An Improved Analysis of NBA Foul Calls with Python

nba_irt.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "title: An Improved Analysis of NBA Foul Calls with Python\n",
    "tags: NBA, Bayesian Statistics, PyMC3\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last April, I wrote a [post](http://austinrochford.com/posts/2017-04-04-nba-irt.html) that used Bayesian item-response theory models to analyze NBA foul call data.  Last November, I [spoke](http://austinrochford.com/talks.html#pydata-nyc) about a greatly improved version of these models at [PyData NYC](https://pydata.org/nyc2017/).  This post is a write-up of the models from that talk.\n",
    "\n",
    "## Last Two-minute Report\n",
    "\n",
    "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 foul 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": [
    "### Loading the data\n",
    "\n",
    "[Russel Goldenberg](http://russellgoldenberg.com/) of [The Pudding](https://pudding.cool/) has been scraping the PDFs that the NBA publishes and transforming them into a CSV for some time.  I am grateful for his work, which has enabled this analysis.\n",
    "\n",
    "We download the data locally to be kind to GitHub."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "from itertools import product\n",
    "import logging\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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 tensor as tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "pct_formatter = StrMethodFormatter('{x:.1%}')\n",
    "\n",
    "sns.set()\n",
    "blue, green, *_ = sns.color_palette()\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": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "SEED = 207183 # from random.org, for reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": 8,
   "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": 9,
   "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": "markdown",
   "metadata": {},
   "source": [
    "The data set contains more than 16,000 plays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16300"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orig_df.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "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, and\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, and\n",
    "* `disadvantaged_team` and `committing_team` indicate how each team is involved in the play."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": 11,
     "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",
    "In this post, we answer two questions:\n",
    "\n",
    "1. How does game context impact foul calls?\n",
    "2. Is (not) committing and/or drawing fouls a measurable player skill?\n",
    "\n",
    "The previous post focused on the second question, and gave the first question only a cursory treatment.  This post enhances our treatment of the first question, in order to control for non-skill factors influencing foul calls (namely intentional fouls).  Controlling for these factors makes our estimates of player skill more realistic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exploratory Data Analysis\n",
    "\n",
    "First we examine the types of calls present in the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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",
       "Name: call_type, dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(orig_df['call_type']\n",
    "        .value_counts()\n",
    "        .head(n=15))"
   ]
  },
  {
   "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": 13,
   "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 0x7f1619124198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(orig_df['call_type']\n",
    "        .str.split(':', expand=True)\n",
    "        .iloc[:, 0]\n",
    "        .value_counts()\n",
    "        .plot(\n",
    "            kind='bar',\n",
    "            color=blue, logy=True, \n",
    "            title=\"Call types\"\n",
    "        )\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": 14,
   "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": 15,
   "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 0x7f15e52739e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(foul_df['call_type']\n",
    "        .str.split(': ', expand=True)\n",
    "        .iloc[:, 1]\n",
    "        .value_counts()\n",
    "        .plot(\n",
    "            kind='bar',\n",
    "            color=blue, logy=True,\n",
    "            title=\"Foul Types\"\n",
    "        )\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": 16,
   "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\n",
    "\n",
    "There are a number of misspelled team names in the data, which we correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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 an NBA season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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 noncalls 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 February 2018), and\n",
    "* dropping unneeded rows and columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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 55% of the rows in the original data set remain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5516564417177914"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clean_df.shape[0] / orig_df.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": 21,
     "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 integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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 one or zero depending on whether or not a foul was called, and\n",
    "* setting `score_committing` and `score_disadvantaged` to the score of the committing and disadvantaged teams, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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 data is ready for analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(n=2).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Modeling\n",
    "\n",
    "We follow George Box's modeling workflow, as <a href=\"http://dustintran.com/talks/Tran_Edward.pdf\">summarized</a> by Dustin Tran:\n",
    "\n",
    "1. build a model of the science,\n",
    "2. infer the model given data, and\n",
    "3. criticize the model given data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Baseline model\n",
    "\n",
    "#### Build a model of the science\n",
    "\n",
    "Below we examine the foul call rate by season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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 0x7f15e751d908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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\n",
    "\n",
    "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; our first model accounts for this difference.\n",
    "\n",
    "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": 26,
   "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": "skip"
    }
   },
   "source": [
    "Foul calls are Bernoulli trials, $y_k \\sim \\textrm{Bernoulli}(p_k).$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "season = df['season'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "with base_model:\n",
    "    y = pm.Bernoulli(\n",
    "        'y', p[season],\n",
    "        observed=df['foul_called']\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Infer the model given data\n",
    "\n",
    "We now sample from the model's posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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",
    "    'nuts_kwargs': {\n",
    "        'target_accept': 0.9\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [β_season]\n",
      "100%|██████████| 1500/1500 [00:07<00:00, 198.65it/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",
    "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": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bfmi = pm.bfmi(base_trace)\n",
    "\n",
    "max_gr = max(\n",
    "    np.max(gr_stats) for gr_stats in pm.gelman_rubin(base_trace).values()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "CONVERGENCE_TITLE = lambda: f\"BFMI = {bfmi:.2f}\\nGelman-Rubin = {max_gr:.3f}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
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Z8drcHAocRtM1TKppVtstRDFIeUFMSzyh8YunmsCAz5zcyPFLvbT3Rnj4+ffHvN4wDA4E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\ndIUQooAkdIUQooD+P8DyYToyq5XaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15cca64048>"
      ]
     },
     "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\n",
    "\n",
    "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": 34,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.4052151 ,  0.30696232],\n",
       "       [ 0.3937377 ,  0.30995026],\n",
       "       [ 0.39881138,  0.29866616],\n",
       "       ..., \n",
       "       [ 0.40279887,  0.31166828],\n",
       "       [ 0.4077945 ,  0.30299785],\n",
       "       [ 0.40207901,  0.29991789]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_trace['p']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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": 36,
   "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>0.403875</td>\n",
       "      <td>0.596125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403875</td>\n",
       "      <td>-0.403875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.403875</td>\n",
       "      <td>0.596125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403875</td>\n",
       "      <td>-0.403875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20151028INDTOR-6</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403875</td>\n",
       "      <td>-0.403875</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  foul_called     p_hat     resid\n",
       "play_id                                          \n",
       "20151028INDTOR-1          1.0  0.403875  0.596125\n",
       "20151028INDTOR-2          0.0  0.403875 -0.403875\n",
       "20151028INDTOR-3          1.0  0.403875  0.596125\n",
       "20151028INDTOR-4          0.0  0.403875 -0.403875\n",
       "20151028INDTOR-6          0.0  0.403875 -0.403875"
      ]
     },
     "execution_count": 36,
     "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": 37,
   "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>-0.000162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-2017</th>\n",
       "      <td>-0.000219</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              resid\n",
       "season             \n",
       "2015-2016 -0.000162\n",
       "2016-2017 -0.000219"
      ]
     },
     "execution_count": 37,
     "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": [
    "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": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NCWJ0FRQ11R6q1kvT9dcHKX1Xlm9NFQVmndztsWyabmdzSKk9pEAyyZZBQUE4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1624d6b9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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)\n",
    "\n",
    "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": [
    "### Possession model\n",
    "\n",
    "#### Build a model of the science\n",
    "\n",
    "The following plot illustrates the fact that only the trailing team has any incentive to committ intentional fouls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": "code",
   "execution_count": 40,
   "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 0x7f1624d731d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_time_axes(\n",
    "    df.pivot_table(\n",
    "        'foul_called',\n",
    "        'seconds_left',\n",
    "        'trailing_committing'\n",
    "      )\n",
    "      .rolling(20)\n",
    "      .mean()\n",
    "      .rename(columns={\n",
    "          0: \"No\", 1: \"Yes\"\n",
    "      })\n",
    "      .rename_axis(\n",
    "          \"Committing team is trailing\",\n",
    "          axis=1\n",
    "      )\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": 41,
   "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 0x7f15ca3e9c88>"
      ]
     },
     "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",
    "\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": 42,
   "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 post, we will use [hierarchical distributions](https://en.wikipedia.org/wiki/Multilevel_model) to model the variation of foul call rates.  For much more information on hierarchical models, consult [_Data Analysis Using Regression and Multilevel/Hierarchical Models_](http://www.stat.columbia.edu/~gelman/arm/).  We use the priors\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 [non-centered parametrization](http://twiecki.github.io/blog/2017/02/08/bayesian-hierchical-non-centered/#The-Funnel-of-Hell-(and-how-to-escape-it%29) of the hierarchical normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def hierarchical_normal(name, shape, σ_shape=1):\n",
    "    Δ = pm.Normal(f'Δ_{name}', 0., 1., shape=shape)\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": 44,
   "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`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "trailing_poss_enc = LabelEncoder().fit(df['trailing_poss'])\n",
    "trailing_poss = trailing_poss_enc.transform(df['trailing_poss'])\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.  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": 47,
   "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 0x7f15c8961cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_time_axes(\n",
    "    df.pivot_table(\n",
    "        'foul_called',\n",
    "        'seconds_left',\n",
    "        'trailing_poss'\n",
    "      )\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": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Hj14MGzaS/ft/Y82az4D8npYePZ7H2NiY1q3bGiROIYRh/buXwcioYgxDFEWh+3t7SPFQ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\nZKRk0KChvPTSaAByc3NZs+Y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K5tThCLIz1bRs74WtvYWhwxHliF5Jw5w5c3B3d0epVDJj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\nIAEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15c88cd7b8>"
      ]
     },
     "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": [
    "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": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "df['remaining_poss'] = (df['seconds_left']\n",
    "                          .floordiv(25)\n",
    "                          .add(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "remaining_poss_enc = LabelEncoder().fit(df['remaining_poss'])\n",
