NUSplash Data Science for FF.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Data Science to Win at Fantasy Football\n",
    "\n",
    "## Taught By Alex Cates\n",
    "\n",
    "\n",
    "## What is Data Science?\n",
    "\n",
    "For me, Data Science is a method of answering questions based on historical data, statistics, simulations, and predictions.  All of that being said, 90% of data science consists of designing your question, quantifying your variables, and collecting the data.\n",
    "\n",
    "### Importantly, Data Science can be done without any advanced mathematics\n",
    "\n",
    "All of the math that I will cover today would be taught in a high school statistics class.  The real magic of data science is not in fancy mathematics, but well posed questions\n",
    "\n",
    "## Why Fantasy Football\n",
    "\n",
    "Fantasy football offers an excellent test bed to explore data science.  There are lots of fun questions that can be asked and, with careful data processing, answered.  The data is relatively straight forward and there are a few straight forward outcome measures to optimize towards (points, wins, final standing, etc.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>week</th>\n",
       "      <th>player</th>\n",
       "      <th>player_id</th>\n",
       "      <th>proteam</th>\n",
       "      <th>position</th>\n",
       "      <th>points</th>\n",
       "      <th>proj_points</th>\n",
       "      <th>fteam</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>Ravens D/ST</td>\n",
       "      <td>-16033</td>\n",
       "      <td>BAL</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.82</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>Broncos D/ST</td>\n",
       "      <td>-16007</td>\n",
       "      <td>DEN</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.84</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "      <td>Vikings D/ST</td>\n",
       "      <td>-16016</td>\n",
       "      <td>MIN</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>8.0</td>\n",
       "      <td>5.06</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>44</td>\n",
       "      <td>0</td>\n",
       "      <td>Saints D/ST</td>\n",
       "      <td>-16018</td>\n",
       "      <td>NO</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.50</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "      <td>Rams D/ST</td>\n",
       "      <td>-16014</td>\n",
       "      <td>LAR</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>9.0</td>\n",
       "      <td>5.18</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  week        player  player_id proteam position  points  \\\n",
       "0           8     0   Ravens D/ST     -16033     BAL     D/ST     6.0   \n",
       "1          12     0  Broncos D/ST     -16007     DEN     D/ST     8.0   \n",
       "2          31     0  Vikings D/ST     -16016     MIN     D/ST     8.0   \n",
       "3          44     0   Saints D/ST     -16018      NO     D/ST     5.0   \n",
       "4          54     0     Rams D/ST     -16014     LAR     D/ST     9.0   \n",
       "\n",
       "   proj_points  fteam  \n",
       "0         6.82      1  \n",
       "1         8.84      1  \n",
       "2         5.06      2  \n",
       "3         6.50      3  \n",
       "4         5.18      4  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pickle\n",
    "from espn_api.football import League\n",
    "\n",
    "df = pd.read_csv('player_performance_2019.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# VORP, VOSP, and VOBP\n",
    "\n",
    "## Value over Replacement\n",
    "\n",
    "The most important concept to help you win is the idea of value over replacement player.  You may have heard of the idea of using tiers instead of rankings, and that is entirely based on value over replacemet.\n",
    "\n",
    "Simply put, value over replacement is how many points a player scored compared to what their replacement would score.\n",
    "\n",
    "So what is a replacement player?\n",
    "\n",
