02_nfl_field_goals_log_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The watermark extension is already loaded. To reload it, use:\n",
      "  %reload_ext watermark\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "\n",
    "from sklearn import preprocessing\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn import metrics\n",
    "\n",
    "import pymc3 as pm\n",
    "import theano.tensor as tt\n",
    "\n",
    "from matplotlib import pylab as plt\n",
    "import seaborn as sns\n",
    "\n",
    "plt.style.use(\"bmh\")\n",
    "\n",
    "import arviz as az\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sklearn          0.22\n",
      "pandas           0.25.2\n",
      "numpy            1.17.3\n",
      "theano           1.0.4\n",
      "matplotlib.pylab 1.17.3\n",
      "seaborn          0.9.0\n",
      "scipy            1.3.1\n",
      "pymc3            3.8\n",
      "arviz            0.6.0\n",
      "last updated: 2019-12-27 10:15:34 PST \n",
      "\n",
      "CPython 3.7.4\n",
      "IPython 7.9.0\n",
      "Git repo: git@github.com:clausherther/nfl-analysis.git\n"
     ]
    }
   ],
   "source": [
    "%watermark -v -d -t -z -u -r -iv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_hdf(\"data/field_goals.hd5\", \"field_goals\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['game_date', 'season_nbr', 'season_type_code', 'season_code', 'game_id',\n",
       "       'play_id', 'quarter', 'home_team_code', 'away_team_code',\n",
       "       'off_team_code', 'def_team_code', 'down', 'play_type', 'yards_to_go',\n",
       "       'yardline_100', 'kicker_player_id', 'kicker_player_name',\n",
       "       'is_within_goal_line', 'field_goal_result', 'is_field_goal_success',\n",
       "       'field_goals', 'successful_field_goals'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Baseline Field Goal % is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8338611090654687"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"successful_field_goals\"].sum()/df[\"field_goals\"].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale(x):\n",
    "    return (x-x.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [],
   "source": [
    "yards_cutoff = 47\n",
    "df_train = df.query(f\"yardline_100 < {yards_cutoff}\").copy()[\n",
    "    [\"yardline_100\", \"yards_to_go\", \"quarter\", \"season_type_code\", \"is_field_goal_success\", \"field_goals\", \"successful_field_goals\"]\n",
    "]\n",
    "df_train.loc[:, \"yardline_100_2\"] = np.power(df_train[\"yardline_100\"], 2)\n",
    "df_train.loc[:, \"is_fourth_quarter\"] = df_train[\"quarter\"].apply(lambda x: True if x == 4 else False)\n",
    "df_train = pd.get_dummies(df_train, columns=[\"season_type_code\"], )\n",
    "\n",
    "feature_columns = [\"yardline_100\"]#, \"yards_to_go\", \"is_fourth_quarter\", \"season_type_code_POST\", \"season_type_code_PRE\"]\n",
    "\n",
    "X = df_train[feature_columns].values\n",
    "\n",
    "y = df_train[\"successful_field_goals\"].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "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>yardline_100</th>\n",
       "      <th>yards_to_go</th>\n",
       "      <th>quarter</th>\n",
       "      <th>is_field_goal_success</th>\n",
       "      <th>field_goals</th>\n",
       "      <th>successful_field_goals</th>\n",
       "      <th>yardline_100_2</th>\n",
       "      <th>is_fourth_quarter</th>\n",
       "      <th>season_type_code_POST</th>\n",
       "      <th>season_type_code_PRE</th>\n",
       "      <th>season_type_code_REG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>29</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>841</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>34</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1156</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>32</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1024</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>121</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13574</th>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13575</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>36</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13576</th>\n",
       "      <td>14</td>\n",
       "      <td>12</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>196</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13577</th>\n",
       "      <td>28</td>\n",
       "      <td>16</td>\n",
       "      <td>2</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>784</td>\n",
       "      <td>False</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13578</th>\n",
       "      <td>16</td>\n",
       "      <td>13</td>\n",
       "      <td>4</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>256</td>\n",
       "      <td>True</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13565 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       yardline_100  yards_to_go  quarter  is_field_goal_success  field_goals  \\\n",
       "0                 2            2        2                   True            1   \n",
       "1                29            7        2                   True            1   \n",
       "2                34            9        3                   True            1   \n",
       "3                32            3        2                   True            1   \n",
       "4                11           10        2                   True            1   \n",
       "...             ...          ...      ...                    ...          ...   \n",
       "13574            10            9        1                   True            1   \n",
       "13575             6            6        2                   True            1   \n",
       "13576            14           12        2                   True            1   \n",
       "13577            28           16        2                   True            1   \n",
       "13578            16           13        4                   True            1   \n",
       "\n",