    "remaining_poss = remaining_poss_enc.transform(df['remaining_poss'])\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": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Lli2r1ACJiIhUwuRAaYI+9blz5xAVFQUAOHToEBwdHTF79mzk5OTg448/rtQA\niYiIVFJDH/CqENRzUFhYCH19fQBATEwM+vXrBwCoW7cu8vLyKi86IiIieucEpVNt2rTBhg0bULt2\nbTx+/Bh9+vQBAJw6dQpmZmaVGiAREZFK2HOgNEEt9vXXX+Orr75CdnY2fH19YWBgALFYjC+++AIr\nV66s7BiJiIjKj8mB0gS1WMeOHXHs2DGZY0ZGRoiKikLjxo0rJTAiIqIKweRAaYJaTCKR4I8//sDt\n27fx6tWrEudnz55d4YERERFVCCYHShPUYt7e3jhy5Ag++OAD6OnpyZwTiURlJgcpKSmIi4vDzZs3\nIRaLAQCGhoawsLBA9+7d8f7775czfCIiIqpogpKDU6dOITIyEpaWlkpVfv36dXz33Xf4/fffYWxs\njNatW8PIyAgikQiPHz/GwYMH8fz5c3z00UeYN2+ezDbMREREFYI9B0oT1GIGBgZo3ry5UhX/8MMP\nCA0NhbOzMw4dOoTWrVuXel1ycjL27NmDSZMmwd3dHf/5z3/k1hkTE4Pw8HAkJCRALBZDJBLB2NgY\n1tbWcHNzQ+fOnZWKkYiIagAmB0oT1GLz5s1DcHAwPDw8pOsdlOXMmTM4ePAgTE1NFV7XunVr+Pr6\nYsqUKViwYIHc5CA8PBzBwcEYPnw4PvroIxgYGAAAMjMzER8fj6lTpyIwMBDDhg0TFB8REdUQTA6U\nJpJIJJKyLnJ2dsaTJ0/w8uVLNGjQAFpasmsnxcbGVlqAbw0ePBjLli2Dra1tqefj4uKwdOlS/Prr\nr0IrrMDoqpdLSw+rO4Qq7ZNP1B1B1fXokbojqNoMDdUdQdX24EElVfzZZ6qV//HHiolDgwhKpxR1\n9QsRHR2N4OBg3L9/H/n5+SXOJyUllVlHamoq2rdvL/e8ra0tUlJSVIqTiIiqIfYcKE1Qi40cOVKl\nm/j5+cHBwQGzZs1C7dq1y1VH69atsW/fPowbN67U85GRkXLHNRARUQ3G5EBpglqssLAQmzZtwvHj\nx5GSkoKCggI0a9YMo0aNwqefflpm+by8PAQGBkJbhb8gT09PzJgxA7t27YKVlZV0zIFYLEZiYiKe\nPXuG0NDQctdPRETVFJMDpQlqsW+++QZRUVFwdXVFy5YtAQC3b9/GTz/9hKKiIkyZMkVh+dGjR2Pv\n3r0YO3ZsuQPt1q0bjh07hoMHD+Lq1avSLaSNjIwwZswYODs7w9jYuNz1ExFRNcXkQGmCWuz06dPY\nunUrWrXLlvEzAAAgAElEQVRqJT3Wv39/ODk5Yd68eWUmByNGjMDUqVOxdu1amJiYlBjQGBkZKSjY\nRo0a4TNVB5YQERGRQoKSg+fPn6NZs2Yljrdu3RoZGRlllvfw8ICJiQns7OzKPeagLIcOHUJWVhYm\nTpxYKfUTEZGGYs+B0gS1WOvWrbF7925MmjRJ5nh4eDhatGhRZvmUlBScO3cOderUKV+UAkRGRuLh\nw4dMDoiISBaTA6UJajEfHx989tlnCAsLQ6tWrSASiXD79m2kpaVh3bp1ZZbv1asXbt26hY4dO6oc\nsDzbtm3DkydPKq1+IiLSUEwOlCaoxWxtbREVFYVDhw7h0X9XObGzs8OQIUMEDQJs27Yt5s6dC1tb\nW5iamkIkEsmc9/b2LrOOtLQ0+Pv74+LFi2jcuDFmzZqFwf9ayGjQoEG4cuWKkI9EREQ1BZMDpQlu\nsYYNG2Ly5MnluklcXBzMzc2Rnp6O9PR0mXP/ThTkWb58OV69eoXFixfjyZMn8Pf3x/379zFjxgzp\nNQIWeyQiIqIyyE0OJkyYgF27dgEARo0apfAhXtZsgx07dsg9d/PmzbJiBACcP38ehw4dkvZU9OnT\nB25ubjA2NpYujCQ00SAiohqEPQdKk9tivXr1kv7+0UcfVcjN0tPTZZZPTk1NxZQpU3Dp0qUyyxYX\nF0NPT0/655YtWyI0NBSffvopTExM8NFHH7HngIiISmJyoDS5LfbP7vrZs2eXOJ+VlSVdpbAsly9f\nxrx585CWllbiXM+ePQXV0a1bNwQGBsLLywvvvfceAKBDhw4ICQmBp6cn5syZw54DIiIq6R0lBz/8\n8AO2b9+OFy9ewMrKCosXL0br1q1x48YNLFu2DNeuXYOBgQFGjhyJWbNmyX1mhYWFYefOnUhNTUXr\n1q3h7e2NLl26AAD27NmDkJAQ6OjoYNGiRejbt6+03JUrV+Dj44MDBw6ovGyAVtmXANevX5dZ3XDe\nvHmws7ODvb29oAGAy5cvx7BhwxAZGQltbW3s27cPS5YsQe/evfHtt98KCnT+/PlISkrCmjVrZI73\n6tUL33//PX7++edSN3UiIiKqbOHh4dizZw+2bt2Ks2fPokuXLti8eTNevXqF6dOnw9bWFqdPn8bm\nzZsRGRmJ8PDwUuv5448/sHr1aixZsgSxsbFwcXHB9OnTkZ6ejhcvXmD16tWIjIzEhg0bsGjRImmP\neWFhIfz9/REQEFAh6wkJSqeWLl0qfc0QFRWFs2fP4v/+7/8QHx+PlStXYufOnQrL3759G+Hh4dDS\n0oJIJIKlpSUsLS1hZmaGr7/+Gps3by4zhiZNmuDgwYPIzs4ucc7a2hr79+/H33//LeTjEBFRTfIO\neg6+//57fPnll2jbti0A4MsvvwQAHD16FHl5eZgzZw60tbXRpk0buLm5ITw8HOPHjy9Rz+7duzFy\n5EhpT4Grqyt27tyJQ4cOwcbGBubm5jAzM4OZmRkKCwuRnp6O9957Dz/++COsrKxgb29fIZ9HUM9B\nUlKS9DXDyZMnMXjwYHTt2hWTJ0/GjRs3yixft25d6UO9Xr16SE1NBQB06dIF58+fVyrg+vXrl3q8\nVq1a0sYkIiKS0tZW7acMqampePToEXJzczFs2DB07doV7u7uePr0Ka5evYq2bdvKbDxoZWWFmzdv\n4vXr1yXqunr1KqysrGSOWVlZISEhocRriLdj8R4+fIjdu3dj6NChmDhxIsaNG4fY2NhyNtYbgtIp\nHR0dFBQUQCQS4cyZM1iyZAmAN90YxcXFZZbv06cPJkyYgIiICHTt2hXe3t4YN24crly5goYNG6r0\nAcrrRfhhtdxXE3iNUHcEVVujRuqOoOr6x5hhKgXbR00quefg6dOnAN4s479lyxbo6OjA29sbX375\nJVq1aoUGDRrIXG9oaIji4mJkZWXBxMRE5lxmZmaJ6w0MDHDnzh20atUKDx8+xP3795Gamgp9fX3U\nr18fHh4e8PDwwIoVKxAYGIgmTZpgzJgx+P3336Gjo1OuzySoxbp27Yq5c+dCW1sbIpEIDg4OKCoq\nwqZNm0pkOKXx9fXF1q1boaenB19fX3zxxRfw8fGBubm5NNEgIiKqFJWcHLx97z9lyhS8//77AN68\nVhg1ahQ++OADudcLHUT/9np9fX189dVXGD9+PPT09LBkyRIcPHgQEokEffr0wZIlS9C5c2cAwHvv\nvYc7d+7AwsKiXJ9JUIstWrQIa9asQXZ2NjZt2gQdHR1kZ2fj+PHj+O6778osr6uri5kzZwIAGjdu\nLF0/gYiISNM1+m93oqGhofRY06ZNAQDPnj1Dbm6uzPVZWVmoVatWqTP+jIyMIBaLS1z/do2f0aNH\nY/To0QDe9DK4uLhg+/btyMnJQb169aRl6tSpU+oYPaEEjTlo2LAhlixZgjVr1qBDhw4A3rzrOHLk\niHTwRVnOnj0LT09PuLm5AXjzSmLv3r3lDJuIiEigSh5zYGpqCmNjY1y7dk167O1WAy4uLrhx44bM\nbLr4+Hi0a9cOurq6Jerq0KEDEhMTZY7Fx8fDxsamxLXffvstXF1dYW5uDn19fZlkIDMzE/r6+mW3\njRzlnsrYvXt39OjRQ9BUxr1798LDwwNGRkbS6zMyMrBhwwZs2bKlnKETEREJUMnJgba2NiZMmIDN\nmzfj9u3byMrKwpo1a+Dk5IR+/frB0NAQ69atQ25uLq5fv44dO3ZIvyinpqZi4MCBuHfvHgBg4sSJ\nOHjwIC5evIjXr19j27ZtyMrKwtChQ2Xuef78eVy9ehWfffYZgDeD9c3MzBAdHY0bN27gxYsXaNmy\nZfmbTMhF/57KeO7cOezYsUPwVMYNGzZg69atsLa2xs8//wzgzeuF0NBQTJ8+HdOmTSv3ByAiIlLo\nHUxldHd3R1ZWFiZMmIDXr1/DyckJixYtgq6uLrZs2SJd28fY2BiffvopRox4M/K7oKAAd+/elfYs\nODg4YMGCBfD390dqaiosLCywZcsWmVcQ+fn5CAwMxPLly2VmQfj5+cHb2xsFBQUIDAwstWdCKJFE\nwJrDnTt3RlxcHLS1tbFgwQLo6Ohg8eLFKCwshL29PS5cuKCwvK2tLS5dugSRSARra2tp70FBQQG6\ndOmilp0UX7x457fUGCM4W0GhwkJ1R1B15eSoO4KqjbMVFDt3rpIqVvUVtotLxcShQQS9Vng7lbGo\nqAhnzpyR7rUgdCpj8+bNcfbs2RLH9+/fDzMzMyVDJiIiosr0TqYyuru7Y86cOejduzcKCwsRGBiI\nGzduID4+HiEhISp/CCIiIrm48ZLSBPUcLFq0CKampqhdu7Z0KmNubi6OHz8OPz+/MssPGDAAO3bs\nQMOGDWFvb49nz57BxsYGhw4dQv/+/VX+EERERHJV8oDE6kjQmIN/KigoUHrFpcjISOm8zH/Ky8vD\nzp07MXXqVKXqqwgccyAfxxwoxjEH8nHMgWIcc6BYpY05OH5ctfIff1wxcWgQQT0HRUVFCAkJgYOD\nAzp16gQAyMnJwfz58/Hy5Uu55QoLC5Gbm4slS5bg1atXyMvLk/m5c+cO1q1bVzGfhIiIiCqEoP6S\nlStX4uLFi/D394eXlxeAN4sgicViLF++HMuWLSu1XFhYGIKCggC8mbFQGnnHiYiIKkQNfTWgCkEt\nduDAAezbtw+mpqbStaAbNGiAFStWwNnZWW65yZMnY9iwYejduzd+/PHHEuf19PTQrl27coZOREQk\nAJMDpQlqsaKiIuna0f+kq6ur8LUCABgbG+PkyZNo3Lhx+SIkIiJSBZMDpQlqsfbt22Pr1q1wd3eX\nHnv58iWCgoLQsWPHMstXZGKQnJyMiIgIJCQkQCwWQyQSwdjYGNbW1tI1pomIiKSYHChN0GyFmzdv\n4vPPP0dhYSHEYjFatmyJx48f47333sPGjRvRpk2bdxEroqKi4OnpCXt7e1hZWcHAwAASiQRZWVmI\nj4/HpUuXsH79evTs2bPMujhbQT7OVlCMsxXk42wFxThbQbFKm61w/rxq5bt1q5g4NIigdKpt27Y4\nfvw4/vjjDzx48AB6enr44IMP4ODggFq1alV2jFLr169HSEgI+vTpU+r5I0eOICQkRFByQERENQR7\nDpQmuMVev36NgQMHAngzjTE2NhbJycmwsLCotOD+7cGDB3BwcJB7vm/fvoIWZSIiohqEyYHSBLXY\n4cOHsXDhQly6dAl5eXkYNWoU0tLSUFBQgKVLl0p3l5Jn1KhR0lkO/6alpYXGjRvD0dFR4XUA0KxZ\nM8TExMjtOYiOjuaYAyIiksXkQGmCWmzDhg1Ys2YNgDfTGgsLC3Hu3DlcvXoVixYtKjM56NevH7Zt\n24a2bdvC0tISWlpaSEpKwp07dzBq1CiIxWKsXLkSKSkpmDNnjtx63N3d4eHhAQcHB+mYAwAQi8VI\nTExEXFwc92ogIiJZTA6UJqjFnjx5gt69ewN48+186NChqFOnDrp06YLHjx+XWf7u3btYsGBBiSTi\nwIEDiI+Px+LFizF+/HjMmjVLYXIwcOBANG/eHBEREYiJiYFYLAbwZrpkhw4d4OPjg1atWgn5SERE\nRCSHoORAX18fqamp0NXVRWxsLKZNmwYAyMjIgK6ubpnlT5w4UeoqioMHD8ayZcvg5+cHCwsL6cNe\nEUtLS44rICIi4dhzoDRBLTZ06FCMGTMGWlpaaNu2LWxsbPDy5Ut4e3ujV69eZZY3MjJCWFgYJk2a\nBC2t/23nEBERgQYNGgAAdu7ciRYtWpTzY7xx4cIF5ObmwtHRUaV6iIioGmFyoDRBLebt7Q0rKytk\nZ2djyJAhAAAdHR00bdoU3t7eZZb39/fHvHnzsHHjRjRu3Bg6OjpISUlBdnY2li1bhsLCQqxduxZr\n165V6cP4+/vj3r17SEpKUqkeIiKqRpgcKE3wls1ZWVnSAYBvpzKam5vD0tJS0I1evHiB06dPIy0t\nDRKJBI0aNULPnj3x3nvvAQByc3NRt27dcn6M/3ny5AmaNGkiIB6Vb1VtcREkxbgIknxcBEkxLoKk\nWKUtgvTkiWrlBTxTqpt3MpUReLNR07Bhw+Ser4jEAAAGDRqEK1euVEhdRERUDbDnQGnlmspYVFSk\n1FTG8+fPIygoCHfu3MHr169LnK/I1wACO0KIiKimYHKgtHJNZRwyZIhSUxn9/Pzw4YcfYurUqahT\np065g+3bt2+Z1xQUFJS7fiIiqoaYHCjtnUxlTEtLQ1BQELRV/AuqU6cOWrRoATs7u1LPSyQSBAUF\nqXQPIiKqZpgcKO2dTGXs1q0bbty4gfbt26sU7KpVqzB16lT4+vrC1NS01GtWrlyp0j2IiIhquncy\nlbFfv37w8vKCo6MjzMzMSuyfMHHiREHBWlhYYMGCBTh79ixGjRpV6jXvv/++oLqIiKiGYM+B0gRP\nZQSAzMxMpKSkoKCgAObm5jAyMhJUTt5GSQAgEolw8uRJoSFUmLZt3/ktNUZysrojqNr09dUdQdWV\nnV32GKSarUjdAVRpEkmzyqm4uFi18v9YvK+mEJROpaamwsvLCxcvXpTOBtDS0oKjoyNWrlwJ/TL+\ntzx16pTqkRIREZVDMVR7uNe81EBgcrB06VLo6upi165daNmyJQDg9u3bWLduHb799lssXry4RJnb\nt29LN0FKLuOraOvWrZWNm4iISBBVFy4TMO6+2hH0WqFXr1747bffpPsgvJWRkQEXFxecPn26RJmO\nHTsiPj4ewJvNkkQiUalrEIhEIrUsd8zXCvLxtYJifK0gH18rlIWvFRSprNcK+fmqla+JyYGgnoPC\nwkLUqlWrxPE6deqUuqgRABw9elT6uzrGFBAREQHsOSgPQa9SunTpAn9/f6SlpUmPpaWlwd/fHx07\ndiy1zD/3N5g/fz6aNm1a4sfAwADu7u4qfgQiIiL5CgtV+6mJBPUcLFy4ELNmzYKjoyPq1asHkUiE\nnJwcdOzYEcHBwXLLJSQkID4+Hn///Td27dpV4rXCw4cP8ejRI9U+ARERkQI19QGvCkHJQePGjREZ\nGYnr169LH+bm5uawsLBQWC4vLw9nzpxBYWEhtm7dWuK8np4e5s2bV46wiYiIqLIIXhkiPz8fGRkZ\nyM7OhkgkwvPnz1FYWKhwSeRu3bqhW7dumDZtGrZs2VIhARMRESmDPQfKE5QcXLhwATNnzkReXh4M\nDQ0BvFkQSV9fHxs3bkSnTp0Uls/Lyyv1eE5ODsaPH49ff/1VybCJiIiEYXKgPEHJga+vLz755BNM\nmzZNuqtibm4utmzZAh8fH5w4caLUchxzQERE6sbkQHmCkoO0tDTMmDFDZgfGunXrYubMmdi2bZvc\nchxzQERE6sbkQHmCkoPOnTsjKSkJ1tbWMsdv3bqFzp07yy3HMQdERESaR9AKidu2bcP27dvRu3dv\ntGjRAsXFxXjw4AGio6Ph4uIiswHT2x0WX716BT09PQDyxxy89fZVxbvEFRLl4wqJinGFRPm4QmJZ\nuEKiIpW1QuLNm6qVr4nPC0HJgaJdFWUq+8cOi9bW1rhy5QqA/y2f/G8SiUTp5ZOvX7+OhIQEiMVi\niEQiGBsbw8bGRrqPg1A18S9bKCYHijE5kI/JQVmYHChSWcnBtWuqlbeyqpg4NImg1wrl2VXxhx9+\nkP6+ffv2UpMDZaSmpmLu3LmIj4+HqakpDAwMIJFIkJWVhadPn6JHjx5YtWqV4G2kiYioZuCYA+UJ\n6jmoCmbOnAlDQ0N4eXnB2NhY5lxqaiq+/fZbFBcXIyQkRFB97DmQjz0HirHnQD72HJSFPQeKVFbP\nwX/3ACw3ObsEVGuCF0FSRXR0NIKDg3H//n3kl7I9lpDXCpcuXUJUVBT0S/mfuXHjxggICMDAgQMr\nJF4iIqo+2HOgvHeSHPj5+cHBwQGzZs1C7dq1y1VHnTp18OLFi1KTAwDIzs4ud91ERFR9MTlQ3jtJ\nDvLy8hAYGKhwqeWyODk5Yfbs2Zg5cyasrKzQoEEDAIBYLEZiYiI2b96M/v37V1TIRERUTTA5UJ6g\np3VYWJjcc1paWmjcuDE6deokXVr530aPHo29e/di7Nix5YsSwNdff43Vq1djwYIFyMnJkTnXoEED\nuLq6Ys6cOeWun4iIqicmB8oTNCBx2LBhSElJQU5ODurXrw+RSCTt4m/QoAGeP38OHR0dbNiwAd26\ndStR/ubNm5g6dSqKiopgYmICLS0tmfORkZGCAy4uLsb9+/eRmZkJADA2Noa5uXmJOsvCAYnycUCi\nYhyQKB8HJJaFAxIVqawBidHRqpXv3bti4tAkgnoOpkyZglOnTsHb2xtmZmYAgMePH2P16tUYMmQI\nPvroI4SGhuLbb78t9UHv4eEBExMT2NnZqTwuQEtLCy1atFCpDiIiqjnYc6A8QT0HTk5O+O2331Cv\nXj2Z4zk5ORg1ahSOHTuGgoIC2NnZ4a+//ipR3tbWFufOnavUlRBdXV1x//59xMbGCrqePQfysedA\nMfYcyMeeg7Kw50CRyuo5OH5ctfIff1wxcWgSQT0HWVlZSElJQevWrWWOp6Wl4fnz5wDe7LD47+Th\nrV69euHWrVvoWImTRT///HNkZ2dXWv1ERKSZ2HOgPEHJwciRI+Hm5oYhQ4agadOm0NbWxpMnT3Do\n0CH06dMH+fn5+OSTTzBmzJhSy7dt2xZz586Fra0tTE1NS6yW6O3trfIH6devn8p1EBFR9cPkQHmC\nkoOFCxeiTZs2iIqKwp9//gmJRIKGDRti8uTJcHNzg66uLnx8fODs7Fxq+bi4OJibmyM9PR3p6eky\n55RZVjk5ORkREREl9lawtraGq6srzM3NBddFREREpdOY5ZOjoqLg6ekJe3t7WFlZyeytEB8fj0uX\nLmH9+vXo2bOnoPo45kA+jjlQjGMO5OOYg7JwzIEilTXmYO9e1cq7uFRMHJpEUM/By5cvsW/fPty+\nfRuvXr0qcX7FihVl1nHt2jXcu3ev1OWTR4wYUWb59evXIyQkRO4OkUeOHEFISIjg5ICIiGoGvlZQ\nnqDk4Msvv8SVK1fQsWNH6OnpKX0Tf39//Pzzz6hTp06JqYwikUhQcvDgwQM4ODjIPd+3b1/4+fkp\nHRsREVVv7zo5WL58ObZv344bN24AAM6fP4/g4GAkJyfDxMQEkydPxvjx40stK5FIsG7dOhw8eBCZ\nmZmwsrKCn58f2rRpAwBYu3YtduzYAUNDQ6xcuRI2NjbSskeOHEFYWBh27Nih8k7IgpKD8+fP4/Dh\nw3j//ffLdZNDhw5h+/bt6N69e7nKA0CzZs0QExMjt+cgOjqaYw6IiEitkpKScODAAemfnz17Bnd3\nd3h5ecHFxQXXrl3D1KlT0bRpU/QuZXWlXbt2Ye/evQgNDYW5uTm2bNmC6dOn48iRI3j06BH27t2L\nEydOIDY2FkFBQQgPDwfwZn+hlStX4vvvv1c5MQAEJgempqaoX79+uW9iYmKCDh06lLs8ALi7u8PD\nwwMODg7SMQfA//ZWiIuLE7xdMxER1RzvqueguLgYAQEB+M9//iN9Hh08eBBNmzbFhAkTAACdOnXC\n8OHDER4eXmpysHv3bkyePBkWFhYAgFmzZiEsLAxnzpzB69evYW1tDUNDQzg5OcnM9AsODoaLiwta\ntWpVIZ9F0JrDCxcuxLJly3Dz5k28fPkSeXl5Mj9lCQgIgL+/P2JiYnDz5k0kJyfL/AgxcOBA/Pzz\nz3j//fcRExODnTt3YufOnfjzzz/xwQcfYO/evXJ7FYiIqOYqLFTtR6jw8HDo6elh6NCh0mNXr15F\n+/btZa6zsrJCQkJCifKvXr1CcnIyrKyspMd0dHTQtm1bJCQkyPQIFBUVSV/zX7p0CRcvXkT79u0x\nbtw4fPLJJ7h+/brwwEshqOdg7ty5yMvLw/79+0s9n5SUpLD89evXceLECfz222/SYyKRCBKJBCKR\nqMzyb1laWpYYV2BtbY1du3YJKv9Pt25lKl2mpqhfv/QNtOiNf/y7p3959KipukOo0jL5345avIue\ng/T0dGzYsAE7duyQOZ6ZmVliAUFDQ0OIxeISdWRlZUEikUh7xt8yMDCAWCxG+/btERQUhIyMDJw5\ncwbt2rVDQUEBAgIC4OvrCy8vL/z8889IT0+Hj4+PzOsNZQlKDjZt2lTuGwDAxo0b4eHhAScnJ5X3\nViAiIlLGu0gOVqxYgTFjxqBly5Z49OiRwmvffjEW6u2KAx988AHGjRuHwYMHo2HDhggODsbWrVth\nY2MDY2NjNGrUCGZmZjAzM8PTp0+Rk5MD/XLOvRaUHJS206IyateuDTc3N+jo6KhUT2k0ZJkGIiKq\npmJjY5GQkIDly5eXOGdkZFSilyAzMxPGxsYlrjU0NISWllaJ67OysmTGIMyaNQsAcP/+fURERGDf\nvn24deuWTCKgp6dXOcnBhAkTpN31o0aNUpjllLXl8rx587Bx40ZMnz69XFMhFVmyZEmF1kdERNVL\nZfccHDx4EKmpqdIBhm+/tHbv3h2fffZZiVfyCQkJsLa2LlFP7dq10aZNGyQkJMDe3h4AkJ+fj+vX\nr2PatGklrg8ICICXlxcMDAygr68v3V/o7QKB8vY7EkJuctCrVy/p705OTipNjdi+fTuePHmC0NBQ\n1K9fH1pasuMghe6kWJrhw4eXuywREVV/lZ0czJ8/H/PmzZP++enTpxg3bhwOHDiAoqIifP/99wgL\nC8Po0aNx+fJl/Prrr9iyZQsAID4+Ht7e3ti3bx/q1KmDiRMnYv369XBycoKZmRnWrVsHExOTEgv8\n7d+/Hzo6Ohg8eDAAoGXLlhCLxbh16xYeP36MFi1aqDTLUG5yMGPGDOnvc+bMKfcNAGDKlCkqlSci\nIiqvyk4ODAwMZAYRFv73hqampgCA0NBQrFy5EqtWrUKTJk0QEBCArl27AgDy8vJw9+5dFBcXAwDG\njRuHjIwMzJw5E1lZWejYsSNCQ0NlXsuLxWLpYkhv6erqwtfXF59++inq1KmD4OBglT6T3L0V/pkF\nleW7775TKQh1EIk4bFgezlZQjLMV5CtjHFaNx9kKisXHV069pQwFUMrXX1dMHJpEbs9B3bp1K+wm\nhYWF2LRpE44fP46UlBQUFBSgWbNmGDVqFD799NMKuw8RERGpTm5yIGQzJaG++eYbREVFwdXVFS1b\ntgQA3L59Gz/99BOKior42oGIiCoNN15SntzkYM+ePRg3bhwAICwsTG4FIpFIuiykPKdPn8bWrVtl\nlnXs378/nJycMG/ePCYHRERUaZgcKE9ucvDTTz9Jk4MffvhBbgVCkoPnz5+jWbOS+3S3bt0aGRkZ\nQmMlIiJSGpMD5clNDo4ePSr9/dSpU3IreLslpSKtW7fG7t27MWnSJJnj4eHhaNGihZA4iYiI6B0R\ntELiW+np6cjPz5f+OTU1FVOmTMGlS5cUlvPx8cFnn32GsLAwtGrVCiKRCLdv30ZaWhrWrVtXvsiJ\niIgEYM+B8gQlB5cvX8a8efOQlpZW4ty/F2Yoja2tLU6ePIlDhw7h4cOHAAA7OzsMGTKk1CUkiYiI\nKgqTA+UJSg6WL1+OYcOGYdCgQXB1dUVERAQSExNx4sQJwbMaCgoKMHjwYDRq1AgAcOfOHbx69Urp\ngK9fv46EhASIxWKIRCIYGxvDxsamwvawJiKi6oXJgfIEJQe3b99GeHg4tLS0IBKJYGlpCUtLS5iZ\nmeHrr7/G5s2bFZY/ffo05s2bh6CgIAwcOBAAcOHCBQQFBWHt2rUySzXLk5qairlz5yI+Ph6mpqYw\nMDCQrh/99OlT9OjRA6tWrYKRkZGQj0RERDUEkwPlaZV9yZsFkd5u6FCvXj2kpqYCALp06YLz58+X\nWX7VqlVYtmyZNDEA3iwRuXLlSsFLPAYGBqJVq1Y4e/Ysfv/9d+zfvx8HDhzAH3/8gdOnT8PIyAiL\nFy8WVBcRERHJJyg56NOnDyZMmIDc3Fx07doV3t7eOHz4MFauXImGDRuWWf7hw4cyicFbjo6OePDg\ngcaQ+pIAACAASURBVKBAL126hK+//rrUMQqNGzdGQEAA4uLiBNVFREQ1R2Ghaj81kaDkwNfXF0OG\nDIGenh58fX1RUFAAHx8fxMTECNoyuXnz5jh27FiJ45GRkTAzMxMUaJ06dfDixQu557Ozs1G7dm1B\ndRERUc3B5EB5gsYcpKWlYebMmQDefEvftWuXUjfx8vLC7NmzsWnTJjRt2hQSiQR3795FWloafvrp\nJ0F1ODk5Yfbs2Zg5cyasrKzQoEEDAG92p0pMTMTmzZvRv39/peIiIqLqr6Y+4FUhd1fGf+rUqRMu\nXrwILS1BHQ2lSk1NxZEjR/Dw4UOIRCKYm5tj6NChgl5LAG9mO6xevRqRkZHIycmROdegQQO4urpi\nzpw50NYWtnQDd2WUj7syKsZdGeXjroyKcVdGxSprV8YyFvEtk5Lfh6sFQcnBqlWroKWlhalTp0Jf\nX19QxadPn4ajo6NSwURHR6N3794KrykuLsb9+/eR+d9/ZcbGxjA3N1c6cWFyIB+TA8WYHMjH5EAx\nJgeKMTmoOgR9zY6KikJ6ejq+//576Ovro1atWjLnY2NjS5RZtmwZoqKiMGPGDDRp0kRh/SkpKdi4\ncSPOnz9fZnKgpaXFJZeJiEgwvlZQnqDkYNq0aUpXvHfvXgQGBmLAgAHo0aMH7Ozs0LZtWxgYGEAk\nEiEzMxO3bt3Cn3/+ibNnz2Lw4MH45ZdflL7PW66urrh//36piQoREdVcTA6Up/C1wsWLF9GlSxeV\nbpCcnIzw8HCcPXsWd+/elTnXokUL9OzZE+PHj1d5hcOoqChkZ2dj5MiRgq7nawX5+FpBMb5WkI+v\nFRTjawXFKuu1grOzauUPHqyYODSJwuTA2toaV65cqbCbFRYWIisrCwBgYGAgePBgZWByIB+TA8WY\nHMjH5EAxJgeKMTmoOhSO4hMwVlEp2traaNiwIRo2bFgpicGUKVMqvE4iItJsXOdAeQqf0CKR6F3F\nUSEuXryo7hCIiKiKqakPeFUoTA5ev36Ndu3alVlJUlJShQUkz/r168u8pqioqNLjICIizcLkQHkK\nkwNtbW1BD+V34fvvv4epqanCdRaKi4vfYURERKQJmBwoT2FyUKtWLTg5Ob2jUBTz9vbGsWPHsH37\ndrmvO6ytrd9xVERERNXPOx2QqIqJEyfCwMAAmzZtkntNVYqXiIiqBg5IVJ7CnoPhw4e/qzgEWbdu\nncLzP/74o+C6RCJO15MnO/tu2RfVYOHhXKFTHomkQN0hVGn29jrqDqFGqqkPeFUo7DkQsh2zuv3z\nVYKqCzYREVH1w54D5alvFaIKwlcJRESkSE19wKui/HswExERUbWk8T0HmvDqg4iI1Ic9B8rT+OSg\nqg2aJCKiqoXJgfI0PjkgIiJShMmB8jjmgIiIiGSw54CIiKo19hwoj8kBERFVa0wOlMfkgIiIqjUm\nB8pjckBERNUakwPlcUAiERERyWDPARERVWvsOVCeRiUH+fn5OHPmDBISEiAWiyESiWBsbAxra2s4\nODigVq1a6g6RiIiqGCYHytOY5CA5ORnTpk1DTk4O2rZtCwMDA0gkEty6dQvbt29H48aNERoaCnNz\nc3WHSkREVQiTA+WJJBqyreGnn34KW1tbzJo1C9rasjlNfn4+QkJCkJycjO+//15QfVocbSGXRHJX\n3SFUaSLR/7d352FRVv3/wN+DsagjKmi4gLkUGrINkjSK4i6KiqISipJkuYILBoqWilTkfpV5SZmP\nFi5kPi0+boW41PWYGqlsBqVgIsH4RVlNGHDO7w9/zOPE5oQ4M8z7dV3zB/c5981nTpPz4XOfc58e\nug5BbwlRqesQ9JpcbqrrEPTauXNNc93G/nuvUj2ZOAyJwXxFXr16FXPnzq2RGACAmZkZQkNDkZKS\nooPIiIiImheDSQ7atm2LW7du1dmem5sLS0vLpxgREREZAiFUjXoZI4OZczB+/HjMmTMHr776Khwc\nHNSJQGFhIdLS0hAXF4dp06bpOEoiItI/Dxp5vsH8Hf3EGExysGjRIlhbWyM+Ph7Xrl1D9VQJExMT\nvPDCC1i4cCH8/f11HCUREemfxiYHxjdXxGAmJD6qoqICxcXFAIB27drBzMxM62twQmLdOCGxfpyQ\nWDdOSKwfJyTWr6kmJEok5Y06XwiLJxSJ4TCYysGjzM3N8eyzz2ocq6iogEqlQsuWLXUUFRER6afG\nVg6MT7P5+3nixIlwc3PTdRhERKR3VI18GR+DrBzUZv369Sgvb1zpiIiImiNWDrTVbJIDZ2dnXYdA\nRER6icmBtgzqtsL333+Pd999F59++ilKSkpqtM+ePVsHURERETUvBpMc7Nq1C8uXL0d2dja+/fZb\n+Pj4ICMjQ6NPUlKSjqIjIiL99aCRL+NjMLcVDh48iJ07d8Ld3R0A8PHHHyM4OBgHDhxA9+7ddRsc\nERHpMeP8gm8Mg0kObt++rbEaYe7cuaiqqsKcOXMQHx8PKysrHUZHRET6yzhXHDSGwdxW6N69OxIT\nEzWOLVy4EB4eHpg1axYUCoWOIiMiIv3W9LcVcnNzERoaCg8PD7z88stYvHix+nspMzMTQUFBcHd3\nx/Dhw/HRRx+hvucP7tu3D2PGjIGbmxv8/f01bpl/8cUXePnllzFo0KAa34nJycnw9vZGRUXFY8Vc\nH4NJDhYsWIBly5Zh+/btGsejo6Mhl8vh4+ODKm7aTUREOjBv3jyYm5sjMTERR48eRVFREVavXo3y\n8nLMnTsXMpkMZ8+eRWxsLA4dOoT4+Phar3PmzBls2bIF0dHR+Omnn+Dn54e5c+eioKAAJSUl2LJl\nCw4dOoTt27dj7dq16iSjqqoKq1evxpo1a2Bubt7o92MwycHIkSOxd+/eWpcsRkZGYufOnZg4caIO\nIiMiIv3WtJWDkpISODo6Ijw8HFKpFNbW1vD398fPP/+MM2fO4P79+wgNDUXr1q3xwgsvYObMmXUm\nBwcOHMCkSZPg7u4Oc3NzBAQEoHPnzjhy5AiysrJgZ2cHW1tbODs7o6qqCgUFBQCAf/3rX3BwcIBc\nLm/cUP1/BjPnAKj9WQYuLi5ITk6GTCaDTCZ77GsJcfhJhtasyOUTdB2CXvvppwu6DkGPGd8z6LWR\nlOSi6xCMVNNOSLS0tERMTIzGsby8PNjY2CA9PR329vZ45pn/fd06ODhg06ZNqKioqPFXfnp6OkaP\nHq1xzMHBAampqTW+41QqFSwsLJCTk4MDBw7gnXfeQWBgIKqqqrBkyZJGJQoGlRzUxgD3jSIioqfq\n6a5WyMrKwo4dO7B27VpcvHgRlpaWGu3t2rWDSqVCcXFxjX2CioqKavRv27YtsrKy0KtXL+Tk5OCP\nP/6AQqGAVCpFmzZtsGTJEixZsgQxMTGIiopCly5dMHXqVJw+fRqmpv9ssy+Dua1ARESk79LS0jBj\nxgwEBwdj/Pjxtfap/qNWIpE81jWr+0ulUoSHh2PatGlYsWIF1q1bh8OHD0MIgWHDhiE/Px/9+vVD\n586d0bFjR2RlZf3j92HwlYPo6Ghdh0BERHrt6Sxl/PHHH7FkyRIsW7YM06dPBwBYWVnh+vXrGv2K\ni4vRokULtG3btsY12rdvj8LCwhr9q5frT5kyBVOmTAHwsMrg5+eHzz77DGVlZWjdurX6nJYtW6K0\ntPQfvxeDrxz4+vrqOgQiItJrTb+UMTk5GUuXLsX69evViQEAODo6IjMzE0qlUn0sJSUFL774IszM\nzGpcx9HREWlpaRrHUlJS4OrqWqPvhg0bEBAQADs7O0ilUo1koKioCFKp9LFir43BJwdERET1a9rk\noKqqCqtWrUJoaChGjBih0ebl5YV27dph27Zt+Ouvv5CRkYG4uDjMnDkTAKBQKODt7Y0bN24AAAID\nA3H48GEkJSWhoqICe/bsQXFxMcaNG6dx3YsXLyI9PR2vvfYaAKBNmzawtbXFDz/8gMzMTJSUlKBn\nz57/ZLAANIPbCkRERPVr2gmJV65cwe+//45NmzZh06ZNGm0nTpzAJ598gujoaAwePBhWVlaYNWuW\neul9ZWUlsrOz1ZUFT09PREZGYvXq1VAoFOjduzc++eQTjVsQSqUSUVFReO+99zRWQbz99tuIiIhA\nZWUloqKiaq1MPC6JMNLp/hIJlzLWhUsZ68eljPXhUsb6mJpyKWN9Hqm8P1ESyaVGnS+EW8OdmhlW\nDoiIqJnjxkvaYnJARETNHDde0haTAyIiauZYOdAWVysQERGRBlYOiIiomWPlQFtMDoiIqJljcqAt\ng0sOMjIykJqaisLCQkgkElhZWcHV1RW9evXSdWhERKSXmBxoy2CSA4VCgUWLFiElJQWdOnVC27Zt\nIYRAcXEx8vPzMWDAAGzevBnt27fXdahERKRXuFpBWwaTHERFRaFXr17YsWOHegOKagqFAhs2bMC6\ndeuwdetWHUVIRETUPBhMcnDp0iWcPHmy1o0kbGxssGbNGnh7e+sgMiIi0m+8raAtg0kOWrZsiZKS\nkjp3mSotLYW5uflTjoqIiPQfkwNtGUxyMGTIEISEhGDBggVwcHCApaUlAKCwsBBpaWmIjY3FyJEj\ndRwlERHpHyYH2jKY5GDlypXYsmULIiMjUVZWptFmaWmJgIAAhIaG6ig6IiLSX5yQqC2D25VRpVLh\njz/+QFFREQDAysoKdnZ2MDHR7mGP3JWxbtyVsX7clbE+3JWxPtyVsX5NtyvjN406X4iJTygSw2Ew\nlYNqJiYm6NGjh67DICIig8HbCtpqNnsrBAQEQC6X6zoMIiLSOw8a+TI+Blc5qMvrr7+O0tJSXYdB\nRER6xzi/4Buj2SQHI0aM0HUIREREzYJBJQeJiYnIyMjA8OHD0adPH5w5cwb79u3DM888gxEjRmDy\n5Mm6DpGIiPQOKwfaMpg5B7t370ZYWBgSExMRFBSEU6dOYfny5ejcuTNsbGzw/vvvY8+ePboOk4iI\n9I6qkS/jYzCVg/j4eOzatQvu7u44duwYVq9ejXfffVd9O2H8+PFYtWoVZs2apdtAiYhIz7ByoC2D\nqRzcvn0b7u7uAICRI0fizp078PLyUrfLZDLk5+frKjwiItJbXK2gLYNJDjp06IDffvsNAGBqaorg\n4GCYmpqq21NSUrhdMxER0RNgMMlBQEAA3njjDSQlJQEAIiIi1G0ff/wxFixYgKCgIF2FR0REeouV\nA20ZzJyD2bNnw9LSEhKJpEbbr7/+ioULFyIwMFAHkRERkX4zzi/4xjC4vRX+zsXFBcnJyVqfJ5Fw\n/4C6cN+J+rm66joC/XX58o+6DkGvHT06SNch6LWxY5vmuhLJR406X4iQJxSJ4TCYykFdDDy3ISKi\nJsfKgbYMZs4BERERPR0GXzmIjo7WdQhERKTXWDnQlsEnB76+vroOgYiI9BqTA20ZfHJARERUPyYH\n2uKcAyIiItLAygERETVzrBxoi8kBERE1c8a5s2JjMDkgIqJmjpUDbTE5ICKiZo7JgbY4IZGIiIg0\nsHJARETNHCsH2mJyQEREzRwnJGrL4JKDjIwMpKamorCwEBKJBFZWVnB1dUWvXr10HRoREeklVg60\nZTDJgUKhwKJFi5CSkoJOnTqhbdu2EEKguLgY+fn5GDBgADZv3oz27dvrOlQiItIrTA60ZTDJQVRU\nFHr16oUdO3bAyspKo02hUGDDhg1Yt24dtm7dqqMIiYiImgeDSQ4uXbqEkydPQiqV1mizsbHBmjVr\n4O3trYPIiIhIv7FyoC2DSQ5atmyJkpKSWpMDACgtLYW5uflTjoqIiPQfkwNtGUxyMGTIEISEhGDB\nggVwcHCApaUlAKCwsBBpaWmIjY3FyJEjdRwlERHpH65W0JbBJAcrV67Eli1bEBkZibKyMo02S0tL\nBAQEIDQ0VEfRERERNR8GkxyYmppi+fLlCA8Pxx9//IGioiIAgJWVFezs7GBiwoc9EhFRbXhbQVsG\nkxxUMzExQY8ePXQdBhERGQwmB9pqNn9uBwQEQC6X6zoMIiLSOw8a+TI+Blc5qMvrr7+O0tJSXYdB\nRER6xzi/4Buj2SQHI0aM0HUIREREzUKzuK0gl8tx+/ZtXYdBRER6ibcVtGUwlYPIyMg62+7du4eY\nmBhYWFggJibmKUZFRET6j8850JbBJAfnzp3D/fv34efnV+MpiSYmJrCxsanz6YlERGTMjPOv/8Yw\nmNsKx48fh5+fH44ePQpbW1uEhISoXxYWFggODkZISIiuwyQiIr3T9LcV8vLyMG/ePHh4eMDLywvr\n1q1DZWVlrX1PnDgBX19fyGQyTJgwAQkJCeq2xMREDB48GB4eHoiPj9c4Lzc3F0OGDMHdu3e1eO//\njMEkB61atcKKFSuwc+dOxMfHIygoCNnZ2boOi4iICCEhIWjXrh0SEhKwf/9+XL58GR988EGNfhkZ\nGQgPD0doaCjOnz+PxYsXY9myZfjtt98ghMDatWuxbds2fPXVV9i6dStKSkrU565duxahoaE1diZu\nCgaTHFTr06cP4uPjMXbsWMycORMffPABhBC6DouIiPRW01YOUlNTcfXqVURERMDS0hJdu3bF3Llz\ncfDgQahUmvMdDh48iIEDB2LEiBEwNzfH8OHDIZfL8eWXX6KgoABVVVVwcXFB165dYWdnh6ysLADA\nsWPHUF5ejsmTJz+ZIWmAwSUH1QICAvDtt98iNzcXxcXFug6HiIj0lqqRr/qlp6ejc+fOGn/R9+3b\nF8XFxbh582aNvn379tU45uDggNTUVEgkEs2oVSpYWFigpKQEmzZtwpw5czB79mxMnToV//nPf7QZ\nAK0ZzITE2lhbW+O7775DRkaG1ucKcbgJIiIydoN0HQBRDU39731RUZF6p+Bqbdu2BfBw5+Du3bs3\n2LewsBAdOnSAhYUFkpKS0KFDB+Tm5qJbt26IiYnBlClTsHfvXvj6+mLYsGEYO3YsBgwYAGtr6yZ5\nTwZbOSAiItJX1be7/14NqEt1v7Vr1+LNN99EYGAgVq5ciatXr+LKlSt44403cOnSJXh5eUEqlcLZ\n2RnJyclNFr9BVw4AcL4BERHplJWVFQoLCzWOVd/u/vvkwfbt29foW1RUpO7n5eWFM2fOAACUSiX8\n/PwQFRUFU1NTlJWVqZfst2zZskm3DDD4ykF0dLSuQyAiIiPm6OgIhUKh8aTelJQUWFtbw87Orkbf\ntLQ0jWOpqalwcXGpcd2dO3eiX79+6NevHwBAKpWqVy8UFRWhdevWT/qtqBl8cuDr66vrEIiIyIg5\nODjA1dUVmzZtQmlpKXJycrBjxw4EBgZCIpHA29sbFy5cAPBwMv2FCxeQkJAApVKJ48ePIykpCQEB\nARrXvHHjBr766iu8+eab6mPu7u44ceIEFAoF0tPTIZPJmuw9SQTr8kRERI2iUCgQFRWFX375Ba1a\ntcKYMWOwbNkytGjRAr1790ZsbCyGDh0KADh58iQ++ugj3Lx5E927d8eSJUswePBgjesFBQVh+vTp\n8Pb2Vh+7du0aFi9ejIKCAixdurRGQvEkMTkgIiIiDQZ/W4GIiIieLCYHT1FmZibGjRuHYcOG1duv\nvuduN1e5ubkIDQ2Fh4cHXn75ZSxevBgKhaLWvhcvXoS/vz/c3Nzg7e2NAwcOPOVon64rV65gxowZ\ncHNzw8CBAxEWFob/+7//q7WvMX52qr333nvo3bt3ne3GODYDBgyAo6MjnJyc1K81a9bU2tcYx4fq\nIeipOHr0qPD09BQLFiwQQ4cOrbPfr7/+KhwdHUVCQoIoLy8XJ0+eFE5OTiIzM/MpRvv0jRs3Tixb\ntkyUlpaKgoICERQUJObMmVOj3+3bt4VMJhP79u0T9+/fF7/88otwc3MTZ8+e1UHUTa+oqEjIZDKx\nZ88eoVQqRUFBgZgxY4aYP39+jb7G+tkRQoirV6+K/v37C3t7+1rbjXVs+vbtK9LS0hrsZ6zjQ3Vj\n5eApuXfvHr744gvI5fJ6+9X33O3mqqSkBI6OjggPD4dUKoW1tTX8/f3x888/1+h7+PBhdO3aFdOn\nT4eFhQXc3Nzg6+tbY/ey5kKpVGLVqlV49dVXYWpqCmtra4wcObLWp4Ia42cHePiI2TVr1iA4OLjO\nPsY4Nvfu3UNlZWWNp/HVxhjHh+rH5OApmTp1Krp06dJgv/qeu91cWVpaIiYmBjY2NupjeXl5Gj9X\nM7bx6dixo3qjFSEErl+/jq+//ho+Pj41+hrb2FSLj4+HhYUFxo0bV2cfYxyb6ofwbNmyBYMGDcKg\nQYOwevVqlJWV1ehrjOND9WNyoGfqe+62scjKysKOHTuwYMGCGm21jU+7du2a/fhkZGTA0dER48aN\ng5OTE5YsWVKjjzF+dgoKCrB9+3asXbu23n7GODbVu/vJ5XIkJibis88+Q3Jycq1zDoxxfKh+TA4M\nxOM+n9vQpaWlYcaMGQgODsb48eMf6xwhRLMfnz59+iAtLQ1HjhxBdnY2wsLCHvvc5jw2MTExmDp1\nKnr27PmPzm/OY9OtWzccPHgQ/v7+MDMzQ8+ePREWFoajR4+ivLz8sa7RnMeH6sfkQM809Nzt5uzH\nH3/Eq6++ipCQEISEhNTax5jHRyKRoFevXggLC8OJEydqrFgwtrH56aefkJqaivnz5zfY19jGpi62\ntrYQQhj9Z4caxuRAz2jz3O3mJDk5GUuXLsX69esxffr0Ovs5OTkZ1fgcP34cfn5+GsdMTB7+b/vM\nM5r7phnbZ+fw4cNQKBQYPHgwPDw81OPk4eGBo0ePavQ1trEBHv4/tXHjRo1j169fh6mpKTp16qRx\n3BjHhxqg49USRicuLq7GUsbRo0eL8+fPCyGE+P3334Wjo6P4/vvvRUVFhTh27JhwdnYWN27c0EW4\nT0VlZaXw8fERe/bsqbU9KChIfPvtt0IIIe7cuSP69esn9u7dK8rLy8X58+eFq6uruHjx4tMM+anJ\nz88Xbm5u4qOPPhL3798XBQUFYvbs2SIgIEAIYdyfnaKiIpGXl6d+Xb58Wdjb24u8vDzx119/GfXY\nCCHEzZs3hbOzs9i9e7eoqKgQ169fF2PHjhVRUVFCCOP+7FDDmBw8JaNGjRKOjo7CwcFB2NvbC0dH\nR+Ho6Chu3bol7O3txalTp9R9ExIShK+vr5DJZGLSpEnNdg1/tZ9//lljTB593bp1SwwdOlTExcWp\n+yclJYlXXnlFyGQy4ePjI77++msdRt/0rly5Il555RXh5OQk5HK5WLp0qcjPzxdCCKP/7DwqJydH\n4zkHHBshzp07J6ZMmSJcXV3F0KFDxfr160VFRYUQguND9ePeCkRERKSBcw6IiIhIA5MDIiIi0sDk\ngIiIiDQwOSAiIiINTA6IiIhIA5MDIiIi0sDkgEhLr732GjZv3vxYfUePHo0DBw40cUSGj+NEpF/4\nnAPSa8OGDYNCoVA/MhgAOnTogOHDh2PJkiWQSqU6jI6IqHli5YD0XmRkJFJTU5GamoqUlBR8+umn\nSEpKanCbXiIi+meYHJBBqd6ZcN68eUhMTIRKpQIAFBcXIzw8HJ6enpDJZJg3bx4KCgoAALdu3ULv\n3r1x6tQpjB07Fi4uLggLC0NOTg6mTZsGV1dXzJw5U70rnRACW7duxdChQyGTyTBu3DicPn1aHcPM\nmTOxfv16AMC2bdswb948fPrppxg4cCBeeukldRvwsPKxd+9eAMCKFSuwbt06vP/+++jfvz/kcjn2\n7Nmj7nvz5k34+fnB2dkZAQEBOH78OHr37o179+7VGIcLFy6gT58+OHv2LEaMGAFnZ2fMmzcPZWVl\n6j6nTp3CxIkTIZPJMGbMGGzfvh3VhcLs7GwEBwfD3d0d7u7umD17Nv78888G2wBg//796nEcPXo0\nzp49q247e/YsfH19IZPJIJfLsWbNGiiVygbbHh0nlUqF2NhYjBo1Cm5ubpg8eTISEhI0xj82NhYR\nERFwc3PD4MGDcezYMXX7zp07MWzYMLi4uGD48OGIi4ur7yNFRLXR5bObiRry930Vqh0+fFi4uLgI\nlUolhBBi/vz5Yt68eeLu3buitLRUrFixQvj7+wsh/vfM/ZCQEFFcXCyuXLki7O3txeTJk0V2dra4\nffu2GDBggNi1a5cQQoivv/5aeHh4iJycHPHgwQOxd+9e4erqKoqLi4UQQsyYMUO8//77QgghPvzw\nQ+Hh4SG2b98uKioqxOnTp4W9vb349ddfa8S/fPly4eHhIf79738LpVIp9u7dKxwcHMTdu3eFEEJM\nnTpVhISEiLKyMpGSkiJGjRol7O3tRVlZWY33f/78eWFvby9CQ0NFYWGhUCgUYvz48eLtt98WQgiR\nmZkpXnzxRXHs2DGhVCrFpUuXhEwmE19++aUQQojg4GARGRkpysvLxb1798TKlSvFokWLGmxLSEgQ\n/fv3F8nJyaKqqkqcOnVK9O3bV1y7dk0olUrh6uoqDh48KFQqlcjPzxeTJk0Se/furbft7+MUFxcn\nBg4cKNLT04VSqRQHDhwQDg4O4vr16+rx9/T0FD/88INQKpVi48aNon///kKlUolffvlFODk5iYyM\nDCGEEMnJyeKll15S/0xEj4eVAzIoKpUKGRkZiI2NxYQJEyCRSHD37l0kJiZi6dKlaN++PaRSKSIi\nIpCcnIysrCz1uVOmTIGlpSVcXFzQoUMHeHh4oHv37ujYsSMcHR1x48YNAMD48eORkJAAW1tbmJiY\nwMfHB3/99ReuX79ea0xCCMydOxdmZmYYMmQILCwsNH7vozp16gQ/Pz+YmprC29sbVVVVuHnzJhQK\nBZKTkzFnzhy0bt0aTk5O8PHxaXA8goOD0a5dOzz77LMIDAzEqVOnAACHDh1C//79MWbMGJiamkIm\nk8HHx0f9F3hJSQlMTU1hZmaGVq1aITo6Gh988EGDbQcPHlRXN1q0aIGhQ4fC09MT33zzDSoqKlBe\nXo5WrVpBIpHAxsYGhw4dQmBgYL1tf3fo0CFMnz4dDg4OMDU1RUBAAGxtbTWqN87Ozhg0aBBMxbLh\nDwAABZ9JREFUTU0xatQoFBUV4c6dOygtLQUAtGrVSt3v/Pnz6N27d4NjSUT/80zDXYh0KyYmRl2q\nV6lUsLCwQGBgIEJCQgA8LMcDwOTJkzXOa9GiBfLy8vDcc88BAGxsbNRt5ubmNX6uLnHfv38fMTEx\n+OGHH1BcXKzuU93+d126dEGLFi3UP1tYWKC8vLzWvra2thr9AKC8vBwKhQIA0LVrV3X7iy++WOs1\nHtWjRw+NOO7cuYMHDx4gJycHzz//vEbfnj174sqVKwCAkJAQhIeH48cff4SnpyfGjBkDuVzeYNvN\nmzfx3//+V30LAHiYHLVp0wZSqRQLFy5EREQEdu3aBU9PT/j6+qJXr171tv1dbbH36NEDeXl5DY6j\nXC7HgAEDMGbMGPTv3x+enp6YNGkS2rdv3+BYEtH/sHJAeu/RCYm7d+9GZWUlfH19YWZmBuB/Xw6n\nT59W90tNTUV6ejoGDhyovs6jKx5q+7laVFQUkpOT8fnnnyMlJQXnzp2rNz6JRPLY76Wu31nN1NRU\nq+tWz7kAoJ5PUN95lZWVAIAhQ4bg9OnTWLZsGe7du4e5c+eqE7D62iwsLLB48WKNcU5LS8PGjRsB\nPEwsTp06hcmTJyM1NRUTJkzAyZMnG2x7lEQiqfU9PJqc1TWOZmZmiI2NxaFDh9CvXz989dVXGDt2\nLHJycuoeRCKqgckBGZT+/fvDx8cHq1atUn8x2traokWLFsjMzFT3U6lUGpPotJGSkoIJEyagZ8+e\nkEgkSEtLeyKx18fa2hoAkJubqz6WkZHR4HnVVRMA+PPPP9GxY0eYmJigW7duNW6DZGVlqasod+/e\nhVQqhY+PDzZv3oyoqCjEx8c32NatWzeNca7+vdX/LQoLC2FjY4PAwEDs3r0bEyZMwKFDhxpse5Sd\nnR2uXbumcSw7O1sde32qqqpQUlKCPn36YOHChfjmm2/Qpk0bjQmNRNQwJgdkcCIiInDjxg18/vnn\nAACpVIpx48Zh8+bNyM3NRUVFBbZt24aZM2fiwYMHWl/fzs4OaWlpUCqVSE9Px/79+2FmZqYu/TeF\nrl274vnnn8fOnTtx//59pKen4/jx4w2e99lnn6GkpAS3b9/G/v37MWLECAAPb7FcuHABCQkJqKqq\nQlJSEo4cOYJJkyahvLwco0ePxr59+6BUKlFRUYH09HQ899xz9bYBwLRp0/Ddd9/h5MmTqKqqwqVL\nlzBx4kRcuHABly9fxvDhw5GUlAQhBO7evYvs7Gx069at3ra/mzJlCvbv34/MzEwolUrExcUhPz8f\nY8aMaXA8du3ahZkzZ+LWrVsAHiYVxcXFtf4eIqob5xyQwWnfvj0iIiKwbt06DB8+HHZ2dnjrrbcQ\nHR0NX19fAICTkxM+/vhjjbkAj+vNN99EeHg4XnrpJTg4OCAmJgbt2rXD22+/jbZt2z7pt6O2YcMG\nrFq1CgMGDIBMJsP8+fOxbNmyem9FjBw5EpMnT0Z+fj4GDhyIsLAwAIC9vT1iYmLw4YcfIiIiAl26\ndMFbb70Fb29vAA+XYG7cuBEbN26EmZkZnJycsHnzZlhYWNTZBgByuRwrV65ETEwMwsLC0KVLF4SH\nh6vnJISFhSEyMhIKhQJt2rSBl5cXFi1aBKlUWmfb3wUEBCAvLw8LFixAUVERXnjhBXz++efo0qVL\ng2MYHByM/Px8+Pv74969e+jYsSNmz56tTpqI6PHwCYlEekIIgaqqKvW8gyNHjmDt2rVISkqq0ffC\nhQsICgrCpUuX0Lp166cdKhE1c7ytQKQnZs2aheXLl+P+/fsoKChAXFwcvLy8dB0WERkhJgdEeuKd\nd95BcXExPD09MX78eNja2mLVqlW6DouIjBBvKxAREZEGVg6IiIhIA5MDIiIi0sDkgIiIiDQwOSAi\nIiINTA6IiIhIA5MDIiIi0vD/AJ2UzxWn+NwlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15c88a1080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.heatmap(\n",
    "    df.pivot_table(\n",
    "        'foul_called',\n",
    "        'trailing_poss',\n",
    "        'remaining_poss'\n",
    "      )\n",
    "      .rename_axis(\n",
    "          \"Trailing possessions\\n(committing team)\",\n",
    "          axis=0\n",
    "      )\n",
    "      .rename_axis(\"Remaining possessions\", axis=1),\n",
    "    cmap='seismic',\n",
    "    cbar_kws={'format': pct_formatter}\n",
    ")\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": 52,
   "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']\n",
    "                            .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": "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": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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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 0x7f15bbf21048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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\")\n",
    "\n",
    "(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.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\sigma_{\\textrm{poss}, c}\n",
    "            & \\sim \\operatorname{HalfNormal}(5) \\\\\n",
    "    \\beta^{\\textrm{poss}}_{t, r, c}\n",
    "        & \\sim \\operatorname{Hierarchical-Normal}(0, \\sigma_{\\textrm{poss}, c}^2)\n",
    "\\end{align*}    \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "call_type = df['call_type'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "with poss_model:\n",
    "    η_game = β_season[season] \\\n",
    "                + β_call[call_type] \\\n",
    "                + β_poss[\n",
    "                    trailing_poss,\n",
    "                    remaining_poss,\n",
    "                    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": 57,
   "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\n",
    "\n",
    "Again, we sample from the model's posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [σ_β_poss_log__, Δ_β_poss, σ_β_call_log__, Δ_β_call, β_season]\n",
      "100%|██████████| 1500/1500 [07:56<00:00,  3.15it/s]\n",
      "There were 5 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 10 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 9 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The number of effective samples is smaller than 25% for some parameters.\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 sampling and good convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bfmi = pm.bfmi(poss_trace)\n",
    "\n",
    "max_gr = max(\n",
    "    np.max(gr_stats) for gr_stats in pm.gelman_rubin(poss_trace).values()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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6pJ+uEELEkEwvCCFEDEnoCiFEDEnoCiFEDEnoCiFEDEnoCiFEDE26ZKy7+/IX1QshxGKT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\nkISuEELE0P8P4jk4RRAQ/rUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15c889c2b0>"
      ]
     },
     "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\n",
    "\n",
    "Again, we calculate residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KQlxcHIKDg6u0DyIi0jAMfAACA9/Pzw+ffPIJwsLC0LJlS4hEIty6dQvp6ekI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15b0c19fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.heatmap(\n",
    "    resid_df.pivot_table(\n",
    "                'resid',\n",
    "                'trailing_poss',\n",
    "                'remaining_poss'\n",
    "            )\n",
    "            .rename_axis(\n",
    "                \"Trailing possessions\\n(committing team)\",\n",
    "                axis=0\n",
    "            )\n",
    "            .rename_axis(\n",
    "                \"Remaining possessions\",\n",
    "                axis=1\n",
    "            )\n",
    "            .loc[-3:3],\n",
    "    cmap='seismic', \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": 63,
   "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": 64,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kuLg4hYaGOvycPHlSJ06csJ8JCAgI0Pvvv681a9aoRYsWmjJliiZNmqSmTZs6HPONN97Q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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15b0a28470>"
      ]
     },
     "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": 65,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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RHq8P7qj8f3VFNYoqqnX6+c0xtu0jv6C0wWNV6/cobeFa74Dk6mD9SO2aln5K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\nW08RSwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15ca3badd8>"
      ]
     },
     "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\n",
    "\n",
    "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": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "MODEL_NAME_MAP = {\n",
    "    0: \"Base\",\n",
    "    1: \"Possession\"\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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": 68,
   "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>var_warn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <td>11610.1</td>\n",
       "      <td>2.11</td>\n",
       "      <td>1541.98</td>\n",
       "      <td>0</td>\n",
       "      <td>56.9</td>\n",
       "      <td>73.43</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Possession</th>\n",
       "      <td>10068.1</td>\n",
       "      <td>82.93</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>88.05</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               WAIC  pWAIC    dWAIC weight     SE    dSE var_warn\n",
       "Base        11610.1   2.11  1541.98      0   56.9  73.43        0\n",
       "Possession  10068.1  82.93        0      1  88.05      0        0"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MVqxY0aG2detWxcfHKzo6Wg8++KAKCwudtebmZqWlpenOO+/U+PHjlZSUJKvV6qyXl5cr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\nVy0OuwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f162514d278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.errorbar(\n",
    "    np.arange(len(MODEL_NAME_MAP)),\n",
    "    comp_df.WAIC,\n",
    "    yerr=comp_df.SE, fmt='o'\n",
    ");\n",
    "\n",
    "ax.set_xticks(np.arange(len(MODEL_NAME_MAP)));\n",
    "ax.set_xticklabels(comp_df.index);\n",
    "ax.set_xlabel(\"Model\");\n",
    "\n",
    "ax.set_ylabel(\"WAIC\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Player item-response theory model\n",
    "\n",
    "#### Build a model of the science\n",
    "\n",
    "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.  For more information on Bayesian item-response models, consult the following references.\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.\n",
    "\n",
    "The item-response theory model includes the season, call type, and possession terms of the previous models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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[\n",
    "                    trailing_poss,\n",
    "                    remaining_poss,\n",
    "                    call_type\n",
    "                ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Each disadvantaged player has an ideal point (per season).\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\sigma_{\\theta}\n",
    "        & \\sim \\operatorname{HalfNormal}(5) \\\\\n",
    "    \\theta^{\\textrm{player}}_{i, s}\n",
    "        & \\sim \\operatorname{Hierarchical-Normal}(0, \\sigma_{\\theta}^2)\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "player_disadvantaged = df['player_disadvantaged'].values\n",
    "n_player = player_enc.classes_.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "player_committing = df['player_committing'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    η_player = θ - b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The sum of the game and player effects determines the foul call probability."