    "There are 3 types of replacement players that matter for Fantasy Football\n",
    "\n",
    "1. Free agents (VORP)\n",
    "2. Non-Starter Caliber (VOSP)\n",
    "3. Your Bench Players (VOBP)\n",
    "\n",
    "lets define them one at a time\n",
    "\n",
    "## VORP - Value Over Free Agents\n",
    "\n",
    "To calculate a player's VORP, we use the following equation\n",
    "\n",
    "Points scored by player - points scored by the best free agent at same position\n",
    "\n",
    "we can do that for each week to account for changing free agents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'D/ST': 10.0, 'K': 16.0, 'QB': 27.26, 'RB': 14.6, 'TE': 14.0, 'WR': 16.3}\n"
     ]
    }
   ],
   "source": [
    "replacement_dict = {}\n",
    "for w, wdf in df.groupby('week'):\n",
    "    replacement_dict[w] = {}\n",
    "    for p, pdf in wdf.groupby('position'):\n",
    "        best_free_agent = pdf[pdf.fteam == 0].points.max()\n",
    "        replacement_dict[w][p] = best_free_agent\n",
    "        \n",
    "print(replacement_dict[5])\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "      <th>week</th>\n",
       "      <th>player</th>\n",
       "      <th>player_id</th>\n",
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       "      <th>position</th>\n",
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       "      <th>3370</th>\n",
       "      <td>3264</td>\n",
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       "      <td>Aaron Jones</td>\n",
       "      <td>3042519</td>\n",
       "      <td>GB</td>\n",
       "      <td>RB</td>\n",
       "      <td>42.2</td>\n",
       "      <td>12.05</td>\n",
       "      <td>9</td>\n",
       "      <td>27.6</td>\n",
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       "    <tr>\n",
       "      <th>3329</th>\n",
       "      <td>3132</td>\n",
       "      <td>5</td>\n",
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       "      <td>3117251</td>\n",
       "      <td>CAR</td>\n",
       "      <td>RB</td>\n",
       "      <td>41.7</td>\n",
       "      <td>18.16</td>\n",
       "      <td>3</td>\n",
       "      <td>27.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5243</th>\n",
       "      <td>5154</td>\n",
       "      <td>8</td>\n",
       "      <td>Tevin Coleman</td>\n",
       "      <td>2979477</td>\n",
       "      <td>SF</td>\n",
       "      <td>RB</td>\n",
       "      <td>35.8</td>\n",
       "      <td>13.10</td>\n",
       "      <td>5</td>\n",
       "      <td>26.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5223</th>\n",
       "      <td>5080</td>\n",
       "      <td>8</td>\n",
       "      <td>Aaron Jones</td>\n",
       "      <td>3042519</td>\n",
       "      <td>GB</td>\n",
       "      <td>RB</td>\n",
       "      <td>34.6</td>\n",
       "      <td>13.76</td>\n",
       "      <td>9</td>\n",
       "      <td>25.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4620</th>\n",
       "      <td>4528</td>\n",
       "      <td>7</td>\n",
       "      <td>Chase Edmonds</td>\n",
       "      <td>3119195</td>\n",
       "      <td>ARI</td>\n",
       "      <td>RB</td>\n",
       "      <td>33.0</td>\n",
       "      <td>4.80</td>\n",
       "      <td>5</td>\n",
       "      <td>25.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3126</th>\n",
       "      <td>3226</td>\n",
       "      <td>5</td>\n",
       "      <td>Eagles D/ST</td>\n",
       "      <td>-16021</td>\n",
       "      <td>PHI</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>35.0</td>\n",
       "      <td>10.39</td>\n",
       "      <td>1</td>\n",
       "      <td>25.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9571</th>\n",
       "      <td>9415</td>\n",
       "      <td>15</td>\n",
       "      <td>Kenyan Drake</td>\n",
       "      <td>2979843</td>\n",
       "      <td>ARI</td>\n",
       "      <td>RB</td>\n",
       "      <td>38.6</td>\n",
       "      <td>10.91</td>\n",
       "      <td>3</td>\n",
       "      <td>24.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1250</th>\n",
