AustinRochford/pydata-nyc-2017-nba-fouls-python.ipynb

## pydata-nyc-2017-nba-fouls-python.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "A Dockerfile that will produce a container with all the dependencies necessary to run this notebook is available [here](https://github.com/AustinRochford/notebooks)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Clear the `theano` cache before each run to avoid subtle bugs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "!rm -rf /home/jovyan/.theano/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "from itertools import product\n",
    "import logging\n",
    "import pickle\n",
    "from warnings import filterwarnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.offsetbox import AnchoredText\n",
    "from matplotlib.ticker import FuncFormatter, StrMethodFormatter\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from theano import shared, tensor as tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# keep theano from complaining about compile locks for small models\n",
    "(logging.getLogger('theano.gof.compilelock')\n",
    "        .setLevel(logging.CRITICAL))\n",
    "\n",
    "# silence PyMC3 warnings (there aren't many)\n",
    "filterwarnings(\n",
    "    'ignore', \".*diverging samples after tuning.*\",\n",
    "    module='pymc3'\n",
    ")\n",
    "filterwarnings(\n",
    "    'ignore', \".*acceptance probability.*\",\n",
    "    module='pymc3'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "pct_formatter = StrMethodFormatter('{x:.1%}')\n",
    "\n",
    "blue, green, *_ = sns.color_palette()\n",
    "\n",
    "# configure pyplot for readability when rendered as a slideshow and projected\n",
    "sns.set(color_codes=True)\n",
    "\n",
    "plt.rc('figure', figsize=(8, 6))\n",
    "\n",
    "LABELSIZE = 14\n",
    "plt.rc('axes', labelsize=LABELSIZE)\n",
    "plt.rc('axes', titlesize=LABELSIZE)\n",
    "plt.rc('figure', titlesize=LABELSIZE)\n",
    "plt.rc('legend', fontsize=LABELSIZE)\n",
    "plt.rc('xtick', labelsize=LABELSIZE)\n",
    "plt.rc('ytick', labelsize=LABELSIZE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "SEED = 207183 # from random.org, for reproducibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Understanding NBA Foul Calls with Python\n",
    "\n",
    "<table border=\"0\">\n",
    "    <tr>\n",
    "        <td><img src=\"https://www.numfocus.org/wp-content/uploads/website.png\" width=400></td>\n",
    "        <td><img src=\"http://data-sports.abs-cbn.com/dev/media-upload/1499473043_nba-secondary-logo-small.jpg\" width=400></td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "\n",
    "## PyData NYC &#8226; Nov 27, 2017 &#8226; [@AustinRochford](https://twitter.com/AustinRochford)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## About Me\n",
    "\n",
    "<center><img src='http://austinrochford.com/resources/img/bball.jpg' width=300></center>\n",
    "\n",
    "### Principal Data Scientist @ [Monetate Labs](http://www.monetate.com/) &#8226; PyMC3 contributor\n",
    "\n",
    "### [@AustinRochford](https://twitter.com/AustinRochford) &#8226; [austinrochford.com](http://austinrochford.com) &#8226; [github.com/AustinRochford](http://github.com/AustinRochford)\n",
    "\n",
    "### [austin.rochford@gmail.com](mailto:arochford@monetate.com) &#8226; [arochford@monetate.com](mailto:arochford@monetate.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## About this Talk\n",
    "\n",
    "<hr style=\"height:5px; visibility:hidden;\" />\n",
    "\n",
    "<script src=\"https://gist.github.com/AustinRochford/0edef7cb3a8916fbe283188ee7df0923.js\"></script>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Last Two Minute Report\n",
    "\n",
    "<center><img src=\"https://upload.wikimedia.org/wikipedia/commons/7/76/Kyrie_Irving_Free_Throw.jpg\" width=700></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Since late in the 2014-2015 season, the NBA has issued [last two minute reports](http://official.nba.com/2017-18-nba-officiating-last-two-minute-reports/).  These reports give the league's assessment of the correctness of fall calls and non-calls in the last two minutes of any game where the score difference was three or fewer points at any point in the last two minutes.\n",
    "\n",
    "These reports are notably different from play-by-play logs, in that they include information on non-calls for notable on-court interactions.  This non-call information presents a unique opportunity to study the factors that impact foul calls.  There is a level of subjectivity inherent in the the NBA's definition of notable on-court interactions which we attempt to mitigate later using season-specific factors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Scraping the data\n",
    "\n",
    "<center><iframe src=\"https://pudding.cool/2017/02/two-minute-report/\" height=400 width=600></iframe></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Loading the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We download the data locally to be kind to GitHub."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%%bash\n",
    "DATA_URI=https://raw.githubusercontent.com/polygraph-cool/last-two-minute-report/32f1c43dfa06c2e7652cc51ea65758007f2a1a01/output/all_games.csv\n",
    "DATA_DEST=/tmp/all_games.csv\n",
    "\n",
    "if [[ ! -e $DATA_DEST ]];\n",
    "then\n",
    "    wget -q -O $DATA_DEST $DATA_URI\n",
    "fi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We use only a subset of the columns in the source data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "USECOLS = [\n",
    "    'period',\n",
    "    'seconds_left',\n",
    "    'call_type',\n",
    "    'committing_player',\n",
    "    'disadvantaged_player',\n",
    "    'review_decision',\n",
    "    'play_id',\n",
    "    'away',\n",
    "    'home',\n",
    "    'date',\n",
    "    'score_away',\n",
    "    'score_home',\n",
    "    'disadvantaged_team',\n",
    "    'committing_team'\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "orig_df = pd.read_csv(\n",
    "    '/tmp/all_games.csv',\n",
    "    usecols=USECOLS,\n",
    "    index_col='play_id',\n",
    "    parse_dates=['date']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16300, 13)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orig_df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The each row of the `DataFrame` represents a play and each column describes an attrbiute of the play:\n",
    "\n",
    "* `period` is the period of the game,\n",
    "* `seconds_left` is the number of seconds remaining in the game,\n",
    "* `call_type` is the type of call\n",
    "* `committing_player` and `disadvantaged_player` are the names of the players involved in the play,\n",
    "* `review_decision` is the opinion of the league reviewer on whether or not the play was called correctly:\n",
    "    * `review_decision = \"INC\"` means the call was an incorrect noncall,\n",
    "    * `review_decision = \"CNC\"` means the call was an correct noncall,\n",
    "    * `review_decision = \"IC\"` means the call was an incorrect call,\n",
    "    * `review_decision = \"CC\"` means the call was an correct call,\n",
    "* `away` and `home` are the abbreviations of the teams involved in the game,\n",
    "* `date` is the date on which the game was played,\n",
    "* `score_away` and `score_home` are the scores of the `away` and `home` team during the play, respectively,\n",
    "* `disadvantaged_team` and `committing_team` indicate how each team is involved in the play."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>play_id</th>\n",
       "      <th>20150301CLEHOU-0</th>\n",
       "      <th>20150301CLEHOU-1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>period</th>\n",
       "      <td>Q4</td>\n",
       "      <td>Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>seconds_left</th>\n",
       "      <td>112</td>\n",
       "      <td>103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>call_type</th>\n",
       "      <td>Foul: Shooting</td>\n",
       "      <td>Foul: Shooting</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>committing_player</th>\n",
       "      <td>Josh Smith</td>\n",
       "      <td>J.R. Smith</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>disadvantaged_player</th>\n",
       "      <td>Kevin Love</td>\n",
       "      <td>James Harden</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>review_decision</th>\n",
       "      <td>CNC</td>\n",
       "      <td>CC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>away</th>\n",
       "      <td>CLE</td>\n",
       "      <td>CLE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>home</th>\n",
       "      <td>HOU</td>\n",
       "      <td>HOU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <td>2015-03-01 00:00:00</td>\n",
       "      <td>2015-03-01 00:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score_away</th>\n",
       "      <td>103</td>\n",
       "      <td>103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score_home</th>\n",
       "      <td>105</td>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>disadvantaged_team</th>\n",
       "      <td>CLE</td>\n",
       "      <td>HOU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>committing_team</th>\n",
       "      <td>HOU</td>\n",
       "      <td>CLE</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "play_id                  20150301CLEHOU-0     20150301CLEHOU-1\n",
       "period                                 Q4                   Q4\n",
       "seconds_left                          112                  103\n",
       "call_type                  Foul: Shooting       Foul: Shooting\n",
       "committing_player              Josh Smith           J.R. Smith\n",
       "disadvantaged_player           Kevin Love         James Harden\n",
       "review_decision                       CNC                   CC\n",
       "away                                  CLE                  CLE\n",
       "home                                  HOU                  HOU\n",
       "date                  2015-03-01 00:00:00  2015-03-01 00:00:00\n",
       "score_away                            103                  103\n",
       "score_home                            105                  105\n",
       "disadvantaged_team                    CLE                  HOU\n",
       "committing_team                       HOU                  CLE"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orig_df.head(n=2).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Research questions\n",
    "\n",
    "1. How does game context impact foul calls?\n",
    "2. Is (not) committing and/or drawing fouls a measurable player skill?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "First we examine the types of calls present in the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Foul: Personal                       4736\n",
       "Foul: Shooting                       4201\n",
       "Foul: Offensive                      2846\n",
       "Foul: Loose Ball                     1316\n",
       "Turnover: Traveling                   779\n",
       "Instant Replay: Support Ruling        607\n",
       "Foul: Defense 3 Second                277\n",
       "Instant Replay: Overturn Ruling       191\n",
       "Foul: Personal Take                   172\n",
       "Turnover: 3 Second Violation          139\n",
       "Turnover: 24 Second Violation         126\n",
       "Turnover: 5 Second Inbound             99\n",
       "Stoppage: Out-of-Bounds                96\n",
       "Violation: Lane                        84\n",
       "Foul: Away from Play                   82\n",
       "Violation: Defensive Goaltending       65\n",
       "Turnover: Stepped out of Bounds        59\n",
       "Violation: Kicked Ball                 58\n",
       "Foul: Technical                        38\n",
       "Turnover: Backcourt Turnover           33\n",
       "Violation: Delay of Game               32\n",
       "Turnover: Out of Bounds                29\n",
       "Turnover: Offensive Goaltending        26\n",
       "Other                                  26\n",
       "Turnover: Palming                      24\n",
       "Turnover: Double Dribble               21\n",
       "Foul: Inbound                          19\n",
       "Foul: Double Personal                  11\n",
       "Violation: Double Lane                  9\n",
       "Violation: Jump Ball                    9\n",
       "Foul: Clear Path                        8\n",
       "Turnover: Discontinue Dribble           7\n",
       "Foul: Flagrant Type 1                   6\n",
       "Turnover: 5 Second Violation            6\n",
       "Turnover: Inbound Turnover              6\n",
       "Turnover: Illegal Screen                5\n",
       "Turnover: 8 Second Violation            5\n",
       "Foul: Double Technical                  5\n",
       "Foul: Delay Technical                   5\n",
       "Turnover: Lane Violation                5\n",
       "Turnover: Kicked Ball Violation         4\n",
       "Ejection: Second Technical              4\n",
       "Turnover: 10 Second Violation           3\n",
       "Turnover: Lost Ball Possession          3\n",
       "Turnover: Punched Ball                  2\n",
       "Turnover: Jump Ball Violation           2\n",
       "Jump Ball                               2\n",
       "Turnover: 24 Second violationCC         1\n",
       "Turnover: Illegal Assist                1\n",
       "Other: Timeout                          1\n",
       "Stoppage: Other                         1\n",
       "Other: Jump Ball                        1\n",
       "Other: Held Ball                        1\n",
       "Turnover: Lost Ball Out of Bounds       1\n",
       "Violation: Other                        1\n",
       "Foul: Punching                          1\n",
       "Instant Replay: Support ruling          1\n",
       "Shot Clock                              1\n",
       "Name: call_type, dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orig_df.call_type.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The portion of `call_type` before the colon is the general category of the call.  We count the occurence of these categories below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIiIJYOETERFJAAufiIhIAlQu/NLSUk3mICIiIg1SufB79OiBb775BhcuXNBkHiIiItIA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\n5Nml4SzZoAMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcde2eebf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(orig_df.call_type\n",