   ]
  },
  {
   "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": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "with irt_model:\n",
    "    η = η_game + η_player"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "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\n",
    "\n",
    "Again, we sample from the model's posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [σ_b_player_log__, Δ_b_player, σ_θ_player_log__, Δ_θ_player, σ_β_poss_log__, Δ_β_poss, σ_β_call_log__, Δ_β_call, β_season]\n",
      "100%|██████████| 1500/1500 [13:55<00:00,  1.80it/s]\n",
      "There were 3 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 1 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 4 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with irt_model:\n",
    "    irt_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "None of the sampling diagnostics indicate problems with convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bfmi = pm.bfmi(irt_trace)\n",
    "\n",
    "max_gr = max(\n",
    "    np.max(gr_stats) for gr_stats in pm.gelman_rubin(irt_trace).values()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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xMa87YLRSmJVMW+847X2eBFcl5ioJ3UXuSH8Nw8ERIv35aFgoKZHAvVSppnRM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\niJTFqS7fEVoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15ca2c64a8>"
      ]
     },
     "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": "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": 81,
   "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": "code",
   "execution_count": 82,
   "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": 83,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zdu1k3bp1xVKZu6Wmpurjjz9WkyZNCt0uPj5eU6ZM0bx589SpUyd9++23eumll/TJJ5+o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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15ca3a5710>"
      ]
     },
     "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": 84,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PH46UlBTY2NigpKQEzs7OAAAHBwcUF8tjQ+QdE2QI7KLWL1Npb15i1T5jGv/W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\nISIiIrapkRARERHbfgGFrYuxU1iHZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15a32a2128>"
      ]
     },
     "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\n",
    "\n",
    "The IRT model is a marginal improvement over the possession model in terms of WAIC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "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": 86,
   "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>var_warn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Base</th>\n",
       "      <td>11610.1</td>\n",
       "      <td>2.11</td>\n",
       "      <td>1566.92</td>\n",
       "      <td>0</td>\n",
       "      <td>56.9</td>\n",
       "      <td>74.03</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Possession</th>\n",
       "      <td>10068.1</td>\n",
       "      <td>82.93</td>\n",
       "      <td>24.94</td>\n",
       "      <td>0.08</td>\n",
       "      <td>88.05</td>\n",
       "      <td>10.99</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IRT</th>\n",
       "      <td>10043.2</td>\n",
       "      <td>216.6</td>\n",
       "      <td>0</td>\n",
       "      <td>0.91</td>\n",
       "      <td>88.47</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               WAIC  pWAIC    dWAIC weight     SE    dSE var_warn\n",
       "Base        11610.1   2.11  1566.92      0   56.9  74.03        0\n",
       "Possession  10068.1  82.93    24.94   0.08  88.05  10.99        0\n",
       "IRT         10043.2  216.6        0   0.91  88.47      0        0"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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27dqlsrIySZKPj4/T+T4+PrJarbLb7Q2eTlw91mq1asCAAU32zdfXU25u5h8y\nvAb8/b1b9HpAR8VcAZrHVXOlzQNDY+x2u0wmkyQpPj7eqfbYY48pLS1Nu3bt0r333tvk+Xa7vdGa\nJMf1m2K1Xvy+XW+Sv7+3iovLW/SaQEfEXAGap6XnSlPho80Dg6+vr+NpwlU2m81pGeG7AgMDVVRU\n5DjGarXK2/v/BllaWipfX1/Z7fYG1y4tLZWkJq8PAACctfn3MISGhurIkSNObRaLRcOHD5ckrV+/\nXjk5OU71kydPKigoSEFBQfLx8XE6v7CwUAUFBQoLC9PQoUNVWFiooqIiRz03N1fdu3dXUFBQK44K\nAICOpc0Dw5QpU1RcXKzNmzerqqpKBw4cUFpamubMmSNJKikpUVJSkvLz81VVVaW3335b+fn5euih\nh2Q2m/XII49o48aNOnv2rMrKyrR69WqNHj1at99+u0JCQhQWFqa1a9eqvLxcZ86c0caNGzV79uxm\nLUkAAIArTPbGFvpbQVRUlM6dO6f6+nrV1tbKw8NDkrRnzx4VFBRozZo1+vLLLxUQEKC5c+cqNjZW\nknTp0iWtXbtWe/fu1cWLF3XHHXfo2WefVVhYmCSppqZGq1atUlZWli5fvqyIiAglJiY6lhwKCwuV\nlJSkQ4cOydPTU9HR0YqPj5fZbLyZsaXXUFmXBZqHuQI0jyv3MLgsMNyICAxA22CuAM3jysDQ5ksS\nAACg/SMwAAAAQwQGAABgiMAAAAAMERgAAIAhAgMAADBEYAAAAIYIDAAAwBCBAQAAGCIwAAAAQwQG\nAABgiMAAAAAMERgAAIAhAgMAADBEYAAAAIYIDAAAwBCBAQAAGCIwAAAAQwQGAABgiMAAAAAMERgA\nAIAhAgMAADBEYAAAAIYIDAAAwBCBAQAAGCIwAAAAQwQGAABgiMAAAAAMERgAAIAhAgMAADBEYAAA\nAIYIDAAAwJBLA8Px48cVExOjCRMmOLV/8cUXmjFjhsLDwzVx4kRt3brVqb5t2zZFR0drxIgReuCB\nB/TRRx85amvWrFFISIhCQ0MdfyNGjHDUy8rKFB8fr7Fjx2rMmDGKj49XRUVF6w4UAIAOxmWBIT09\nXXPnzlX//v2d2ouLixUXF6fY2Fjt27dPy5cv19q1a/W3v/1NkpSRkaHVq1crKSlJBw8e1K9+9Su9\n8MILys3NlSSVlpZq1qxZslgsjr/Dhw87rp+QkCCbzaaPP/5YaWlpstlsevHFF101bAAAOgSXBYbK\nykpt3759umlUAAAUdklEQVRdkZGRTu2pqakKDAzUrFmz1LlzZ4WHh2vq1Knatm2bJOny5ctatGiR\nIiIi5ObmpqioKPXr10+HDh2SdOUJgre3d6P3vHDhgjIzM7Vo0SL16NFD3bt319NPP62MjAyVlJS0\n7oABAOhAXBYYpk+froCAgAbtR48e1ZAhQ5zaQkJCZLFYJElTp07Vo48+6qhVV1erpKREvXr1kiTZ\nbDbl5ORo8uTJGjlypB599FHHuXl5eTKZTAoODnacHxwcLLvdrmPHjrX4GAEA6Kjc2roDNptNAwcO\ndGrr1q2brFZro8cvW7ZMPXv21H333SdJCggIUKdOnbR27Vp5eXlpw4YNeuKJJ7R3717ZbDZ5eXnJ\nbDY7znd3d5eXl9c1r/9tvr6ecnMzGx73ffj7N/40BIAz5grQPK6aK20eGBpjt9tlMpmc2urq6pSY\nmKh9+/bp/fffl7u7uyRp5cqVTsfFx8crNTVVe/fulZeXV7Ov3xir9eJ1jqBx/v7eKi4ub9FrAh0R\ncwVonpaeK02Fjzb/WKWvr2+D/9u32Wzy8/NzvK6urtb8+fN19OhRbd26VYGBgde8ntlsVp8+fVRU\nVCQ/Pz9VVFSopqbGUa+pqdHFixedrg8AAJrW5oEhNDRUR44ccWqzWCwaPny443V8fLwuXbqkTZs2\nqWfPno722tpaLVu2TCdPnnS01dTUKD8/X0FBQRo8eLBMJpPy8vIc9SNHjshsNiskJKQVRwUAQMfS\n5oFhypQpKi4u1ubNm1VVVaUDBw4oLS1Nc+bMkSTt3r1bFotFGzZsaLDE4ObmptOnTysxMVFFRUWq\nrKzU6tWr5e7urvvvv19+fn6Kjo7Wq6++qgsXLqi4uFivvPKKpkyZIh8fn7YYLgAANyST3W63u+JG\nUVFROnfunOrr61VbWysPDw9J0p49e1RQUKA1a9boyy+/VEBAgObOnavY2FhJ0uOPP66DBw86bVyU\nrnx6YtmyZSopKdGKFSuUnZ2turo6DR06VM8//7xuu+02SVJFRYWSk5OVnZ0tk8mk8ePHKyEhQV26\ndDHsc0uvobIuCzQPcwVoHlfuYXBZYLgRERiAtsFcAZrnR7XpEQAAtH8EBgAAYIjAAAAADBEYAACA\nIQIDAAAwRGAAAACGCAwAAMAQgQEAABgiMAAAAEPt8uetAfx4Ld6wT2azSSvnRbZ1VwB8C08YAACA\nIQIDAAAwRGAAAACG2MMAAMANyNX7fXjCAAAADBEYAACAIQIDAAAwRGAAAACGCAwAAMAQgQEAABgi\nMAAAAEMEBgDtxoG8QtkqqlRkvaTf/OGADuQVtnWXAPx/fHETgHbhQF6h3kw96nh9trjS8XpUSK+2\n6haA/48nDADahU/2n75G+1cu7QeAxhEYALQL57652Gj7+QuVLu4JgMYQGAC0CwE9PBtt79Pdy8U9\nAdAYAgOAdmFS5IBrtPd3bUeAG0BbbBBm0yOAduHqxsa3d+eprt6uvv43a1JkfzY8At/RVhuEecIA\noN0YFdJL3W6+ST19uyj55xGEBaARbbVBmMAAAMANpK02CBMYAAC4gbTVBmECAwAAN5C22iDs0sBw\n/PhxxcTEaMKECU7tX3zxhWbMmKHw8HBNnDhRW7dudapv3rxZ0dHRCg8P14wZM5STk+OoVVdXKykp\nSffcc49GjRqluLg4FRb+327R8+fPKy4uTqNGjdL48eOVnJysmpqa1h0oAACtZFRIL82bMkTmTiZJ\nUl//mzVvypBW3/PjssCQnp6uuXPnqn9/5wRUXFysuLg4xcbGat++fVq+fLnWrl2rv/3tb5Kkzz//\nXK+88opeeukl7d+/Xw8++KDmzZunb775RpK0bt06HT58WJs2bVJWVpZ8fX21cOFCx/UXLFigbt26\nKTMzU1u2bNHhw4e1fv16Vw0bAIAW1xYbhF0WGCorK7V9+3ZFRkY6taempiowMFCzZs1S586dFR4e\nrqlTp2rbtm2SpK1bt2ratGm68847ddNNN+mRRx5Rnz59tHv3btXV1SklJUXz589XUFCQvL29tXjx\nYuXm5urYsWOyWCzKy8vTkiVL1LVrVwUGBmrevHnasWOH6uvrXTV0AABueC4LDNOnT1dAQECD9qNH\nj2rIkCFObSEhIbJYLI56SEhIo/WvvvpK5eXlTnU/Pz/17t1bFotFR48eVZ8+feTn5+eoDxkyRKWl\npcrPz2/J4QEA0KG1+Rc32Ww2DRw40KmtW7duslqtjnrXrl2d6j4+Pjp16pRsNpvj9XfrVqtVdru9\n0XMlyWq1asCAAU32zdfXU25u5u89pqb4+3u36PWAjsZsvrIuy1wBmubqudLmgaExdrtdJpOpyXpz\nzm/suKttTV3/Kqu18c+6Xi9/f28VF5e36DWBjqauzi6z2cRcAQy0xlxpKny0eWDw9fV1PE24ymaz\nOZYRGquXlpbKz8/PcYzVapW3t7dT3dfXV3a7vdFzJTktUwAAgKa1+fcwhIaG6siRI05tFotFw4cP\nlyQNHTq0QT03N1dhYWEKCgqSj4+PU72wsFAFBQUKCwvT0KFDVVhYqKKiIqdzu3fvrqCgoFYcFQAA\nHUubB4YpU6aouLhYmzdvVlVVlQ4cOKC0tDTNmTNHkjR79mylpqYqJydHVVVVevfdd1VaWqqYmBiZ\nzWY98sgj2rhxo86ePauysjKtXr1ao0eP1u23366QkBCFhYVp7dq1Ki8v15kzZ7Rx40bNnj27WUsS\nAFxvzfwx+kPC/W3dDQDfYbIbbQhoIVFRUTp37pzq6+tVW1srDw8PSdKePXtUUFCgNWvW6Msvv1RA\nQIDmzp2r2NhYx7k7duzQu+++q8LCQg0aNEhLly7VsGHDJEk1NTVatWqVsrKydPnyZUVERCgxMdGx\n5FBYWKikpCQdOnRInp6eio6OVnx8vMxm482MLb2Gyh4GoHmYK4CxxRv2yWw2aeW8SOODm6mpPQwu\nCww3IgID0DaYK4AxVweGNl+SAAAA7V+bf0oCAAB8f2vmj3Hp0zieMAAAAEMEBgAAYIjAAAAADBEY\nAACAIQIDAAAwRGAAAACGCAwAAMAQgQEAABgiMAAAAEMEBgAAYIjAAAAADBEYAACAIQIDAAAwRGAA\nAACGTHa73d7WnQAAAO0bTxgAAIAhAgMAADBEYAAAAIYIDAAAwBCBAQAAGCIwAAAAQwQGAB3SwYMH\nFRoaqosXL7Z1V4AOge9huA4TJkxQYWGhOnXqJJPJpJtvvlkjRozQ4sWLNWDAgLbuHnDdvv3eliQP\nDw/dfvvtWrhwoe6666427h3w4zFnzhwNHTpUzz77rAYNGiR3d3eZTCZJkslkUq9evTR58mTFxcXJ\nw8NDCQkJ2rVrlyTJbrerpqZGHh4ejuu98847Gjly5A/qE08YrtNzzz0ni8Wi3NxcpaWlSZIWLVrU\nxr0Cfrir722LxaLs7GxNmjRJ8+bN04kTJ9q6a8CP1uuvv+6Yl//85z/18ssv66OPPtLvfvc7SdKy\nZcsc9ddff12SHK8tFssPDgsSgaFFdO/eXZMmTdK///1vSZLVatWvf/1rjRkzRj/5yU/02GOP6eTJ\nk47jP/roI0VFRSksLEx33323Xn31VV190FNaWqrFixdr7NixGjFihOLi4vTNN9+0ybiAzp07a86c\nObrlllv0l7/8RdXV1Vq5cqXuvfdejRw5UrNmzVJOTo7j+Kbe29f7vq+vr9eqVas0duxYhYWFKTo6\nWunp6Ya1AwcOaNCgQaqsrJQkFRYWasGCBRo9erTGjh2rBQsWqKCgQJJ09uxZDRo0SNnZ2YqNjVVY\nWJhmzpzpqAPtSadOnTRs2DA9+uijyszMdN19XXanDuz8+fNKSUnR5MmTJUlr1qzRN998o8zMTO3b\nt0/+/v564YUXJEkFBQV6/vnn9dvf/laHDx/W+++/r9TUVH3++eeSrvzfXUVFhdLS0vT3v/9dvr6+\n+uUvf9lWQwMkSXV1dXJzc9O6dev097//Xe+9956ys7M1cuRIxcXFqbS0tMn39g9533/yySdKS0vT\njh07dPjwYS1dulQvvPCCrFZrk7Xv+uUvfyl3d3dlZmZq9+7dunTpkuLj452Oee+99/TWW2/pz3/+\ns6xWq/74xz+2+j9b4HrV1NS49H5uLr1bB7JixQqtWrXKsVY0fPhw/eIXv5AkJSYmqra2Vp6enpKk\nqKgox3JFRUWF6uvr5enpKZPJpFtuuUVZWVnq1KmTSkpK9NlnnyktLU2+vr6SpCVLligyMlKnTp3S\nrbfe2jaDxY/WxYsX9eGHH+rrr7/Wz372Mz344INKSEhQv379JF35j/CmTZu0f/9+DRw48Jrv7RMn\nTlz3+76srEydOnVS586dZTKZNH78eB06dEidOnVqsvZt//rXv2SxWPTGG2/I29vb0feZM2eqpKTE\ncdyMGTPUs2dPSdLo0aOdngwC7UVtba3+93//Vx988IHmzJnjsvsSGK7Tc889p0cffVSSVF5eri1b\ntmjatGnatWuXysrKtHLlSlksFscO7atJ8LbbbtOMGTM0a9YshYWF6a677tKDDz6oPn36KD8/X5L0\n0EMPOd3LbDbr/PnzBAa4xNUwLF1Zkhg0aJD+8Ic/qGvXriorK9PAgQMdx3p4eCgwMFDnz59XVFTU\nNd/bP+R9P2nSJO3atUsTJkxQZGSkxo0bp6lTp8rT07PJ2redOXNGXl5e6t27t6Pt6nw6f/68fHx8\nJEl9+/Z11Lt06aKqqqoW/CcLXL+FCxc6Nj3W1dXJ19dXTz75pJ588kmX9YEliRbg7e2tefPmydfX\nV7t27dK8efPk4+Oj9PR0HTlyRK+++qrjWJPJpJdeekmffvqpfvrTn+qvf/2roqOjlZubq86dO0uS\n/vKXvzhtVjl69Cg71OEy3970ePDgQX3wwQe68847HfWr/9L6tpqamibf2z/kfd+tWzft2LFD77zz\njgYOHKjf//73mjp1qsrLy5usfVdj/b7a96u++2QCaC++velx+fLlqqur07Rp0675vm4NzI4WVl1d\nra+//lpz5sxRjx49JElHjx511Ovr62Wz2dS/f3/9/Oc/144dOxQaGqpdu3apb9++MpvNOn78uNPx\n586dc/k4gO/y8fGRj4+P06clrr7f+/Xr1+R7+4e876urq1VRUaHw8HDFx8dr9+7d+uabb7Rv374m\na98WFBSkiooKFRYWOtpOnTolk8nkWF4BbhSxsbG64447lJyc7NL7EhhaQHV1tTZv3qzz58/rvvvu\nk6enp/75z3+qurpaGRkZOnjwoKQru7TT09M1depUx78cz58/r8LCQvXr108333yzYmJi9PLLL+vr\nr79WVVWVXn/9dc2ZM0d1dXVtOURAkvTwww/r97//vb7++mtdvnxZ69evV5cuXXT33Xc3+d7+Ie/7\nZcuW6b//+78dn5rIy8tTdXW1+vXr12Tt24KDgzVs2DCtXr1alZWVunDhgl577TWNHz9efn5+Lvwn\nCLSMpKQkffbZZ8rKynLZPdnDcJ2+vc570003KTg4WG+99ZYGDRqkl156SatWrdLrr7+uCRMm6LXX\nXtPPf/5zTZo0SZmZmTp58qSeeuopWa1W+fr66oEHHtDs2bMlSQkJCXrppZc0depUSVJoaKjefPNN\nmc3mNhsrcNXChQtVVlammTNn6vLlywoNDdWmTZvk5eWlSZMmXfO9bTabr/t9/8wzzygpKUmTJk1S\nVVWVAgIClJycrMGDBzdZO3DggFPfX375ZSUnJ2vChAny8PDQuHHjtHTpUpf/MwRawi233KKnnnpK\niYmJGjlypGMfTmvimx4BAIAhliQAAIAhAgMAADBEYAAAAIYIDAAAwBCBAQAAGCIwAAAAQwQGADeE\nCRMm6IMPPmjxYwE0D4EBQIuZMGGCwsLCVFlZ2aCWnp6uQYMG6fXXX2+DngH4oQgMAFqUp6en9u7d\n26A9LS1N3bt3b4MeAWgJBAYALWr8+PHatWuXU5vNZlNOTo4iIiIcbX/+858VGxurESNGKDo6Wr/7\n3e909Ytna2trtWzZMo0aNUpjx47Vli1bnK5XX1+vN954Q/fdd5+GDx+u2NhY5ebmtv7ggB8xAgOA\nFvXTn/5U//znP51+GfLTTz/VmDFjHD9l/eWXX2rBggWaN2+evvjiCy1fvlx/+MMf9OGHH0qSPvzw\nQ33yySf64IMPtHfvXp04ccLxA1OS9P7772vXrl168803lZOTo5kzZ+rxxx+XzWZz7WCBHxECA4AW\n5e3trXvvvVepqamOtrS0NMcPS0nSzp07FRERoejoaLm7u2vEiBGOH2eTpMzMTE2aNEm33367PD09\n9fTTT6u2ttZxfkpKih5//HHdeuutcnd313/8x3+ob9++2rNnj+sGCvzIEBgAtLjY2FhHYDh79qxO\nnz6tcePGOepnzpzRwIEDnc659dZbde7cOUlXfgq+T58+jlrXrl2d9j/k5+dr5cqVCg0Ndfz9+9//\n1vnz51tzWMCPGj9vDaDFjR07Vi+88IKOHTumv/71r3rggQfk5mb8r5uamhpJUnV1dYPat9s6d+6s\npKQkPfDAAy3XaQBN4gkDgBZnNpsVExOj9PR0paena8qUKU71fv366eTJk05tp06dUv/+/SVJPXv2\ndHpaYLVaVVpa6nT+8ePHnc4/e/ZsSw8DwLcQGAC0itjYWH3yySeqqanRsGHDnGoPPfSQDhw4oMzM\nTNXW1ionJ0e7d+/WtGnTJEl33323Pv30U508eVKVlZVat26dbrrpJsf5M2fO1NatW5WTk6O6ujp9\n9tlniomJ0alTp1w6RuDHhCUJAK0iODhYXbt21cSJExvU7rjjDq1YsUKvvfaalixZooCAACUkJDiO\n/c///E+dPXtWs2bNkru7u37xi1+oX79+jvMfeughFRQU6Ne//rXKyso0YMAAvfzyy7r11ltdNj7g\nx8Zkv/rBZwAAgGtgSQIAABgiMAAAAEMEBgAAYIjAAAAADBEYAACAIQIDAAAwRGAAAACGCAwAAMAQ\ngQEAABj6fxG/tSwlIRNtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15b05fcdd8>"