       "      <td>1294</td>\n",
       "      <td>2</td>\n",
       "      <td>Patriots D/ST</td>\n",
       "      <td>-16017</td>\n",
       "      <td>NE</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>35.0</td>\n",
       "      <td>6.35</td>\n",
       "      <td>5</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3643</th>\n",
       "      <td>3272</td>\n",
       "      <td>5</td>\n",
       "      <td>Will Fuller V</td>\n",
       "      <td>3052876</td>\n",
       "      <td>HOU</td>\n",
       "      <td>WR</td>\n",
       "      <td>39.7</td>\n",
       "      <td>6.89</td>\n",
       "      <td>9</td>\n",
       "      <td>23.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>112</td>\n",
       "      <td>0</td>\n",
       "      <td>Saquon Barkley</td>\n",
       "      <td>3929630</td>\n",
       "      <td>NYG</td>\n",
       "      <td>RB</td>\n",
       "      <td>39.9</td>\n",
       "      <td>15.10</td>\n",
       "      <td>8</td>\n",
       "      <td>23.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "      Unnamed: 0  week               player  player_id proteam position  \\\n",
       "3370        3264     5          Aaron Jones    3042519      GB       RB   \n",
       "3329        3132     5  Christian McCaffrey    3117251     CAR       RB   \n",
       "5243        5154     8        Tevin Coleman    2979477      SF       RB   \n",
       "5223        5080     8          Aaron Jones    3042519      GB       RB   \n",
       "4620        4528     7        Chase Edmonds    3119195     ARI       RB   \n",
       "3126        3226     5          Eagles D/ST     -16021     PHI     D/ST   \n",
       "9571        9415    15         Kenyan Drake    2979843     ARI       RB   \n",
       "1250        1294     2        Patriots D/ST     -16017      NE     D/ST   \n",
       "3643        3272     5        Will Fuller V    3052876     HOU       WR   \n",
       "243          112     0       Saquon Barkley    3929630     NYG       RB   \n",
       "\n",
       "      points  proj_points  fteam  vorp  \n",
       "3370    42.2        12.05      9  27.6  \n",
       "3329    41.7        18.16      3  27.1  \n",
       "5243    35.8        13.10      5  26.9  \n",
       "5223    34.6        13.76      9  25.7  \n",
       "4620    33.0         4.80      5  25.6  \n",
       "3126    35.0        10.39      1  25.0  \n",
       "9571    38.6        10.91      3  24.4  \n",
       "1250    35.0         6.35      5  24.0  \n",
       "3643    39.7         6.89      9  23.4  \n",
       "243     39.9        15.10      8  23.3  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['vorp'] = df.apply(lambda x: x.points - replacement_dict[x.week][x.position], axis = 1)\n",
    "\n",
    "df.sort_values('vorp', ascending = False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'D/ST': 0.0, 'K': 4.0, 'QB': 13.6, 'RB': 1.5, 'TE': 0.9, 'WR': 5.3}\n"
     ]
    },
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       "      <th>9571</th>\n",
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       "      <td>Kenyan Drake</td>\n",
       "      <td>2979843</td>\n",
       "      <td>ARI</td>\n",
       "      <td>RB</td>\n",
       "      <td>38.6</td>\n",
       "      <td>10.91</td>\n",
       "      <td>3</td>\n",
       "      <td>34.6</td>\n",
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       "    <tr>\n",
       "      <th>2357</th>\n",
       "      <td>1912</td>\n",
       "      <td>3</td>\n",
       "      <td>Mike Evans</td>\n",
       "      <td>16737</td>\n",
       "      <td>TB</td>\n",
       "      <td>WR</td>\n",
       "      <td>37.0</td>\n",
       "      <td>9.20</td>\n",
       "      <td>7</td>\n",
       "      <td>34.0</td>\n",
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       "      <th>5865</th>\n",
       "      <td>5772</td>\n",
       "      <td>9</td>\n",
       "      <td>Christian McCaffrey</td>\n",
       "      <td>3117251</td>\n",
       "      <td>CAR</td>\n",
       "      <td>RB</td>\n",
       "      <td>34.6</td>\n",