    "        .str.split(':', expand=True).iloc[:, 0]\n",
    "        .value_counts()\n",
    "        .plot(kind='bar', color=blue, logy=True, title=\"Call types\")\n",
    "        .set_ylabel(\"Frequency\"));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We restrict our attention to foul calls, though other call types would be interesting to study in the future."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "foul_df = orig_df[\n",
    "    orig_df.call_type\n",
    "           .fillna(\"UNKNOWN\")\n",
    "           .str.startswith(\"Foul\")\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We count the foul call types below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IyMjzmEqlwu3btz/6GocPH4arqysaNGiQ5/l2dnb4z3/+A19fXyQlJcHOzg7u7u6YNGmS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\nwWAwmgH/D//ehRlp4rH9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcde0dd2320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(foul_df.call_type\n",
    "        .str.split(': ', expand=True).iloc[:, 1]\n",
    "        .value_counts()\n",
    "        .plot(kind='bar', color=blue, logy=True, title=\"Foul Types\")\n",
    "        .set_ylabel(\"Frequency\"));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We restrict our attention to the five foul types below, which generally involve two players.  This subset of fouls allows us to pursue our second research question in the most direct manner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "FOULS = [\n",
    "    f\"Foul: {foul_type}\"\n",
    "    for foul_type in [\n",
    "        \"Personal\",\n",
    "        \"Shooting\",\n",
    "        \"Offensive\",\n",
    "        \"Loose Ball\",\n",
    "        \"Away from Play\"\n",
    "    ]\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Data transformation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<center><img src=\"https://c1.staticflickr.com/5/4003/4633000725_8817dcedb9_b.jpg\" width=400></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "There are a number of misspelled team names in the data, which we correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "TEAM_MAP = {\n",
    "    \"NKY\": \"NYK\",\n",
    "    \"COS\": \"BOS\",\n",
    "    \"SAT\": \"SAS\",\n",
    "    \"CHi\": \"CHI\",\n",
    "    \"LA)\": \"LAC\",\n",
    "    \"AT)\": \"ATL\",\n",
    "    \"ARL\": \"ATL\"\n",
    "}\n",
    "\n",
    "def correct_team_name(col):\n",
    "    def _correct_team_name(df):\n",
    "        return df[col].apply(lambda team_name: TEAM_MAP.get(team_name, team_name))\n",
    "    \n",
    "    return _correct_team_name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We also convert each game date to NBA season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def date_to_season(date):\n",
    "    if date >= datetime.datetime(2017, 10, 17):\n",
    "        return '2017-2018'\n",
    "    elif date >= datetime.datetime(2016, 10, 25):\n",
    "        return '2016-2017'\n",
    "    elif date >= datetime.datetime(2015, 10, 27):\n",
    "        return '2015-2016'\n",
    "    else:\n",
    "        return '2014-2015'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We clean the data by\n",
    "\n",
    "* restricting to plays that occured during the last two minutes of regulation,\n",
    "* imputing incorrect non-calls when `review_decision` is missing,\n",
    "* correcting team names,\n",
    "* converting game dates to seasons,\n",
    "* restricting to the foul types discussed above,\n",
    "* restricting to the plays that happened during the [2015-2016](https://en.wikipedia.org/wiki/2015%E2%80%9316_NBA_season) and [2016-2017](https://en.wikipedia.org/wiki/2016%E2%80%9317_NBA_season) regular seasons (those are the only full seasons in the data set as of November 2017),\n",
    "* and dropping unneeded rows and columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "clean_df = (foul_df.where(lambda df: df.period == \"Q4\")\n",
    "                   .where(lambda df: (df.date.between(datetime.datetime(2016, 10, 25),\n",
    "                                                      datetime.datetime(2017, 4, 12))\n",
    "                                     | df.date.between(datetime.datetime(2015, 10, 27),\n",
    "                                                       datetime.datetime(2016, 5, 30)))\n",
    "                         )\n",
    "                   .assign(\n",
    "                       review_decision=lambda df: df.review_decision.fillna(\"INC\"),\n",
    "                       committing_team=correct_team_name('committing_team'),\n",
    "                       disadvantged_team=correct_team_name('disadvantaged_team'),\n",
    "                       away=correct_team_name('away'),\n",
    "                       home=correct_team_name('home'),\n",
    "                       season=lambda df: df.date.apply(date_to_season)\n",
    "                    )\n",
    "                   .where(lambda df: df.call_type.isin(FOULS))\n",
    "                   .dropna()\n",
    "                   .drop('period', axis=1)\n",
    "                   .assign(call_type=lambda df: (df.call_type\n",
    "                                                   .str.split(': ', expand=True)  \n",
    "                                                   .iloc[:, 1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "About 50% of the rows in the full data set remain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5516564417177914"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clean_df.shape[0] / orig_df.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>play_id</th>\n",
       "      <th>20151028INDTOR-1</th>\n",
       "      <th>20151028INDTOR-2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>seconds_left</th>\n",
       "      <td>89</td>\n",
       "      <td>73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>call_type</th>\n",
       "      <td>Shooting</td>\n",
       "      <td>Shooting</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>committing_player</th>\n",
       "      <td>Ian Mahinmi</td>\n",
       "      <td>Bismack Biyombo</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>disadvantaged_player</th>\n",
       "      <td>DeMar DeRozan</td>\n",
       "      <td>Paul George</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>review_decision</th>\n",
       "      <td>CC</td>\n",
       "      <td>IC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>away</th>\n",
       "      <td>IND</td>\n",
       "      <td>IND</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>home</th>\n",
       "      <td>TOR</td>\n",
       "      <td>TOR</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <td>2015-10-28 00:00:00</td>\n",
       "      <td>2015-10-28 00:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score_away</th>\n",
       "      <td>99</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score_home</th>\n",
       "      <td>106</td>\n",
       "      <td>106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>disadvantaged_team</th>\n",
       "      <td>TOR</td>\n",
       "      <td>IND</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>committing_team</th>\n",
       "      <td>IND</td>\n",
       "      <td>TOR</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>disadvantged_team</th>\n",
       "      <td>TOR</td>\n",
       "      <td>IND</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>season</th>\n",
       "      <td>2015-2016</td>\n",
       "      <td>2015-2016</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "play_id                  20151028INDTOR-1     20151028INDTOR-2\n",
       "seconds_left                           89                   73\n",
       "call_type                        Shooting             Shooting\n",
       "committing_player             Ian Mahinmi      Bismack Biyombo\n",
       "disadvantaged_player        DeMar DeRozan          Paul George\n",
       "review_decision                        CC                   IC\n",
       "away                                  IND                  IND\n",
       "home                                  TOR                  TOR\n",
       "date                  2015-10-28 00:00:00  2015-10-28 00:00:00\n",
       "score_away                             99                   99\n",
       "score_home                            106                  106\n",
       "disadvantaged_team                    TOR                  IND\n",
       "committing_team                       IND                  TOR\n",
       "disadvantged_team                     TOR                  IND\n",
       "season                          2015-2016            2015-2016"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clean_df.head(n=2).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We use `scikit-learn`'s [`LabelEncoder`](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html) to transform categorical features (call type, player, and season) to integer ids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "call_type_enc = LabelEncoder().fit(\n",
    "    clean_df.call_type\n",
    ")\n",
    "n_call_type = call_type_enc.classes_.size\n",
    "\n",
    "player_enc = LabelEncoder().fit(\n",
    "    np.concatenate((\n",
    "        clean_df.committing_player,\n",
    "        clean_df.disadvantaged_player\n",
    "    ))\n",
    ")\n",
    "n_player = player_enc.classes_.size\n",
    "\n",
    "season_enc = LabelEncoder().fit(\n",
    "    clean_df.season\n",
    ")\n",
    "n_season = season_enc.classes_.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We transform the data by\n",
    "\n",
    "* rounding `seconds_left` to the nearest second (purely for convenience),\n",
    "* transforming categorical features to integer ids,\n",
    "* setting `foul_called` equal to zero if a foul was not called, or one if it was,\n",
    "* setting `score_committing` and `score_disadvantaged` to the score of the committing and disadvantaged teams, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "df = (clean_df[['seconds_left']]\n",
    "              .round(0)\n",
    "              .assign(\n",
    "                call_type=call_type_enc.transform(clean_df.call_type),\n",
    "                foul_called=1. * clean_df.review_decision.isin(['CC', 'INC']),\n",
    "                player_committing=player_enc.transform(clean_df.committing_player),\n",
    "                player_disadvantaged=player_enc.transform(clean_df.disadvantaged_player),\n",
    "                score_committing=clean_df.score_home.where(\n",
    "                    clean_df.committing_team == clean_df.home,\n",
    "                    clean_df.score_away\n",
    "                ),\n",
    "                score_disadvantaged=clean_df.score_home.where(\n",
    "                    clean_df.disadvantaged_team == clean_df.home,\n",
    "                    clean_df.score_away\n",
    "                ),\n",
    "                season=season_enc.transform(clean_df.season)\n",
    "              ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The resulting `DataFrame` is ready for analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>play_id</th>\n",
       "      <th>20151028INDTOR-1</th>\n",
       "      <th>20151028INDTOR-2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>seconds_left</th>\n",
       "      <td>89.0</td>\n",
       "      <td>73.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>call_type</th>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>foul_called</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>player_committing</th>\n",
       "      <td>162.0</td>\n",
       "      <td>36.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>player_disadvantaged</th>\n",
       "      <td>98.0</td>\n",
       "      <td>358.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score_committing</th>\n",
       "      <td>99.0</td>\n",
       "      <td>106.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score_disadvantaged</th>\n",
       "      <td>106.0</td>\n",
       "      <td>99.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>season</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "play_id               20151028INDTOR-1  20151028INDTOR-2\n",
       "seconds_left                      89.0              73.0\n",
       "call_type                          4.0               4.0\n",
       "foul_called                        1.0               0.0\n",
       "player_committing                162.0              36.0\n",
       "player_disadvantaged              98.0             358.0\n",
       "score_committing                  99.0             106.0\n",
       "score_disadvantaged              106.0              99.0\n",
       "season                             0.0               0.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(n=2).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Modeling\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <td>\n",
    "            <img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/GeorgeEPBox.jpg/1200px-GeorgeEPBox.jpg\" width=300>\n",
    "        </td>\n",
    "        <td>\n",
    "            George Box (via <a href=\"http://dustintran.com/talks/Tran_Edward.pdf\">Dustin Tran</a>):\n",
    "            <ol>\n",
    "                <li>Build a model of the science</li>\n",
    "                <li>Infer the model given data</li>\n",
    "                <li>Criticize the model given data</li>\n",
    "            </ol>\n",
    "        </td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Build a model of the science"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def make_foul_rate_yaxis(ax, label=\"Observed foul call rate\"):\n",
    "    ax.yaxis.set_major_formatter(pct_formatter)\n",
    "    ax.set_ylabel(label)\n",
    "    \n",
    "    return ax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Below we examine the foul call rate by season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5+WH58uXYsmWL6B327t0bFy5cQG5uLpYtW4b58+fX2U8QhMdad/Bw1qNLly4IDAyEr68v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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcde30b9588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_foul_rate_yaxis(\n",