      ]
     },
     "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": {},
   "source": [
    "We now produce two `DataFrame`s containing the estimated player ideal points per season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "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": 89,
   "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": 90,
   "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>-0.016516</td>\n",
       "      <td>-0.323127</td>\n",
       "      <td>0.272022</td>\n",
       "      <td>θ</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.003845</td>\n",
       "      <td>-0.289842</td>\n",
       "      <td>0.290248</td>\n",
       "      <td>θ</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.008519</td>\n",
       "      <td>-0.289715</td>\n",
       "      <td>0.304574</td>\n",
       "      <td>θ</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.031367</td>\n",
       "      <td>-0.240853</td>\n",
       "      <td>0.339297</td>\n",
       "      <td>θ</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.037530</td>\n",
       "      <td>-0.320010</td>\n",
       "      <td>0.226110</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 -0.016516 -0.323127  0.272022     θ       0       0\n",
       "1  0.003845 -0.289842  0.290248     θ       0       1\n",
       "2  0.008519 -0.289715  0.304574     θ       1       0\n",
       "3  0.031367 -0.240853  0.339297     θ       1       1\n",
       "4 -0.037530 -0.320010  0.226110     θ       2       0"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "irt_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "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": 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 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>-0.069235</td>\n",
       "      <td>0.013339</td>\n",
       "      <td>-0.016516</td>\n",
       "      <td>0.003845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.003003</td>\n",
       "      <td>0.001853</td>\n",
       "      <td>0.008519</td>\n",
       "      <td>0.031367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.084515</td>\n",
       "      <td>0.089058</td>\n",
       "      <td>-0.037530</td>\n",
       "      <td>-0.002373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.028946</td>\n",
       "      <td>0.004360</td>\n",
       "      <td>0.003514</td>\n",
       "      <td>-0.000334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.001976</td>\n",
       "      <td>0.280380</td>\n",
       "      <td>0.072932</td>\n",
       "      <td>0.005571</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "param          b                   θ          \n",
       "season         0         1         0         1\n",
       "player                                        \n",
       "0      -0.069235  0.013339 -0.016516  0.003845\n",
       "1      -0.003003  0.001853  0.008519  0.031367\n",
       "2       0.084515  0.089058 -0.037530 -0.002373\n",
       "3      -0.028946  0.004360  0.003514 -0.000334\n",
       "4      -0.001976  0.280380  0.072932  0.005571"
      ]
     },
     "execution_count": 92,
     "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 be correlated with defensive ability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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22mkxe/bsmDt3brz55ptx8cUXx8477xyNGjWK3/zmNzFp0qTskoE1a9bExIkTi130c+Nj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\nDgAAAAAAgJP5P2+0kWjVvWZmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15c8058c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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\n",
    "\n",
    "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": [
    "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 may to be due to the hack-a-Shaq phenomenon.  In 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": 94,
   "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": 95,
   "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>0.351946</td>\n",
       "      <td>-0.026786</td>\n",
       "      <td>0.762273</td>\n",
       "      <td>b</td>\n",
       "      <td>86</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.320737</td>\n",
       "      <td>-0.027064</td>\n",
       "      <td>0.713128</td>\n",
       "      <td>b</td>\n",
       "      <td>23</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.280380</td>\n",
       "      <td>-0.071020</td>\n",
       "      <td>0.695970</td>\n",
       "      <td>b</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.279678</td>\n",
       "      <td>-0.057249</td>\n",
       "      <td>0.647667</td>\n",
       "      <td>b</td>\n",
       "      <td>462</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.271735</td>\n",
       "      <td>-0.106795</td>\n",
       "      <td>0.676231</td>\n",
       "      <td>b</td>\n",
       "      <td>78</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean       low      high param  player  season\n",
       "0  0.351946 -0.026786  0.762273     b      86       0\n",
       "1  0.320737 -0.027064  0.713128     b      23       0\n",
       "2  0.280380 -0.071020  0.695970     b       4       1\n",
       "3  0.279678 -0.057249  0.647667     b     462       1\n",
       "4  0.271735 -0.106795  0.676231     b      78       0"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_bot_irt_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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NTQUejRomJCSo7ZcvX873MerVq8epU6eytF27do1atWrlWdwKIURZ49iiphR3Il/k/6DF\nJCMjg6CgIC5evEhiYiJbtmzJ91x1Bc3b25uIiAj+/PNPPD09872fTqfjzz//JDQ0lD59+gDQoEED\njh8/zrVr10hOTmbp0qUYGBio+xgaGnLt2jWSkpLIyMjIcjwfHx927tzJnj17yMjI4NixY3h7exMZ\nGVkwFyqEEEKUQTKyV0zeeecd4uLi1JE9d3d3/Pz8iiWWevXq0bJlS0xNTalatWqufZ98QUNPTw9z\nc3PGjx+vFnv9+vUjPDyc7t27U716dSZNmsTvv/+u7t+rVy927txJp06d2LJlS5ZjOzs7M3HiRKZP\nn84nn3xCnTp1GDduHM7OZeNBdSGEEKIwaBRFkYl4yjidToenpycTJkxQ3/B92ZXFt9Dk7bvCI7kt\nPJLbwiF5LTwlNbe5vY0rI3tlXEZGBosWLcLY2LjYbiMLIYQQovDIM3tl2LVr17C1tSU8PJx58+bJ\nSxBCCCFEKSQje2VYnTp10Gq1xR2GEEIIIQqRDOUIIYQQQpRiUuy9IHd3d9asWZOlbf369Tg4OHDy\n5MkCOUdISAi3b9/OcVtkZCSWlpbqihM2NjZ07dqVefPmPdOExkIIIYQoneQ2bgHbsWMHs2bNYvny\n5TRr1uyFj6fT6Zg+fTqtWrWiWrVqT+13+PBhKlasiE6n48SJEwwbNgwzMzPeeuutF45BCCFE8YuM\niSc04iLXbt2nTnVjejg3kEmVRb7IyF4BOnToEJMmTSIoKAhbW1u1PS0tjcDAQNzc3LCxsWHQoEFc\nvHhR3W5pacnOnTvx8fHBxsaG3r17qytJ2NnZkZSURN++fZk/f36eMZQrVw5ra2usrKy4cOGC2h4e\nHk6/fv2ws7PDxcWFwMBAdeRv0qRJWdajbdmyJZaWluq+f/75JwMGDFD3Xbp0qbotKCiI4cOHs2jR\nIhwcHGjXrh3bt29n27ZtdOrUCXt7exYtWqT2T0pKYsKECXTo0AFHR0d8fX05c+ZMllysXLmSDh06\nEBQUlOf5hRCiLIiMiWfJ1mhib6agUxRib6awZGs0kTHxxR2aeAnIyF4B+eeff/j444+ZNWsW7dq1\ny7Jtzpw5aLVafv75Z0xNTfnuu+9455132L17N+XLlwdgxYoVzJw5k5o1azJixAiCgoJYtGgR27dv\np3PnzoSEhNC0adM843j48CF//fUXWq2WESNGAI+WMvPz82Ps2LEMHDiQK1eu0L9/f5o2bUr//v0J\nDAwkMDAQeLSW7VtvvaWe6/r164wYMYLPP/8cb29vLl68yPDhw6lSpYo6IfQ///yDq6srhw4dYtas\nWQQGBtK1a1d+++03QkNDmTRpEj4+PlSrVo1JkyaRmJjIpk2bMDY2JiAggJEjR7Jr1y709PQA2Llz\nJyEhIVSvXj1f5xfiZTLu2/DiDqFE0dPTkJkp073m5U5yWo7ty7fHEPz7uWztktfCU1C5nf1+u7w7\nFRAp9grAmTNnCAoKwtrami5dumTZptPp+OWXX5g7dy61atUCYPTo0axdu5bDhw/ToUMHAHr06EHD\nhg0BcHV1JSQk5JlicHJyAh4Va4qiMGzYMNq0aQOAkZERBw8exNjYGI1GQ7169bCxseHEiRP0798/\ny3EWLlxISkoKEydOBGD79u00bNiQfv36AdCkSRMGDx7Mpk2b1GJLX1+fQYMGodFocHV1ZfXq1bzz\nzjsYGRnh5uaGTqfjypUr6Ovrs2vXLtasWaOuAzxmzBhcXV2JiYlRV+bw9PTEzMws3+fPiampMfr6\nes+Uw9Igt0k1xYspqNzq6WkK5DilieQkb5m6nIuLTJ3y1PxJXgtPQeS2KH9fS7FXALZt24a/vz8L\nFixg5cqVDB06VN12+/ZtUlJS+PDDD9Fo/vfDodPpuH79uvrd3Nxc/VyhQgXS0nL+V9zTPPnM3qVL\nl5g8eTLjxo1j7ty5APz222/88MMPXL16lczMTDIyMvDy8spyjPDwcNasWcPGjRsxNDQE4PLly/z7\n779qIQagKIparAHUrFlTvbbH+9WsWTPL97S0NK5evYqiKDRp0iTLvhUrViQuLk49R926ddXt+Tl/\nThIT7+cnbaVKSZ3VvTQoyNzOGCHL/z1Jfm7zZ/KKSGJvpmRrNzerRICvQ7Z2yWvhKajcFvSfj6yg\nUchGjx7NoEGDqFevHqNGjaJJkybqiJ2RkREAa9eupXXr1k89RkFNaFyuXDkaNmzI2LFj6d+/P59/\n/jmnTp3iyy+/ZObMmXh4eGBgYJBtHd5bt24xfvx4vvjiCxo1aqS2GxkZ0b59e5YvX/7Ucz5ZxObW\nltu2hw8fqp8f387N7/mFEKK06+HcgCVbo3Nor18M0YiXjbygUQD09R/VzB06dGD06NF88skn6ssR\nlStXxtTUVH3h4rHY2NgiiS01NZWoqCgsLCzo1asXBgYGZGZmZpkWRlEUxo8fT4cOHfD29s6yf/36\n9Tlz5gw6nU5tu337Nqmpqc8ci7m5ORqNhrNnz6pt8fHxpKSkUK9evRz3KcjzCyHEy8qxRU1G9G6J\nuVkl9MppMDerxIjeLeVtXJEvUuwVsOHDh9OuXTtGjRrFvXuPhmh9fHxYvHgxp0+fJiMjg/Xr1+Pl\n5UVSUlKex3s8Mnjx4kWSk5PzFUN8fDxBQUE4ODhQp04dLCwsuHnzJrGxsSQkJBAQEECVKlW4ceMG\nAEuXLuX69etMnjw527F69uxJcnIyQUFBPHjwgGvXrjFs2DCWLFmS35SoqlSpgoeHBwsWLCAhIYHk\n5GRmz55N06ZNadWqVY77FOT5hRDiZebYoiYBvg4sG+9GgK+DFHoi36TYKwTTp0+nfPnyjBkzhszM\nTEaNGoW7uztDhgzB3t6eTZs2sXTpUqpUqZLnsapXr46HhweffPIJc+bMeWo/JycndeqU119/ndq1\na7Nw4UIAXnvtNdzc3OjVqxevv/461tbWjB07luPHj+Pv78/69eu5dOkSDg4OWaZgOXLkCCYmJnz3\n3XccPHgQR0dH3nzzTezt7Xn//fefKzdffvklpqam9OrVi65du5Kens7y5cufetu3oM8vhBBClDUa\nRVHk3WxR6pTFB5PlgezCI7ktPJLbwiF5LTwlNbe5vaAhI3tCCCGEEKWYFHtCCCGEEKWYFHtCCCGE\nEKWYFHtCCCGEEKWYFHsvMSsrKw4cOJBnv8GDBzNz5swiiCh/LC0t2b9/f47bjhw5gpWVFffvl70V\nMIQQQojCICtolEDu7u7Ex8dnWVWjevXqdO7cmY8//phKlSoBoNVqizSuzz77jC1btqiTSANUqlQJ\nOzs7xo4dq67t+yLs7e2L/LqEEKKki4yJJzTiItdu3adOdWN6ODeQefZEvsnIXgk1YcIEtFotWq2W\nqKgoli9fztGjR/nqq6+KNa6uXbuqcWm1WkJDQzE2NmbYsGGkp6cXa2xCCFEaRcbEs2RrNLE3U9Ap\nCrE3U1iyNZrImPjiDk28JGRk7yWg0Who3LgxI0eOZMKECeh0OsqVK4elpSWLFy/Gzc2NBw8eMH36\ndHbu3Ak8Gh384osvMDY2zna8CRMmcPHiRfr378+MGTM4dOgQ5cuXByAhIQEXFxfWrVuHtbV1nrG9\n8sorTJgwAWdnZ06ePIm1tTWDBw+mVatWfPrpp8CjpeE6d+7Mtm3baNq0KQBXr17Fx8eHf//9l0aN\nGjFt2jSaN29OZGQkQ4YM4dixY1SsWJH4+HimTp3K0aNH0dfXx8bGhkmTJlGrVq2CSq8QRWbct+HF\nHUKJo6enITNTpnvNzZ3ktBzbl2+PIfj3czluk7wWnrxyO/v9dkUYTf5IsfcSefjwIYqi5LjaxNdf\nf82pU6fYsWMH5cqVY+TIkcyZMyfbEmjLli3j2LFjrFu3DiMjI6ZOncrBgwfp3LkzAHv37sXCwiJf\nhd6TcT2rtWvXMn/+fCwsLJgyZQp+fn7s3bs3Wz8/Pz8sLCzYvXs3mZmZ+Pv74+/vz9q1a3M9vqmp\nMfr6es8c18sut0k1xYspiNzq6eW8UkxZJ3nJXaYu58IiU6fkmjvJa+HJLbcl8fewFHsvAZ1Ox+nT\np1m8eDG9e/fOVuwpisLmzZuZOnUq1apVAyAwMJCbN29m6bdnzx5++OEHfv75Z0xNTQHw8PBg69at\narG3c+dOevfune/Y4uPjmTZtGo0bN6Zly5b53q9Xr15YWloCj9YT3rx5M2fPns3S5+TJk2i1WhYt\nWkTlyo/+8vj5+eHj40NCQgKvvPLKU4+fmFj2XvAoqbO6lwYFldsZI5wLIJrSRX5u8zZ5RSSxN1Oy\ntZubVSLA1yHHfSSvhSev3BZX3nMrMqXYK6GmT5+uvkGr0+kwMjJi0KBBfPDBB9n6JiYmkpSURN26\nddW2V199lVdffVX9fvr0adatW8cnn3xCvXr11PY+ffrw3nvvkZycjE6n4/Dhw3z55ZdPjWv37t1Y\nWVkBj4rMhw8f0rt3b1auXImeXv5H0po0aaJ+fhx3fHy8ejsZ4MqVK1SsWDHLLdtGjRoBEBcXl2ux\nJ4QQpUUP5wYs2RqdQ3v9YohGvIzkBY0S6skXNFauXMnDhw/x8vLCwMAgW9/HI325LXN85MgR3N3d\nWbp0KXfu3FHb7e3tMTMzY9euXezbtw8rKyssLCyeepwnX9D4448/MDU1xcnJiZo1n/5WmE6ny9b2\n5JvGjxkaGj712v7reW4dCyHEy8ixRU1G9G6JuVkl9MppMDerxIjeLeVtXJFvUuy9BBwcHOjRowef\nf/55joWTqakpVapU4fz582rbqVOn2Lhxo/p9wIABzJkzhwYNGjBlyhS1XaPR4OXlxa5du/jtt9+e\n6Rauqakpn376KTNmzODGjRtqu4GBAampqer3y5cvZ9v3yVivXr0KkO2lCwsLC5KTk4mPj8+yn0aj\nyTI6KYQQpZ1ji5oE+DqwbLwbAb4OUuiJZyLF3kti/PjxXLx4kR9//DHH7X379mXFihVcv36du3fv\nEhgYyIkTJ9Ttenp6aDQapk+fzoEDB9i+fbu6zdvbm4iICP788088PT2fKa4+ffrQvHnzLFPCNGjQ\ngIiICBITE0lISOCnn37Ktt+2bdu4ePEiqampLF++HEtLy2wjis2aNcPa2ppZs2aRkpLC7du3Wbhw\nIR07dpRbuEIIIUQ+SbH3kjA1NWX8+PHMnz+fK1euZNvu7+9P27Zt6dmzJx4eHpibmzNu3Lhs/czN\nzZkwYQIBAQFcv34dgHr16tGyZUucnZ2pWrXqM8f21Vdf8ccffxAaGgqAr68vVatWpVOnTgwZMoQh\nQ4Zk22fw4MGMHz8eJycnzpw5w9dff53jsefOncvdu3dxd3fH29ubunXrMmfOnGeOUQghhCirNEpu\nD3qJMkGn0+Hp6cmECRPo1KlTcYdTIMriW2jy9l3hkdwWHslt4ZC8Fp6Smlt5G1c8VUZGBosWLcLY\n2BhXV9fiDkcIIYQQBUxu45Zh165dw9bWlvDwcObNm5fjG7JCCCGEeLnJyF4ZVqdOHbRabXGHIYQQ\nQohCVOKGco4cOYKVlRX37xf+Cgjvvvsuc+fOLfTzFAd3d3fWrFlT3GEIIYQQopgVabF38eJFPv30\nU1xcXLC2tsbFxYUPP/yQmJgYtY+9vT1arRZjY+NCj+f777/H39//ufdXFIUuXbpga2tLcnLyM+2r\n0+lYsWJFvvvHxsayY8eOZw1RCCGEEGVckRV7//77L6+//joVKlRg06ZNHD9+nHXr1lG9enUGDBhA\nVFRUUYVSYA4fPkxGRgavvvoqv/766zPtGxMTw9KlS/Pd//Gkx0IIIUqXyJh4Jq+I5L2Z+5m8IpLI\nmPi8dxLiGRRZsRcQEICrqytfffUVZmZmaDQazM3N+fLLL/nkk0/Q13/0+GBkZCSWlpakpDxa9Dk6\nOprBgwdjb2+Pk5MT48ePV0fRYmNjsbS0JCwsDG9vb2xsbPDx8VHnjwsJCaFXr15s3rwZNzc37Ozs\nGDt2LJmZmcCjud4erz974cIFhg4dStu2bWnbti2+vr5cu3Yt12vauHEjnp6edO/eneDg4CzbIiMj\nsbOz49ChQ3Tr1g1bW1uGDx9OcnIyx44d48033+TOnTtYWVkRFhYGwE8//UT37t1p3bo1Hh4eHDhw\nAIClS5cdhiInAAAgAElEQVQye/ZsdV3a9PR00tPTmTFjBm5ubtjb2zNw4ECOHj2aY5wZGRkMHTqU\njz76CEVR8tzX0tKS/fv3q99DQkJwdHTMd8579OjBxo0bcXFxoW3btnz//feEh4fj4eGBra0tX3zx\nhXpsd3d3Vq5cia+vL61bt6ZLly78+eef6vb4+Hg++OADnJyccHFx4YMPPlDPJYQQL7vImHiWbI0m\n9mYKOkUh9mYKS7ZGS8EnClSRvKBx+/Ztjh07xurVq3Pc/s477zx1348//hgPDw9++OEHEhMTGTJk\nCMuWLWPMmDFqn1WrVrF06VL09fUZOHAgK1euZMKECcCjN061Wi2hoaFcunSJfv364enpSefOnbOc\nZ+rUqdSuXZvFixeTmZnJtGnTmDlzJgsWLMgxrsTERHbv3s2GDRswMzNj9uzZnD17liZNmqh9Hjx4\nwLZt29iwYQP37t2jb9++hISEMGTIEKZOncrMmTOJjIwEYM+ePSxYsIBly5bRsmVLDh48iJ+fH1u2\nbGH48OGcP3+e+/fvs3DhQgBmzpzJH3/8wapVq6hVqxbffPMNI0eOZO/evZiYmGSJddq0aaSmprJ4\n8WI0Gg3z5s3L975Pk1fOY2Nj2bdvH6tXr2bevHl06dKFX375hRMnTvD222/z5ptv0qpVKwB++OEH\n5s2bR8uWLfnuu+94//33CQsLw9DQED8/PywsLNi9ezeZmZn4+/vj7+/P2rVr8xWnECXNuG/DizuE\nEkVPT0NmZtmd7vVOclqO7cu3xxD8+7nnPm5Zz2th+m9uZ7/frhijyZ8iKfYer/hQv379Z9538+bN\nlC9fHj09PapXr067du2yLAMG0L9/f2rUqAGAk5MT58797y9IcnIyH330EcbGxjRv3pz69etz7ty5\nbMVeUlISFhYWGBgYoNFomDp1aq5TkWzZsoUGDRrQvHlzANq3b09wcDCfffaZ2ken0zF06FCqVKlC\nlSpVsLa2zhLbkzZs2EDfvn2xtrYGwM3NDRcXFzZv3pzjc4XBwcFMmjRJXSPWz8+P1atXExERQbdu\n3dR+q1evJjw8nHXr1mFoaPhM++Ymt5w/ePCA4cOHY2BgQKdOnZg1axbe3t5UqlQJJycnjI2NuXTp\nklrsdezYETs7OwCGDx/O8uXL+fPPPzEzM0Or1bJo0SIqV66sxurj40NCQkKuS6aZmhqjr6+Xr2sp\nTXKbVFO8mILKrZ6epkCOU5qU5Zxk6nIuyDJ1ygvnpSzntbA9mduX4fdukRR7Gs2jpDy+fQpw7Ngx\n3n77beDRiw61a9dm9+7d2faNiIjg22+/5cKFC2RkZJCZmUmbNm2y9DE3N1c/V6hQgbS0//1LycTE\nhCpVqqjfjYyMsmx/7IMPPmDcuHH88ccfuLi44OnpibOz81OvKTg4GC8vL/W7l5cXgYGBfPLJJxgY\nGOQrtiddvnyZsLCwLG/QKoqiFjlPunv3LklJSVlGEQ0MDKhbty5xcXFqW1hYGAcOHGDRokWYmpo+\n0755ye26qlSpQsWKFQHUArNmzf8t2m1gYJClf8OGDdXPxsbGVK1alRs3bpCamkrFihWpVauWur1R\no0YAxMXF5VrsJSYW/tvcJU1JndW9NCjI3M4Y8fTfK2VRWf+5nbwiktibKdnazc0qEeDr8NzHLet5\nLUz/zW1JyXNuRWeRPLPXoEEDNBpNltEfOzs7tFotWq2WgICALIXgY+fOneOjjz6iZ8+ehIeHo9Vq\neeutt7L1y20E7nGhmZdOnTqxf/9+/P39SUlJYcSIEerzfP/1999/c+bMGYKCgrC1tcXW1pbPP/+c\nhIQE9u3b91znNzIy4qOPPlJzotVqOXHiBLNnz36ma3v48KH6+dixY7i5uTF//nzS09Ofad8n5fRn\n86w5z63/f4+vKIp6jKfl72mxCiHEy6SHc4OntD/7nTAhnqZIij0TExPat2/PypUrc9yu0+lybP/3\n33/R09Nj6NChVKhQAXj0wkZhSEhIoFKlSvTo0YO5c+cyZcoU1q1bl2PfjRs34uzszLZt29i8eTOb\nN29my5Yt9OrVK9uLGvlVr149Tp06laXt2rVrOebGxMQEExMTzp49q7alp6dz9epV9dYswPvvv8/c\nuXNJT09Xn/XLz74GBgakpqaq2x/fhi8sly9fVj+npKRw584datWqhYWFBcnJycTH/+9B5fPnz6PR\naLJcpxBCvKwcW9RkRO+WmJtVQq+cBnOzSozo3RLHFjXz3lmIfCqyt3E///xzoqOj+eijj4iNjQXg\nzp07bNy4ka+//lp9Vu1JFhYWpKenc+LECZKTk1m0aBEPHjzg5s2bOY42Pa/U1FQ8PDxYu3Yt6enp\npKWlER0dneMzhsnJyfz6668MGDCA+vXrZ/lv0KBBhIWF5et2qJGRESkpKcTHx/PgwQN8fHzYuXMn\ne/bsISMjg2PHjuHt7a2+wGFoaMi1a9dISkoiIyODfv36sWzZMq5evUpqaioLFiygQoUKdOjQQT2H\nnp4eRkZGzJo1ix9++EF94zavfRs0aMCePXt4+PAh//77L3v37i2IND/VwYMH0Wq1pKWlsWzZMipV\nqkTbtm1p1qwZ1tbWzJo1i5SUFG7fvs3ChQvp2LFjrrdwhRDiZeLYoiYBvg4sG+9GgK+DFHqiwBVZ\nsdeoUSN++eUXjI2N8fHxwcrKim7duvHbb78xceJEvv7662z7tG7dmnfeeYehQ4fi4eFB+fLl+b//\n+z+SkpJyvJ37vIyMjAgKCiIkJAQHBwc6dOjAhQsXclxdIzQ0FENDQ9zd3bNts7W1Va8zL05OTtSv\nX58uXbqwZ88enJ2dmThxItOnT8fOzo6JEycybtw49bnBXr16ERsbS6dOnYiLi+PDDz+kdevW+Pj4\n4OrqysmTJ1m9erX6rNyTrK2t8fX15dNPPyU5OTnPfSdOnEhUVBRt27Zl9uzZvPfee8+a0mfSt29f\n5s+fj4ODA9u2beObb75Rn3ucO3cud+/exd3dHW9vb+rWrcucOXMKNR4hhBCiNNEoiiLvZoti4+7u\nzrvvvlugxTuUnAdmi5I8kF14JLeFR3JbOCSvhaek5rbYX9AQQgghhBDFQ4o9IYQQQohSrEjm2RPi\naf47VY0QQgghCpaM7AkhhBBClGJS7JUCISEhODo6FncY+RYUFETfvn2LOwwhhBCiTJBiL5/c3d1p\n2bIlVlZWWFlZ0alTJ8aPH59tIuT82rRpE5aWlupkxyVR27ZtadWqFZaWlpw+fbq4wxFCCCHEc5Bi\n7xlMmDABrVbLsWPHWLFiBTVq1OCNN97g4MGDz3ysjRs30q1bN0JCQp66gkhxO3r0KL/99ltxhyGE\nEKVGZEw8k1dE8t7M/UxeEUlkTHzeOwnxgqTYew7ly5encePGjB07lmHDhvHFF1+oa7XevXuXcePG\n4eLigq2tLSNHjuTWrVtZ9j9//jxRUVFMmjSJ1NRUwsLCsmwfPHgwixcvZvz48djZ2eHq6sqOHTvU\n7VFRUXh5eWFjY8Pbb7/NzZs31W2xsbFYWlqydu1aHB0dCQkJAWDnzp14e3tjY2ODu7t7viZ+zkl6\nejozZszAzc0Ne3t7Bg4cqK7MAY9GQL/55htee+01JkyYAMDvv/9Ot27dsLW1ZfTo0dy/fz/LMUND\nQ+nVqxe2trZ07NiRxYsXq9tCQkLo1asXmzdvxs3NDTs7O8aOHVugK6gIIURRiIyJZ8nWaGJvpqBT\nFGJvprBka7QUfKLQydu4L2jIkCF8++23HDt2DEdHRyZMmICiKGzbto3y5cszbdo0/Pz8WL9+vbrP\nxo0bcXV1xczMjB49ehAcHJxlmTOAtWvX8n//939MmzaNBQsWMGXKFDw9PdHpdIwePRoPDw82bNjA\n6dOnGT16dLa4IiIi2LNnD5UqVeLEiRN8+umnLFiwABcXF6Kiohg2bBg1atTIdt68zJs3jz/++INV\nq1ZRq1YtvvnmG0aOHMnevXsxMTEBYPv27SxZsoQGDRqQlJTExx9/zMcff8zAgQM5cuQIY8aMwdzc\nHHhUnI4bN45vv/2WTp06ERUVxcCBA7GysqJ9+/bAozWCtVotoaGhXLp0iX79+uHp6Unnzp2fKXYh\nisK4b8OLO4SXip6ehszMsjG3/53ktBzbl2+PIfj3cwV6rrKU16Iy+/12xR3Cc5Ni7wWZmJhQrVo1\nrly5wquvvsrevXvZtm0bpqamAIwfPx5nZ2fOnz9Po0aNePjwIZs3b+arr74CwMvLi4EDB5KQkJBl\nvVdra2u1EHvttddYtmwZt2/f5urVq8TFxTFq1CgMDQ3VZecej+A95u3tTeXKj2bT/uWXX3B1daVj\nx47Ao2XdvL292bRp0zMXe8HBwUyaNIl69eoB4Ofnx+rVq4mIiKBbt24AdOjQgYYNGwJw6NAhDAwM\nGDx4MHp6erRv3x4nJyd1fWRzc3MiIiLUQtHa2pqGDRty4sQJtdhLTk7mo48+wtjYmObNm1O/fn3O\nnTuXa7FnamqMvr7eM11baZDbDOrixeQ3t3p6mkKOpPQpKznL1OVcfGXqlELJQVnJa1F58nfAy/a7\nVoq9ApCRkYGenh6XL18G4PXXX8+yXU9Pj7i4OBo1asSePXvIyMjAzc0NeFTcWFhYsHXrVt555x11\nn8cjX/Bo7V6A1NRUrl+/jrGxMVWrVlW3Py6snlS3bl318+XLl4mIiMDKykptUxQFa2vrZ7rOu3fv\nkpSURJMmTdQ2AwMD6tatS1xcnNpWp04d9fP169epUaMGenr/K7waNmyoFnsA69atIzg4mPj4eBRF\n4eHDh6Snp6vbTUxMqFKlivrdyMiItLSc/4X8WGLi/Vy3l0YldQmf0uBZcjtjhHMhR1O6lKWf28kr\nIom9mZKt3dysEgG+DgV6rrKU16LyOJ8lNbe5FaBS7L2guLg4EhMTady4MQYGBgDs37+f6tWr59g/\nODiY5OTkLFOlpKenExwcnKXYK1cu58cpnyyCHsup8HmyuDIyMuKNN95gypQp+bqmnGg0mhw/P/b4\nmUUAff3//VjlFe/GjRtZvHgxQUFBODk5oa+vj7e391PPLYQQL6sezg1YsjU6h/b6xRCNKEuk2HtB\nixYtomHDhrRq1Yr79++jp6fHqVOn1GJPp9Nx/fp16tSpw9WrVwkPD2fRokVZRscSExPx8fHh+PHj\ntG7dOtfz1ahRg/v373Pnzh11dO/SpUu57lOvXj3+/vvvLG3x8fG88sorlC9fPkv7oUOHOHDgAJ9/\n/jnw6BYqQLVq1TAxMcHExISzZ8/SokUL4FExd/XqVfW2bk7x3rhxA51OpxawFy9eVLdrtVrs7Oxw\ncXFRz5fX9QghxMvIsUVNAEIjLhF3O4Xa1SrSw7m+2i5EYZG3cZ/TjRs3+PLLLwkNDSUwMJBy5cpR\nqVIlevbsydy5c7l69SppaWkEBQUxePBgMjMzCQ4OpnHjxnTu3Jn69eur/9nY2NCuXTuCg4PzPG/r\n1q2pWrUqS5cuJT09nX/++Yc9e/bkuk///v2Jiopi/fr1pKenc/bsWXx8fNiyZUu2vlWqVGHt2rXs\n2bOH9PR01qxZg5WVlfo8Yb9+/Vi2bBlXr14lNTWVBQsWUKFChac++9euXTvu37/P2rVrSU9P58CB\nAxw7dkzdbm5uzoULF0hMTOT69et88cUX1K5dm/h4eTtNCFH6OLaoSYCvA8vGuxHg6yCFnigSUuw9\ng+nTp2NlZUWrVq3o1asXiYmJrFu3jrZt26p9Jk2aROPGjfHy8qJ9+/b8888/LFmyBI1GQ0hICP36\n9cvx2K+//jqhoaHZpiX5LyMjI7755hv++OMP7O3tmTt3Lr6+vrnu07BhQ+bNm8eqVato06YNw4cP\np3///jnGYm1tzZQpU5g+fTpOTk5cvXqVuXPnqts//PBDWrdujY+PD66urpw8eZLVq1dTsWLFHM9d\nq1Yt5s6dy48//oiDgwMbNmzgrbfeUrf7+PjQuHFj3N3defvtt/Hy8uK9995j+/btzJs3L9frEkII\nIUTeNIqiyLvZotQpiQ/PFraS+tBwaSC5LTyS28IheS08JTW3ub2gISN7QgghhBClmBR7QgghhBCl\nmBR7QgghhBClmBR7QgghhBClmBR7ZVxsbCyWlpacPn26uEN5qqCgIPr27QtAZGQklpaWpKRkn4Ve\nCCGEENlJsVeKREVFYWVlRcuWLbOs0FFU1qxZg6OjIzqdLkv7wIEDs0y3ApCZmYm9vT3r1q0ryhCF\nEKJYRcbEM3lFJO/N3M/kFZFExsicoqLwSbFXilhbW6PVapk6dWqxnN/V1ZU7d+4QHf2/5YBSUlL4\n999/iY6OzjIad+LECZKSkp46GbMQQpQ2kTHxLNkaTezNFHSKQuzNFJZsjZaCTxQ6WS6tDIiPj2fq\n1KkcPXoUfX19bGxsmDRpErVq1VL7XL58mS+++ILTp09jaWnJnDlzMDc3JzIyklGjRrFw4UICAwOJ\nj4/H3t6er7/+mkqVKmU5T7169WjQoAFhYWFYWVkB8Oeff9KkSRMUReHIkSN06tQJgLCwMJo0aULd\nunUB+PHHH1mzZg03b96kevXqjBgx4qkTUAvxMhn3bXhxh1Ci6elpyMwsG9O93knOvo45wPLtMQT/\nfq5Az1WW8lpUZr/frrhDeG5S7JUBfn5+WFhYsHv3bjIzM/H398ff35+1a9eqfdavX8/ChQspX748\nb7/9NkuWLFFHCB88eMC2bdvYsGED9+7do2/fvoSEhDBkyJBs5+rQoQNhYWGMHDkSgPDwcNq0aYNO\npyM8PFwt9iIiInB1dQXg6NGjzJw5k40bN9K8eXP279+Pn58fdnZ2NGrU6Lmu2dTUGH19vefa92WW\n26Sa4sU8b2719DQFHEnpU1ZylKnLufjK1CmFkoOyktei8uTvgJftd60Ue6XcyZMn0Wq1LFq0iMqV\nH/1w+vn54ePjQ0JCgtpvwIAB1Kz5aI1GV1fXLOvX6nQ6hg4dSpUqVahSpQrW1tacO5fzv0I7dOjA\nunXrSElJoWLFioSHhzN+/Hh0Op267NqDBw/4+++/ef/99wFo06YNERERVKlSBQB3d3cqVKhATEzM\ncxd7iYm5LztXGpXUWd1LgxfJ7YwRzgUcTelSln5uJ6+IJPZm9pfLzM0qEeDrUKDnKkt5LSqP81lS\nc5tbASrFXil35coVKlasmOWW7eMCKi4uDhMTEwDMzc3V7UZGRqSlZb3d8OT2ChUqZNv+mKOjI3p6\nehw5coTmzZtz6dIl7O3t0el0XLhwgRs3bvDvv/9Svnx52rRpA0BGRgbffvstv/32G7dv3wYgPT2d\n9PT0AsiAEEKUDD2cG7Bka3QO7fWLIRpRlkixV0ppNJocPz/p4cOHefbJ7/bHjIyMsLe3JywsjMTE\nRFq3bo2xsTEAVlZWhIeH8++//+Lo6IiBgQEA33zzDdu3b+fbb7+lVatWlCtXDnt7+3ydTwghXhaO\nLR7dPQmNuETc7RRqV6tID+f6arsQhUWKvVJg1apVGBoaMmDAAADu3btH9erVAbCwsCA5OZn4+Hj1\nNu358+fRaDTUq1eP+/cL/nanq6srISEh3L9/H2fn/93CcnJy4ujRo0RHR/PGG2+o7VqtFnd3d6yt\nrYFHo5FJSUkFHpcQQhQ3xxY1pbgTRU6mXikFMjIyCAoK4uLFiyQmJrJlyxb15YdmzZphbW3NrFmz\nSElJ4fbt2yxcuJCOHTvyyiuvFEo8rq6unD59moiICNq1+9/bS87OzkRERHD69OksU66Ym5tz8uRJ\n7t+/z4ULF5gxYwY1a9YkPl6mIxBCCCFelIzslQLvvPMOcXFx6sieu7s7fn5+6va5c+cSEBCAu7s7\nBgYGuLq68tlnnxVaPA0aNKBu3bokJCSoo3UAtra23Lp1CwsLCywsLNT2kSNHMmbMGNq1a0eDBg2Y\nMmUKhw4d4rvvvsPU1LTQ4hRCCCHKAo2iKDIRjyh1SuKbUoWtpL4hVhpIbguP5LZwSF4LT0nNbW5v\n48ptXCGEEEKIUkyKPSGEEEKIUkyKPSGEEEKIUkyKvWJiaWnJ/v37izuMF/LZZ58xevTo4g5DCCGE\nELmQYg/o27cv06dPz9J25coVLC0t+eWXX7K079y5k1atWpGcnFyUIeabpaUl7u7u5PTezbJly7C0\ntCQkJCRfx0pKSmL9+vVP/S6EEEKIkk+KPR7NCxcWFpalLSwsDGNjY8LDw7O0h4eHY2dnR6VKlYoy\nxGeSmprKkSNHsrVv27aNatWq5fs4ERERWYq7/34XQgiRu8iYeCaviOS9mfuZvCKSyBiZP1QUPSn2\neFTsnTlzJsskvuHh4fTp04fw8PAso2Th4eHqhMVpaWkEBgbi5uaGjY0NgwYN4uLFi2rfZcuW4e7u\nTuvWrencuTOrV6/O8fy5Heftt98mMDAwS/+VK1fSo0ePp15Px44d2bJlS5a206dPk5ycTOPGjdU2\nRVGYN28ebm5u2Nra0rNnT/XW8vbt2xkzZgwxMTFYWVmxaNGiLN8vXLigHue7777DycmJ9u3bs3Tp\n0nxdV8eOHdmzZ4/a19fXN8s1nTx5EisrK1JTU9m0aRMeHh7Y2NjQoUMH5s+fn+PIpRBClCSRMfEs\n2RpN7M0UdIpC7M0UlmyNloJPFDmZVBlo3bo1JiYmhIWF0bdvX3Q6HZGRkaxatYrQ0FBOnTpFs2bN\niI2N5fLly2qxN2fOHLRaLT///DOmpqZ89913vPPOO+zevRutVktQUBAbN27E0tKSqKgo3nvvPRwc\nHLC0tMxy/tyO06dPH2bNmsVnn32Gvv6jP65du3bRu3fvp15P9+7dGTNmDJMnT8bQ0BCArVu30q1b\nN7Rardpvy5YtrF+/nuDgYOrUqcPPP//MJ598woEDB+jZsycXLlxg//796m1fRVGyfAc4evQoHTp0\n4ODBg2zZsoXJkyfTu3dvatWqlet1OTo68tdff9GlSxcyMzOJiYmhQoUKJCYmYmpqytGjR7G1teXO\nnTtMnDiRFStW4OzszMWLF/H19aV169a4ubkVzA+AEAVk3LfheXcSWejpacjMLJ3/eLuTnJZj+/Lt\nMQT/fq5Qz12a81oUZr/fLu9OLxEp9gA9PT3atWunFnsnTpxAT08PS0tLHB0dCQsLo1mzZoSHh1Or\nVi2aNm2KTqfjl19+Ye7cudSqVQuA0aNHs3btWg4fPoxOpwPA2NgYAGtraw4fPky5clkHU/M6zmuv\nvcaUKVMICwujY8eO3Lhxg+PHjzN37tynXk/Dhg1p1KgRe/fupXv37iiKQmhoKIsXL85S7PXq1YvO\nnTtTufKjiRh79OhBQEAA586dw9bWNl+5q1mzprrOba9evZg0aRLnz5+nRo0auV6Xk5MTGzZsACA6\nOpr69etTq1YttQA8evQo7dq1Izk5GZ1Oh7GxMRqNhoYNG7Jnz55sefwvU1Nj9PX18nUNpUluk2qK\nF5Of3OrpaYogktKntOYtU5dzsZWpU4rkmktrXotCXn/fX7bftVLs/X+urq7Mnj0bRVEIDw/H2dkZ\njUaDk5MTe/fuxdfXl/DwcHVN19u3b5OSksKHH36IRvO/v1A6nY7r16/j5eVFu3bt8PT0xMHBARcX\nF/r06ZNt+a+8jmNsbEy3bt3YunUrHTt2ZPfu3bRp04Y6derkej1eXl5s3bqV7t27c+TIEUxMTLKN\nKD548IDp06dz8OBB7t69q7anp6fnO2/m5ubqZyMjI+DR7du8rsvFxYXJkyeTlpbGkSNHaNu2LTVq\n1FCLvb/++ouhQ4fSuHFj+vfvz8CBA7GxsaF9+/b07duX2rVr5xpXYuL9fF9DaVFSZ3UvDfKb2xkj\nnIsgmtKlNP/cTl4RSezNlGzt5maVCPB1KNRzl+a8FoXccldScysraORDhw4dSExM5OTJk4SFheHs\n/OiXtrOzM0ePHiUtLY3Dhw+rt3AfFzZr165Fq9Wq/0VHR/PGG29gYGDA4sWLCQ4Opk2bNoSEhNC9\ne3euXLmS5bx5HQfA29ubvXv38uDBgzxv4T7Wo0cPIiMjSUhIYNu2bXh5eWXrM2XKFI4fP86PP/5I\nVFRUtpdR8uPJQu5Zrqt27drUrl0brVbLkSNHaNOmDba2tvz1119cvnyZBw8e0KpVKzQaDVOnTuXX\nX3+lc+fOHDhwAE9PT6Kiop45ViGEKEo9nBs8pb1+0QYiyjwp9v4/MzMzmjdvTnh4OFFRUbRr9+h+\nfcOGDalatSrBwcHcu3dPba9cuTKmpqacOnUqy3FiY2MByMjIICkpiWbNmuHn58fmzZupXLkyu3fv\nztI/r+MAODg48Morr7Bp0yaOHz+Oh4dHntdTtWpVXFxc+PXXX9m7dy89e/bM1icqKorevXvTqFEj\nNBoNJ06cyEem8ic/1+Xk5MTRo0f5+++/sbOzo3nz5ly4cIFDhw7h4OCAnp4eOp2OO3fuUL9+fXx9\nfdmwYQNWVlbZXkARQoiSxrFFTUb0bom5WSX0ymkwN6vEiN4tcWxRs7hDE2WMFHtPcHV1Zd26ddSq\nVSvLbVJnZ2d+/PHHbFOu+Pj4sHjxYk6fPk1GRgbr16/Hy8uLpKQkVqxYweDBg9Xi5sKFC9y9e5d6\n9eplO29ux4FHo2deXl58/fXXuLq6UqVKlXxdj7e3NytWrKBFixaYmZll225hYcGJEydIT08nOjqa\nn376CQMDA/WtZENDQ27dukViYiLp6enZvuclr+tycnJi8+bN1KhRAxMTE/T19WnWrBlr165Vi+od\nO3bg5eWlFo1xcXHEx8fnmEchhChpHFvUJMDXgWXj3QjwdZBCTxQLKfae0KFDBy5fvqzewn3MycmJ\nixcvqs/rPTZq1Cjc3d0ZMmQI9vb2bNq0iaVLl1KlShWGDh2KnZ0d/fv3p3Xr1owaNQpfX1+6dOmS\n7by5Hecxb29v7t27l69buI+5urry4MGDHG/hAowdO5aLFy9ib29PYGAg/v7+eHt788UXX3DgwAG6\ndP7IZAQAACAASURBVOlCuXLlcHNzIyoqKtv3vOR1XY/z2qZNG3UfOzs7zp49q/4Z9OjRg759+zJ8\n+HCsra0ZMGAAnTt3ZtCgQfnOgxBCCFGWaRSZsOylcPToUT7++GP2799P+fLlizucEq8kPjxb2Erq\nQ8OlgeS28EhuC4fktfCU1NzKCxovuZs3bzJt2jTee+89KfSEEEII8Uyk2CvhlixZQrdu3bC1tWXw\n4MHFHY4QQgghXjIyz14JN2LECEaMGFHcYQghhBDiJSUje0IIIYQQpZgUeyWQh4cHP//8c6GeY/Dg\nwcycOfO597e0tGT//v0FGJEQQgghCoPcxn0O7u7uJCQkEBYWRsWKFbNs27FjB2PGjOGDDz7gww8/\nfK7j79y584Xiu3HjBt999x379+8nISEBExMTnJyc8PPzo0GDBi90bCGEEPkXGRNPaMRFrt26T53q\nxvRwbiBz7YkiJyN7z8nY2Jhdu3Zla9+2bRvVqlUrhogeiY+Pp1+/fsTFxbF69WqOHz/OTz/9hEaj\n4Y033uDSpUvFFpsQQpQlkTHxLNkaTezNFHSKQuzNFJZsjSYyJr64QxNljIzsPaeOHTuyZcsW+vTp\no7bduXOHo0eP0r59+yx9f/zxR9asWcPNmzepXr06I0aMoF+/fgAEBQXxzz//ULVqVfbu3ctff/1F\n165deffdd3nrrbfQ6XQsXbqUkJAQbt26RcOGDRk5ciRdu3bNMa558+ZRrVo1vvvuO3XdWgsLC/4f\ne/cel+P9P3D8dXdXkgidzHKI7du+yFkphGaKQpvDMstmIWfZiDC2corZlohsDjOMSUja0JbDaJlt\nJmFGoTuEiVbpePf7w889fUtC6S7v5+Ph8XB/ruv6XO/rXfLuuq7P57N48WLmz5/P9evXadLk3rqM\narWagIAAzVJuPj4+uLu7A5CcnMy8efM4ceIEarWajh078vHHH2Nubl7snJ6entjZ2XHu3DkOHz6M\nhYUFQUFB7Ny5k7CwMGrWrElAQADdu3cH4M8//2ThwoUkJCSgo6ODu7s7U6dORU9Pj/DwcFavXk2v\nXr3YtGkTERER3Lp1i4ULF3Lu3Dl0dXVxcHDA39+/zCuJCPG0vObto6BApiStCEqlotrm9nZGTont\nX0aeJuzAhQo9d3XOa2VZMs6hskN4YlLsPaFXX32VqVOnkpqaioXFvVvy3333HQ4ODhgYGGj2O378\nOIGBgWzbto3//ve/xMTEMH78eNq3b0+zZs0AiI+PZ+LEiSxevBilUlnkPJs3b2bjxo2sXr2al19+\nme3bt+Pj48Pu3bs1x9+nVqvZv38/M2bM0BR6D5o1a1aRz1FRUcybN4/p06ezcuVK/P396dOnDzVq\n1GD27NmYmZlx+PBhcnJyGDduHIGBgSxdurTEfHz77bcEBQWxcOFC3nnnHUaNGsXYsWM5cuQIH330\nEZ988gndu3fn7t27jBw5Eg8PD1avXs3NmzeZMGECy5Yt44MPPgDg5s2bKBQKjh07hq6uLiNHjsTV\n1ZWNGzeSmZnJ1KlTWbVqFb6+vg/9+tSrZ4iurvKh26ur0ibVFE9HqSz+b0qUj+qa2wJ1ycVWgbrw\nmVxzdc1rZXnw52tV+1krxd4Tql27Nj179iQiIoJRo0YB9x7hjhw5ssjj3Q4dOhAbG6u5C+Xk5ETN\nmjU5ffq0plhTKBQMGzYMHZ3iT9XDwsJ46623aNGiBQAeHh6sW7eOmJiYYsXerVu3yMjIwMrKqkzX\n0KZNG83dNjc3N0JCQrh27RpNmjQhNDQUAH19ffT19XFycmLLli0P7atdu3a0a9cOuLcM2o4dO/Dw\n8EChUODo6Mju3bsBOHDgAHl5eYwfPx6Ahg0bMmbMGPz9/TXFXkZGBqNGjdJMIJ2eno6BgQG6uroY\nGxsTGhpaYq4elJaWVaYcVCfaOqt7dbBmdm/JbQWpzt+3c9bEobqRWazd0swIfy/bCj13dc5rZbmf\nT23NbWkFqBR7T8Hd3Z1PPvmEUaNGoVKpuHjxIo6OjkWKvfz8fEJCQvj+++/5+++/AcjNzSU3N1ez\nT4MGDR5avCQnJ/PSSy8VabOysuLq1asPjUutVpcpfktLS83fa9SoAUBOzr3HDqdOneKzzz7j7Nmz\n5ObmolarNXcwS9KgQYMifZmbm2vuLtaoUUNzvcnJydy+fRsbG5tiMd/fx8jIqMgj2vfff5958+ax\nc+dOunbtipubG61bty7TNQohRGVxtW9KaERCCe1NKiEa8TyTARpPoWvXrqSlpXHmzBkiIyPp27cv\nurpF6+cVK1YQGRnJsmXL+OOPP4iPjy/2rtn/Prp9kEKhKPGR7IPF4n0mJiYYGxvz119/lSn+kvoF\nuHPnDqNHj6ZVq1bExMQQHx9f6iNToFix+rC+a9SogZWVFfHx8UX+JCQkoK+vDxTPx+DBgzlw4ABe\nXl6oVCo8PDzYuHFjma5RCCEqi10LC7z7t8TSzAiljgJLMyO8+7eU0bjimZNi7ykolUrc3NyIiooi\nKiqK/v37F9snPj4eJycnWrdujY6ODsnJyaSnp5f5HI0aNeL8+fNF2pKSkjSDLB6kUCjo3bs3GzZs\nID8/v9j2CRMm8O233z7ynImJiWRmZuLl5aUpTBMSiv92+iSaNGlCSkoKGRkZmrY7d+7wzz8PvyV+\n69Yt6tWrx8CBAwkJCWHcuHFs3bq1XOIRQoiKZNfCAn8vW77w7Ym/l60UeqJSSLH3lNzd3dmzZw95\neXklPlq0tLTk7NmzZGVlkZSUxKJFi7CwsCA1tWxD7wcNGsTmzZv5888/yc3N5euvv+batWv06dOn\nxP0nT55MdnY2I0aM4MKFCxQWFpKcnMy0adNISEjQvKNXmoYNG6Kjo8Pvv//O3bt32bp1K0lJSdy5\nc4fs7Owyxf0wXbt2xczMjAULFvDPP/9w69Ytpk2bRkBAQIn7X7t2DUdHR/bv309BQQEZGRmcO3eO\nxo0bP1UcQgghxPNCir2n9Morr1CnTh0GDBhQ4vYxY8ago6ODg4MDU6ZMYfTo0bz55pusXLmy1AEP\n93l4eDBgwADGjRuHvb09e/bsYcOGDTRs2LDE/c3MzNi2bRtWVlaMGDGCNm3aMHz4cGrVqsXWrVtL\nfe/uPgsLC3x9fZk7dy7du3fnwoULLFu2jLp169K7d+9HHl8aXV1dQkJCSE5O1rx/Z2Jiwpw5c0rc\nv0GDBixevJigoCDat29Pr169AB66vxBCCCGKUhQWFspEPKLa0caRUhVNW0eIVQeS24ojua0YkteK\no625LW00rtzZE0IIIYSoxqTYE0IIIYSoxqTYE0IIIYSoxqTYe87t3LkTR0fHyg6jiJCQEDw8PCo7\nDCGEEKJakAEaVYSTkxOpqamayYtNTEywtbXFy8sLa2vrSosrKSmJ4OBgjh07xj///EPt2rWxt7dn\n2rRpmJubV1pc2vjybEXT1peGqwPJbcWR3FYMyWvF0dbcygCNasLPz4/4+Hh+++031qxZg7m5OYMH\nD+bQoUOVEk9WVhbDhw+nfv367Nq1ixMnTvDNN99w69YtxowZUykxCSGENok7ncqcNXGMDIxhzpo4\n4k6XbY5VIcqTFHtVkJ6eHs2bN2fq1KmMGjWKDz/8kLy8PODe2rPe3t7Y2dnRqVMnxo4dy/Xr1zXH\nWltbs27dOrp160ZwcDDh4eHY2dlptl+4cIERI0Zga2tLjx49mD59+kNXt/jrr7+4fv06o0aNwsTE\nBIVCQaNGjViwYAEjR47ULOmWkJCAp6cnnTp1onPnzvj6+mpW0FCpVFhbW7Np0ybs7OwIDw8nODiY\nN954Q3OeI0eO4O7uTtu2benXrx8HDx4s95wKIUR5izudSmhEAqobmagLC1HdyCQ0IkEKPvHM6T56\nF6HNhg8fTkhICL/99ht2dnbMnj0bMzMzDh8+TE5ODuPGjSMwMJClS5dqjtm7dy/h4eGYmpqyY8cO\nTXtubi7vvfceffr0ISQkhNu3bzN27FgCAgJYvHhxsXM3atQIfX19VqxYgY+PD/Xr1wfuTcrct29f\nzX4+Pj44Ozuzfv160tLSGD58OF988QVTpkzR7BMbG0t0dDRGRkYsX75c056amsqECRPw9/fHxcWF\nvXv3MnHiRPbt20eDBg3KNZdCVJRpIUcrOwStpVQqKCionm8T3c7IKbH9y8jThB24UKHnrs55rWhL\nxjlUdgjlToq9Ks7Y2BgTExOSk5Oxs7MjNDQUAH19ffT19XFyciq2UkefPn0wMzMr1tehQ4dIT0/H\nx8cHAwMDatasiZeX10NXq6hfvz6LFy8mICCAsLAwXnnlFWxtbenVqxcdO3bU7Ldz50709PRQKpWY\nmpri4ODAqVOnivTl7u5O7drF3zf47rvvePHFF+nXrx8Abm5u6OjoaN5dfJh69QzR1VWWuk91VNo7\nG+LpPE1ulUpFOUZS/VTX/BSoSy62CtSFz+Saq2teK1pZ/q1XtZ+1UuxVA/n5+SiV9wqbU6dO8dln\nn3H27Flyc3NRq9XFlkh78cUXS+xHpVJhaWmJgYGBpq1Zs2ZkZWVx+/Zt6tatW+yYPn360KtXL44f\nP86xY8eIjY1l/fr19O7dm6CgIBQKBbGxsYSEhJCUlER+fj4FBQV06NChTDFdvny52LYH7xo+TFpa\n1iP3qW609aXh6uBpc7vI274co6leqvP37Zw1cahuZBZrtzQzwt/LtkLPXZ3zWtEelTdtza0M0KjG\nrl69SlpaGs2bN+fOnTuMHj2aVq1aERMTQ3x8PL6+vsWOuV8YlkShKPk3wfvvBJZET08Pe3t7Jk+e\nzJYtW/jiiy/Yu3cvv/zyCxcuXGDy5Mm4ublx9OhR4uPjefvtt8sck0KhQK1WP/TcQgihrVztmz6k\nvcmzDUQ896TYq+KWL1+OlZUVrVq1IjExkczMTLy8vKhTpw5wb3BEWTVq1AiVSkVOzr/vmSQmJlKr\nVi1MTEyK7R8dHc3atWuLtXfu3Bk9PT0yMjI4c+YMSqWSESNGULNmzSeKKSkpqUjbli1buHChYt93\nEUKIp2XXwgLv/i2xNDNCqaPA0swI7/4tsWth8eiDhShHUuxVUdevX2fu3Lns2bOHefPmoaOjQ8OG\nDdHR0eH333/n7t27bN26laSkJO7cuUN2dvYj++zWrRt16tTh888/Jzc3F5VKxerVq3F3dy/xHbla\ntWrx6aefsn79em7fvg3AjRs3WLx4MbVq1aJDhw40atSI3NxcTp06RUZGBsuXL+fu3bvcuHGDgoKC\nR8bk5ubG9evX2bRpE7m5uURHR7Nw4UJq1Kjx+EkTQohnzK6FBf5etnzh2xN/L1sp9ESlkGKvClm4\ncCE2Nja0atWKfv36kZaWxpYtWzSDISwsLPD19WXu3Ll0796dCxcusGzZMurWrUvv3r0f2b++vj7B\nwcHEx8fj4OCAp6cn3bp1Y8aMGSXub29vz8qVKzl48CAuLi60atWK/v37k5qayjfffIOxsTFt2rTh\n3XffZcSIETg7O6Onp8eCBQtIT08v8XHu/zI1NWXdunV88803dOrUiaCgIJYtW4alpeXjJU8IIYR4\nTskKGqJa0saXZyuatr40XB1IbiuO5LZiSF4rjrbmtlwGaMyaNatcghFCCCGEEM9OmYu948ePc/ny\n5YqMRQghhBBClLMyz7M3YMAAxo4dS7du3WjYsGGxqTKGDRtW7sEJIYQQQoinU+ZiLywsDIB9+/YV\n26ZQKKTYE0IIIYTQQmUu9n788ceKjEM8hfDwcAIDA4mLi6vsUMokODiYmJgYwsPDKzsUIYQQotp7\nrKlX0tPT+fbbb1m2bJmm7eLFi+Udk1ZycnKiZcuW2NjYYGNjQ48ePfD19eXPP/98ov527NiBtbV1\nkVxqm44dO9KqVSusra05d+5cZYcjhBBCiCdQ5mLv5MmTdO/enY0bN/LFF18AkJKSwuuvv86BAwcq\nKj6t4ufnR3x8PL/99htr1qzB3NycwYMHc+jQocfua9u2bbi4uBAeHq61y4EdP36c77//vrLDEEKI\nKinudCpz1sQxMjCGOWviiDudWtkhiedUmYu9jz76iJkzZxIREaFZP/XFF1/kk08+ISgoqMIC1EZ6\neno0b96cqVOnMmrUKD788EPN2rF37txh2rRpdO3alXbt2jFmzBhu3rxZ5PjExEROnjzJ7Nmzyc7O\n5siRI0W2e3p6smrVKnx9fWnfvj2Ojo5ERUVptp88eZIBAwbQtm1b3nnnHW7cuKHZplKpsLa2ZtOm\nTdjZ2Wkele7duxd3d3fatm2Lk5MT27dvf6Jrz83NZdGiRfTs2ZNOnTrx1ltvcfz4cc12JycnVqxY\nQe/evfHz8wPgwIEDuLi40K5dOyZNmkRWVlaRPvfs2UO/fv1o164d3bt3Z9WqVZpt4eHh9OvXj507\nd9KzZ0/at2/P1KlTy7T6hhBCVJa406mERiSgupGJurAQ1Y1MQiMSpOATlaLM7+wlJibyxhtvAGiK\nPYCePXsyderU8o+sihg+fDghISH89ttv2NnZ4efnR2FhIbt370ZPT4/58+czfvx4tm7dqjlm27Zt\nODo6YmZmhqurK2FhYXTr1q1Iv5s2bWLBggXMnz+foKAgPv74Y/r06YNarWbSpEk4Ozvz7bffcu7c\nOSZNmlQsrtjYWKKjozEyMuLUqVNMnz6doKAgunbtysmTJxk1ahTm5ubFzvson332GYcPH+arr76i\nQYMGrFixgjFjxvDDDz9gbGwMQGRkJKGhoTRt2pT09HR8fHzw8fHhrbfe4pdffmHKlCmaFTBUKhXT\npk0jJCSEHj16cPLkSd566y1sbGzo0qULAFeuXCE+Pp49e/Zw6dIlBg0aRJ8+fXj11VcfK3YhysO0\nkKOVHUK1olQqKCiofnP7387IKbH9y8jThB2o+LW9q2teK9uScQ6VHcITKXOxZ25ujkqlokmTJkXa\nf//9d2rXfviszdWdsbExJiYmJCcn8/LLL/PDDz+we/du6tWrB4Cvry/29vYkJibSrFkz8vLy2Llz\nJx999BFwb0qbt956i1u3blG/fn1Nv61bt9YUYr179+aLL77g77//JiUlhatXrzJ27Fhq1KiBjY2N\n5nHwg9zd3TVfl+3bt+Po6Ej37t0BaNeuHe7u7uzYseOxi72wsDBmz55N48aNARg/fjxff/01sbGx\nuLi4APfW2LWysgLgp59+Ql9fH09PT5RKJV26dKFz586oVCoALC0tiY2N1RSKrVu3xsrKilOnTmmK\nvYyMDCZPnoyhoSH//e9/adKkCRcuXCi12KtXzxBdXeVDt1dXpc2gLp7O/dwqlYpH7CkeV3XMaYG6\n5EKrQF34zK63Oua1st3/OVDVftaWudjr378/o0ePZvjw4ajVar7//nvOnj3LN998w/DhwysyRq2X\nn5+PUqnUTDo9cODAItuVSiVXr16lWbNmREdHk5+fT8+ePYF7xU2jRo2IiIjg3Xff1Rzz4NqvBgYG\nAGRnZ3Pt2jUMDQ2pW7euZvv9wupBL774oubvly9fJjY2FhsbG01bYWEhrVu3fqzrvHPnDunp6bz0\n0kuaNn19fV588UWuXr2qaWvYsKHm79euXcPc3LzIvIxWVlaaYg9gy5YthIWFkZqaSmFhIXl5eeTm\n5mq2GxsbU6dOHc1nAwMDcnJK/q35vrS0rFK3V0fauoRPdfBgbhd521dyNNVLdf2+nbMmDtWNzGLt\nlmZG+HvZVvj5q2teK9uNG/9obW5LK0DLXOyNHz8eIyMjvvnmGxQKBXPmzKFx48b4+voWK26eJ1ev\nXiUtLY3mzZujr68PQExMDKampiXuHxYWRkZGBnZ2dpq23