       "       successful_field_goals  yardline_100_2  is_fourth_quarter  \\\n",
       "0                           1               4              False   \n",
       "1                           1             841              False   \n",
       "2                           1            1156              False   \n",
       "3                           1            1024              False   \n",
       "4                           1             121              False   \n",
       "...                       ...             ...                ...   \n",
       "13574                       1             100              False   \n",
       "13575                       1              36              False   \n",
       "13576                       1             196              False   \n",
       "13577                       1             784              False   \n",
       "13578                       1             256               True   \n",
       "\n",
       "       season_type_code_POST  season_type_code_PRE  season_type_code_REG  \n",
       "0                          0                     1                     0  \n",
       "1                          0                     1                     0  \n",
       "2                          0                     1                     0  \n",
       "3                          0                     1                     0  \n",
       "4                          0                     1                     0  \n",
       "...                      ...                   ...                   ...  \n",
       "13574                      0                     0                     1  \n",
       "13575                      0                     0                     1  \n",
       "13576                      0                     0                     1  \n",
       "13577                      0                     0                     1  \n",
       "13578                      0                     0                     1  \n",
       "\n",
       "[13565 rows x 11 columns]"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((13565, 1), (13565,))"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline, make_pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(1, include_bias=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = LogisticRegression(random_state=SEED).fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipeline = make_pipeline(poly, clf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('polynomialfeatures',\n",
       "                 PolynomialFeatures(degree=1, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('logisticregression',\n",
       "                 LogisticRegression(C=1.0, class_weight=None, dual=False,\n",
       "                                    fit_intercept=True, intercept_scaling=1,\n",
       "                                    l1_ratio=None, max_iter=100,\n",
       "                                    multi_class='auto', n_jobs=None,\n",
       "                                    penalty='l2', random_state=42,\n",
       "                                    solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                                    warm_start=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipeline.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.00638754]), array([[-0.10327504]]))"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.intercept_, clf.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8371544415775893"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipeline.score(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = pipeline.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9834131957242904"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(y_pred)/len(y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.18037063966256306"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.r2_score(y, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "metrics.plot_roc_curve(pipeline, X, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "metrics.plot_confusion_matrix(pipeline, X, y, values_format=\":,\", normalize=\"all\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y_pred_proba = pipeline.predict_proba(X)[:, 1]\n",
    "# threshold_list = [0.5,0.55,0.6,0.65,.7,.75,.8,.85,.9,.95]\n",
    "\n",
    "# _, axes = plt.subplots(3, 4, figsize=(18, 14))\n",
    "# axes = axes.flatten()\n",
    "# for i, t in enumerate(threshold_list):\n",
    "#     ax = axes[i]\n",
    "#     y_pred_ = np.array([1 if y > t else 0 for y in y_pred_proba])\n",
    "#     test_accuracy = metrics.accuracy_score(y, y_pred_)\n",
    "#     cfm = metrics.confusion_matrix(y, y_pred_, normalize=\"all\")\n",
    "#     sns.heatmap(cfm, cmap=\"GnBu\", annot=True, cbar=False, ax=ax)\n",
    "#     ax.set_title(f\"T: {t:.2} A: {test_accuracy:.2%}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train.loc[:, \"y_pred\"] = y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "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>yardline_100</th>\n",
       "      <th>field_goals_success_percent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.992337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.980132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.981308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.983914</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   yardline_100  field_goals_success_percent\n",
       "0             1                     1.000000\n",
       "1             2                     0.992337\n",
       "2             3                     0.980132\n",
       "3             4                     0.981308\n",
       "4             5                     0.983914"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_grp_train = pd.DataFrame(\n",
    "    df_train\n",
    "     .groupby(\"yardline_100\")[[\"field_goals\", \"successful_field_goals\"]]\n",
    "     .sum()\n",
    "     .apply(lambda x: x[\"successful_field_goals\"]/x[\"field_goals\"], axis=1)\n",
    "     .reset_index()\n",