    "    df.pivot_table('foul_called', 'season')\n",
    "      .rename(index=season_enc.inverse_transform)\n",
    "      .rename_axis(\"Season\")\n",
    "      .plot(kind='bar', rot=0, legend=False)\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "There is a pronounced difference between the foul call rate in the 2015-2016 and 2016-2017 NBA seasons.  This change in foul call rates is due to a rule change between these seasons meant to [cut down on hack-a-Shaq](https://www.usatoday.com/story/sports/nba/2016/07/12/nba-approves-rule-changes-hack-a-shaq-situations/87013528/) fouls.\n",
    "\n",
    "Our first model accounts for this difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Each season has a different foul call rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We use [`pymc3`](http://docs.pymc.io/) to specify our models.  Our first model is given by\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\beta^{\\textrm{season}}_s \n",
    "        & \\sim N(0, 5) \\\\\n",
    "    \\eta^{\\textrm{game}}_k\n",
    "        & = \\beta^{\\textrm{season}}_{s(k)} \\\\\n",
    "    p_k\n",
    "        & = \\textrm{sigm}\\left(\\eta^{\\textrm{game}}_k\\right).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "We use a logistic regression model with different factors for each season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "\n",
    "with pm.Model() as base_model:\n",
    "    β_season = pm.Normal('β_season', 0., 5., shape=n_season)\n",
    "    p = pm.Deterministic('p', pm.math.sigmoid(β_season))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Foul calls are like flipping a weighted coin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$y_k \\sim \\textrm{Bernoulli}(p_k)$$\n",
    "\n",
    "When building models, we will wrap each feature in a Theano [`shared`](http://deeplearning.net/software/theano/library/compile/shared.html) variable in order to eventually facilitate posterior predictive sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "season = shared(df.season.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "with base_model:\n",
    "    y = pm.Bernoulli(\n",
    "        'y', p[season],\n",
    "        observed=df.foul_called.values\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Infer the model given data\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <td>\n",
    "            <img src=\"https://upload.wikimedia.org/wikipedia/commons/1/18/Bayes%27_Theorem_MMB_01.jpg\" width=400>\n",
    "        </td>\n",
    "        <td>\n",
    "            <img src=\"https://i.pinimg.com/736x/ce/42/5c/ce425cdcb13afce4636d419f4ba786b0--stanislaw-ulam-richard-feynman.jpg\" width=360>\n",
    "        </td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "PyMC3 provides an accessible interface to state-of-the art Bayesian inference algorithms.  Throughout this talk, we will use PyMC3 to perform [Hamiltonian Monte Carlo inference](https://en.wikipedia.org/wiki/Hybrid_Monte_Carlo) (HMC).\n",
    "\n",
    "Unfortunately there is not enough time in this talk to do these deep topics justice.  For the curious:\n",
    "\n",
    "* [_Probabilistic Programming and \n",
    "Bayesian Methods for Hackers_](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers#pymc3) is an accessible, open-source introduction to Bayesian statistics using PyMC3.\n",
    "* [_Statistical Rethinking_](http://xcelab.net/rm/statistical-rethinking/) is an acessible introduction to Bayesian data analysis originally using [Stan](http://mc-stan.org/), whose examples have been [ported to PyMC3](https://github.com/pymc-devs/resources/tree/master/Rethinking).\n",
    "* [_Bayesian Analysis with Python_](https://www.amazon.com/Bayesian-Analysis-Python-Osvaldo-Martin/dp/1785883801) is an accessible introduction to Bayesian statistics using PyMC3.\n",
    "* [_Bayesian Data Analysis_](http://www.stat.columbia.edu/~gelman/book/) (commonly known as BDA3) is an excellent reference on applied Bayesian statistics.\n",
    "* [_A Conceptual Introduction to Hamiltonian Monte Carlo_](https://arxiv.org/abs/1701.02434) pairs an intuitive conceptual motivation of HMC algorithms with extensive references to the rigorous mathematics of HMC.\n",
    "* [_The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo_](https://arxiv.org/abs/1111.4246) is the seminal paper on the NUTS algorithm that is central to modern Bayesian statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "NJOBS = 3\n",
    "\n",
    "SAMPLE_KWARGS = {\n",
    "    'draws': 1000,\n",
    "    'njobs': NJOBS,\n",
    "    'random_seed': [\n",
    "        SEED + i for i in range(NJOBS)\n",
    "    ]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1500/1500 [00:06<00:00, 235.48it/s]\n"
     ]
    }
   ],
   "source": [
    "with base_model:\n",
    "    base_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Convergence diagnostics\n",
    "\n",
    "> The folk theorem [of statistical computing] is this: When you have computational problems, often there’s a problem with your model.\n",
    "\n",
    "&mdash; <a href=\"http://andrewgelman.com/2008/05/13/the_folk_theore/\">Andrew Gelman</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We rely on three diagnostics to ensure that our samples have converged to the posterior distribution:\n",
    "\n",
    "* Energy plots: if the two distributions in the energy plot differ significantly (espescially in the tails), the sampling was not very efficient.\n",
    "* Bayesian fraction of missing information (BFMI): BFMI quantifies this difference with a number between zero and one. A BFMI close to (or exceeding) one is preferable, and a BFMI lower than 0.2 is indicative of efficiency issues.\n",
    "* [Gelman-Rubin statistics](http://blog.stata.com/2016/05/26/gelman-rubin-convergence-diagnostic-using-multiple-chains/): Gelman-Rubin statistics near one are preferable, and values less than 1.1 are generally taken to indicate convergence.\n",
    "\n",
    "For more information on energy plots and BFMI consult [_Robust Statistical Workflow with PyStan_](http://mc-stan.org/users/documentation/case-studies/pystan_workflow.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bfmi = pm.bfmi(base_trace)\n",
    "max_gr = max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(base_trace).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "CONVERGENCE_TITLE = lambda: f\"BFMI = {bfmi:.2f}\\nGelman-Rubin = {max_gr:.3f}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
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2aPzutb0cbJEBgDg2SOiKCeXZ1/dhmHD2khpOqCvjvGW1mCasfWOf3aUJkRcSumLC6OyJ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\nhBAWktAVQggLSegKIYSF/j/pXxkbICveKQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdca6596d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(pm.energyplot(base_trace, legend=False, figsize=(6, 4))\n",
    "   .set_title(CONVERGENCE_TITLE()));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Criticize the model given data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We use the samples from `p`'s posterior distribution to calculate [residuals](https://en.wikipedia.org/wiki/Errors_and_residuals), which we use to criticize our models.  These residuals allow us to assess how well our model describes the data-generation process and to discover unmodeled sources of variation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.39621111,  0.30601358],\n",
       "       [ 0.40373111,  0.31909179],\n",
       "       [ 0.40255341,  0.3074904 ],\n",
       "       ..., \n",
       "       [ 0.40184561,  0.30958139],\n",
       "       [ 0.40790953,  0.30464071],\n",
       "       [ 0.39905963,  0.31899429]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_trace['p']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3000, 2)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_trace['p'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid_df = (df.assign(p_hat=base_trace['p'][:, df.season].mean(axis=0))\n",
    "              .assign(resid=lambda df: df.foul_called - df.p_hat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>foul_called</th>\n",
       "      <th>p_hat</th>\n",
       "      <th>resid</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>play_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.403732</td>\n",
       "      <td>0.596268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403732</td>\n",
       "      <td>-0.403732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.403732</td>\n",
       "      <td>0.596268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403732</td>\n",
       "      <td>-0.403732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-6</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403732</td>\n",
       "      <td>-0.403732</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  foul_called     p_hat     resid\n",
       "play_id                                          \n",
       "20151028INDTOR-1          1.0  0.403732  0.596268\n",
       "20151028INDTOR-2          0.0  0.403732 -0.403732\n",
       "20151028INDTOR-3          1.0  0.403732  0.596268\n",
       "20151028INDTOR-4          0.0  0.403732 -0.403732\n",
       "20151028INDTOR-6          0.0  0.403732 -0.403732"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resid_df[['foul_called', 'p_hat', 'resid']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The per-season residuals are quite small, which is to be expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>resid</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>season</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-2016</th>\n",
       "      <td>-0.000019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-2017</th>\n",
       "      <td>0.000026</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              resid\n",
       "season             \n",
       "2015-2016 -0.000019\n",
       "2016-2017  0.000026"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(resid_df.pivot_table('resid', 'season')\n",
    "         .rename(index=season_enc.inverse_transform))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Intentional fouls\n",
    "\n",
    "<hr style=\"height:5px; visibility:hidden;\" />\n",
    "\n",
    "<center>\n",
    "<table>\n",
    "    <tr>\n",
    "        <td><img src=\"https://static1.squarespace.com/static/5150aec6e4b0e340ec52710a/t/51525c33e4b0b3e0d10f77ab/1364352052403/Data_Science_VD.png\" width=400></td>\n",
    "        <td><img src=\"https://sports.cbsimg.net/images/visual/whatshot/tdhugdj.jpg\" width=500></td>\n",
    "    </tr>\n",
    "</table>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Anyone who has watched a close basketball game will realize that we have neglected an important factor in late game foul calls &mdash; [intentional fouls](https://en.wikipedia.org/wiki/Flagrant_foul#Game_tactics).  Near the end of the game, intentional fouls are used by the losing team when they are on defense to end the leading team's possession as quickly as possible.\n",
    "\n",
    "The influence of intentional fouls in the plot below is shown by the rapidly increasing of the residuals as the number of seconds left in the game decreases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def make_time_axes(ax,\n",
    "                   xlabel=\"Seconds remaining in game\",\n",
    "                   ylabel=\"Observed foul call rate\"):\n",
    "    ax.invert_xaxis()\n",
    "    ax.set_xlabel(xlabel)\n",
    "    \n",
    "    return make_foul_rate_yaxis(ax, label=ylabel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PozEc2iAiItIDQ3qeRmMYSBAREelB7ednSPl5Go3h0AYREZEeGNLzNBrDQIKIiEgPDOl5\nGo3h0AYRERGpjYEEERERqY2BBBEREamNgQQRERGpjYEEERERqY2zNoiIGmAstzAm0iYGEkREDTCW\nWxgTaZOkhzb69+8PHx8f+Pr6Kv/FxsbWu21KSgrGjBmDgIAAPPfcc0hNTVWuO3r0KAYNGoTg4GDs\n2rVL9L7r169j8ODBuHv3rlbrQkSGx1huYWzoiksVSErOxLItaUhKzkRxmaLOurlrf6yzjnRD0j0S\nhYWF+OKLL9CzZ89Gt8vJycH8+fOxZs0aDBw4ED///DPmzJmDvXv3omvXroiLi0NiYiJat26NcePG\nISwsDI6OjgCAuLg4zJo1C66urrqoEhEZEDdnG2VPRPVr0r3GeoZqrqvGXiPdkmyPRElJCSorK5Un\n/Mbs3r0bAwYMwLBhw2BlZYWhQ4eiX79+2LNnD27fvo179+6hV69e6NChAzw9PXH58mUAwKFDh1Be\nXo7x48druzpEZIAmD++GIC93dGrrgCAvd4O9hbGha6xniL1G+ifZHgm5XA4A+PDDD5Geng4AGDJk\nCBYsWAB7e3vRtllZWXjqqadEy7y9vXHixAmYmZmJlldVVcHa2hqFhYVISEhAfHw8XnvtNRQWFiIy\nMhKjR4/WYq2IyJAYyy2MDV1jPUPsNdI/yQYS1b0I/fr1w8qVK5Gbm4s5c+YgNjYWq1evFm1bUFBQ\np+fCyckJMpkMrVu3hrW1NdLT09G6dWtcv34djz32GJYvX44XXngBn3/+OcaMGYPQ0FCEhYWhf//+\naNWqVYPlcnGxRYsWFhqvr5ubg8b3aajYFmJsDzG2x0Om0hZvTeqNpH1nkHe3FG1cbfH6+F5wtGvZ\n5DpTp6vjQ7KBxGOPPYbdu3crX3fp0gVz585FVFQU/vWvf8Ha2rrJfVT3RsTFxSEmJgaVlZX45z//\niezsbJw+fRpLly5F//798cEHH8De3h5+fn44c+YMQkNDG9ynTFba/MrV4ubmgPz8oqY3NAGP2hbG\nPj2Px4YY2+MhU2uLV0d6Kf9fUVqB/NIK0brq9qi9zlRp+vhoLCiRbCBRHw8PDwiCgPz8fHh6eiqX\nu7i4QCaTibYtKChQJlCGhITg2LFjAACFQoFx48YhPj4elpaWKC4uVg6V2NjYoKjIdL6YxoDT84iI\n9EuyyZZnzpzBqlWrRMsuXboES0tLtG3bVrTcx8cHmZmZomUZGRno1atXnf1+8skn6N27N3r37g0A\nsLe3R2FhIYAHwYednZ0mq0FaxkQroocamyZJpC2SDSRcXV3x+eefY8uWLVAoFLh8+TLWrVuHCRMm\nwNLSEiNGjMBvv/0GAJg4cSJ+++03pKamQqFQ4Ntvv0V6ejomTpwo2ufVq1exf/9+xMTEKJf16dMH\nKSkpyMvLQ1ZWFgICAnRaT2qe2olVTLQiU1bdQ3f1ZhHScm5h2+EL+i4SmQDJDm14enri3//+Nz78\n8EOsW7cOLi4uGDFiBN566y0AwJUrV1Ba+iBf4YknnsCaNWuQmJiIhQsXolOnTtiwYQM6duwo2ufS\npUsxf/58ODg8HOuZN28eZs+ejbVr12LOnDmNJlqS9FRPx6uZI0FkqthDR/pgJgiCoO9CGBJtJDeZ\nWtJUY9gWYmwPMbbHQ/W1RVJypujmTEFe7pLOGdJksjSPDTEmWxIR0SMztB46JksbBwYSRERGwtBu\noMWhGOMg2WRLIiIybkyWNg7skSAiIr0wtKEYqh8DCSIi0gtDG4qh+nFog4iIiNTGHgkiIlIy9ufX\nkOYxkCAiIiVOyaRHxUCCVMYrFSLjxymZ9KgYSJDKeKVCZPzcnG2U3+/q10SNYSBBKuOVCpHx45RM\nelQMJEhlvFIhMn6ckkmPioEEqYxXKkREVBsDCVIZr1SIqBqTr6kaAwkiInpkTL6maryzJRERPTIm\nX1O1Rnskxo8fDzMzM5V2tHfvXo0UiIiIpI/J11St0UBiyJAhuioHEREZECZfU7VGA4mZM2eqtJPd\nu3drpDBERGQYmHxN1R4p2fLq1avIzs6GQqFQLsvLy0NSUhImTJig8cIRERGRtKkcSOzbtw9LliyB\njY0NSktL4eDggMLCQrRt2xbTp0/XZhmJiIhIolSetfHxxx9j48aNOHnyJCwtLfH7778jNTUVPj4+\neOqpp7RZRiKDUlyqQFJyJpZtSUNSciaKyxRNv4mIyECp3CNx69YtDB48GACUMzk8PT0xb948zJs3\nD/v379dKAYkMjanMr+cNiVTDdiJjp3Ig4e7ujpycHHh5ecHV1RVZWVno2bMn2rZtiytXrmizjEQG\nxVTm15tKwNRctdvpz+tyONm1ZFBBRkPlQCIiIgIvvPACfv31VwwfPhyvv/46hgwZgvPnz6NHjx7a\nLCORQTGV+fWmEjA1V+12kRVVQFZUweCLjIbKgURkZCR69uwJe3t7xMTEwNraGhkZGfDy8kJ0dLQ2\ny2i0qrs8C0oUcLZryauTBhha17CpzK83lYCpuWq3U03aDL4M7XtDhuuRpn/27t37wZtatMBbb72l\nlQKZkppdntV4dVKXoXWhm8r8elMJmJqrZjvJSxSQFVUo12kz+DK07w0ZLpUDidmzZze6ft26dc0u\njKlh17Bq2E7SZCoBU3PVbKfiMgW2Hb6gk+CL3xvSFZUDCVtbW9Hr+/fv49q1a7h27RrGjBmj8YKZ\nAnYNq4btRMZCl8EXvzekKyoHEsuXL693+cGDB/HHH39orECmpPpqpGaOBNXFLnSiR8fvDemKmSAI\nQnN2cP/+ffTt2xdpaWmaKpOk5efXnzTVHG5uDlrZryFiW4ixPcTYHg+xLcTYHmKabg83N4cG16nc\nI1FWVnd8rby8HCkpKWjZkpnA9Ojqyyp303ehjBQz+IlIW1QOJAICApR3tKzJwsICMTExGi1UtRs3\nbiA+Ph5//PEHrK2tMXToULzzzjuwtLSss21KSgqSkpJw7do1eHp6YtasWXj66acBAEePHkV8fDwq\nKiowZ84cTJw4Ufm+69evIyIiAvv374erq6tW6kH1qy+rfOk/+umzSEaLGfxExkkKFwkqBxKfffZZ\nnUDCysoKHh4eaNWqlcYLBjx4jHnXrl2RmpqKoqIizJw5E+vWrasTuOTk5GD+/PlYs2YNBg4ciJ9/\n/hlz5szB3r170bVrV8TFxSExMRGtW7fGuHHjEBYWBkdHRwBAXFwcZs2axSBCD5hVrjtsayLjJIWL\nBJUDieDgYG2Wo46MjAxkZ2fjk08+gaOjIxwdHREVFYWlS5di7ty5MDd/+Lyx3bt3Y8CAARg2bBgA\nYOjQoejXrx/27NmD6dOn4969e+jVqxeAB88HuXz5Mvz9/XHo0CGUl5dj/PjxOq0bPcCscvWocwXC\ntiYyTlK4SGg0kOjbt2+9wxn1OXHihEYKVC0rKwvt2rUT9RT07NkTcrkc165dQ6dOnUTb1n4Cqbe3\nN06cOFGn/FVVVbC2tkZhYSESEhIQHx+P1157DYWFhYiMjMTo0aM1Wg9qGLPKVVM7cKi8dx+n/7wD\nQPUrELY1aYIUutFJTAoXCY0GEgsXLlT+Pz8/H7t27cLw4cPRpUsXVFRU4OrVqzh69CimTZum8YIV\nFBQohx+qOTk5AQBkMpkokGhoW5lMhtatW8Pa2hrp6elo3bo1rl+/jsceewzLly/HCy+8gM8//xxj\nxoxBaGgowsLC0L9//0aHalxcbNGihYXmKvr/NZYRa6zcUH9OhCm2RWN2/3hZ1HVpbyPOESooUTTZ\nZg21tSHi8fGQrtviv1vTRMeilVULLIwM0mkZGmOKx8Zbk3ojad8Z5N0tRRtXW7w+vhcc7R4Ed7pq\nj0YDieeff175/1deeQXr16+Hj4/4ymfUqFFYs2YNIiIitFPCGqpnqqraS1K9XVxcHGJiYlBZWYl/\n/vOfyM7OxunTp7F06VL0798fH3zwAezt7eHn54czZ84gNDS0wX3KZKXNr0gtnLb0ENtCzM3NAbl5\n4vaoqhLP2Ha2a2kybcbj4yF9tEXtYzE3r0gyfw9TPjZeHeml/H9FaQXySyukOf3z9OnT6Natbneo\nt7c3zp49q17JGuHq6gqZTCZaJpfLletqcnFxqbNtQUGBcruQkBAcO3YMAKBQKDBu3DjEx8fD0tIS\nxcXFsLe3BwDY2NigqMg0D0SSrtpdl90fc0YLC/NmDVMYaxe1qvUy1vprmxS60Ul6VA4kOnbsiDVr\n1uD1119XDiMUFhbi448/hoeHh8YL5uPjg7y8PNy6dQvu7u4AgLNnz6JVq1bw9PSss21mZqZoWUZG\nhjLBsqZPPvkEvXv3Vj6AzN7eHoWFhXBxcUFBQQHs7Ow0Xhei5qgvv6G5Jz0pZHprg6r1Mtb6axtz\nbag+KgcSy5Ytw+zZs7FlyxbY2DyIQsvKyuDk5ISPPvpI4wXz9vaGv78/EhISsGTJEhQUFCApKQkR\nEREwMzPDiBEjEB8fj+DgYEycOBHPP/88UlNTERISgqNHjyI9PR1Lly4V7fPq1avYv38/kpOTlcv6\n9OmDlJQUhIaGIisrCwEBARqvC1FzaOP5DFLI9NYGVetlrPXXtoaORfbwmDaVAwk/Pz8cPXoUGRkZ\nyMvLg0KhgLu7O3r16gUrKyutFG7dunWIj4/HsGHDYGtri5EjRyI6OhoAcOXKFZSWPshXeOKJJ7Bm\nzRokJiZi4cKF6NSpEzZs2ICOHTuK9rd06VLMnz8fDg4Px3rmzZuH2bNnY+3atZgzZ47W7olBVJs+\nf3w13UUtlROJqvViF71msYfHtDUaSJSXl8Pa2hrAw1tkd+vWTZQrUVVVhbKyMmUvhSa1adMGGzdu\nrHfd+fPnRa+HDRumvI9EQ7Zu3Vpn2RNPPIGDBw+qX0giNenzx1fTXdRSOZGoWi920WsWe3hMW6OB\nRHBwMM6cOQOg4VtkC4IAMzMznDt3TjslJDJS+vzx1fRwiVROJKrWS5eP8zYF7OExbY0GEv/5z3+U\n/6/vap6I1GdMP77GVBd6dOzhMW2NBhJ9+vRR/v/JJ5+EXC5X3hSquLgYJ06cgKenJ7y8vBraBRE1\nwJh+fI2pLvTo2MNj2lROtjx06BAWL16MU6dOoaysDOPHj8etW7dQWVmJ9957D2PHjtVmOYk0RiqJ\ngcb042tMddEEqRxjRLqgciDx0UcfYe3atQCAL7/8Evfv38cvv/yCrKwsxMXFMZAgyWnox1wqiYFk\nvDRxjDEYIUOhciDx999/Y9CgQQCAn376Cc8++yxsbGzQp08fXL9+XWsFJFJXQz/m+kwM5MnBNGji\nGGPAS4bCvOlNHrC3t0deXh5kMhlOnDiBIUOGAADu3LmDli35Q0jS09CPee1EQF0mBlafHK7eLEJa\nzi1sO3xBZ59NuqOJY0wqM2GImqJyj8SoUaPw4osvwtzcHN26dYO/vz9KSkqwYMECDBw4UJtlJFJL\nQzMJ9JkYyJODadDEMWasNw0j46NyILFgwQJ4e3ujqKgIzz77LADA0tISHTp0wIIFC7RWQCJ11fwx\nd3GwQuW9+1i2Jc0g7rxIhk0TyafGetMwMj4qBxJmZmYYPXo0rl69iuzsbPTr1w8tW7ZEfHy8yo/1\nJtKlmj/mScmZkvgR5TRJqqmxXgJjvWkYNZ/UepdUDiTu3LmDGTNm4MyZM2jRogUyMjJw48YNREZG\nYtOmTejSpYs2y0nULFL5EdX2NEmp/cBom6HXV5e9BOwNMx5S611SOdlyyZIlePzxx/HLL78oeyDa\ntm2LUaNG4V//+pfWCki6VVyqQFJyJpZtSUNSciaKyxT6LpJG6DPBUpdMLZnT0OurywB38vBuCPJy\nR6e2DgjycmdvmAGTyoVRNZV7JH799Vf8/PPPsLW1VQYSZmZmiI6OZrKlEZFapKsppjKkILUfGG0z\n9PrqspeANw0zHlLrXVI5kLCzs8O9e/fqLL9z5w4EQdBooUh/DP2HuSGm8iMqtR8YbTP0+ppKgEua\nJbXjRuVAom/fvvjnP/+Jt956CwBw9+5dnD9/HgkJCQgNDdVaAUm3DP2H2dRJ7QdG2wy9vqYS4JJm\nSe24MRNU7E4oLCzE22+/je+///7BG83MYG5ujlGjRmHx4sVwcHDQakGlIj+/qOmNHpGbm4NW9quO\n4jIFth3A5+/QAAAgAElEQVTWX/KalNpCCtgeYmyPh9gWYmwPMU23h5tbw+d4lXskHB0dsXHjRty9\nexd//fUXrKys4OHhAXt7e+Tm5ppMIGHspBbpEpHmGfpsF5KWJmdtFBcXY8GCBQgMDERAQADWr1+P\nnj17wsvLC/b29ti6dStGjx6ti7ISEZEGGPpsF5KWJnsk1q5di4sXL2L58uVQKBTYtGkTEhMTMWbM\nGLzzzjv43//+h6VLl+qirEREpAHGmlRN+tFkIPH9999j8+bNyhtOde3aFS+//DK2bNmCkSNH4t//\n/jecnZ21XlCqH7soiehRMamaNKnJQOLOnTuiu1Z2794d5eXl+PTTTxEUFKTVwlHTjPW+D0SkPYY+\n24WkReVky2pmZmawsLBgECER7KIkokfFpGrSJJVvkU3SZCq3fiYiImlqskfi/v372LFjh+julfUt\ni4iI0E4JqVHsopQG5qoQkalqMpBwd3fH5s2bG11mZmbGQEJP2EUpDcxVISJTpdKsDSJqHHNViMhU\nMUeCSAOYq0JEpuqRZ20QUV3MVSEiU8VAgkgDmKtCRKaKQxtERESkNvZIEBERGYnqqegFJQo427XU\nyVR0BhJEpMT7YZCm8ZjSrZpT0atpe9hVsoHEjz/+iKioKFhaWoqWf/bZZwgMDKyzvUKhwPLly/HD\nDz+grKwMAQEBiI+PR5s2bQAAixYtwrfffgtPT0+sW7cOnTp1Ur538+bNuHDhAj744AOt1kkqNPHF\n5o+DceL9MEjTeEzplj6moks2kJDL5ejatSu+/vprlbZfs2YN/vjjD2zbtg3Ozs54//33MWvWLOze\nvRvHjx/HuXPn8H//93/Yvn07NmzYgNWrVwMAcnNzsX37duzbt0+b1ZEUTXyx+eNgnGr/6OTdLUFS\nciYDxnowmFYN77GiW/p4sqtkA4nCwkI4OjqqtO39+/exZ88evP/++/D09AQAzJ8/H/3798e5c+dw\n7tw59O3bFzY2Nhg8eDD27t2rfG9cXBzefPNNuLq6aqUeUqSJLzZ/HIxT7R+horJ7uMaAsV4MplXD\nR5brVvXU85o5Etom2UCioKAAd+7cweTJk5GTk4O2bdti2rRpGDNmTJ1t//e//6GoqAje3t7KZa6u\nrmjbti0yMjJE296/fx/W1tYAgIMHD6KyshJmZmZ44YUX4OTkhGXLlqFDhw7arZyeaeKLzR8H41T7\nfhg375RAVlShXM+A8SEG06rhPVZ0q3oqupubA/Lzi5p+gwZINpBwdHSEh4cH5s6diyeeeALfffcd\n5s+fj9atW2PAgAGibQsKCgAATk5OouVOTk6QyWTw8/PDypUrUVxcjO+++w49evSAXC7H6tWrsXLl\nSsydOxfffPMNfv75Z/zrX//Cxo0bGyyXi4stWrSw0Hh93dwcNL7Phrw1qTeS9p1B3t1StHG1xevj\ne8HRrm6XrLxEgX83sF3Nfbg6WgMQsHz7qUb3pypdtoUh0GV7uAFY+o9+ytcrt6bhr/wS5WuPNg56\n//vo+/OrebRxEAXT+mgbqbRFY2ofU1r9LANoD13SVXtINpCIjIxEZGSk8nVYWBiOHDmCffv21Qkk\nGiIIAszMzNCvXz/4+flh8ODB6Ny5M9auXYtVq1ZhwoQJkMvl8PHxgZOTE0JCQrBs2bJG9ymTlTar\nXvXRZeRY7dWRXsr/V5RWIL+0os42ScmZyq7bi38VoKLinqjrtnofTW33KPTRFlKm7/aYMLgLKiru\nKa8mJwzuotfy6Ls9atJ320ipLaSA7SGm6fZoLCiRTCCRnJyMJUuWKF/XHpIAgA4dOuDMmTN1llfn\nN8hkMjg4PKysXC6Hi4sLAGDZsmXKICE9PR1nzpxBbGwsDh48CHt7ewCAjY0Niop4IFZTteuWXbzG\ni3fsbBjbhugByQQSY8eOxdixY5WvP/vsM7Rv3x5PP/20ctmlS5eUyZQ1eXp6wsnJCZmZmXjssccA\nAHl5ebh58yb8/f1F2yoUCsTFxeHdd9+FpaUl7O3tlcFDQUEB7OzstFE9g6RqHoQx5UswE5+I6NFI\n9hbZFRUVWLZsGbKzs6FQKPD111/jp59+wksvvQQASE1NRXh4OADAwsICEydORFJSEnJzc1FYWIgP\nPvgAffv2RdeuXUX7/fjjj9GnTx8EBAQAAAICApCRkYFbt24hJSUFwcHBuq2ohE0e3g1BXu7o1NYB\nQV7uDSZJqbqdIajOxL96swhpObew7fAFfReJiEjSJNMjUdu0adNQXl6OmTNnQiaToXPnzti4cSP8\n/PwAAEVFRbh69apy+1mzZqG0tBQvv/wyysvL8eSTT2LNmjWifV65cgUHDhzAl19+qVzWqlUrTJ8+\nHaNGjULbtm2xbt06ndTPEKjadWtMXbwcpiEiejRmgiAI+i6EIdFGMg+ThB7Sd1vUTBwFgCAvd70G\nSfpuD6lhezzEthBje4iZZLIlkRRwzrs06fJBRFLMk6mvTG56LRHRQwwkiGowpmEaqdDEiVmXDyKS\n4h0r6yuTru7NQNQUBhJEpFWaODHrMndFinkyUiwTUTUGEkSkVeqcBGv3Yjjbi3swtDnFWIrTmaVY\nJqJqDCSISKvUOQnW7sUI6NoaQV7uOnkQkRTzZKRYJqJqDCSISKvUOQnW7rWQFVVg6dQgnWTmSzFP\nRoplIqrGQIKItEqdkyC78nVLijNVyHAwkCAiyWFXvm5JcaYKGQ4GEkQkOezK1y3OCqHmYCBBWsUu\nU2oMjw9p4FASNQcDCSMixR9ldplSY3h8SAOHkqg5GEgYESn+KLPLlBrD40MaOJREzSHZx4jTo5Pi\nj3LtLlJ2mVJNPD6IDB97JIyIFMc52WVKjeHxQWT4GEgYESn+KBt6l6kU806MiaEfH0TEQMKo8EdZ\n86SYd0JEJCUMJIhX3Y2QYt4JEZGUMJAgXnU3Qop5J0REUsJAgnjV3Qgp5p0QEUkJAwky+avuxoZ2\nmHdCRNQ4BhISpcu8BV1edUsxH4NDO0RE6mMgIVG6PLnp8qpbiidtDu0QEamPd7aUKGM9uUmxXry7\nIhGR+tgjIVHGmrcgxXoxoVI1UhyWIiL9YyAhUcZ6cpNivZhQqRopDksRkf4xkJAoYz25GWu9TIEU\nh6WISP8YSBCRSqQ4LNUYDsUQ6QYDCSJSiRSHpRrDoRgi3WAgQUQqMbRhqdpDL3l3S5CUnMkeCiIN\nYyBBREap9lBMUdk9XGMPBZHGMZAgIqNUeyjm5p0SyIoqlOuZLEqkGQwkiMgo1R6KSUrOxF/5JcrX\nUk8WJTIUDCSIjBRnLYgZWrIokaHQ+y2yt2/fDj8/P2zYsEG0XBAErF+/HsOGDUOfPn0QGRmJixcv\nNrifGzduIDo6GsHBwQgJCcGyZctQWVkJALh79y4mT56MgIAAREdHo6KiQvTeqKgo7N27V/OVI9Kj\n6lkLV28WIS3nFrYdvqDvIulVdQ/F0qlBeH2sj0kHVUSapNdAYubMmUhJSUGbNm3qrNuxYwf279+P\njz76CD/99BMCAwMRFRVVJwiouS9nZ2ekpqZix44d+OOPP7Bu3ToAwKeffoquXbvi999/BwAkJycr\n33fo0CGUlpZi/PjxWqghkf7wBlJEpAt6DSS8vLywZcsWODg41Fm3c+dOTJkyBd27d4etrS1mzJiB\noqIiHD9+vM62GRkZyM7OxoIFC+Do6IgOHTogKioKu3fvRlVVFbKzsxESEgJLS0sMHDgQWVlZAICi\noiIkJCQgPj4eZmZmWq8vkS7xYWREpAt675GwsLCos7y8vBx//vknvL29lcssLS3RrVs3ZGRk1Nk+\nKysL7dq1g6urq3JZz549IZfLce3aNVGQUFVVBWtrawDAqlWr8Pzzz2PPnj0YN24cFi1a1GCPB5Gh\nmTy8G4K83NGprQOCvNyZE0BEWiHJZEu5XA5BEODk5CRa7uTkBJlMVmf7goICODo61tkWAGQyGXx9\nfXH06FH07dsXx44dw+jRo3Hy5EmcOnUKUVFROHDgAPbt24fY2Fjs3LkTU6dObbBsLi62aNGibvDT\nXG5udXtlTBXbQkzd9nADsPQf/TRbGAng8fEQ20KM7SGmq/aQZCDREEEQHnlbMzMzREZGYvbs2ejf\nvz8GDhyIZ555BuHh4YiLi8ORI0cwaNAgmJmZISQkBMnJyY0GEjJZaXOrUYebmwPy84ua3tCIVc8w\nKChRwNmupcnPMKjGY0OM7fEQ20KM7SGm6fZoLCjRWSCRnJyMJUuWKF/XN0RRzdnZGebm5nV6H+Ry\nObp3715ne1dX13q3rV7n4uKCrVu3Ktdt3LgRAQEB6NOnD/bv3w87OzsAgK2tLYqKpHcgmsI0vprP\nRahmyncdZGBFRIZCZ4HE2LFjMXbsWJW2tbKyQteuXZGRkYF+/R50zSoUCuTk5GD69Ol1tvfx8UFe\nXh5u3boFd3d3AMDZs2fRqlUreHp6ira9evUq9u7dq5y5YW9vrwweZDKZMqiQElN4+BBnGIgxsCIi\nQ6H3+0g0JCIiAtu2bcOFCxdQWlqKNWvWwN3dHQMGDAAArF69Gu+99x4AwNvbG/7+/khISEBRURH+\n+usvJCUlISIios5sjNjYWMTExChzKoKCgvD999+jvLwcqampCA4O1m1FVWAKJ1nOMHjQC5GUnIll\nW9KQdeWOaJ0x/s2JyDjoLUciLS0Nr776KgCgsrISOTk5+PjjjxEUFIT//ve/CA8Px507d/DGG29A\nLpfDz88PmzZtgqWlJQAgPz8fpaUP8xXWrVuH+Ph4DBs2DLa2thg5ciSio6NFn3ngwAFYW1sjLCxM\nuSw0NBRHjhxB//79ERwcjBdffFEHtX80tR8+ZIwn2eoZBTW78k1Nfb0Q1Yzxb05ExsFMeJQMRtJK\nMk9TSTHFZQpsO2zcORLVTDlhatmWNFHAaGvVAh3c7ZkjUYMpHx+1sS3E2B5iRplsSeqr/fAhMk61\ne556dnbF0n/0448jEUkaAwkiieBDpYjIEDGQIJII9jwRkSGS7KwNIiIikj4GEkRERKQ2Dm0QETWT\nPu8+awp3viVpYyBBRNRM+rz7rCnc+ZakjUMbRETNpM+7z5rCnW9J2hhIEBE1kz5v8c7by5O+cWiD\niKiZ9HkPEN5/hPSNgQQRUTPp8x4gvP8I6RuHNoiIiEht7JEgIpIATuMkQ8VAgsjEafoEpu7+TP1E\nymmcZKgYSBCZOE2fwNTdn9RPpNoOdDiNkwwVAwkiE6fpE5i6+5P6iVTbgU7tx8hzGicZCiZbEpk4\nTd+HQN39Sf1+CNoOdCYP74YgL3d0auuAIC93TuMkg8EeCSITp+n7EKi7P6nfD0HbPQacxkmGioEE\nkYnT9AlM3f1J/UQq9UCHSF8YSBARqUDqgQ6RvjCQINIiU5/SSETGj4GEkeIJTLtUbV+pT2kkImou\nBhJGiicw7VK1faU+pVHXGOASGR8GEkaKJzDtUrV9eW8AMQa4RMaHgYSR4glMu1RtX2b6izHAJTI+\nDCSMFE9g2qVq+zLTX4wBLpHxYSBhpHgC0y62r3oY4BIZHwYSRAbM0JIXGYARGR8GEkQGjMmLRKRv\nfGgXkQFj8iIR6RsDCSIDJvUnZhKR8ePQBpEBY/IiEemb3nsktm/fDj8/P2zYsEG0fNWqVfD29oav\nr6/yX0BAQIP7uXHjBqKjoxEcHIyQkBAsW7YMlZWVAIC7d+9i8uTJCAgIQHR0NCoqKkTvjYqKwt69\nezVfOSItq05eXDo1CK+P9ZF0oiURGSe9BhIzZ85ESkoK2rRpU2edXC7HpEmTkJGRofz3xx9/NLov\nZ2dnpKamYseOHfjjjz+wbt06AMCnn36Krl274vfffwcAJCcnK9936NAhlJaWYvz48RquHRmb4lIF\nkpIzsWxLGpKSM1FcptB3kYiI9E6vgYSXlxe2bNkCBweHOusKCwvrXV6fjIwMZGdnY8GCBXB0dESH\nDh0QFRWF3bt3o6qqCtnZ2QgJCYGlpSUGDhyIrKwsAEBRURESEhIQHx8PMzMzjdaNmkedk7a2T/TV\nMySu3ixCWs4tbDt8QaP7JyIyRHrNkZg5c2aD6woKCpCeno7Ro0fj5s2b6N69OxYuXAhfX98622Zl\nZaFdu3ZwdXVVLuvZsyfkcjmuXbsmChKqqqpgbW0N4MHwyfPPP489e/bgt99+Q48ePbB06VJYWVlp\nsJaaZQj3DdBEGdWZ1qjtqZCcISENhvAdIDIlkk22bN++PczNzZGQkAA7Ozts3LgRr7zyCo4cOSIK\nGIAHQYejo6NomZOTEwBAJpPB19cXR48eRd++fXHs2DGMHj0aJ0+exKlTpxAVFYUDBw5g3759iI2N\nxc6dOzF16tQGy+XiYosWLSw0Xl83N9V6X/67NU10srSyaoGFkUEaL09zNLeMbm4OKCgR9yYUlCia\nbCN13vMoPNo4iG7v7NHGQaP7b4guPsOQ7P7xsuS/A7rCY0OM7SGmq/aQbCCxYsUK0et58+bhq6++\nwpEjRzBx4sQm3y8IAgDAzMwMkZGRmD17Nvr374+BAwfimWeeQXh4OOLi4nDkyBEMGjQIZmZmCAkJ\nQXJycqOBhExW2qx61cfNzQFX/ndHpaus3LyiOq/z84vqbKdPzSmjm5sD8vOL4GwnrruzXcsm96HO\nex7FhMFdUFFxT/k3mjC4i9bbvro96AE3NweD+A7oAo8NMbaHmKbbo7GgRGeBRHJyMpYsWaJ8nZGR\n8Ujvt7CwQLt27XDr1q0661xdXSGTyUTL5HK5cp2Liwu2bt2qXLdx40YEBASgT58+2L9/P+zs7AAA\ntra2KCrSz4Goare8ITz0SBNlVGdao7anQvL2ztJgCN8BIlOis0Bi7NixGDt2rErb3rt3DytWrMBL\nL72Exx9/HABQWVmJa9euwdPTs872Pj4+yMvLw61bt+Du7g4AOHv2LFq1alVn+6tXr2Lv3r3KmRv2\n9vbK4EEmkymDCl1TdfzdEO4boIkyqnPS5oneNBjCd4DIlEhyaKNFixa4evUq4uLisHr1atjZ2WHt\n2rWwtLTEM888AwBYvXo1ysrKsHjxYnh7e8Pf3x8JCQlYsmQJCgoKkJSUhIiIiDqzMWJjYxETE6PM\nqQgKCsJnn32GSZMmITU1FcHBwTqvL6D6VZYhnCwNoYxkuHh8EUmL3qZ/pqWlKW80lZ2djaSkJPj6\n+uLVV18FAHzwwQdo27Ytxo4di9DQUFy+fBmfffaZsscgPz9fNMyxbt06FBcXY9iwYYiMjERISAii\no6NFn3ngwAFYW1sjLCxMuSw0NBTt2rVD//79UV5ejhdffFEHta9r8vBuCPJyR6e2Dgjyctf4VRbv\ngUBERNpgJlRnJZJKtJHMo4skoaTkTGUOBgAEeblL8qpOlbYwpel/TCATY3s8xLYQY3uIGWWyJemX\nMd0DgY/OJiKSDr0/a4N0w5ieEmlMQRERkaFjj4SJMKZMd07/IyKSDgYSJsKYMt2NKSgiIjJ0DCTI\n4BhTUEREZOiYI0FERERqY48EEZEBqZ7+XFCigLNdS6Oe/kyGgYEEEZEBqTn9uRqH+kifOLRBRGRA\nOP2ZpIaBBBGRATGme8KQceDQBhGRAame7lwzR4JInxhIEBEZkOrpz3y2BEkFhzaIiIhIbQwkiIiI\nSG0MJIiIiEhtDCSIiIhIbQwkiIiISG0MJIiIiEhtDCSIiIhIbQwkiIiISG0MJIiIiEhtDCSIiIhI\nbQwkiIiISG0MJIiIiEhtDCSIiIhIbQwkiIiISG0MJIiIiEhtDCSIiIhIbQwkiIiISG1mgiAI+i4E\nERERGSb2SBAREZHaGEgQERGR2hhIEBERkdoYSBAREZHaGEgQERGR2hhIEBERkdoYSBAREZHaGEho\n0fnz5zFq1CiEhoaKlqelpWHixIkIDAzE4MGD8cEHH+DevXvK9SkpKRgzZgwCAgLw3HPPITU1VddF\n14qG2uP333/HhAkTEBgYiBEjRmDnzp2i9du3b8fIkSMRGBiICRMmID09XZfF1olz585hypQpCAoK\nQr9+/fDmm2/i77//BtB0+xir//znPxg0aBD8/f0xadIk/PnnnwAeHEeRkZHo06cPhg4disTERJjK\n7XDef/99dO/eXfnaFI+N69evY9asWQgODkbfvn0xe/Zs5OXlATDtYwMAbty4gejoaAQHByMkJATL\nli1DZWWl9j9YIK04ePCg8NRTTwlvvPGGMGTIEOXy69evC/7+/sJnn30mKBQKIScnRxgwYICwefNm\nQRAE4dy5c4KPj4+QmpoqlJeXC999953g6+srnD9/Xl9V0YiG2uPWrVtCQECAsH37dqGsrEw4efKk\nEBgYKPz444+CIAjCDz/8IAQGBgppaWlCeXm5sHPnTiEwMFDIz8/XV1U0rrKyUhgwYICwatUqoaKi\nQigsLBRmzZolvPTSS022j7HauXOn8PTTTwvnz58XiouLhdWrVwvz5s0TysrKhJCQEOHDDz8UiouL\nhQsXLgghISHCjh079F1krcvOzhaefPJJoVu3boIgNP3dMVajRo0S5s2bJxQVFQm3b98WIiMjhenT\np5v0sVFt3LhxwsKFCwW5XC7k5uYKY8eOFVatWqX1z2WPhJaUlJTgiy++QL9+/UTLb9++jXHjxiEy\nMhKWlpbo3r07QkNDkZaWBgDYvXs3BgwYgGHDhsHKygpDhw5Fv379sGfPHn1UQ2Maao+vvvoKHTp0\nwKRJk2BtbY3AwECMGTMGu3btAgDs3LkTzz//PPr06QMrKytMnDgR7dq1wzfffKOPamjFjRs3kJ+f\nj+effx4tW7aEg4MDwsLCcO7cuSbbx1h98sknmD17Nrp16wY7OzvMnTsXCQkJOHbsGMrKyjBr1izY\n2dmha9eumDx5stG3R1VVFWJjY/HKK68ol5nisVFYWAgfHx/Mnz8f9vb2aNWqFSZMmIC0tDSTPTaq\nZWRkIDs7GwsWLICjoyM6dOiAqKgo7N69G1VVVVr9bAYSWvLiiy+iffv2dZb7+flhyZIlomU3b95E\nmzZtAABZWVno2bOnaL23tzcyMjK0V1gdaKg9mqpvVlYWvL29G1xvDDp06AAvLy/s2rULxcXFkMlk\nOHjwIEJDQ432eGhMXl4ecnNzUVpaitGjRyMoKAjR0dG4efMmsrKy0K1bN7Ro0UK5vbe3Ny5cuICK\nigo9llq7du3aBWtra4waNUq5zBSPDUdHRyxfvlz5ewk8CMTbtGljssdGtaysLLRr1w6urq7KZT17\n9oRcLse1a9e0+tkMJPTsm2++QVpamvJKo6CgAI6OjqJtnJycIJPJ9FE8rauvvs7Ozsr6NtQeBQUF\nOiujtpmbmyMxMRHff/89evfujb59++LGjRuIjY1tsn2M0c2bNwE8+G58/PHH+Pbbb6FQKDB37twG\n26OqqgpyuVwfxdW627dv46OPPkJcXJxouSkeG7VdvnwZSUlJeOONN0zy2Kipod9KAFo/JhhI6NG+\nffuwdOlSrF+/Hp06dWp0WzMzM90USgIEQWi0voKRJU8pFAq8/vrrGD58ONLT0/HTTz/B3d0d8+bN\nq3f7ptrH0FX/fV977TW0a9cOrVu3xty5c3Hy5ElRUnLt7Y21TZYvX44XX3wRXbp0aXJbYz82asrM\nzMTLL7+MV155BaNHj653G2M/Npqiq/ozkNCTjRs3IiEhAZs3b8bAgQOVy11cXOpEjwUFBaLuKmPS\nVH3rWy+Xy42qPU6cOIGrV69izpw5cHBwQJs2bfDmm2/ip59+grm5uUkdDwDQunVrAA+uJqt16NAB\nAJCfn1/v8WBhYaG8+jImJ06cQEZGBl5//fU660ztt6Km48ePY8qUKZg5cyZmzpwJAHB1dTWpY6O2\nhupfvU6bGEjowbZt27Br1y7s3LkTgYGBonU+Pj7IzMwULcvIyECvXr10WUSd8fX1bbS+9bXH2bNn\n4e/vr7Myatv9+/fr9LJUX3k/+eSTJnU8AEDbtm3h6uqK7Oxs5bLc3FwAwLhx43D+/HkoFArlurNn\nz6JHjx5o2bKlzsuqbV999RXy8vIwaNAgBAcHY9y4cQCA4OBgdOvWzeSODQA4c+YM5syZg5UrV2LS\npEnK5T4+PiZ1bNTm4+ODvLw83Lp1S7ns7NmzaNWqFTw9PbX74VqfF2Litm3bJpru+Ndffwn+/v5C\nZmZmvdtfvHhR8PHxEY4cOSJUVFQIhw4dEvz8/ISrV6/qqshaVbs97ty5I/Tu3Vv4/PPPhfLycuHX\nX38V/P39hd9//10QBEE4fvy44O/vr5z++emnnwrBwcFCQUGBvqqgcXfv3hWefPJJ4YMPPhBKSkqE\nu3fvCjNmzBDCw8ObbB9jtX79eiEkJET4888/hYKCAuHVV18Vpk+fLlRUVAihoaFCQkKCUFJSIpw7\nd04YMGCAcODAAX0XWSsKCgqEGzduKP/98ccfQrdu3YQbN24Iubm5JndsVFZWCs8++6ywZcuWOutM\n7dioT3h4uDB//nyhsLBQuHbtmhAWFiYkJiZq/XPNBMHIBpwlYvjw4fj7779RVVWFe/fuKSPiqKgo\nJCYmwtLSUrR9+/btcfjwYQDAd999h8TERFy7dg2dOnXCW2+9hUGDBum8DprUUHukpKTg5s2bWLVq\nFS5cuID27dtj2rRpGDt2rPK9u3fvxpYtW5CXl4fu3bvj7bffhp+fn76qohWZmZlYuXIlcnJyYGlp\niaCgILzzzjto27YtTp482Wj7GKPKykqsXLkSX3/9NSoqKjB48GDExcXB2dkZly5dwrvvvovMzEy4\nurpiwoQJmDZtmr6LrBO5ubkYOnQozp8/DwAmd2ykp6cjIiKi3h6GlJQUlJeXm+yxATyY8RQfH4+T\nJ0/C1tYWI0eOxLx582BhYaHVz2UgQURERGpjjgQRERGpjYEEERERqY2BBBEREamNgQQRERGpjYEE\nERERqY2BBBEREamNgQQR4e2338abb76p72I8ssWLFzf4TJLaXn31VaxevVrjZbh+/Tp8fX3x559/\navoBYzIAAAuqSURBVHzfRIaA95Eg0oJ79+7h3//+Nw4ePIibN2/C0tISXbp0weuvv46QkBB9F6+O\nt99+G6WlpVi/fr2+i0JEBoY9EkRasHLlShw+fBgffvgh0tPTcezYMYSFheGNN95AVlaWvotHRKQx\nDCSItODnn3/Gs88+ix49esDCwgK2traIjIzEqlWr4OjoCACoqqpCYmIinn76afTq1Qtjx47F2bNn\nlfu4e/cu3nrrLfTu3RsDBgzAihUrcP/+fQBAYWEh3nnnHQwcOBDBwcF47bXXcPHiReV7u3fvjsOH\nD+Oll16Cv78/nnvuOeVtlQFgz549CA0NRWBgIJYuXarcLwDcvn0bM2fORHBwMAICAjBp0iTk5OTU\nW88NGzbgtddew7x58+Dv74/79++joqIC7733HoYMGQJ/f39ERETg6tWrorJ9/fXXGD9+PPz8/PDK\nK6/gxo0biIqKQkBAAJ5//nn89ddfyu23bt2KZ555BgEBAXj66aexd+9e5bqaQzL79+/H6NGjkZyc\njCFDhiAwMBAxMTHKuk2ePBkrV65Uljs6OhqbN2/GgAEDEBQUpFxX3fZTpkyBn58fRo8ejePHj6N7\n9+64cOFCnTbIzc0VrQsNDcWePXswffp0BAQE4JlnnsGvv/5ab/tV/y369++P3r174/3330d8fLxo\nmKmx+m/YsAHTp09HYmIinnzySfTv3x/ffPMNvv76awwePBhBQUFITExUbi+XyzF//nw89dRTCAgI\nQHR0NG7fvt1g2YhUwUCCSAueeOIJHDhwABkZGaLlYWFhyifxbd26FV9++SU2bdqE9PR0vPTSS5gy\nZQoKCgoAPBj/r6ysxLFjx7B3715899132LJli3Jdbm4uDhw4gB9++AFubm6Ijo4WBQT/+c9/8P77\n7+OXX36Bk5MTNmzYAAC4cuUKlixZggULFuDXX39FYGAgvvvuO+X71q1bh7KyMhw9ehS//fYb+vbt\ni8WLFzdY14yMDPj7++PkyZOwsLBAQkICMjIysHPnTvz2228ICgrC1KlTUVlZqXzPzp07sXHjRhw8\neBCnT5/G1KlTMWPGDBw/fhz37t1T1jM9PR0rV67E2rVrcerUKbzzzjtYsmQJLl++XG9Z/v77b2Rk\nZODgwYPYvn07vv32Wxw7dqzebU+fPg2FQoEffvgBq1atwn//+19lwPTuu++ioqICP/74IxITE7Fu\n3boG61+fzZs3Y+bMmfjtt9/g6+srClJqunTpEhYvXozFixfjl19+gYuLCw4ePKhcr0r9T58+DWdn\nZ/z8888ICwvDe++9h99//x0pKSl4++238dFHH+HOnTsAgHfeeQfFxcX4+uuvcfz4cbi4uGDGjBmP\nVDei2hhIEGnBokWL0KpVK7zwwgsICQnBvHnzcODAAZSWliq32bNnD6ZMmYIuXbrA0tIS4eHh8PDw\nQEpKCmQyGX744QdER0fDwcEB7dq1w4cffojevXtDLpfjyJEjmD17Nlq3bg1bW1vMmTMHubm5okdv\nP/vss+jcuTNsbW0xaNAgXLp0CQCQmpqKrl27YsSIEWjZsiXGjh2Lzp07K99XWFgIS0tLWFtbo2XL\nlpg1a5boKrg2MzMzREREwMLCAlVVVdi3bx+io6PRtm1bWFlZ4c0330RJSYnoqvzZZ59FmzZt4Onp\nia5du6JHjx7w8/ODvb09goKClD0YvXv3xokTJ+Dt7Q0zMzOEhobCxsZGVM+aiouLMXv2bNja2qJH\njx7o2LGjst61CYKAqKgotGzZEoMHD4a1tTUuX76MqqoqfPfdd5g6dSpcXFzQsWNHvPTSS03/0WsI\nCQmBn58fWrZsiaFDhzZYhuq/RVhYGKysrBAVFQV7e3vlelXq36JFC+WDrAYNGgSZTIapU6fC2toa\nQ4YMQVVVFf766y/cvXsXR48exZw5c+Di4gJ7e3ssWLAAZ86caTAwI1JFC30XgMgYtW3bFjt27MCl\nS5fw66+/Ii0tDe+++y4+/PBDfPbZZ+jSpQuuXbuGFStWiK5WBUHAjRs3kJubi6qqKnTo0EG5rvqJ\np9nZ2RAEAU888YRyXZs2bWBnZ4cbN27A19cXAODh4aFcb2Njg4qKCgAPnhDYvn17UXk7d+6s7DGY\nNm2aMil04MCBGDZsGIYOHQozM7MG62pu/uCa5M6dOygpKcGsWbNE21dVVeHmzZui91SzsrJCmzZt\nRK8VCgWAB0mrGzduREpKivKqWqFQKNfX5uTkpBw6AgBra2tlvWtr37696KmI1tbWKC8vR0FBARQK\nhajte/ToUe8+GtJQ29eWl5cn+hxzc3N0795d+VqV+rdp00bZ1lZWVsplNV9XVFTg2rVrAIDx48eL\nymBhYYEbN26gS5cuj1RHomoMJIi06PHHH8fjjz+OiIgIyOVyvPTSS/jkk0+wfPlyWFtbIz4+HmFh\nYXXel5mZCeBBYNGQ+k7sNYcPqk/utdV3ElYoFMr9+fr64vvvv8fx48dx7NgxLFy4EAMGDGhwRkft\nkzEAbN++Hb169Wqw7LXL1lBZP/roI3zzzTfYuHEjfHx8YG5ujqCgoAb321Cw8yjbVre5paVlk+Vr\niKrbC4KAFi3EP8M136tK/eurR33Lqv82P/zwA1q3bq1S+YhUwaENIg27efMm4uLiUFRUJFru5OSE\nXr16obi4GADw2GOPiRIggQeJe8CDK1pzc3NcuXJFuS49PR0pKSnw8PCAmZmZ6L4FeXl5KCkpwWOP\nPdZk+dzd3XHjxg3RsprJkIWFhTA3N8fQoUPx7rvvIikpCYcPH4ZMJmty3w4ODnBxcWmwXo8qIyMD\noaGh8PPzg7m5Of766y8UFhaqtS9VOTs7w8LC4v+1c/cgybVhHMD/JbX0ZRS1OAiFLX05tBgZ5BDB\nKbdIyIakqDaJCMRPchBCKPqwrCUIomhrK90iG4SGoC+owLByKEkj0sye4QXBh/fhUVF4hv9vO2e4\nr3MfDtwX93WdG8FgMHXv8vKyILFqa2vx+PiYuv75+Ul7d/mcv0QigUgkShs/mUymxSfKBRMJojyr\nqanByckJZmZmcHt7m/qTwePx4PDwECqVCgCg0Wiws7MDv9+P7+9veL1eCIKAu7s7iMViqFQqrKys\nIBwOIxQKwWKxIBAIoLKyEr29vVhcXMTr6yve398xPz8PmUyG5ubmvz6fUqnE9fU1PB4P4vE49vf3\n0xb6wcHBVMNlIpHA+fk5xGIxqqqqMpq/RqPB2toabm5ukEgksLu7C7VandMCKJFIcHV1hY+PD9zf\n38PhcKC+vh6hUCjrsTIlEonQ2dmJra0tRCIRBAIB7O3tFSSWUqnExcUFvF4v4vE43G53Wh9NPudf\nXl4OQRDgdDoRDAYRi8WwtLQErVab1qRLlC2WNojyrKSkBNvb21heXsbY2BheXl5QXFyMxsZGmM1m\nqNVqAP/Vqp+fn6HX6xGJRCCVSuF0OlO1aofDAZPJhJ6eHpSVlUEQBIyOjgIALBYLbDYb+vv7kUwm\n0dHRgc3NzYy29tva2mAymWC32xGJRNDX14eBgYHUjsPCwgLsdjsUCkWqZu9yuTLerp+cnEQ0GsXI\nyAhisRiamprgdrvTehcyNTExAb1eD4VCAalUCpvNhuPjY7hcLlRXV2c9XqbMZjNmZ2fR3d0NmUyG\nqakpjI+PZ13i+JvW1lZMT0/DarXi6+sLw8PD6OrqwufnJ4D8z99oNGJubi71Dba0tGB9fT2tPEWU\nLZ5sSUT0P+LxOEpLSwEAZ2dnGBoagt/vR0VFRcHiAIBOp0NDQwMMBkNe4xAVCksbRES/MRgM0Ol0\neHt7QzQaxcbGBuRyed6TiIeHB8jlchwdHSGZTMLn8+H09PSfPEad6E+4I0FE9JtwOAyr1Qqfz4ei\noiK0t7fDaDSmDhPLp4ODA6yuruLp6Ql1dXXQarXQarV5j0NUKEwkiIiIKGcsbRAREVHOmEgQERFR\nzphIEBERUc6YSBAREVHOmEgQERFRzphIEBERUc5+AS4F5o4s5Z3gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcde4feafd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_time_axes(\n",
    "    resid_df.pivot_table('resid', 'seconds_left')\n",
    "            .reset_index()\n",
    "            .plot('seconds_left', 'resid', kind='scatter'),\n",
    "    ylabel=\"Residual\"\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Build a model of the science, take two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "df['trailing_committing'] = (df.score_committing\n",
    "                               .lt(df.score_disadvantaged)\n",
    "                               .mul(1.)\n",
    "                               .astype(np.int64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The following plot illustrates the fact that only the trailing team has any incentive to committ intentional fouls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T4mlT2xejXIsyuW59Pj1RYUXDX+v+29raFrW5uroCkJycXGJRH7VajVKpxMbGpsSx7Ozs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\n4tWxcHMXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdbbafad30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_time_axes(\n",
    "    df.pivot_table('foul_called', 'seconds_left', 'trailing_committing')\n",
    "      .rolling(20).mean()\n",
    "      .rename(columns={0: \"No\", 1: \"Yes\"})\n",
    "      .rename_axis(\"Committing team is trailing\", axis=1)\n",
    "      .plot()\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Intentional fouls are only useful when the trailing (and committing) team is on defense.  The plot below reflects this fact; shooting and personal fouls are almost always called against the defensive player; we see that they are called at a much higher rate than offensive fouls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jD1lZWUmSChYsqKZNm2rUqFFpWiAAAEB6sknJQjt27NC2bduUNWtWSziysrJS9+7dVadO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\nfAAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdbbb638d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = (df.pivot_table('foul_called', 'call_type')\n",
    "        .rename(index=call_type_enc.inverse_transform)\n",
    "        .rename_axis(\"Call type\", axis=0)\n",
    "        .plot(kind='barh', legend=False))\n",
    "ax.xaxis.set_major_formatter(pct_formatter);\n",
    "ax.set_xlabel(\"Observed foul call rate\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We continue to model the differnce in foul call rates between seasons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "with pm.Model() as poss_model:\n",
    "    β_season = pm.Normal('β_season', 0., 5., shape=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Throughout this talk, we will use [hierarchical distributions](https://en.wikipedia.org/wiki/Multilevel_model) to model the variation of foul call rates across different categories (in this instance, call types).  For much more information on hierarchical models, consult [_Data Analysis Using Regression and Multilevel/Hierarchical Models_](http://www.stat.columbia.edu/~gelman/arm/).\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\sigma_{\\textrm{call}}\n",
    "        & \\sim \\operatorname{HalfNormal}(5) \\\\\n",
    "    \\beta^{\\textrm{call}}_{c}\n",
    "        & \\sim \\operatorname{Hierarchical-Normal}(0, \\sigma_{\\textrm{call}}^2)\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "For sampling efficiency, we use an [offset parametrization](http://twiecki.github.io/blog/2017/02/08/bayesian-hierchical-non-centered/#The-Funnel-of-Hell-(and-how-to-escape-it)) of the hierarchical normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def hierarchical_normal(name, shape, σ_shape=1):\n",
    "    Δ = pm.Normal(\n",
    "        f'Δ_{name}', 0., 1., shape=shape\n",
    "    )\n",
    "    σ = pm.HalfNormal(f'σ_{name}', 5., shape=σ_shape)\n",
    "    \n",
    "    return pm.Deterministic(name, Δ * σ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Each call type has a different foul call rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "with poss_model:\n",
    "    β_call = hierarchical_normal('β_call', n_call_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We add score difference and the number of possessions by which the committing team is trailing to the `DataFrame`.  We assume that at most three points can be scored in a single possession (while this is not quite correct, [four-point plays](https://en.wikipedia.org/wiki/Four-point_play) are rare enough that we do not account for them in our analysis)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "df['score_diff'] = (df.score_disadvantaged\n",
    "                      .sub(df.score_committing))\n",
    "\n",
    "df['trailing_poss'] = (df.score_diff\n",
    "                         .div(3)\n",
    "                         .apply(np.ceil))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "trailing_poss_enc = LabelEncoder().fit(df.trailing_poss)\n",
    "trailing_poss = shared(\n",
    "    trailing_poss_enc.transform(df.trailing_poss)\n",
    ")\n",
    "n_trailing_poss = trailing_poss_enc.classes_.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The plot below shows that the foul call rate (over time) varies based on the score difference (quantized into possessions) between the disadvanted team and the committing team."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CiHuUsaCA7BMnsPX2xqF+A4vWrTPqWRz+DYm51+lVpxv96/e+4zIcGjQEQBsT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\nELQiggZBEARBELQiggZBEARBELTy/zzLCzMZz7OWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdbbb600b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_time_axes(\n",
    "    df.pivot_table('foul_called', 'seconds_left', 'trailing_poss')\n",
    "      .loc[:, 1:3]\n",
    "      .rolling(20).mean()\n",
    "      .rename_axis(\n",
    "          \"Trailing possessions\\n(committing team)\",\n",
    "          axis=1\n",
    "      )\n",
    "      .plot()\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The plot below reflects the fact that intentional fouls are disproportionately personal fouls; the rate at which personal fouls are called increases drastically as the game nears its end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Hj14MGzaS/ft/Y82az4D8npYePZ7H2NiY1q3bGiROIYRh/buXwcioYgxDFEWh+3t7SPFQ\nJT1psTxMhCxrWq2WYcMG8MYbU2nXzq/Y9VW0Nvzgg3nY2toxceLkxxcuAxWt/cobab/ie5baMDU5\nm61rT2PvZMmgl31LJGl45na5FM8OjUbDV1+tw9LSgjZt2hk6nDJ34sSfHDlyiK+/3mroUIQQpSwr\nM5eYOylkpKnIy9Oi0Wi5F5VSaXoZQJIGUYpiY2MZNqwfderUY+7cDwwy78CQhg3rT25uLrNnz6Nq\nVVdDhyOEKCE6nY6sjFzS03JIT80h7m4ad2+nkJSQ+dDyjs5WFX4uw98kaRClxtXVlYMHTxg6DIP5\n9tsfDB2CEKIEZWfl8seeq9y7k4L2f1b2NTY2wqOGA+5e9tg7WmJsYoRSaYTS2AgHJ6tK0csAkjQI\nIYQQj5WRlsNP2y+Rcj8LJ2cr7J0ssbY1x8bODCdna6pWszXo8s5lRZIGIYQQ4hFSkrL4adtFMtJU\nNG3lSdsutSrMYkwlTZIGIYQQogiJcens3X6J7Cw1rTvV5Lk21Z/ZhAEkaRBCCCEeKj01hz1bL6LK\n0dChe10aNdd/CfzKqvIPwAghhBBPSKvV8sdPVyRh+B+SNAghhBD/468/I4mNTqOOtzMNn6tm6HDK\nDUkaRKU2adJ/WLXqUwA2bFjD2LEjDByREKK8i45M4tyJ29jam9OxR/1neg7D/5I5Dc+gAQN6M3To\nS/TvP9jQoTzSpEn/ISTk4v9vj63AwsKcevUaMH36NNzcaho6PCFEJZSVmcsfP13FyEhBtxd9MDOX\nj8l/k54GUa4NHDiUgwdPcPDgcbZv3427uyfjx49HtkwRQpS0rMxc9u++QnammtadauHiZmvokMod\nSaHEAy5fvsSqVZ9y69ZN7OzsadeuAxMnTsbExASAP/88yoYNq4mOjsbFxYVu3QIZNWosCoWC27ej\nWLbsI65duwKAj09jpk+fiatr/jLKu3Z9zw8/bCcm5h4uLlV5442ptG2r3yZW1tbW9OwZxI8/fk9a\nWip2dvaoVCpWrlzGsWNHyMrKokaNGkyePI1GjZqUTuMIISodrVbHlQv3OH3kFrkqDTXqONG0lYeh\nwyqXJGkoYTvD93I+PqTI80ojBXnakv2W/JxLY/rVCSqRupKTk5gy5TXGjXuVFStWc/duNG+++TrW\n1ta88soEIiLCmTnzLebMWUjHjp25du0KU6e+TpUqzgQFvcgnnyymalVXPvroE7RaLcuXL+Wzzz5l\n/vwPOXr0MOvWfcHSpcupX9+bU6dO8O67b/HVV99So8bjhxuSk5PZuXM7fn5+2NnZA7B16ybOnz/L\n119vw9ramrVrP2f27LfZteuXEmkPIUTlFh+TxtF910mIzcDUTIlfQB0aNq8m8xiKIMMTopD9+/dR\npYozgwcPx9TUlJo1a9GnT3+OHDkIwN69u2nWrAX+/gEYGxvTqFETunbtztGjhwDIyEjHxMQEU1NT\nLCwsmD59JvPnfwjATz/t4vnne+Pj0wilUkn79h1o1aoNv/32c5HxfPfdVvz92+Hv347evbtx9eoV\n3nrrrYLzL700mnXrvsbe3h5jY2O6du1OQkI8iYmJpdhKQojKIDoymV2bz5MQm0Hdhi4MHdeKxi09\nnrnN9Z6E9DSUsH51gh75rb+87yN/795dvLxqFDrm5VWDuLi4gvM1a9b8n/NeXLmS37syZsx/mDdv\nNqdOnaB167Z06RJAy5atALh7N5ozZ06xc+eOgmu1Wi3W1tZFxjNw4FAmTZoCQE5ODgcO/M7w4cNZ\nuXINdevWJzk5ieXLP+bChbNkZv6zw5xanfv0jSCEqPTiY9L4bedlAJ4f0BivOk4GjqhikKRBPOBh\n3XIajfrfJR44r1bnn2/Xzo+dO/dy4sSfHD9+jOnT/0u/fgOZNGkKZmZmjBv3Ki+9NPqp4jI3N6dX\nrxf4889D7NnzI2++OYM5c95FqVSyfv1mXF1duXHjOmPGDHuq+oUQz4bk+1n8vCMEjTqP7n0aSsLw\nBKQPRhTi7u5BZGRkoWNRUZG4u3v863zE/5yPwsPDE4CUlBQsLa0ICOjBnDkLeOutd9i9e+f/X+vJ\nzZvhha6NjY1Fq9U+cZwqVQ4AV6+G8sILfQsmWoaFXX3iuoQQz46MdBV7t18kJ1tNxx71qFXf2dAh\nVSiSNIhCAgJ6cP9+At99tw2NRkN4+A127fqenj17A9Cr1wucP3+WI0cOodFouHjxPH/8sY+ePYNQ\nqXIYMqQvP/ywA7VajUqlIizsGh4e+QlH374DOHz4AMeOHUaj0RAScpExY4Zx7lywXrFpNBoOHz7A\nmTNn6NHjeQCqVXPnypVQNBoNZ8/+VTD3IiEhvhRaRwhRkeVkq9m7PX+3ylYda+LTTFZ6fFIKnTzw\n/kglPf+gPMxpGDCgNwkJ8f+/aNI/PvpoGb6+bTh9+iTr139BVFQUjo6OBAW9yLBhIwsmB+3b9wvf\nfvsN9+7dpWpVN4YOfYlevV4A4Ny5YD7/fAWRkRGYmJji7d2QN96YWvB0xK5d3/Ptt5u4fz8RV1dX\nhg0bQVBQn4fGWXhxJ1AqjfHyqsGkSa/RrFkbAM6e/YuPPlpAcnISzZo155133mPBgvcJCbnAF198\nyaefLqFBAx8mTZrChg1rOHHiTzZs2FQKrVpxlIffwYpM2q/4DNGG6lwNe7ZdJP5eOo1butO+a50K\n+4REabefs7NNkeckaXiMypg0VHTShsUj7Vc80n7FV9ZtmJen5dfvQ7hzK5l6DaviH9SgwiYMYNik\nQYYnhBBCVFparY6De69y51YyXrUd6fy87CVRHJI0CCGEqLT+/OMG4VcTcPWwo1ufhiiV8rFXHNJ6\nQgghKqXoyGRCz93D0dmK5wc0wsRE+fiLxCNJ0iCEEKLS0el0nD6S/3i4f68GmJmbGDiiykGSBiGE\nEJVORFgC8THp1G7gjLNr0RP7xJORpEEIIUSlotVqOX30FgoFtOr4+M3whP4kaRBCCFGpXLsUS2pS\nNt5N3bB3tDR0OJWKJA1CCCEqDY06j+A/IzE2NqJl+xqGDqfSkaRBCCFEpRFy9i6ZGbk09vXAysbM\n0OFUOmWeNGzYsIGOHTvSrFkzhg0bRnh4/gZGYWFhjBw5kpYtW9K1a1dWrVrFoxar3LJlCz179qR5\n8+YMGjSI4OB/9i/Yvn07bdq0oUOHDhw4cKDQdRcvXiQwMBCVSlU6b7ASOXDgd4KCuvHqqy8DsH37\nFgIDu/D++zNL