NxcwsLCihR7Ojolv075YBF0X0mFz4PF\nlYGBAYMHD+bjjz8u0zWV5MFH9w/+/b777ywC6Or++231qHi3bdvGqlWrCA4OpnPnzujq6uLu7v7Q\ncwshRFXgat+U0IiEEtqblLC3EBWrzMVeQkIC7777bpGCRMDy5cuxsrKiVatWZGVloVQq+fPPPzXF\nnlqt5tq1azRs2JCUlBSOHj3K8uXLi9wdS0tLY+jQofzxxx+0adOm1POZm5uTlZXF7du3NXf3Ll26\nVOoxjRs35vfffy/SlpqaSv369dHT0yvS/tNPP3Hw4EHNWsgZGRkAmJiYYGxsjLGxMefPn6dFixbA\nvWIuJSVF81i3pHivX7+OWq3WFLAPTtcTHx9P+/bt6dq1q+Z8j7oeIYTQdnYtLADYE3uJq39n8oJJ\nLVztm2jahXiWyjwa980336RPnz6sWrWKK1euVGRMVcL169eZO3cue/bsYd68eejo6GBkZISbmxtL\nly4lJSWFnJwcgoOD8fT0pKCggLCwMJo3b86rr75KkyZNNH/atm2Lg4ODZpWS0rRp04a6deuyevVq\ncnNzOXHiBNHR0aUeM2TIEE6ePMnWrVvJzc3l/PnzDB06lF27dhXbt06dOmzatIno6Ghyc3PZuHEj\nNjY2mvcJBw0axBdffEFKSgrZ2dkEBQVRs2bNh7775+DgQFZWFps2bSI3N5eDBw/y22+/abZbWlqS\nlJREWloa165d48MPP+SFF14gNVVGrAkhqja7Fhb4e9nyhW9P/L1spdATlabMxd5PP/3Ee++9x6+/\n/oqzszPDhg1j69atpKenV2R8WmXhwoXY2NjQqlUr+vXrR1paGlu2bKFjx46afWbPnk3z5s0ZMGAA\nXbp04cSJE4SGhqJQKAgPD2fQoEEl9j1w4ED27NlTbFqS/2VgYMCKFSs4fPgwnTp1YunSpXh5eZV6\njJWVFZ999hlfffUVHTp0YPTo0QwZMqTEWFq3bs3HH3/MwoUL6dy5MykpKSxdulSzfeLEibRp04ah\nQ4fi6OjI2bNn+frrr6lVq1aJ527QoAFLly5lw4YN2Nra8u233/L2229rtg8dOpTmzZvj5OTEO++8\nw4ABAxg5ciSRkZF89tlnpV6XEEIIIR5NUVhY+Nhjs9PT04mJieG7777j+PHj2NvbM3jwYBwdHSsi\nRiEemza+PFvRtPWl4epAcltxJLcVQ/JacbQ1t6UN0His5dLuUyqVFBYWolAoyM/P59atW8yfP583\n3nhDMyJVCCGEEEJUvjIP0CgoKODQoUNEREQQExODmZkZAwYMYObMmTRq1IjCwkKCgoLw9fVly5Yt\nFRmzEEIIIYQoozIXe126dCE/P18zwW+nTp2KbFcoFEyYMIG1a9eWe5BCCCGEEOLJlLnY8/Pzw9nZ\nWTPB74MOHTqEo6Mjurq67N27t1wDFEIIIYQQT67M7+wNGDCA/Px8/vjjD3755RfNn8jISCZPnqzZ\n74UXXqiQQEX1ExISgoeHBwBxcXFYW1uTmXlvxnlra2tiYmIqMzwhhBCiWijznb0DBw4wZcoU7t69\ni0Kh4P4g3ho1ajBgwIAKC1CUzsnJidTUVM2Exfr6+rz88stMnDhRs7bso5w5c4a///5bM7Hx/35+\n3Hhu3brFkSNHik3HEhUVxZQpU5gwYQITJ05k3LhxjBs37rHPIYQoXdzpVPbEXuTKzSwamhriat9U\n5ngT4jlW5jt7S5cuZerUqfz888/o6elx/Phx1q1bR/fu3Rk5cmRFxigewc/Pj/j4eOLj4zly5Aiu\nrq54e3tz/vz5Mh0fFhbGkSNHHvr5cRkaGrJv375i7bt378bExOSJ+xVCPFrc6VRCIxJQ3chEXViI\n6kYmoREJxJ2WicqFeF6V+c6eSqVi2LBhwL3BGEZGRtjb21OnTh38/PzYtGlThQUpys7AwABPT0++\n/fZbYmJieOmll0hLS8Pf35+4uDhycnJo2bIlc+fOpXnz5sydO5etW7eio6PD3r176datW5HPnTt3\nJi0tjZUrV2rOsW/fPmbPns1PP/2kWQ/4Qd27d2fXrl28/vrrmrbbt29z/PjxIncbg4ODiYmJITw8\nvNRrOnjwIJ9++imXL1/GwMCA3r17M2vWrBLPLZ7OtJCjlR2CVlIqFRQUPPaUpJXidkbxtbIBvow8\nTdiBC884mkerSrmtSp4kr0vGOVRQNKKylbnYq1evHlevXuWFF16gdu3aXLp0iSZNmvCf//yH06dP\nV2SM4gkUFBSgq3vvy7tkyRJu3rzJ/v370dXVZebMmcyaNYstW7bw8ccfk5iYSKtWrZg+fTpAkc/H\njx/n3XffJS0tjXr16gH3ij0XF5eHFluvvvoqU6dOJTU1FQuLe4+OvvvuOxwcHEoc4FOavLw8fHx8\nmDlzJoMGDeL69euMHTuWbdu2aX75KEm9eobo6iof61zVQWmTapaFUqkop0iqn6qSmwJ1yf/BF6gL\ntfYatDWuqu5x8/q0Pz+eJ1UtV2Uu9vr168fAgQPZt28fjo6OTJgwgX79+nHq1CkaNWpUkTGKx5CV\nlcX27dtJSUmhV69eAHz00Ufk5+djaGgIgLOzM++//36Z+uvQoQMNGjQgKiqKYcOGkZuby4EDB1i1\natVDj6lduzY9e/YkIiKCUaNGAfce4Y4cObLEx7ulycnJITs7G0NDQxQKBRYWFoSFhWneUXyYtLTS\nl52rjspjVvdF3vblFE31oq0z5pdkzpo4VDcyi7Vbmhnh72VbCRGVrirltip5krzK16FstPV7tlxW\n0JgyZQrTp0+nVq1azJo1i1deeYXw8HDu3r3LkiVLyiVQ8WTur9lrY2ND9+7d2bt3L2vWrNEU4Zcu\nXWLixInY2trSqlUr3n//ffLy8srUt0KhwN3dnd27dwMQGxtLnTp16NChQ6nHubu7ExERAdx7BeDi\nxYtPtJyekZER48ePx9fXlzfeeINPP/2UpKSkx+5HiOeFq33Th7Q3ebaBCCG0Rpnv7AGaUbe1atWS\nAk+L+Pn58fbbb5e4Ta1W4+3tTdu2bYmKisLU1JTo6GjGjx9f5v4HDBjA8uXLSU5OZu/evfTr1w+F\novTHA127dmXWrFmcOXOGgwcP0rdvX81j5cc1YcIEBg8eTHR0NNHR0axZs4agoCDNnUshxL/uGrOG\niQAAIABJREFUj7rdE3uJq39n8oJJLVztm8hoXCGeY6X+77t48eIyd+Tr6/vUwYjyd/PmTVJSUli6\ndCmmpqYAJCQkPFYfjRo1omPHjnz33XdER0fzzTffPPIYpVKJm5sbUVFRHDx4kHnz5j1R/ABpaWlY\nWFgwbNgwhg0bhp+fH2FhYVLsCfEQdi0spLgTQmiUWuzFx8eXqZNH3eURlad+/foYGhpy4sQJWrZs\nSUxMDL/88guAZgBFjRo1UKlUpKenU7t27WKf7z/KXbRoEY0bN6Z58+ZlOre7uzvjxo2jRo0atG7d\n+oni//333/Hy8mL16tV06NCBtLQ0kpKSnrg/IYQQ4nlTarH39ddfA3DhwgViYmLQ1dWlV69eWFpa\nPpPgxNPT1dUlICCAwMBAgoODcXJyYtmyZXh5eeHq6sr+/ft54403mD17Nq+99hqHDx8u9llfXx8X\nFxcCAgIeawLtV155hTp16uDi4vLE8bdr1473338fPz8/UlNTqV27Nt27d2fSpElP3KcQQgjxPFEU\n3l8K4yGOHj3KmDFjaNq0KQUFBVy5coW1a9fSrl27ZxWj0AIqlYp+/frx448/aqZg0WbaOFKqomnr\nCLHqQHJbcSS3FUPyWnG0NbdPNRo3ODgYX19fIiIi2LNnD++//z6ffvppuQYotNs///zD3LlzGThw\nYJUo9IQQQgjxr0cWe+fPn2fIkCGaz4MGDeLcuXMVGpTQHrt376Zbt27UqVOnzHPzCSGEEEJ7PHIu\njNzc3CIrJdSsWZPs7OwKDUpoj379+tGvX7/KDkMIIYQQT6jMkyqLquGXX37BxsaGrCztXEEiPDwc\nOzu7yg5DCCGEeG488s5eQUEBmzdv5sFxHCW1lbZOqfiXk5MTqampmuW+TExMsLW1xcvLC2tr66fu\nv1OnTmWeMud/xcXFMXz4cM2dXKVSiZmZGX379mXSpEkolc/fWrNCCCFEVffIYs/c3Jwvv/yy1DaF\nQiHF3mO4v+JFXl4ely9fZseOHQwePJjly5c/0ZJi5e3nn3+mVq1aqNVqTp06xahRozAzM3voKh1C\nCO0SdzqVPbEXuXIzi4amhrjaN5VJloV4jj2y2Pvxxx+fRRzPJT09PZo3b87UqVOpUaMGH374IdHR\n0ejp6XHnzh3mzZtHbGwsmZmZ2NnZMW/ePOrXr4+joyOTJ09m8ODBmr4++OADCgsLefPNNxk+fDi/\n/fYbtWrVwtrammXLlrF+/XrOnDlD48aNWbJkSZnuIuro6NC6dWtsbGyKrEd74cIF5s2bR0JCAoaG\nhtjZ2TF79mxq17437Pv3338nMDCQv/76i3r16tGjRw98fX2LvPt5X2xsLBMmTGDdunW0bt2aY8eO\n8emnn3Lu3DkMDQ0ZPnw4o0ePBu6NDD9x4gR169blhx9+4Ndff5W7jUL8j7jTqYRG/LtKjupGpuaz\nFHxCPJ+ebLFSUe6GDx9OSEgIv/32G3Z2dvj5+VFYWMju3bvR09Nj/vz5jB8/nq1bt9K7d29++OEH\nTbGXm5vLwYMHCQwMLLHvNWvWEBgYiIWFBd7e3gQHB7N8+fJHxpSXl8evv/5KfHw83t7emnO99957\n9OnTh5CQEG7fvs3YsWMJCAhg8eLF/P3334wYMQIfHx82bNjA5cuXGTlyJLVr12by5MlF+k9MTMTH\nx4fAwEBat27NtWvX8Pb2ZtasWbi7u3Px4kVGjx5NnTp18PDwAO6t6jJx4kQWL14shd4zNi3kaGWH\nUGmUSgUFBaVOSao1bmfklNj+ZeRpwg5ceMbRPFpVym1VUlpel4xzeMbRiMomxZ6WMDY2xsTEhOTk\nZF5++WV++OEHdu/erZnXztfXF3t7exITE+nTpw9eXl5kZWVhaGhIbGwsCoWCbt268fvvvxfr29XV\nFSsrKwAcHR0JDw8vNZbOnTsD997NLCwsZNSoUXTo0AGAQ4cOkZ6ejo+PDwYGBtSsWRMvLy/mzJkD\nQGRkJObm5rz77rsAvPTSS3h4eBAZGVmk2LtfJE6YMEGzxm1kZCRWVlYMGjRIc6ynpyc7duzQFHv3\nXxm4/87jw9SrZ4iu7vNXDJY2qebTUiqf72URq8r1F6hL/g++QF2otdegrXFVdQ/La0X+nHheVLUc\nSrGnRfLz81EqlVy+fBmAgQMHFtmuVCq5evUq9vb2GBsbc/jwYZydndm3bx+vvfZaiY9JgSLL29Ws\nWZOcnJJ/87/vwXf2Ll26xJw5c5g2bRpLly5FpVJhaWmJgYGBZv9mzZqRlZXF7du3SU5OplmzZkX6\na9asGVeuXNF8VqvVTJo0iVq1auHp6alpv3z5MmfOnMHGxkbTVlhYiKmpqeZzgwYNHlnoAaSlaedo\n5IpU0bO6L/K2r7C+tZ22zphfkjlr4lDdyCzWbmlmhL+XbSVEVLqqlNuqpLS8Sr6fjrZ+zz7VChri\n2bh69SppaWk0b95cU0jFxMQQHx+v+ZOQkECXLl3Q0dHB2dmZ6OhoCgoK+PHHH3F1dX1o32Upjh52\nnJWVFVOnTiUyMpJbt24B9+6ulSQvL++h2+9vA0hPT6du3bpcunSJqKgoTbuBgQFdunQpcs2nTp3i\nwIEDmn3k0a0QpXO1b/qQ9ibPNhAhhNaQYk9LLF++HCsrK1q1aoWlpSVKpZI///xTs12tVhe5O+bi\n4sKhQ4c4duwYCoVC8+i1ImVnZ9OoUSNUKlWRu4OJiYnUqlULExMTGjduTGJiYpHjEhMTadLk3/9o\njI2NCQoKws/Pj48++ojU1FQAmjRpwl9//YVardbs+/fff8sk3kI8BrsWFnj3b4mlmRFKHQWWZkZ4\n928pgzOEeI5JsVfJrl+/zty5c9mzZw/z5s1DR0cHIyMj3NzcWLp0KSkpKeTk5BAcHIynpycFBQUA\ndOjQAQMDA5YvX46Li0uF3fFKTU0lODgYW1tbGjZsqFk67fPPPyc3NxeVSsXq1atxd3dHR0cHNzc3\nrl+/zoYNG8jLy+Ps2bNs3ryZ119/XdOnQqFAoVAwaNAg2rdvz8yZMwFwc3MjIyOD4OBg7t69y5Ur\nVxg1ahShoaEVcm1CVFd2LSzw97LlC9+e+HvZSqEnxHNOir1KsHDhQmxsbGjVqhX9+vUjLS2NLVu2\n0LFjR80+s2fPpnnz5gwYMIAuXbpw4sQJQkNDNUWdQqHA2dmZ48eP07dv33KNr3PnztjY2GBjY8PA\ngQN54YUXWLZsGQD6+voEBwcTHx+Pg4MDnp6edOvWjRkzZgBQv359li1bRkREBHZ2dkyaNIm3336b\nESNGlHiugIAAEhIS2LRpE8bGxqxcuZJDhw5hZ2fHm2++SadOnRg3bly5Xp8QQgjxPFEUPrgMhhDV\nhDa+PFvRtPWl4epAcltxJLcVQ/JacbQ1tzJAQwghhBDiOSXFnhBCCCFENSbFnhBCCCFENSbFnhBC\nCCFENSbFnqhSZsyYwaRJkyo7DCGEEKLKkOXSqignJydSU1M1q2Po6+vz8ssvM3HiRLp06VJh542N\njWXNmjWcPHmSnJwcTExM6NGjB+PHj8fExKTCziuEKF3c6VT2xF7kys0sGpoa4mrfVObXE0IAcmev\nSvPz89MsK3bkyBFcXV3x9vbm/PnzFXK+bdu2MWbMGHr27ElMTAy//vorwcHB/PXXXwwZMoSMjIwK\nOa8QonRxp1MJjUhAdSMTdWEhqhuZhEYkEHc6tbJDE0JoAbmzV00YGBjg6enJt99+S0xMDC+99BJp\naWn4+/sTFxdHTk4OLVu2ZO7cuTRv3hwAa2trVq1aRc+ePQEIDw8nMDCQuLi4Yv2np6ezYMECZsyY\nwdChQzXtLVu2ZOXKlXz99ddkZWVhZGQEwIYNG9i4cSM3btzA1NQUb29vBg0aBEBSUhL+/v7Ex8cD\n0KZNGwICAmjYsCFwr6hct24dV69exdLSkmHDhuHh4VFxyRMPNS3kaGWHoBWUSgUFBdo7JentjJwS\n27+MPE3YgQvPOJrHo+25rYqWjHOo7BCElpFir5opKChAV/fel3XJkiXcvHmT/fv3o6ury8yZM5k1\naxZbtmx57H5/+ukn8vPzGThwYLFtRkZGjB07VvP5+PHjBAYGsm3bNv773/8SExPD+PHjad++Pc2a\nNSMgIIAXXniBVatWUVBQwPz58wkMDCQoKIiYmBgWLFjAypUr6dixI4cPH2bcuHE0adIEe3v7Msdb\nr54huroVs4ScNittUs0noVQqyrW/qkybc1GgLrlYKlAXanXc91WFGKuS+z8HyvvngfhXVcutFHvV\nRFZWFtu3byclJYVevXoB8NFHH5Gfn4+hoSEAzs7OvP/++0/Uv0qlomHDhujr6z9y3w4dOhAbG0ud\nOnWAe+8X1qxZk9OnT9OsWTPS09Np1KgR+vr6KBQKAgICNO8ehoWF0bdvXzp37gxAz549sbe3Z//+\n/Y9V7KWlZT3BVVZtFTGr+yLvsue8OtPWGfPvm7MmDtWNzGLtlmZG+HvZVkJEZaftua2Kbtz4R/Ja\ngbQ1t6UVoFLsVWELFy4kMDAQuPcY19ramjVr1tCoUSMALl26xKJFi4iPjycr617xk5eX98Tny8/P\nL/J59erVBAcHA1BYWEj//v1ZsGAB+fn5hISE8P333/P3338DkJubS25uLgATJkxg2rRpHD58mK5d\nu9KnTx9NIZecnFxkjWCAZs2aoVKpnjhuIao7V/umhEYklNDepBKiEUJoGyn2qjA/Pz/efvvtErep\n1Wq8vb1p27YtUVFRmJqaEh0dzfjx4x/aX0FBwUO3NWvWjGvXrpGVlaW5Uzh69GhGjx4N3JsSRa1W\nA7BixQoiIyMJCQmhVatW6Ojo0KlTJ01fPXr0ICYmhoMHD/Ljjz/i7e3NsGHDmD59OgAKRfFHOk9T\npApR3d0fdbsn9hJX/87kBZNauNo3kdG4QghAir1q6+bNm6SkpLB06VJMTU0BSEgo+pu/vr4+2dnZ\nms/JyckP7c/BwQEjIyM2bNjAmDFjim1Xq9WaR7Hx8fE4OTnRunVrTb/p6emafW/dukX9+vVxdXXF\n1dWVHTt24O/vz/Tp02ncuHGx0cSJiYk0bdr08RIgxHPGroWFFHdCiBLJ1CvVVP369TE0NOTEiRPk\n5uayd+9efvnlFwBSU+9Nx9C0aVOio6PJy8vjzJkz/PDDDw/tz9DQkLlz57J8+XJWrFjBnTt3KCws\nRKVS8fnnnxMVFYWNjQ0AlpaWnD17lqysLJKSkli0aBEWFhakpqaSnZ2Ns7MzmzZtIjc3l5ycHBIS\nEmjS5N7jpsGDB7Nnzx6OHz9Ofn4++/fv5+eff8bd3b2CMyaEEEJUT1LsVVO6uroEBASwdu1aOnfu\nzP79+1m2bBktWrTA1dWVtLQ0Zs6cycmTJ+nYsSNLlixh5MiRpfbZt29f1q9fz4kTJ3jttddo06YN\nw4YNIzk5ma+//pphw4YBMGbMGHR0dHBwcGDKlCmMHj2aN998k5UrV7Jz506Cg4MJDw/H1taWbt26\nkZSUxNKlSwHo3r07EydOZNasWXTq1ImQkBBCQkI0dwmFEEII8XgUhYWFMsGRqHa0caRURdPWEWLV\ngeS24khuK4bkteJoa25LG40rd/aEEEIIIaoxKfaEEEIIIaoxKfaEEEIIIaoxKfa01HvvvacZtCCE\nEEII8aSk2HsMTk5ObNy4sVh7eHg4dnZ25XqutWvX8sEHH5Rrn2Xh5OREy5YtsbGxoXXr1jg4ODB+\n/HguXrz4zGMRQgghxNOTYk8U4+fnR3x8PCdPnmT37t0AT7ymrhCiYsWdTmXOmjhGBsYwZ00ccadT\nKzskIYSWkWKvAiQkJODp6UmnTp3o3Lkzvr6+ZGRkAKBSqbC2tmbTpk3Y2dkRHh5OeHg4Li4ufPLJ\nJ7Rr147k5GQ8PT01694mJSUxYsQIOnbsSMeOHfHy8uLKlSua823bto2+ffvSrl07+vXrx5YtWzTb\nZsyYgb+/P4sWLcLW1hZ7e3vWr19f5msxMTHB1dWVpKQkTVtaWhpTpkzBwcGBDh06MHz4cC5cuKDZ\n7uTkxIoVK+jduzd+fn6aaz5y5Aju7u60bduWoUOHcu3aNc0xe/fu1WxzcnJi+/b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IAAAg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15b94512b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plot_latent_params(\n",
    "    top_bot_irt_df[top_bot_irt_df['param'] == 'θ']\n",
    "                  .sort_values('mean')\n",
    ")\n",
    "ax.set_xlabel(r\"$\\hat{\\theta}$\");\n",
    "ax.set_title(\"Top and bottom ten\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The top ten players in terms of committing skill include many defensive standouts (Danny Green &mdash; twice, Gordon Hayward, Paul George).\n",
    "\n",
    "The bottom ten players include many that are known to be defensively challenged (Ricky Rubio and James Harden).  Dwight Howard was, at one point, a fierce defender of the rim, but was well past his prime in 2015, when our data set begins.  Chris Paul's presence in the bottom is somewhat surprising."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AxMSE3NzcEmMVQogXkZ97M60xXH+1W1dCNOJ59EIVXFevXiUjI4PmzZtz584dRo8eTf/+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\nJeTHaeQJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15b039a940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plot_latent_params(\n",
    "    top_bot_irt_df[top_bot_irt_df['param'] == 'b']\n",
    "                  .sort_values('mean')\n",
    ")\n",
    "ax.set_xlabel(r\"$\\hat{b}$\");\n",
    "ax.set_title(