    ")\n",
    "df_grp_train.columns = [\"yardline_100\", \"field_goals_success_percent\"]\n",
    "df_grp_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_yards = df_grp_train[\"yardline_100\"].values\n",
    "y_probs = df_grp_train[\"field_goals_success_percent\"].values\n",
    "# x_yards, y_probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(46, 2)"
      ]
     },
     "execution_count": 272,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred_prob = pipeline.predict_proba(x_yards.reshape(-1, 1))\n",
    "y_pred_prob.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'plt' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-dc88a1f57030>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0m_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_yards\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_probs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"observed\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m# ax.plot(\"yardline_100\", \"field_goals_success_percent\", data=df_grp_train, label=\"prediction\", color=\"red\", linestyle=\"dashed\")\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_yards\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred_prob\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"prediction\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"red\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinestyle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"dotted\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;31m# ax = df_.plot.scatter(x=\"yardline_100\", y=\"field_goals_success_percent\", figsize=(15, 8))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'plt' is not defined"
     ]
    }
   ],
   "source": [
    "_, ax = plt.subplots(1, 1, figsize=(12, 8))\n",
    "ax.scatter(x_yards, y_probs, label=\"observed\")\n",
    "# ax.plot(\"yardline_100\", \"field_goals_success_percent\", data=df_grp_train, label=\"prediction\", color=\"red\", linestyle=\"dashed\")\n",
    "ax.plot(x_yards, y_pred_prob[:, 1], label=\"prediction\", color=\"red\", linestyle=\"dotted\")\n",
    "# ax = df_.plot.scatter(x=\"yardline_100\", y=\"field_goals_success_percent\", figsize=(15, 8))\n",
    "\n",
    "vals = ax.get_yticks()\n",
    "_ = ax.set_yticklabels(['{:,.1%}'.format(x) for x in vals])\n",
    "# ax.set_xscale(\"logit\")\n",
    "\n",
    "# reverse the x axis\n",
    "ax.set_xlim(ax.get_xlim()[1], 0)\n",
    "# ax.set_xticks(yard_lines_5)\n",
    "# ax.set_xticklabels(yard_lines_5)\n",
    "ax.set_xlabel(\"Yards from Goal Line\")\n",
    "ax.set_ylabel(\"Field Goal Success %\")\n",
    "ax.set_title(\"Field Goal Success % by Yard Line\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'chains': 3,\n",
       " 'cores': 3,\n",
       " 'draws': 4000,\n",
       " 'tune': 2000,\n",
       " 'target_accept': 0.95,\n",
       " 'random_seed': [42, 43, 44]}"
      ]
     },
     "execution_count": 274,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_chains = 3\n",
    "n_cores = 3\n",
    "n_draws = 4000\n",
    "n_tunes = int(n_draws/2)\n",
    "\n",
    "SEED = 42\n",
    "\n",
    "SAMPLE_KWARGS = {\n",
    "    \"chains\": n_chains,\n",
    "    \"cores\": n_cores,\n",
    "    \"draws\": n_draws,\n",
    "    \"tune\": n_tunes,\n",
    "    \"target_accept\": 0.95,\n",
    "    \"random_seed\": [SEED+s for s in np.arange(0, n_chains)]\n",
    "}\n",
    "SAMPLE_KWARGS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_grp_yards.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_train[\"yardline_100\"]\n",
    "y = df_train[\"successful_field_goals\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as logit_model_1:\n",
    "    \n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sd=1)\n",
    "#     beta = pm.StudentT(\"beta\", nu=40, mu=0, sd=1)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sd=1)\n",
    "\n",
    "\n",
    "    mu = alpha + beta*X\n",
    "    p = pm.Deterministic(\"p\", pm.math.sigmoid(mu))\n",
    "    bd = pm.Deterministic(\"bd\", -alpha/beta)\n",
    "    y_obs = pm.Bernoulli(\"y_obs\", p=p, observed=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pm.model_to_graphviz(logit_model_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with logit_model_1:\n",
    "    logit_trace_1 = pm.sample(**SAMPLE_KWARGS)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf.intercept_, clf.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "az.plot_trace(logit_trace_1, combined=True, compact=True, var_names=[\"alpha\", \"beta\"], divergences=None);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_trace_1[\"alpha\"].mean(), logit_trace_1[\"beta\"].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, ax = plt.subplots(1, 1, figsize=(12, 8))\n",
    "ax.scatter(x_yards, y_probs, label=\"observed\")\n",
    "# ax.plot(\"yardline_100\", \"field_goals_success_percent\", data=df_grp_train, label=\"prediction\", color=\"red\", linestyle=\"dashed\")\n",
    "# ax.plot(x_yards, y_pred_prob[:, 1], label=\"prediction\", color=\"red\", linestyle=\"dotted\")\n",
    "# ax = df_.plot.scatter(x=\"yardline_100\", y=\"field_goals_success_percent\", figsize=(15, 8))\n",
    "az.plot_hpd(X, logit_trace_1[\"p\"], color=\"red\", credible_interval=.5, ax=ax, fill_kwargs={'alpha': .9})\n",
    "az.plot_hpd(X, logit_trace_1[\"p\"], color=\"C2\", ax=ax, fill_kwargs={'alpha': .4})\n",
    "\n",
    "\n",
    "vals = ax.get_yticks()\n",
    "_ = ax.set_yticklabels(['{:,.1%}'.format(x) for x in vals])\n",
    "# ax.set_xscale(\"logit\")\n",
    "\n",
    "# reverse the x axis\n",
    "# ax.set_xlim(ax.get_xlim()[1], 0)\n",
    "# ax.set_xticks(yard_lines_5)\n",
    "# ax.set_xticklabels(yard_lines_5)\n",
    "ax.set_xlabel(\"Yards from Goal Line\")\n",
    "ax.set_ylabel(\"Field Goal Success %\")\n",
    "ax.set_title(\"Field Goal Success % by Yard Line\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = logit_trace_1[\"p\"].mean(axis=0)\n",
    "idx = np.argsort(X)\n",
    "plt.plot(X, p);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}