9b7+/u04efJ4qd5DCFH55Ko0nD91GzNzY55r7WnocCqlMt0ae9u2bWzfvp3169fj\n7u7OmjVrWL16NQsWLGD8+PG8+OKLfPHFF9y7d49x48bh5OTE0KFDH6jn8OHDLFu2jDVr1tC4cWN2\n7drF+PHj2bdvH6ampixbtowffviBpKQkJk6ciL+/PwqFAo1Gw3vvvcecOXMwM3u2M9AbN67zzTdf\ncv78WbKysnBwcKBduw6MGjWWKlWqALB580YCAnowefKbAHz11XrGjHmFwYOHl2psBw+eKNX6hRCV\nU1hILKocDa061JBHLEtJmfY0rFu3jsmTJ1OvXj2srKyYOnUqS5cu5fDhw2RnZ/P6669jZWVF3bp1\nGTFiBNu2bXtoPVu3bqVv3760bNkSMzMzhgwZgpubG3v37iUiIgJPT088PDxo0qQJGo2GxMREAL78\n8kt8fHxo27ZtWb7tcic4+AwTJozB1dWNTZu2c/DgcVasWE1cXCyvvDKCuLhYADIyMvD09CxYcjUj\nIx0Pj+qGDF0IIR5Kp9MRcvYuSqUCn+dk98rSUmZJQ1xcHNHR0WRlZdG7d298fX2ZMGECsbGxhIaG\nUq9ePYyN/+n48PHx4fr16w8dRggNDcXHx6fQMR8fH0JCQh5YU1yr1WJubs6dO3fYunUrQUFBDB8+\nnMGDB3Py5MnSebPlmFarZfHihfTu3YeJEyfj4OAIgLu7Bx99tAxnZxdWrfqUAQN6ExNzjxUrljFm\nzDD8/dsBMHPmW8ye/TYAhw8fYMyYYQQE+DFgQG9+/nlPwX0WLnyfZcs+YuXKT+jZ05+goG7s2PFt\nwflff93L0KH9CAjwo0+fnqxb90XBcJSfX0uOHz/G558v57XXXikU/5kzp2jcuDEZGRmoVCo+/XQJ\n/fsHERDgx8SJ47hz53aptp8Qony6HZFEanI2dXyqYmFpauhwKq0yG56Ijc3/9rp3717Wrl2LiYkJ\n06dPZ+rUqdSuXRtbW9tC5e3t7dFqtaSmpuLi4lLoXEpKygPl7ezsiIiIoHbt2ty5c4eoqCji4uKw\ntrbGxsaGKVOmMGXKFD744APmzp1LtWrVGDhwIIcOHcLEpOhuLAcHS4yN9V969NZXX3P/RNHJSJTe\nNenPqV1bao4ZpVfZkJAQ7t27y/jxrzx0J7OXXx7NrFmzCA4OJjAwkJdffpmXXnoJgPr167Nq1Sq6\ndOnC5cuXWbjwfZYvX46fnx+XLl1i3Lhx1K5dnQ4dOmBubsKhQ38wffp0Zs9+hx07drBo0SKGDRuE\nSqXigw/msWHDBtq2bUtkZCRjx46lbVtfunTpAoCdnQX9+r3Itm1bMDLKxcnJCYDTp4/RqVMnatZ0\nY+HChYSHh7Fjx3YcHBz44osvmDp1Ivv373/kz1Q8ehc78XjSfsVX0m34+4+hAHQMqPtM/HwM9R7L\nLGn4+1vk2LFjcXNzA2Dq1Kn0798fLy+vIsvruxvZ3+Wtra156623GDp0KObm5syfP589e/ag0+nw\n9/dn/vz5tGjRAgBnZ2ciIiKoX79+kfUmJ2fp/yaB7Oxc8vK0RZ5XKo0eef5pZGfn6r1NamjodUxM\nTDAzs3voNU5ObqhUKq5cuUlenpaMjJxC5VJTs0lISGfz5m20bt0WH5/mJCVl4eFRhx49nmfr1h00\naNCMnBw1Vao406FDN1JScvD19UOj0XDx4jUsLS3RarWoVJCYmIG1dRW2bt2FkZFRwb1SU7Np1KgG\nrq5u7NnzC0FBfdBqtfzxxx/MmjWLuLhUvv/+B+bMWYBSaUVaWi5Dh45h06bN7Nt3iNatn+0hqEeR\nrZ2LR9qv+Eq6DZPvZ3HzWv6mVMZmykr/8zHk1thlljT8PbnO3t6+4Ji7uzsACQkJZGUV/nBOTU1F\nqVRiZ2f3QF0ODg4kJyc/UN7RMb+rfcCAAQwYMADI75Xo168fX3/9NRkZGVhZWRVcY2FhQXp6yTa8\n88AhOA8cUvT5cvAfjk6nK/LJlL8PPy5Zu3s3mrNnzxQMW/xdr7d3w4LXbm7uBX83MzMHQKXKwcen\nIb1792XixFdo2LAxrVq1oWfPIKpWdX3gPl26BHD06BGCgvoQEnKJrKxsunTpQlRULFlZmcyaNb1Q\nrHl5ecTHxz2+EYQQlcbls3cBaNLS/TElRXGVWdLg6uqKo6MjV65coUmTJgBER0cD0K9fP2bPnk1u\nbi6mpvljUZcuXcLb27vg9b81atSIy5cvM3DgwIJjly5dYuTIkQ+UXbx4MUOGDMHT05P09PRCSUJK\nSgrW1tYl+j7Lu+rVvdBoNNy9e4fq1Ws8cP727UgsLCxwcan6yHrMzMzo3bsP06a9U2QZI6OHJx4K\nhYIZM2YyfPhIjh49zOHDB9i8eSMrVqzGx6dRobL+/t149dWxZGdnc/ToQfz8OmJhYVGQhKxatY6G\nDRs97DZCiGeAKkdD2OVYrGzMqFG3iqHDqfTKbCKksbExw4YNY/Xq1dy8eZPU1FQ+/fRTOnfuTEBA\nAPb29qxcuZKsrCyuXbvGpk2bGDFiBJA/iTIwMJDIyEgAhg8fzp49ewgODkalUrFx40ZSU1MJCgoq\ndM8zZ84QGhrKyy/nrzNgY2ODh4cHR48eJSwsjLS0NGrVqlVWTVAu1KlTDy+vGuzYsfWh53fu/I7O\nnbsWmpT6MB4enty8eaPQsYSEeDQazWNj0Gq1pKWl4uHhybBhI1i7diPe3g3Zt++XB8rWr98AFxcX\nzpw5xdGjhwkI6AHkD0PZ29s/EENMzL3H3l8IUXmEhcSizs2jUfNqKJWyXmFpK9MWnjBhAgEBAQwb\nNoxOnTphY2PDRx99hKmpKWvXriUkJISOHTvyxhtvMHr0aPr06QOAWq3m1q1b5ObmAuDn58c777zD\ne++9R7snezFnAAAgAElEQVR27fj9999Zu3ZtoaGM3Nxc5s6dy7x58wp9AM6ePZs5c+YwduxY5s6d\n+9CejMpMoVAwffpMfv11L8uXf0xS0n0g/8N25sy3SEiI59VXX39sPb179+HKlVB27975/z+fCF57\n7RV+++3nx1574MDvjB49jJs38xf2iouLJSEhHnf3hy/G0qVLADt2fEtGRgatWrUpON6nzwC++eZL\nIiLC0Wg07N69k9Gjh5b4kJMQonzKf8wyGqVSgXdTN0OH80wo08WdTExMmDVrFrNmzXrgXO3atdm4\nceNDr/Pw8CAsLKzQsUGDBjFo0KAi72VqasrPPz/4Aebr68uhQ4eeLPBKpmnT51i9+iu++modI0cO\nJisrG0dHR/z8OjJt2rs4ODg8to7q1b2YO3cR69evZvnypTg6OvHCC30JCnrxsdcGBPQgKiqSt96a\nTEpKCvb29vj7d6Nfv4EPLe/v341Nm74iKOjFQk9FjBz5MhkZ6bzxxgRUKhW1a9dlyZLl2NhU/pnT\nQgi4dT2RtJQcGjRxlccsy4hC96i1mkWJT1osDxMhKzppw+KR9iseab/iK4k21Ol07Nx0jvh76Qx5\nxReHKlaPv6iSMOTTEzIAJIQQosKJuZNK/L10atR1eqYSBkOTpEEIIUSFc/5U/uqvz7WRpe3LkiQN\nQgghKpT78RncjkjCzcMOV/cH1/IRpUeSBiGEEBXK+dPSy2AokjQIIYSoMNJSsgm/Eo+jsxXVazsa\nOpxnjiQNQgghKoxLf0Wj00Gz1p56700kSo4kDUIIISqE5PuZXL0Ug7WtGXW8XR5/gShxkjQIIYQo\n9zLSVezdfgmNWkvrTrVkyWgDkVYXQghRrqly1Py84xIZaSpadaxJvYaP3lBPlB5JGkSFNmnSf1i1\n6lNDhyGEKCUadR6/fH+ZpIRMGrdwp3lbeWLCkMp07wlRPgwY0JuEhHiUSiWQvydIzZq1GTv2P/j6\ntnnM1UIIUTby8rTs332F2OhU6ng70z6gjkx+NDBJGp5Rb7wxlf79BwOgUuXw008/Mn36f/nyyy3U\nrPlsbRcuhCh/clUa9u0KJToyGY8aDvj38paEoRyQ4QmBmZk5AwYMwdOzOidOHEOlUvHpp0vo3z+I\ngAA/Jk4cx507twvK+/m1ZNu2zfTp05MNG9aQk5PDokVzCQrqRrduHXj55Zc4e/avgvKXL19iwoSX\n6dGjE4MGvcinny5FrVYD8MsvPzFq1BB+++1n+vcPonv3TsybN5u8vDwAVCoVS5d+wIsvBtKtW0fG\njRvJ+fPny7aBhBBlKitDxe5vLxAdmYxXHScC+zdCaSwfV+WB9DSUsBMHbxJxLb7I80ZKI7R52hK9\nZ60GLrTzr13serRaLUqlktWrV3H16hW++GIDdnb2fPPNl0ye/Co7duzG2Dj/V+bIkYNs2LAJR0cn\nNm36irCwa2ze/B02Njb88stPzJs3mx9+2Et6ehpTprzGuHGvsmLFau7ejebNN1/H2tqaV16ZAEBs\nbAxXr4ayefN3REff5pVXRuLvH4CfXye2bt3E+fNn+frrbVhbW7N27edMnjyZH354cNtzIUTFl5KU\nxd7tl0hPzcG7qRsde9TFyEgShvJCfhKC7Oxsvv9+GzEx9+jQoTM//7yHkSNfxsWlKmZmZowdO56s\nrKxCvQddunTDyakKCoWCjIx0lEol5ubmKJVKevfuw48//oqxsTH79++jShVnBg8ejqmpKTVr1qJP\nn/4cOXKwoK7MzExeeeVVLCwsqFu3Pp6e1YmMvAXASy+NZt26r7G3t8fY2JiuXbsTFxdHYmJimbeT\nEKJ0ZWflsmvTedJTc/D1q0GnwHqSMJQz0tNQwtr5137kt/7S3gddXytWLOOzz5YDYGpqRp06dVm2\n7DPMzc3Jyspk1qzphcYP8/LyiI+PK3jt6upW8Pe+fQdy7NgR+vTpSatWbWjXzo+AgB4YGxtz795d\nvLxqFLq3l1cN4uL+qcvGxhYbm3/2bzczM0elUgGQnJzE8uUfc+HCWTIzMwvKqNW5JdMQQohyIywk\nlpxsNS39atDSr4ahwxEPIUnDM+rfEyH/LSMjA4BVq9bRsGGjIq//+8kLADe3amze/B3nzgVz/Pgx\nPvtsObt2fc9nn60DeOjkJY1GXfB3I6OiJzfNmfMuSqWS9es34+rqyo0b1xkzZtjj36AQokLR6XRc\nvRiDUqmgcQt3Q4cjiiD9PqIQa2tr7O3tuXnzRqHjMTH3irwmOzsbjUaNr29rpkyZxrp1XxMaGkJ4\n+A3c3T2IjIwsVD4qKhJ3dw+94rl6NZQXXuiLq6srAGFhV5/sDQkhKoTYu2mkJGVTs74z5hYmhg5H\nFEGSBvGAPn0G8M03XxIREY5Go2H37p2MHj2U9PSHD6vMnPkWS5Z8QHp6OlqtltDQEExMTKha1ZWA\ngB7cv5/Ad99tQ6PREB5+g127vqdnz956xVKtmjtXroSi0Wg4e/avgrkQCQlFTzYVQlQ8Vy/GAODd\nxO0xJYUhyfCEeMDIkS+TkZHOG29MQKVSUbt2XZYsWV5o3sG/zZgxi6VLP2DAgCC0Wh2entWZP/8j\nHBwcAFiwYDHr13/BunVf4OjoSP/+gxgyZLhesUydOoOPPlrA3r0/0qxZc9555z0WL57Pm2++zhdf\nfFli71kIYTiqHA03r8Vja2+Ou5e9ocMRj6DQ6XQ6QwdRnpX0pMXyMhGyIpM2LB5pv+KR9iu+/23D\n0PP3OLrvOq061qRFOy8DRlYxlPbvoLPzw78gggxPCCGEMLCrF2NQKKBBY1dDhyIeQ5IGIYQQBpMY\nl05CbDrVazthZWNm6HDEY0jSIIQQwmCuXowFwLupTICsCCRpEEIIYRAadR7XQ+OwtDbFq7ajocMR\nepCkQQghhEFcPHOHXJUG7yZuslx0BSE/JSGEEGUuIy2Hc6duY2FlQrPWnoYOR+jpiZKGyMhITp48\nWfBantYUQgjxNE4ejkCj1tKmUy1MzWTJoIpCr6Th/v37DBkyhJ49e/Kf//wHgJiYGLp3705ERESp\nBiiEEKJyuR1xn/Ar8bi42VBfHrOsUPRKGmbPnk3t2rU5ceJEweZDrq6uBAUFsXDhwlINUAghROWh\n1er47cfLALQPqPPQDe1E+aVX0nDq1ClmzpyJg4NDwQ9YoVAwYcIEQkJCSjVAUfYWLnyfWbOml8m9\nYmNj8Pdvx61b0mMlxLPg2qUYYu+mUa9hVVzd7QwdjnhCeg0kWVlZodFoHjh+//59mddQAWk0GjZt\n+oo//thHfHwcxsYm1KhRg5EjX6ZtW79Sv/+5c8GYm5vj49MIV1c3Dh48Uer3FEIYXq5Kw+mjtzAx\nVdKmcy1DhyOegl49DW3atOHdd98lPDwcgKSkJE6ePMnrr7+Ov79/qQYoSt5nny3n0KE/eP/9hfz2\n22F27vwZf//uvP32m4SFXSv1+2/btoWrV0NL/T5CiPIlIiyBnCw1bTvVltUfKyi9ehpmz57N22+/\nTVBQEADt27fHyMiIoKAgZs2aVaoBipJ35sxJevR4nrp16wNgYWHBwIFDcHR0KrST5ddfb+C777Zi\nZKRk0KChvPTSaAByc3NZs+Y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K5tThCLIz1bRs74WtvYWhwxHliF5Jw5w5c3B3d0epVDJj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\nIAEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdcab8b5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_time_axes(\n",
    "    df.pivot_table('foul_called', 'seconds_left', 'call_type')\n",
    "      .rolling(20).mean()\n",
    "      .rename(columns=call_type_enc.inverse_transform)\n",
    "      .rename_axis(None, axis=1)\n",
    "      .plot()\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### The shot clock\n",
    "\n",
    "<center><img src=\"https://cdn-s3.si.com/s3fs-public/styles/marquee_large_2x/public/2017/08/22/nba-shot-clock-invention.jpg\" width=700></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Due to the NBA's [shot clock](https://en.wikipedia.org/wiki/Shot_clock), the natural timescale of a basketball game is possessions, not seconds, remaining."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "df['remaining_poss'] = (df.seconds_left\n",
    "                          .floordiv(25)\n",
    "                          .add(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "remaining_poss_enc = LabelEncoder().fit(df.remaining_poss)\n",
    "remaining_poss = shared(\n",
    "    remaining_poss_enc.transform(df.remaining_poss)\n",
    ")\n",
    "n_remaining_poss = remaining_poss_enc.classes_.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Below we plot the foul call rate across trailing possession/remaining posession pairs.  Note that we always calculate trailing possessions (`trailing_poss`) from the perspective of the committing team.  For instance, `trailing_poss = 1` indicates that the committing team is trailing by 1-3 points, whereas `trailing_poss = -1` indicates that the committing team is leading by 1-3 points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Lli2r1ACJiIhUwuRAaYI+9blz5xAVFQUAOHToEBwdHTF79mzk5OTg448/rtQA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\nIiINTA6IiIhIA5MDIiIi0vD/AJ2UzxWn+NwlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdbbac7ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.heatmap(\n",
    "    df.pivot_table('foul_called', 'trailing_poss', 'remaining_poss')\n",
    "      .rename_axis(\n",
    "          \"Trailing possessions\\n(committing team)\", axis=0\n",
    "      )\n",
    "      .rename_axis(\"Remaining possessions\", axis=1),\n",
    "    cmap='seismic', cbar_kws={'format': pct_formatter}\n",
    ")\n",
    "ax.invert_yaxis();\n",
    "ax.set_title(\"Observed foul call rate\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The heatmap above shows that the foul call rate increases significantly when the committing team is trailing by more than the number of possessions remaining in the game.  That is, teams resort to intentional fouls only when the opposing team can run out the clock and guarantee a win.  (Since we have quantized the score difference and time into posessions, this conclusion is not entirely correct; it is, however, correct enough for our purposes.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_foul_diff_heatmap(*_, data=None, **kwargs):\n",
    "    ax = plt.gca()\n",
    "\n",
    "    sns.heatmap(\n",
    "        data.pivot_table(\n",
    "            'diff',\n",
    "            'trailing_poss',\n",
    "            'remaining_poss'\n",
    "        ),\n",
    "        cmap='seismic', robust=True,\n",
    "        cbar_kws={'format': pct_formatter}\n",
    "    )\n",
    "    \n",
    "    ax.invert_yaxis()\n",
    "    ax.set_title(\"Observed foul call rate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "call_name_df = df.assign(\n",
    "    call_type=lambda df: call_type_enc.inverse_transform(\n",
    "        df.call_type.values\n",
    "    )\n",
    ")\n",
    "\n",
    "diff_df = (pd.merge(\n",
    "                call_name_df,\n",
    "                call_name_df.groupby('call_type')\n",
    "                         .foul_called.mean()\n",
    "                         .rename('avg_foul_called')\n",
    "                         .reset_index()\n",
    "             )\n",
    "             .assign(diff=lambda df: df.foul_called - df.avg_foul_called))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Difference from call type average"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The heatmaps below are broken out by call type, and show the difference between the foul call rate for each trailing/remaining possession combination and the overall foul call rate for the call type in question"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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ye0ZCiMpFxogLIXRJWXPa7du3gYKe2mFhYezdu5esrCxmzJhR5Hw+eXl5ygl5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\n7lzmzp2b6f6iRYvi4+OjNXvn28aMGaP1MtPCwoIFCxZkeU0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8MQAREREYGxunG2ceExOD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X//foSHh+PcuXNwcHCAh4cHnj17hrS0NOzfvx+xsbHw9fXFypUrpe3y8/MREhKCoKAgPiwkIr4j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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdcb84d518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(sns.FacetGrid(diff_df, col='call_type', col_wrap=3, aspect=1.5)\n",
    "    .map_dataframe(plot_foul_diff_heatmap)\n",
    "    .set_axis_labels(\n",
    "        \"Remaining possessions\",\n",
    "        \"Trailing possessions\\n(committing team)\"\n",
    "    )\n",
    "    .set_titles(\"{col_name}\"));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "These plots confirm that most intentional fouls are personal fouls.  They also show that the three-way interaction between trailing possesions, remaining possessions, and call type are important to model foul call rates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* The foul call rate changes based on the number of possessions trailing and remaining and the call type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "    \\sigma_{\\textrm{poss}, c}\n",
    "            & \\sim \\operatorname{HalfNormal}(5) \\\\\n",
    "    \\beta^{\\textrm{poss}}_{t, r, c}\n",
    "        & \\sim \\operatorname{Hierarchical-Normal}(0, \\sigma_{\\textrm{poss}, c}^2)\n",
    "\\end{align*}    \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "with poss_model:\n",
    "    β_poss = hierarchical_normal(\n",
    "        'β_poss',\n",
    "        (n_trailing_poss, n_remaining_poss, n_call_type),\n",
    "        σ_shape=(1, 1, n_call_type)\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* The foul call rate is a combination of season, call type, and possession factors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\\eta^{\\textrm{game}}_k = \\beta^{\\textrm{season}}_{s(k)} + \\beta^{\\textrm{call}}_{c(k)} + \\beta^{\\textrm{poss}}_{t(k),r(k),c(k)}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "call_type = shared(df.call_type.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "with poss_model:\n",
    "    η_game = β_season[season] \\\n",
    "                + β_call[call_type] \\\n",
    "                + β_poss[\n",
    "                    trailing_poss, remaining_poss, call_type\n",
    "                ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "p_k\n",
    "    & = \\operatorname{sigm}\\left(\\eta^{\\textrm{game}}_k\\right)\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "with poss_model:\n",
    "    p = pm.Deterministic('p', pm.math.sigmoid(η_game))\n",
    "    y = pm.Bernoulli('y', p, observed=df.foul_called)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Infer the model given data, take two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1500/1500 [06:34<00:00,  3.80it/s]\n"