       "      <td>19.60</td>\n",
       "      <td>3</td>\n",
       "      <td>33.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1250</th>\n",
       "      <td>1294</td>\n",
       "      <td>2</td>\n",
       "      <td>Patriots D/ST</td>\n",
       "      <td>-16017</td>\n",
       "      <td>NE</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>35.0</td>\n",
       "      <td>6.35</td>\n",
       "      <td>5</td>\n",
       "      <td>32.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4232</th>\n",
       "      <td>3794</td>\n",
       "      <td>6</td>\n",
       "      <td>Stefon Diggs</td>\n",
       "      <td>2976212</td>\n",
       "      <td>MIN</td>\n",
       "      <td>WR</td>\n",
       "      <td>36.5</td>\n",
       "      <td>6.41</td>\n",
       "      <td>1</td>\n",
       "      <td>31.2</td>\n",
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       "    <tr>\n",
       "      <th>5243</th>\n",
       "      <td>5154</td>\n",
       "      <td>8</td>\n",
       "      <td>Tevin Coleman</td>\n",
       "      <td>2979477</td>\n",
       "      <td>SF</td>\n",
       "      <td>RB</td>\n",
       "      <td>35.8</td>\n",
       "      <td>13.10</td>\n",
       "      <td>5</td>\n",
       "      <td>31.2</td>\n",
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       "    <tr>\n",
       "      <th>3643</th>\n",
       "      <td>3272</td>\n",
       "      <td>5</td>\n",
       "      <td>Will Fuller V</td>\n",
       "      <td>3052876</td>\n",
       "      <td>HOU</td>\n",
       "      <td>WR</td>\n",
       "      <td>39.7</td>\n",
       "      <td>6.89</td>\n",
       "      <td>9</td>\n",
       "      <td>31.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Unnamed: 0  week               player  player_id proteam position  \\\n",
       "3370        3264     5          Aaron Jones    3042519      GB       RB   \n",
       "3329        3132     5  Christian McCaffrey    3117251     CAR       RB   \n",
       "3126        3226     5          Eagles D/ST     -16021     PHI     D/ST   \n",
       "9571        9415    15         Kenyan Drake    2979843     ARI       RB   \n",
       "2357        1912     3           Mike Evans      16737      TB       WR   \n",
       "5865        5772     9  Christian McCaffrey    3117251     CAR       RB   \n",
       "1250        1294     2        Patriots D/ST     -16017      NE     D/ST   \n",
       "4232        3794     6         Stefon Diggs    2976212     MIN       WR   \n",
       "5243        5154     8        Tevin Coleman    2979477      SF       RB   \n",
       "3643        3272     5        Will Fuller V    3052876     HOU       WR   \n",
       "\n",
       "      points  proj_points  fteam  vorp  \n",
       "3370    42.2        12.05      9  38.4  \n",
       "3329    41.7        18.16      3  37.9  \n",
       "3126    35.0        10.39      1  35.0  \n",
       "9571    38.6        10.91      3  34.6  \n",
       "2357    37.0         9.20      7  34.0  \n",
       "5865    34.6        19.60      3  33.1  \n",
       "1250    35.0         6.35      5  32.0  \n",
       "4232    36.5         6.41      1  31.2  \n",
       "5243    35.8        13.10      5  31.2  \n",
       "3643    39.7         6.89      9  31.1  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_replacement_dict = {}\n",
    "for w, wdf in df.groupby('week'):\n",
    "    new_replacement_dict[w] = {}\n",
    "    for p, pdf in wdf.groupby('position'):\n",
    "        best_free_agent = pdf[(pdf.fteam == 0)].sort_values('proj_points', ascending = False).iloc[0]['points']\n",
    "        new_replacement_dict[w][p] = best_free_agent\n",
    "        \n",
    "print(new_replacement_dict[6])\n",
    "        \n",
    "df['vorp'] = df.apply(lambda x: x.points - new_replacement_dict[x.week][x.position], axis = 1)\n",
    "\n",
    "df.sort_values('vorp', ascending = False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why is Vorp Important\n",
    "\n",
