585  \n",
       "martiti02  5402.69  0.260127  0.280295  \n",
       "posadjo01  4644.69  0.261575  0.283693  \n",
       "strawda01  4233.69  0.247376  0.270415  \n",
       "willibe02  5749.69  0.285621  0.305538  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yankee_1998_career = (\n",
    "    yankee_1998_career\n",
    "    .assign(low = lambda df: df.apply(lambda x: qbeta(x['alpha1'], x['beta1'], q=2.5), axis=1))\n",
    "    .assign(high = lambda df: df.apply(lambda x: qbeta(x['alpha1'], x['beta1'], q=97.5), axis=1))\n",
    ")\n",
    "\n",
    "yankee_1998_career"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    "## Section 4.4 - Credible Intervals and Confidence Intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### TODO: Figure 4.4"
   ]
  }
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