     ]
    }
   ],
   "source": [
    "with poss_model:\n",
    "    poss_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The BFMI and Gelman-Rubin statistics for this model indicate no problems with HMC sampling and good convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bfmi = pm.bfmi(poss_trace)\n",
    "max_gr = max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(poss_trace).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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J6AohRApNuSKtr+/SJ9ULIcRC4/Gcfwc4aekKIUQKSegKIUQKSegKIUQKSegKIUQKSegK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdb6d466d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(pm.energyplot(poss_trace, legend=False, figsize=(6, 4))\n",
    "   .set_title(CONVERGENCE_TITLE()));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Criticize the model given data, take two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "resid_df = (df.assign(p_hat=poss_trace['p'].mean(axis=0))\n",
    "              .assign(resid=lambda df: df.foul_called - df.p_hat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The following plots show that, grouped various ways, the residuals for this model are relatively well-distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4TJkyBS4uLrC2tlbMXSyVSpGcnIz4+HiEhoZWax9ERKRlGPgABAZ+YGAgPvvs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdac8c64e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.heatmap(\n",
    "    resid_df.pivot_table('resid', 'trailing_poss', 'remaining_poss')\n",
    "      .rename_axis(\"Trailing possessions\\n(committing team)\", axis=0)\n",
    "      .rename_axis(\"Remaining possessions\", axis=1)\n",
    "      .loc[-3:3],\n",
    "    cmap='seismic',  cbar_kws={'format': pct_formatter}\n",
    ")\n",
    "ax.invert_yaxis();\n",
    "ax.set_title(\"Observed foul call rate\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "N_BIN = 20\n",
    "\n",
    "bin_ix, bins = pd.qcut(\n",
    "    resid_df.p_hat, N_BIN,\n",
    "    labels=np.arange(N_BIN),\n",
    "    retbins=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZAFwdpx4AJ+I+GQBcHUEBcCLukwHA1XHqAXAi7pMBwNURFAAn4j4ZAFwdpx4A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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdac8a2668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = (resid_df.groupby(bins[bin_ix])\n",
    "              .resid.mean()\n",
    "              .rename_axis('p_hat', axis=0)\n",
    "              .reset_index()\n",
    "              .plot('p_hat', 'resid', kind='scatter'))\n",
    "\n",
    "ax.xaxis.set_major_formatter(pct_formatter);\n",
    "ax.set_xlabel(r\"Binned $\\hat{p}$\");\n",
    "\n",
    "make_foul_rate_yaxis(ax, label=\"Residual\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JIj3SZDIkexmISMok/YVUPXv2RGBgIIKCglT/kpKS6l03IyMDw4YNQ2hoKJ5//nkcOHBA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\nBOgoNX78VQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdac7bee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = (resid_df.groupby('seconds_left')\n",
    "              .resid.mean()\n",
    "              .reset_index()\n",
    "              .plot('seconds_left', 'resid', kind='scatter'))\n",
    "make_time_axes(ax, ylabel=\"Residual\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Model selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Now that we have two models, we can engage in [model selection](https://en.wikipedia.org/wiki/Model_selection).  We use the [widely applicable Bayesian information criterion](http://www.jmlr.org/papers/volume14/watanabe13a/watanabe13a.pdf) ([WAIC](http://www.stat.columbia.edu/~gelman/research/published/waic_understand3.pdf)) for model selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "MODEL_NAME_MAP = {\n",
    "    0: \"Base\",\n",
    "    1: \"Possession\"\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "comp_df = (pm.compare(\n",
    "                (base_trace, poss_trace),\n",
    "                (base_model, poss_model)\n",
    "             )\n",
    "             .rename(index=MODEL_NAME_MAP)\n",
    "             .loc[MODEL_NAME_MAP.values()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Since smaller WAICs are better, the possession model clearly outperforms the base model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "      <th>dSE</th>\n",
       "      <th>warning</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <td>11609.8</td>\n",
       "      <td>1.98</td>\n",
       "      <td>1543.34</td>\n",
       "      <td>0</td>\n",
       "      <td>56.98</td>\n",
       "      <td>73.35</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Possession</th>\n",
       "      <td>10066.5</td>\n",
       "      <td>81.92</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>87.93</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               WAIC  pWAIC    dWAIC weight     SE    dSE warning\n",
       "Base        11609.8   1.98  1543.34      0  56.98  73.35       1\n",
       "Possession  10066.5  81.92        0      1  87.93      0       1"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FihXtalu3blVcXJyioqL04IMPqqCgwFlrampSamqq7rjjDo0bN06JiYmyWq3OellZmRIT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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcde4aaab38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.errorbar(\n",
    "    np.arange(len(MODEL_NAME_MAP)), comp_df.WAIC,\n",
    "    yerr=comp_df.SE, fmt='o'\n",
    ");\n",
    "ax.set_xticks(np.arange(len(MODEL_NAME_MAP)));\n",
    "ax.set_xticklabels(comp_df.index);\n",
    "ax.set_xlabel(\"Model\");\n",
    "ax.set_ylabel(\"WAIC\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Research questions\n",
    "\n",
    "1. ~~How does game context impact foul calls?~~\n",
    "2. Is (not) committing and/or drawing fouls a measurable player skill?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Build a model of the science, take three"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<center><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Graph_of_Bailey_Scores_of_Supreme_Court_Justices_1950-2011.png/800px-Graph_of_Bailey_Scores_of_Supreme_Court_Justices_1950-2011.png\" width=650></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We now turn to the question of whether or not committing and/or drawing fouls is a measurable skill.  We use an [item-response theory](https://en.wikipedia.org/wiki/Item_response_theory) (IRT) model to study this question.\n",
    "\n",
    "Unfortunately there is not enough time in this talk to do Bayesian item-response theory justice. For the curious:\n",
    "\n",
    "* [_Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation_](http://www.stat.columbia.edu/~gelman/research/published/171.pdf) is an excellent introduction to applied Bayesian IRT models and has inspired much of this work.\n",
    "* [_Bayesian Item Response Modeling &mdash; Theory and Applications_](http://www.springer.com/us/book/9781441907417) is a comprehensive mathematical overview of Bayesien IRT modeling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Item-response theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DhgxB0aJFERQUhMmTJ6NBgwZ4//338dZbb2H06NEAgI8++gi+vr4YMGAAGjdu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\nEREZDBsLIiIiMhg2FkRERGQw/w9xWHbyYVL42gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdac387828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_aspect('equal');\n",
    "\n",
    "x = y = np.linspace(-3, 3, 100)\n",
    "C = sp.special.expit(\n",
    "    np.subtract.outer(x, y)\n",
    ")\n",
    "\n",
    "poly = ax.pcolor(x, y, C, cmap='bwr')\n",
    "\n",
    "ax.text(\n",
    "    -4., -3.5, \"Liberal\",\n",
    "    fontdict={'size': LABELSIZE}\n",
    ");\n",
    "ax.text(\n",
    "    3.1, -3.5, \"Conservative\",\n",
    "    fontdict={'size': LABELSIZE}\n",
    ");\n",
    "ax.text(\n",
    "    -4.85, 3.1, \"Conservative\",\n",
    "    fontdict={'size': LABELSIZE}\n",
    ");\n",
    "\n",
    "cbar = fig.colorbar(poly, ax=ax)\n",
    "cbar.ax.yaxis.set_ticks(np.linspace(0, 1, 5));\n",
    "cbar.ax.yaxis.set_major_formatter(pct_formatter);\n",
    "\n",
    "ax.set_ylabel(\"Case ideal point\");\n",
    "ax.set_xlabel(\"Justice ideal point\");\n",
    "ax.set_title(\"Probability justice issues\\nconservative opinion on case\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V1qxZU+zdu1f06tVLNGjQQLz//vsiMjJSCCHE48ePxaRJk0SzZs2Em5ub6Nq1q/j999+l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\no3+n6pIGDRogISFB7bmcnBw0b95coRUZTtOmTVV37KyqqkJWVha2b9+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a7dq1w88//6zz\nusvKygSfs7GxwcSJExEREVGtTt9gH6B6cmJVVZXqvXzce/q4xuVxQUdEZBj8G0Ykkw0bNqjdbKi4\nuFgVbGNtbQ0AatkmD+9rAAiH7ghp27Ytrl+/rvZ/4bt27cLp06fx9NNPIzs7GyUlJaqxwsJCFBcX\n1/hamjVrpnYGoKKiAtnZ2Wo/VzNg5/r166isrNQ72Ad4cEbkodLSUhQUFKBFixZo06YNSkpKVN/j\nBx6E1JmZmYkKNyIiw2NjQSSTiooKLF++HJcvX0Z+fj527typCrJq3Lgx7O3tsXfvXty/fx9//PEH\nUlNTVccKhe7Y2NgAAC5fvqzWJACAj48P7Ozs8Pnnn+Pu3bs4efIkZs2ahcrKSnh7e6Np06ZYsGAB\niouLcevWLUyZMgUffvhhja/Fx8cHx44dw8mTJ3Hv3j2sWrVK7YxFaGgo9u7di3379qGiogInT57E\ngAEDkJycLCrYpyaHDh1CWloa7t27hy+++AJ2dnZwd3fHCy+8gM6dOyMxMRGlpaXIy8vDsmXL4Ovr\ni8aNG4ua+yGh95WIxGNjQSSTESNGoG/fvhg8eDD69u2LF154QXX639zcHHPmzMGPP/4Id3d3bNmy\nBcOHD1cdKxS64+joiICAAEyaNAmLFi1S+5lWVlbYsGED/vjjD7z00kuYPn06Zs+eja5du8LCwgIr\nVqzA1atX4e3tjaCgIDRp0gSzZ8+u8bX07dsXI0aMQHR0NHx8fFBeXq72FVcvLy/MmDEDCQkJ6Nat\nG2bMmIEpU6bAy8tLVLBPTR5+BfSll17Cjz/+iM8//1x1TcjixYtRWFgIPz8/DBgwAK1atar2vogh\n9L4SkXgMyCKiWq02hGcRkXg8Y0FEREQGw8aCiIiIDIZbIURERGQwPGNBREREBsPGgoiIiAyGjQUR\nEREZDBsLIiIiMhg2FkRERGQw/w9xWHbyYVL42gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdac387828>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "with pm.Model() as irt_model:\n",
    "    β_season = pm.Normal('β_season', 0., 5., shape=n_season)\n",
    "    β_call = hierarchical_normal('β_call', n_call_type)\n",
    "    β_poss = hierarchical_normal(\n",
    "        'β_poss',\n",
    "        (n_trailing_poss, n_remaining_poss, n_call_type),\n",
    "        σ_shape=(1, 1, n_call_type)\n",
    "    )\n",
    "    \n",
    "    η_game = β_season[season] \\\n",
    "                + β_call[call_type] \\\n",
    "                + β_poss[trailing_poss, remaining_poss, call_type]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "player_committing = shared(df.player_committing.values)\n",
    "player_disadvantaged = shared(df.player_disadvantaged.values)\n",
    "n_player = player_enc.classes_.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Each disadvantaged player has an ideal point (per season)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "    \\sigma_{\\theta}\n",
    "        & \\sim \\operatorname{HalfNormal}(5) \\\\\n",
    "    \\theta^{\\textrm{player}}_{i, s}\n",
    "        & \\sim \\operatorname{Hierarchical-Normal}(0, \\sigma_{\\theta}^2)\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    θ_player = hierarchical_normal(\n",
    "        'θ_player', (n_player, n_season)\n",
    "    )\n",
    "    θ = θ_player[player_disadvantaged, season]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Each committing player has an ideal point (per season)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "    \\sigma_{b}\n",
    "        & \\sim \\operatorname{HalfNormal}(5) \\\\\n",
    "    b^{\\textrm{player}}_{j, s}\n",
    "        & \\sim \\operatorname{Hierarchical-Normal}(0, \\sigma_{b}^2)\n",
    "\\end{align*}    \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    b_player = hierarchical_normal(\n",
    "        'b_player', (n_player, n_season)\n",
    "    )\n",
    "    b = b_player[player_committing, season]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Players affect the foul call rate through the difference in their ideal points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\\eta^{\\textrm{player}}_k = \\theta_k - b_k$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    η_player = θ - b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Game and player effects combine to determine the foul call rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\\eta_k = \\eta^{\\textrm{game}}_k + \\eta^{\\textrm{player}}_k$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    η = η_game + η_player"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    p = pm.Deterministic('p', pm.math.sigmoid(η))\n",
    "    y = pm.Bernoulli(\n",
    "        'y', p,\n",
    "        observed=df.foul_called\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Infer the model given data, take three"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1500/1500 [08:45<00:00,  2.85it/s]\n"
     ]
    }
   ],
   "source": [
    "with irt_model:\n",
    "    irt_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bfmi = pm.bfmi(irt_trace)\n",
    "max_gr = max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(irt_trace).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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0hRAigSR0hRAigSR0hRAigSR0hRAigS44Zay7+/In1QshxHyTlXX+pdjS0hVCiASS0BVC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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdadd4e160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(pm.energyplot(irt_trace, legend=False, figsize=(6, 4))\n",
    "   .set_title(CONVERGENCE_TITLE()));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Criticize the model given data, take three"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "resid_df = (df.assign(p_hat=irt_trace['p'].mean(axis=0))\n",
    "              .assign(resid=lambda df: df.foul_called - df.p_hat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The binned residuals for this model are more asymmetric than for the previous models, but still not too bad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "N_BIN = 50\n",
    "\n",
    "bin_ix, bins = pd.qcut(\n",
    "    resid_df.p_hat, N_BIN,\n",
    "    labels=np.arange(N_BIN),\n",
    "    retbins=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QUIfXH8VLy8ize5yeme+imgAAblaJQaJLly5lVY8iLly4oIsXL9o+8EvywQcfqGPHjrrn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\nAQAATPv/F5ml3DxVMx0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdbbbeabe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = (resid_df.groupby(bins[bin_ix])\n",