    "We can look at the value of vorp by comparing how a the total vorp of a fantasy team relates to where that team finished"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>Unnamed: 0</th>\n",
       "      <th>lid</th>\n",
       "      <th>team</th>\n",
       "      <th>week</th>\n",
       "      <th>vosp</th>\n",
       "      <th>vorp</th>\n",
       "      <th>reg_standing</th>\n",
       "      <th>final_standing</th>\n",
       "      <th>score</th>\n",
       "      <th>outcome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>38734302</td>\n",
       "      <td>Anthony Vlahos</td>\n",
       "      <td>0</td>\n",
       "      <td>41.76</td>\n",
       "      <td>17.10</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>156.52</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>38734302</td>\n",
       "      <td>Anthony Vlahos</td>\n",
       "      <td>1</td>\n",
       "      <td>98.72</td>\n",
       "      <td>86.31</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>87.82</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>38734302</td>\n",
       "      <td>Anthony Vlahos</td>\n",
       "      <td>2</td>\n",
       "      <td>6.72</td>\n",
       "      <td>-1.24</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>134.62</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>38734302</td>\n",
       "      <td>Anthony Vlahos</td>\n",
       "      <td>3</td>\n",
       "      <td>26.90</td>\n",
       "      <td>-50.77</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>115.84</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>38734302</td>\n",
       "      <td>Anthony Vlahos</td>\n",
       "      <td>4</td>\n",
       "      <td>-1.26</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>132.12</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0       lid            team  week   vosp   vorp  reg_standing  \\\n",
       "0           0  38734302  Anthony Vlahos     0  41.76  17.10            10   \n",
       "1           1  38734302  Anthony Vlahos     1  98.72  86.31            10   \n",
       "2           2  38734302  Anthony Vlahos     2   6.72  -1.24            10   \n",
       "3           3  38734302  Anthony Vlahos     3  26.90 -50.77            10   \n",
       "4           4  38734302  Anthony Vlahos     4  -1.26  -0.05            10   \n",
       "\n",
       "   final_standing   score  outcome  \n",
       "0              11  156.52     True  \n",
       "1              11   87.82    False  \n",
       "2              11  134.62     True  \n",
       "3              11  115.84    False  \n",
       "4              11  132.12    False  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vorp_df = pd.read_csv('vorp_splash.csv')\n",
    "vorp_df.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 16)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "team_vorp_df = vorp_df.groupby(['lid', 'team']).sum()\n",
    "sns.lmplot(x = 'vorp', y = 'outcome', data = team_vorp_df)\n",
    "plt.ylim([0,16])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x193a8cbfd48>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Yfhl7FlwW8SOiTV0fD3WqTMHZ1xRbvLH/3nqoy8KPQJCktrzyMqTG9H4QbQVgy76dve+bPdxDvG1IqveOGsFkz/Divt47ami2aycNsCRlBsaShjHFpMYw/Jo5kR6y7aHN3b4mqfEMv3p+tPEeWV90e5CkXqUiNaHXY7RrkKi37uumGpi7b3Zvl219SVBgSWoosKRhTBmqSE1g5NXdLWfTP8cf+XGXbY2NjWx95TVGpqYW+Y6uTmglAK/tO9Z7vOyuLtuSnqQGQy3RkoYxxqmRqalMu+aWyI+786G7u2xrbGzklVcaqBo/vbSD6AgAsntbe9113/4dfTo/F4IxZ68y7cxzet13RFsw4ceJpkO97ruz5c2Sz6EskkZzczPvHDpUdEzFQO04tJ/RYuMnjBksqsZP5zMfvyPy4/7bo9/qsi2O2SamnXkOSy6KdrXrpc/+a8n7lkXSMMYYF4KBvA1MPXNar/tWtgW1mmNNJ0o69q6WEjpXxKAskkY6neaEDnM2InxEemLkxzXGDA1Tz5zG33zotsiP+w+/uivyY0ahLJKGb83NzbzTcrLbEdz9tavlJKObm4vGaznU/biK/tp7EI5p13jGmPJlU6MbY4wp2ZCraYjIVcC9wDDgX1R1Wcyn1EU6neZY+wEnc0+dlk4XjXeavOVkRPj4SV3jNTc3c/BQz4Px+uPgAaC9eE2qtaX7wXj91ZqF5larSRnTF0MqaYjIMOCfgI8BTcCvReRhVX053jMzpv+am5vRlkPdDsbrL83up7nVevaZaA2ppAFcCDSoaiOAiDwIXANY0vAonU5DxVtOphFJn1O8JtVS+ZaTaUTSVcVrUrS83eMI7n7Jvj0oajbNzc20t7xddDDeQLRn99LcejTSY5rBZ6gljclA7jDQJuBDMZ2LMZFIp9NkK4c5mUYkXRVvz77m5maOt7xTdCDeQB3P7qK5dXTkxzU9G2pJo9itZl5Dt4gsBhYDTJvWe99pYwql02neqmxzMvdUsZqNb+l0