chapter_07.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Chapter 07 - Beta Binomial Regression\n",
    "### Setup Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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",
       "    </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  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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\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)\n",
    "\n",
    "career_eb = career_eb.assign(alpha1 = lambda x: alpha0 + x['H'],\n",
    "                             beta1 = lambda x: beta0 + x['AB'] - x['H'])\n",
    "career_eb.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Figure 7.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Matplotlib doesn't have an easy way to get a trendline, so we'll have to do it on our own. Yes, I know this is easier with Seaborn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def calculate_trend(x, y):\n",
    "    z = np.polyfit(x, y, 1)\n",
    "    p = np.poly1d(z)\n",
    "#     print(\"y = {:.6f}x + ({:.6f})\".format(z[0],z[1]))\n",
    "    return p(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Since the x-axis is on a log scale, we'll need to fit our linear trendline to `log(AB)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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XH7S0ZOHzTPJcbsf7a/dnmNcLMVtBfbcrHWl6vNv0ALZTmkE9ShA2uQCIcpEQxu9k9hqu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\nYd8EvKiaWRQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fcea978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = career_eb.query(\"AB > 10\")['AB'].values\n",
    "y = career_eb.query(\"AB > 10\")['average'].values\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(x, y, color='k')\n",
    "plt.plot(x, calculate_trend(np.log(x), y), color='steelblue', linewidth=2)\n",
    "\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Number of at-bats (AB)')\n",
    "plt.ylabel('Raw batting average (H / AB)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Figure 7.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "There might be a more elegant way of doing this, but the code below is pretty straight-forward for anyone familiar with matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SHugE+TBjLRh02+7der6LxaJv+YxfwOfV8cStfjjMqm+359RvYvFbpBJm8o9r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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111bf0c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=2, nrows=1, sharey=True, figsize=(12, 6))\n",
    "\n",
    "axes[0].scatter(x, y, color='k')\n",
    "axes[1].scatter(x, career_eb.query(\"AB > 10\")['eb_estimate'], color='k')\n",
    "\n",
    "axes[0].plot(x, calculate_trend(np.log(x), y), color='steelblue', linewidth=2)\n",
    "axes[1].plot(x, calculate_trend(np.log(x), career_eb.query(\"AB > 10\")['eb_estimate']),\n",
    "             color='steelblue', linewidth=2)\n",
    "\n",
    "prior = alpha0 / (alpha0 + beta0)\n",
    "axes[0].axhline(prior, color='r', linestyle='--', linewidth=2)\n",
    "axes[1].axhline(prior, color='r', linestyle='--', linewidth=2)\n",
    "\n",
    "axes[0].set_title('Raw')\n",
    "axes[1].set_title('With EB Shrinkage')\n",
    "\n",
    "axes[0].set_xlabel('AB')\n",
    "axes[1].set_xlabel('AB')\n",
    "\n",
    "axes[0].set_ylabel('average')\n",
    "axes[1].set_ylabel('average')\n",
    "\n",
    "axes[0].set_xscale('log')\n",
    "axes[1].set_xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Section 7.3 - Step 1: Fit the model across all players"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "from pymc3 import Model, Beta, Binomial, Normal, traceplot, find_MAP\n",
    "from pymc3 import glm"
   ]
  },
  {
   "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",
       "      <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  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "career_eb.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MCMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as model:\n",
    "    alpha = ''\n",
    "    beta = ''\n",
    "    \n",
    "    true_average = Beta('true_average', alpha=alpha, beta=beta)\n",
    "    hits = Binomial('hits', n='AB', p=true_average)\n",
    "    \n",
    "    map_estimate = find_MAP(model)\n",
    "    \n",
    "    print(map_estimate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GLM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as glm_model:"
   ]
  }
 ],
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