    "              .resid.mean()\n",
    "              .rename_axis('p_hat', axis=0)\n",
    "              .reset_index()\n",
    "              .plot('p_hat', 'resid', kind='scatter'))\n",
    "ax.xaxis.set_major_formatter(pct_formatter);\n",
    "ax.set_xlabel(r\"Binned $\\hat{p}$\");\n",
    "make_foul_rate_yaxis(ax, label=\"Residual\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KiuSxIZpCdxjJjyncqiYnxtLe3F9pniGNf2swSISGhuLkyZMA6n9EtiAIMDMz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\nJERERCRnfwOOn5C9ktVAOwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcd9d74da58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = (resid_df.groupby('seconds_left')\n",
    "              .resid.mean()\n",
    "              .reset_index()\n",
    "              .plot('seconds_left', 'resid', kind='scatter'))\n",
    "make_time_axes(ax, ylabel=\"Residual\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Model selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The IRT model represents a marginal improvement over the possession model in terms of WAIC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "MODEL_NAME_MAP[2] = \"IRT\"\n",
    "\n",
    "comp_df = (pm.compare(\n",
    "                (base_trace, poss_trace, irt_trace),\n",
    "                (base_model, poss_model, irt_model)\n",
    "             )\n",
    "             .rename(index=MODEL_NAME_MAP)\n",
    "             .loc[MODEL_NAME_MAP.values()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "      <th>dSE</th>\n",
       "      <th>warning</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <td>11609.8</td>\n",
       "      <td>1.98</td>\n",
       "      <td>1567.2</td>\n",
       "      <td>0</td>\n",
       "      <td>56.98</td>\n",
       "      <td>73.91</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Possession</th>\n",
       "      <td>10066.5</td>\n",
       "      <td>81.92</td>\n",
       "      <td>23.86</td>\n",
       "      <td>0.1</td>\n",
       "      <td>87.93</td>\n",
       "      <td>10.98</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IRT</th>\n",
       "      <td>10042.6</td>\n",
       "      <td>215.56</td>\n",
       "      <td>0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>88.4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               WAIC   pWAIC   dWAIC weight     SE    dSE warning\n",
       "Base        11609.8    1.98  1567.2      0  56.98  73.91       1\n",
       "Possession  10066.5   81.92   23.86    0.1  87.93  10.98       1\n",
       "IRT         10042.6  215.56       0    0.9   88.4      0       1"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p5syZys7OdtSqq6uVmJioe+65R+Hh4YqNjVVhYaGjfuHCBcXGxio8PFwRERFKSkpSTU1N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\npoEDBzq1devWTVa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aqrvvvluvvPKKrj7oKS0t1dKlSzV+/HiNHDlSsbGx+vrrr9tkXEDn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\nGAAAgCECAwAAMPT/AC4cuSvhMaHqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcdbbb7df98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.errorbar(\n",
    "    np.arange(len(MODEL_NAME_MAP)), comp_df.WAIC,\n",
    "    yerr=comp_df.SE, fmt='o'\n",
    ");\n",
    "ax.set_xticks(np.arange(len(MODEL_NAME_MAP)));\n",
    "ax.set_xticklabels(comp_df.index);\n",
    "ax.set_xlabel(\"Model\");\n",
    "ax.set_ylabel(\"WAIC\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Is committing and/or drawing fouls a measurable player skill?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def varname_to_param(varname):\n",
    "    return varname[0]\n",
    "\n",
    "def varname_to_player(varname):\n",
    "    return int(varname[3:-2])\n",
    "\n",
    "def varname_to_season(varname):\n",
    "    return int(varname[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "irt_df = (pm.trace_to_dataframe(\n",
    "                irt_trace, varnames=['θ_player', 'b_player']\n",
    "            )\n",
    "            .rename(columns=lambda col: col.replace('_player', ''))\n",
    "            .T\n",
    "            .apply(\n",
    "               lambda s: pd.Series.describe(\n",
    "                   s, percentiles=[0.055, 0.945]\n",
    "               ),\n",
    "               axis=1\n",
    "            )\n",
    "            [['mean', '5.5%', '94.5%']]\n",
    "            .rename(columns={\n",
    "                 '5.5%': 'low',\n",
    "                 '94.5%': 'high'\n",
    "            })\n",
    "            .rename_axis('varname')\n",
    "            .reset_index()\n",
    "            .assign(\n",
    "                param=lambda df: df.varname.apply(varname_to_param),\n",
    "                player=lambda df: df.varname.apply(varname_to_player),\n",
    "                season=lambda df: df.varname.apply(varname_to_season)\n",
    "            )\n",
    "            .drop('varname', axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>low</th>\n",
       "      <th>high</th>\n",
       "      <th>param</th>\n",
       "      <th>player</th>\n",
       "      <th>season</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.015132</td>\n",
       "      <td>-0.312961</td>\n",
       "      <td>0.276028</td>\n",
       "      <td>θ</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.003946</td>\n",
       "      <td>-0.284629</td>\n",
       "      <td>0.283364</td>\n",
       "      <td>θ</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.010513</td>\n",
       "      <td>-0.277971</td>\n",
       "      <td>0.290268</td>\n",
       "      <td>θ</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.037012</td>\n",
       "      <td>-0.239934</td>\n",
       "      <td>0.337692</td>\n",
       "      <td>θ</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.034668</td>\n",
       "      <td>-0.311093</td>\n",
       "      <td>0.229465</td>\n",
       "      <td>θ</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean       low      high param  player  season\n",
       "0 -0.015132 -0.312961  0.276028     θ       0       0\n",
       "1 -0.003946 -0.284629  0.283364     θ       0       1\n",
       "2  0.010513 -0.277971  0.290268     θ       1       0\n",
       "3  0.037012 -0.239934  0.337692     θ       1       1\n",
       "4 -0.034668 -0.311093  0.229465     θ       2       0"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "irt_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "player_irt_df = irt_df.pivot_table(\n",
    "    index='player',\n",
    "    columns=['param', 'season'],\n",
    "    values='mean'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>param</th>\n",
       "      <th colspan=\"2\" halign=\"left\">b</th>\n",
       "      <th colspan=\"2\" halign=\"left\">θ</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>season</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.064689</td>\n",
       "      <td>0.006621</td>\n",
       "      <td>-0.015132</td>\n",
       "      <td>-0.003946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.006142</td>\n",
       "      <td>0.004387</td>\n",
       "      <td>0.010513</td>\n",
       "      <td>0.037012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.090107</td>\n",
       "      <td>0.092868</td>\n",
       "      <td>-0.034668</td>\n",
       "      <td>-0.003519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.022949</td>\n",
       "      <td>-0.002456</td>\n",
       "      <td>0.005822</td>\n",
       "      <td>-0.003961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.006999</td>\n",
       "      <td>0.288897</td>\n",
       "      <td>0.068338</td>\n",
       "      <td>0.007508</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "param          b                   θ          \n",
       "season         0         1         0         1\n",
       "player                                        \n",
       "0      -0.064689  0.006621 -0.015132 -0.003946\n",
       "1      -0.006142  0.004387  0.010513  0.037012\n",
       "2       0.090107  0.092868 -0.034668 -0.003519\n",
       "3      -0.022949 -0.002456  0.005822 -0.003961\n",
       "4      -0.006999  0.288897  0.068338  0.007508"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "player_irt_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The following plot shows that the committing skill appears to be somewhat larger than the disadvantaged skill.  This difference seems reasonable because most fouls are committed by the player on defense; committing skill is quite likely to to be correlated with defensive ability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_latent_params(df):\n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    n, _ = df.shape\n",
    "    y = np.arange(n)\n",
    "\n",
    "    ax.errorbar(\n",
    "        df['mean'], y,\n",
    "        xerr=(df[['high', 'low']]\n",
    "                .sub(df['mean'], axis=0)\n",
    "                .abs()\n",
    "                .values.T),\n",
    "        fmt='o'\n",
    "    )\n",
    "\n",
    "    ax.set_yticks(y)\n",
    "    ax.set_yticklabels(\n",
    "        player_enc.inverse_transform(df.player)\n",
    "    )\n",
    "    ax.set_ylabel(\"Player\")\n",
    "    \n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcd9d65d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(\n",
    "    ncols=2, nrows=2, sharex=True,\n",
    "    figsize=(16, 8)\n",
    ")\n",
    "(θ0_ax, θ1_ax), (b0_ax, b1_ax) = axes\n",
    "\n",
    "bins = np.linspace(\n",
    "    0.9 * irt_df['mean'].min(),\n",
    "    1.1 * irt_df['mean'].max(),\n",
    "    75\n",
    ")\n",
    "\n",
    "θ0_ax.hist(\n",
    "    player_irt_df['θ', 0],\n",
    "    bins=bins, normed=True\n",
    ");\n",
    "θ1_ax.hist(\n",
    "    player_irt_df['θ', 1],\n",
    "    bins=bins, normed=True\n",
    ");\n",
    "\n",
    "θ0_ax.set_yticks([]);\n",
    "θ0_ax.set_title(\n",
    "    r\"$\\hat{\\theta}$ (\" + season_enc.inverse_transform(0) + \")\"\n",
    ");\n",
    "\n",
    "θ1_ax.set_yticks([]);\n",
    "θ1_ax.set_title(\n",
    "    r\"$\\hat{\\theta}$ (\" + season_enc.inverse_transform(1) + \")\"\n",
    ");\n",
    "\n",
    "b0_ax.hist(\n",
    "    player_irt_df['b', 0],\n",
    "    bins=bins, normed=True, color=green\n",
    ");\n",
    "b1_ax.hist(\n",
    "    player_irt_df['b', 1],\n",
    "    bins=bins, normed=True, color=green\n",
    ");\n",
    "\n",
    "b0_ax.set_xlabel(\n",
    "    r\"$\\hat{b}$ (\" + season_enc.inverse_transform(0) + \")\"\n",
    ");\n",
    "\n",
    "b0_ax.invert_yaxis();\n",
    "b0_ax.xaxis.tick_top();\n",
    "b0_ax.set_yticks([]);\n",
    "\n",
    "b1_ax.set_xlabel(\n",
    "    r\"$\\hat{b}$ (\" + season_enc.inverse_transform(1) + \")\"\n",
    ");\n",
    "\n",
    "b1_ax.invert_yaxis();\n",
    "b1_ax.xaxis.tick_top();\n",
    "b1_ax.set_yticks([]);\n",
    "\n",
    "fig.suptitle(\"Disadvantaged skill\", size=18);\n",
    "fig.text(0.45, 0.02, \"Committing skill\", size=18)\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The latent ability parameters tend to lie in the interval $[-0.2, 0.2]$, so these skills are small, if they exist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcd9d65d0b8>"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "top_bot_irt_df = (irt_df.groupby('param')\n",
    "                    .apply(\n",
    "                        lambda df: pd.concat((\n",
    "                                df.nlargest(10, 'mean'),\n",
    "                                df.nsmallest(10, 'mean')\n",
    "                            ),\n",
    "                            axis=0, ignore_index=True\n",
    "                        )\n",
    "                    )\n",
    "                    .reset_index(drop=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>low</th>\n",
       "      <th>high</th>\n",
       "      <th>param</th>\n",
       "      <th>player</th>\n",
       "      <th>season</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.347551</td>\n",
       "      <td>-0.028239</td>\n",
       "      <td>0.758395</td>\n",
       "      <td>b</td>\n",
       "      <td>86</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.328016</td>\n",
       "      <td>-0.028768</td>\n",
       "      <td>0.707518</td>\n",
       "      <td>b</td>\n",
       "      <td>23</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.288897</td>\n",
       "      <td>-0.089046</td>\n",
       "      <td>0.677624</td>\n",
       "      <td>b</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.285537</td>\n",
       "      <td>-0.084353</td>\n",
       "      <td>0.689011</td>\n",
       "      <td>b</td>\n",
       "      <td>78</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.279316</td>\n",
       "      <td>-0.049866</td>\n",
       "      <td>0.634959</td>\n",
       "      <td>b</td>\n",
       "      <td>462</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean       low      high param  player  season\n",
       "0  0.347551 -0.028239  0.758395     b      86       0\n",
       "1  0.328016 -0.028768  0.707518     b      23       0\n",
       "2  0.288897 -0.089046  0.677624     b       4       1\n",
       "3  0.285537 -0.084353  0.689011     b      78       0\n",
       "4  0.279316 -0.049866  0.634959     b     462       1"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_bot_irt_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We now examine the top and bottom ten players in each ability, across both seasons.\n",
    "\n",
    "The top players in terms of disadvantaged ability tend to be good scorers (Jimmy Butler, Ricky Rubio, John Wall, Andre Iguodala).  The presence of DeAndre Jordan in the top ten seems to be due to the hack-a-Shaq phenomenon.  Future work, it would be interesting to control for the disavantage player's free throw percentage in order to mitigate the influence of the hack-a-Shaq effect on the measurement of latent skill.\n",
    "\n",
    "Interestingly, the bottom players (in terms of disadvantaged ability) include many stars (Pau Gasol, Carmelo Anthony, Kevin Durant, Kawhi Leonard).  The presence of these stars in the bottom may somewhat counteract the pervasive narrative that referees favor stars in their foul calls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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