mv2VB5xMI5KuKmHq4wQJekq+46R77K6WHYxuHnxJcagljSYgdxKbKUBefV9VVwIrAebMmRPtk1NjTJ+k02neqTzmbBqRdNVpeduC7udHio7eHqh92R0cb4u2c0tfBUnq7T6N4C7FjpY3Gd38Tkn7DrWk8WtgloicC7wBfA7IlPKNOw/tL2kakT3vvA3AxNFnlHRCOw/tp3qyDe4zphwFPSVPOBvcd1p6ROTHHahek4aInAb8FXApQVPQ08AKVe19GsqIqWqbiNwArCfocrtKVXtdXHvmzJklxzixPVjzYESJiaB68sQ+Hd8Y4046nWbk8FZnc0+lJlRGfty+SKfTnGg/5GTuqRHpsSXtW0pN44fA28B3wvLngR8Bn+nX2Q2Qqj4KPNqX7+nLVMYdk4ktX768T+dljDHloJSk8S5VfX9O+QkR+Z2rE0qKXSVOI7L3nWA91Amjex+cv6vlJLMGfGbGGNN/pSSN34rIRar6LICIfAh4xu1pDW19aa5qDadLPm3Keb3uO6uHY+87WNrcUwfDFUfHlbCS6b6DMH5S7/sZY8pHKUnjQ8AXRaRjnt5pwDYReRFQVX2fs7Mbonw3h/UlSR0Ik9T4Sb0nqfGT+nZsY0zylZI0rnJ+FmZAyuGZTWu2tLmn2sJFyoaX8EyvNQtUDey8hqr27N6SRoS3HwrWBq8Y2/v4i/bsXiizcRrlqMekISIVwBpVne3pfMwQcehAaRMWHg56MDOmhB7Mhw5Ausgqln2p7WxvCWpS51X1XpOiqodjZw+XNo3IofC51dgS+u9nD3ebpDS7v6S5p/RQ8AOVsb3/QDW7H4qMCO/bz3M/AOeVkgyqzrKaaRnoMWmoaruI/E5Epqnq4FxGynjXp4vOO8FFPH1O7xfx9DnFjz2Ym/tOJakSZh/oJkn1Ld7hMF4JXcKrincHL4eaqU+7WnaWNCJ87zt7AJgwurTu/LtadjKL6gGdmwulNE9NAl4SkeeAziGDqvpJZ2dlBrWkX3R8v7+k/zyTrG+dXoJlXk+bUtqAvVlUFz3+zpY3SxoRvuedoJY4cfT4Xvfd2fIm1UQ3TuObJR3JGGOKOJ7dVfKEhScO7QVgxNgJJR2Xqng7oQ/mWvCJ7W8BMGJK78mgmrElH7vXpKGqPxeRicAfhZueU9W9JR3dGFPW+vqMY3tLKwDnFcwpVVTVrKLH37d/R8lzTx1seROAcWcWeZhW5LipCfE2Fw2GWmkp04j8KbAceJJgltnviMjNqvrTSM/EGJM4fbnIwcAvdH1NUgffDpqMSpkeJDWheHNRuSmleep24I86ahciUgU8DljSMMYMKr6TVDnqfe4KqChojsqW+H3GGGMSppSaxloRWQ90jAT6LH2cMNAYY0wylJI03gReBM4neKaxUlVXOz0rY4wxg1IpSeMM4DpgP/Ag8AunZ2SMMWbQ6vXZhKp+U1X/ELgeSAM/F5HHnZ+ZMcaYQacvD7T3EjRVZYHeR94YY4xJnF6Thoh8WUSeBDYCZwN/btOhG2NMeSrlmcZ04CZVfcH1yRhjjBncSplG5FYfJ2KMMWbws0F6xhhjSmZJwxhjTMliSRoi8hkReUlE2kVkTsFrt4lIg4i8KiLzc7ZfFW5rEBFrMjPGmBjEVdPYCvwxsCl3o4i8B/gc8IcEa5P/s4gME5FhwD8BC4D3AJ8P9zXGGONRKb2nIqeq2wBEpPCla4AHVfU48LqINAAXhq81qGpj+H0Phvu+7OeMjTHGwOB7pjEZ2JVTbgq3dbfdGGOMR85qGuFUI8WWw7pdVR/q7tuKbFOKJzftJu5iYDHAtGnTSjhTY4wxpXKWNFT1yn58WxMwNac8BWgOv+5ue2HclcBKgDlz5hRNLMYYY/onlmcaPXgYqBORbxNMjjgLeI6gBjJLRM4F3iB4WJ4ZaLAVK1bQ2NiYt2379u3AqRW9cs2cObPPK4MZY0ySxNXldqGINAEfBtaEizyhqi8BPyF4wL0OuF5VT6pqG3ADsB7YBvwk3DdyI0aM4Pjx47S2tro4vDHGDGlx9Z5aDRRdyElV7wTuLLL9USJeMbBYrWH58uU8/vjjTJ48uWhtwxhjytlg6z0Vq2w2S319PQD19fXs378/5jMyxpjBZbA904jVqlWraG9vB6C9vZ3777/fahvGmD4r9rz0tdde4/jx49x0001UVlbmvTaUnpda0sjxxBNPdCkP5aRhD/qNGTza29tpb29n7969TJ48dIeZWdLIUThCvciI9QEZDHcfp512WqTHM8lQ7G8Tuv/7tBuMnhX+bLLZLF/60pcAePvtt7ntttsYP358DGc2cJY0clx++eU8/vip5c+vuOIK5zFd3n2U4z/1kSNHaGxspLGxkZkzZyYunm9tbW20t7fT1NTEueeeG/fpDFl1dXV5Td8PPPAAX/nKV2I+q/6xpJGjtrY2L2nU1tZGevxidx/XXnstAC0tLdx3331D9u7Dt+7ujLdv346qctNNN/Gud70r7zUXd8e7du2ivb2dZcuWsXLlykiPXUxrays7d+5k//79kf6tFPu5ZLNZMplgONRQvzuOW319PW1tbUCQiOvr6y1pJEVFRQXt7e1UVLjvWFZXV9c5HqS1tdXL3Uc2m+Wuu+5iyZIlibsAHDlyBNVgEoDjx49z9OhRTj/99EiOXSxJHTlyhOPHjwOwY8cObrjhhs54A01QPTUXtbW1ccMNN+TVTF0kxHvvvbdL+Zvf/GakMcpFTU0Na9asQVUREWpqauI+pX6zpJGjrq6u86Kjqs4v4hs3buxSdp006urq2Lp1q7fqsc8748WLF+eVT5w4wX333RdZzEK7du3KK+/cubNL7SZKra2tnXer2WyWCRMmdHkOFqVf/epXeeVnn33WWaykW7BgAY888ggQXFs+8YlPRHp8n51eLGnk2LhxY17ScH0RHz9+PG+88UZnOZVKOYsFwYVmw4YNqCobNmxg0aJFkV7Ii/3hvvrqq7S3t/MXf/EXzJgxI++1qO+Od+zY0WN5IIqd5/z58/PKx48fZ/ny5c7ifec732Hbtm2d5fPOO2/INnGUm7Vr1yIinTWNNWvWOP/duer0Ykkjx7hx4zh69Ghe2aU333wzr7x7926n8Xw/jGttbe2M19LSQmtrq9M74zFjxnD48OG8sku+4z322GNdyi5/fx1NtbnloaqnZ2DQ9W486hua+vr6vBvSqJ9p+Oz0YkkjR+FF2/VFPPcfslg5aq4fxhX+4X7rW9/KK1dVVXH77bdHFq9Q4XxhrucP6/hZdleO2smTJ3ssR83332ccfHVBr6mpYd26dbS1tTF8+HB7pmH6p6KiIu8f3/Wd3MUXX5zXO+ySSy5xGu/pp5/OKz/11FNO45199tl5zX1VVVVO41155ZWd7dQdZZd8J6kk6e5OvKNjiOueYZlMhg0bNgDB//miRYucxXLNkkaOSZMm5dUuJk2a5DTexRdfnHchvfjii53GK9RRXfZ1fNfxCmuGzc1Fl1yJTCaT6UwaIuL8QuC7OcylwTKY0FfHkFQqxbx581izZg3z5s0b0j0Xh24jpQPV1dV55VmzZnmNH/UI9ELPPPNMj+WoTZgwocdy1OJoTumoHbr+3QHccMMNeeUbb7zReUzfcge7ulbYMcT1BKWZTIbZs2cP6VoGWE0jz/PPP59X3rx5s9N4v/zlL/PKv/jFL5zGmzBhQl6PItcX8cLmtmHDhjmNN2zYsLzmPtfx6urq8sb1uL5bLfx7fO6557jsssucxXOpu8GEPqfa8N0xJJVKcc899zg7vi9W08hRU1PTeaEZNmyY84dVvptvCu/eXN/N+e4dVjjti+vfX7GOBS4VTqjpOl5h0vWRhAsv4i75/v0lhSWNHJlMJi9puK5GFl7kXM91NXfu3M5mFBFh7ty5TuMVtrm7boOvra3Ne39RTwNTyPdNhu/eU0lPwjU1NXl/L0O5R1Mx2WyWr33ta5E3u1nSyNHxsEpEvDysyr3IVVRUcN111zmNl8lkGD48aJGsrKx0nhR9d4FNpVKdifDKK690/vvLZDKdF+6TJ08O+bbqQrW1tZ1NjBUVFV6ScMffp49uqQsWLMgbOxH1KO245T7kj5IljQI+H1alUinS6TQA6XTa+UUulUoxf/58b0nx7LPP7rHsQm1tLe9973udX+AADhw4kFc+ePCg03iFsyC7XpMhlUp1Xrjnzp3rJQnnJinX/4Nr167NK69Zs8ZpPFd3/t3FcvWQ35JGgY6HVT66xGWz2c7nCnv27PHyx+QzKfoeLAnw+9//npdeeinSKUS6c/fdd+eVly1b5jTe9ddfn1f2MYWIzyTsu6ZfbO43l1zd+XcXy9XzIUsaMSo2QaJrPpNiYe8pH9NQLF26lPb29i6j0V1wOddVMYVt/K4vcuD37wX83tQUvieXc7/57t7r8vmQJY0YJb33xuWXX55Xdv2g//nnn+8c/Hb48GF++9vfOo1XOPjT9WDQJ598Mq9c2JvKBZ9NKuA3Sfns3ee7Z5jL50OxJA0RWS4ir4jIFhFZLSLjcl67TUQaRORVEZmfs/2qcFuDiNwax3lHzfeDP998P0hdunRpXtl1bcN1F+ne4vmI77NJxTfXyzvn8n2D6PL5UFw1jceA2ar6PuA/gdsAROQ9wOeAPwSuAv5ZRIaJyDDgn4AFwHuAz4f7Rs7nnZXvB3++pVKpzvmtLr30Uud3j7lTbBQrRy3ucSiua26+m1R881kT9t092+XzoViShqpuUNWO2daeBaaEX18DPKiqx1X1daABuDD8aFDVRlU9ATwY7hs5n3dWvh/8xWHkyJEAjBgxwnks3+NCRo8e3WM5aoU1N9ddtH03qfhWWPN1WRPOZDJ5zy993CC6ej40GJ5p1AIdfd8mA7nLoTWF27rbHqk47qySMh9NMdlslk2bNgGwadMm5z/PJUuW5JXvuOMOp/GOHTvWYzlquV1ga2pqnN9kJP2ZW9K5ej7kLGmIyOMisrXIxzU5+9wOtAEdtzDFGhW1h+3F4i4Wkc0isnnfvn19Ouc47qx8907xqa6uLu+i4/rnecEFF3Su0X366afzgQ98wGm8OCxcuJBRo0bx6U9/2nmswlmXXU+lD36bh1etWtVjOUod87BQKyIAAA6fSURBVJQBnfOUDVXOkoaqXqmqs4t8PAQgItcCVwOL9NQTvSZgas5hpgDNPWwvFnelqs5R1Tl9XU/B7qyiVV9fn5eEffw8zzjjDADOPPNM57F8P2OAYEDa0aNHnQ9EKyZpD9599kZL0rUlrt5TVwF/C3xSVY/kvPQw8DkRGSki5wKzgOeAXwOzRORcERlB8LD84ajPK+m9mXy74IILeixHraGhIW+wZLH1GqK0cOHCvLLru3/fzaeFsy67noU5m82ybt06VJV169Y5f38+e6Ml6doS1zON+4AzgMdE5AUR+S6Aqr4E/AR4GVgHXK+qJ8OH5jcA64FtwE/CfSOV9N5MvhVetF9//XWn8XyP0PY9DUUcff199vjx3Zzps6aYpGtLXL2nqlV1qqqeH378Zc5rd6rqear6LlVdm7P9UVX9L+Frd7o4r1Qq1bk+wUc/+tFEPmfwKXfpVYCmpian8eIeoe26ySGOvv4+Z33OXYq4WDlqPnujJamn5GDoPTUo+R64lUTTp0/vsTzU4/lucvAdz/eFruO9dVeOmu/eaAsWLOD000/3NpuuTY3uge8uokl3yy235JVvvdXtQH7f8TKZTF5zkes78TiaOHx2Cfc9OBNOTcjoeswL+O/EYFOje5D0wUy+VVdXd97tT58+nZkzZyYqnm9xNHH47BLuu6YI/t6f704M2WyW9evXo6qsX7/epkZ3JUnd4gaLW265hVGjRjm/648jXl1dXd7Kbz5uMpI8GNR3TdEn3zekLjsVWNLIkaRucYNFdXU1q1ev9nbX7zNefX193sp9Pm4ykjwYNMk1Rd83pBs3bsybtiTKafQtaeRIUrc4457dZETPd83UF9/dlydMmNBjeSAsaeRIUrc4457dZETPd83UF98TFnYMcu2uPBCWNAokuc3YRMtuMsxgNXfu3LznbXPnzo3s2JY0CiS5zdhEz24youV7pUBffE9YmMlk8pJGEhZhMiYR7CYjWqtWreLFF1/k/vvvj/tUIpWknpmWNEyiJPVOtRxks9nOi2l9fX2ifoe+O0247A5uScMkSlLvVMvBqlWr8sYyJOl36LvThMvu4JY0ykyS78STfKdaDgrXs3C5voVvvjtNuKzZWNIoMz4XufEtyXeq5aCjOaW78lDns9OEPQg3kYhjDXSfknyn2iHJNcXLL788r+xjJUSffHaaSKVSpNNpANLpdKQxLWmUkaRPyJj0O1XwX1P0maQK17eora11HjOpstkszc3BitjNzc02YaHpnyR1+ysm6XeqcdQUfSapVCrFJZdcAsCll15q3ZgHwCYsNJFI+lxJSb9T9V1TjCNJjRw5Mu+z6R+bsNBEIulzJeWuxDZ37tzE3an6rinGkaQ6FkH7+c9/nsjnNr7YhIUmEuWwBnrHSmxJq2WA/5pi0pNUktmEhSZySV0DPcnTeviuKSY9SSWZTVhoImFroA9tvgeIJT1JJVkmk8n7Wdo4DdMvVv0f+nwOEEt6kkqyVCrF/PnzERHmz58/9MdpiMjficgWEXlBRDaISDrcLiLyjyLSEL7+wZzvuVZEXgs/ro3jvIc6q/4Pfb6b35KcpJLO1e8urprGclV9n6qeDzwC/I9w+wJgVvixGFgBICLjga8DHwIuBL4uImd5P+shzqr/pq+SnKSSztXvLpakoaotOcXRQMdT2WuAH2rgWWCciEwC5gOPqep+VT0APAZc5fWkE8Cq/2awS3JHhqSI7ZmGiNwpIruARZyqaUwGduXs1hRu6257seMuFpHNIrJ537590Z/4EGbVf2PMQDlLGiLyuIhsLfJxDYCq3q6qU4EHgBs6vq3IobSH7V03qq5U1TmqOqeqqiqKt5IoVv035pQkTwDpirOkoapXqursIh8PFexaB3w6/LoJmJrz2hSguYftpo+s+m/MKUleKsCVuHpPzcopfhJ4Jfz6YeCLYS+qi4BDqrobWA/ME5Gzwgfg88JtxhjTL0lfKsCVuJ5pLAubqrYQJIAbw+2PAo1AA/A94K8AVHU/8HfAr8OP/xluM8aYfrFxS/0jSZ1OAmDOnDm6efPmuE/DGDMILVy4kCNHjnSWR40axerVq2M8o8FDRJ5X1TnFXrMR4caYsmTjlvrHkoYxpizZuKX+saRhjClLNm6pf4bHfQLGGBOXTCbDjh07rJbRB5Y0jDFlq2PckimdNU8ZY4wpmSUNY4wxJbOkYYwpWzb3VN9Z0jDGlC2be6rvLGkYY8qSzT3VP5Y0jDFlyeae6h9LGsaYslRfX09bWxsAbW1t1NfXx3xGQ4MlDWNMWbK5p/rHkoYxpizZ3FP9Y0nDGFOWbO6p/rFpRIwxZcvmnuo7SxrGmLJlc0/1nTVPGWOMKZklDWOMMSWzpGGMMaZkljSMMcaUTFQ17nNwRkT2ATv68a1nA29FfDoWz+JZPIs3VN7bdFWtKvZCopNGf4nIZlWdY/EsnsWzeEM1lqt41jxljDGmZJY0jDHGlMySRnErLZ7Fs3gWb4jHchLPnmkYY4wpmdU0jDHGlMySRg4RWSUie0Vkq6d4U0XkCRHZJiIviciNjuOdJiLPicjvwnjfdBkvjDlMRH4rIo+4jhXG+72IvCgiL4jIZsexxonIT0XklfB3+GGHsd4VvqeOjxYRuclVvDDmfwv/TraKyI9F5DTH8W4MY73k4r0V+/8WkfEi8piIvBZ+PstxvM+E769dRCLt1dRNvOXh3+cWEVktIuMGGseSRr7vA1d5jNcG/I2qvhu4CLheRN7jMN5xoEZV3w+cD1wlIhc5jAdwI7DNcYxCV6jq+R66Nt4LrFPVPwDej8P3qaqvhu/pfOAC4Aiw2lU8EZkMfBWYo6qzgWHA5xzGmw38OXAhwc/yahGZFXGY79P1//tWYKOqzgI2hmWX8bYCfwxsijBOT/EeA2ar6vuA/wRuG2gQSxo5VHUT4G11eVXdraq/Cb9+m+CiM9lhPFXVw2GxMvxw9lBLRKYAnwD+xVWMuIjImcBlwP0AqnpCVQ96Cj8X2K6q/Rm42hfDgdNFZDgwCmh2GOvdwLOqekRV24CfAwujDNDN//c1wA/Cr38AfMplPFXdpqqvRhWjhHgbwp8nwLPAlIHGsaQxSIjIDOADwK8cxxkmIi8Ae4HHVNVlvP8N3AK0O4xRSIENIvK8iCx2GGcmsA/417D57V9EZLTDeLk+B/zYZQBVfQO4B9gJ7AYOqeoGhyG3ApeJSEpERgEfB6Y6jNdhoqruhuAmDpjgIWZcaoG1Az2IJY1BQETGAP8O3KSqLS5jqerJsIljCnBh2CwQORG5Gtirqs+7OH4PLlHVDwILCJr7LnMUZzjwQWCFqn4AeIdomzaKEpERwCeBf3Mc5yyCu/BzgTQwWkT+q6t4qroN+HuC5pR1wO8Imm9NBETkdoKf5wMDPZYljZiJSCVBwnhAVX/mK27YlPIk7p7hXAJ8UkR+DzwI1IjI/3EUq5OqNoef9xK0+V/oKFQT0JRTU/spQRJxbQHwG1Xd4zjOlcDrqrpPVVuBnwEXuwyoqver6gdV9TKCZpbXXMYL7RGRSQDh570eYnolItcCVwOLNIIxFpY0YiQiQtAmvk1Vv+0hXlVH7wkROZ3gwvCKi1iqepuqTlHVGQTNKfWq6uxOFUBERovIGR1fA/MImj0ip6pvArtE5F3hprnAyy5iFfg8jpumQjuBi0RkVPh3OhfHHRpEZEL4eRrBw2If7/Nh4Nrw62uBhzzE9EZErgL+Fvikqh6J5KCqah/hB8Ef6W6gleBO8jrH8S4laIPfArwQfnzcYbz3Ab8N420F/oenn+vlwCMe4swkaNb4HfAScLvjeOcDm8Of538AZzmONwrIAmM9/d6+SXBTsRX4ETDScbynCBLv74C5Do7f5f8bSBH0mnot/DzecbyF4dfHgT3AesfxGoBdOdeX7w40jo0IN8YYUzJrnjLGGFMySxrGGGNKZknDGGNMySxpGGOMKZklDWOMMSWzpGGMMaZkljRM2RGRr4ZTmR8QkX5P/SEih3vfq8v3LOlvvJ7OQUTSIvLTKI9tTDE2TsOUHRF5BVigqq8P8DiHVXWM6+/xeTxjemM1DVNWROS7BCPHHw4XGbov3P59EflHEfmFiDSKyJ+E28eIyEYR+U24uNM1JcaZJCKbwgWTtorIR0RkGcFU4y+IyAPhfv8Rzsj7Uu6svCJyWETulGDBrGdFZGK4/VwR+aWI/FpE/i5n/xkdi++IyJdE5Gcisi5cXOjunP2uE5H/FJEnReR7He/fmFJZ0jBlRVX/kmBdiCuAAwUvTyKY2uVqYFm47RiwUIOZc68A/iGci6k3GYIpIs4nWFToBVW9FTiqwWJKi8L9alX1AmAO8FURSYXbRxOsL/F+ggV7/jzcfi/BzLp/BLzZQ/zzgc8C7wU+K8EqkWngvxMs+PUx4A9KeB/G5LGkYcwp/6Gq7ar6MjAx3CbAUhHZAjxOsEjWxO4OkOPXwJ+JyDeA92qwyFYxXxWR3xEskDMV6Fit7gTQsUTu88CM8OtLODWR3496iL9RVQ+p6jGC+ZymE8z4+3NV3a/BzLVOp1c3yWRJw5hTjud83VGbWARUAReEtYY9QK9rZWuwitplwBvAj0Tki4X7iMjlBDMNfzisUfw259iteuqB40mC9Ts6D9/H99Lx/aXUkIzpkSUNY3o2lmAxqVYRuYLgjr1XIjI9/L7vEUx/37HWRmu4hkrHsQ+o6hER+QOCZqPePMOptboX9bRjEc8BHxWRs8IlXD/dx+83Ju/uxRjT1QPA/xORzQRTS5e6/sjlwM0i0gocBjpqGiuBLSLyG4LlN/8ybPp6laCJqjc3AnUiciPB4l0lU9U3RGQpwZLCzQTNVof6cgxjrMutMWVERMao6uGwprEaWKWqq+M+LzN0WPOUMeXlGyLyAsHCSq8TLB5lTMmspmHMAIjIe+nai+m4qn4ojvMxxjVLGsYYY0pmzVPGGGNKZknDGGNMySxpGGOMKZklDWOMMSWzpGGMMaZk/x+ppY1yKkjFqQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x = 'final_standing', y = 'vorp', data = vorp_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VOSP - Value Over non-Starting Player\n",
    "\n",
    "VOSP or value over starting player is calculated the same as vorp, but instead of the replacement level player being the best free agent, we can define that as the next replacement for a starter caliber player of the week.\n",
    "\n",
    "For instance, In a 10 team league which starts 1 QB, the 11th best QB of the week would define our replacement level.\n",
    "\n",
    "We can do the same calculations as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'D/ST': 5.0, 'K': 6.0, 'QB': 18.22, 'RB': 8.5, 'TE': 5.2, 'WR': 7.6}\n"
     ]
    },
    {
     "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>week</th>\n",
       "      <th>player</th>\n",
       "      <th>player_id</th>\n",
       "      <th>proteam</th>\n",
       "      <th>position</th>\n",
       "      <th>points</th>\n",
       "      <th>proj_points</th>\n",
       "      <th>fteam</th>\n",
       "      <th>vorp</th>\n",
       "      <th>vosp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3264</th>\n",
       "      <td>5</td>\n",
       "      <td>Aaron Jones</td>\n",
       "      <td>3042519</td>\n",
       "      <td>GB</td>\n",
       "      <td>RB</td>\n",
       "      <td>42.2</td>\n",
       "      <td>12.05</td>\n",
       "      <td>9</td>\n",
       "      <td>38.4</td>\n",
       "      <td>31.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3272</th>\n",
       "      <td>5</td>\n",
       "      <td>Will Fuller V</td>\n",
       "      <td>3052876</td>\n",
       "      <td>HOU</td>\n",
       "      <td>WR</td>\n",
       "      <td>39.7</td>\n",
       "      <td>6.89</td>\n",
       "      <td>9</td>\n",
       "      <td>31.1</td>\n",
       "      <td>30.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3132</th>\n",
       "      <td>5</td>\n",
       "      <td>Christian McCaffrey</td>\n",
       "      <td>3117251</td>\n",
       "      <td>CAR</td>\n",
       "      <td>RB</td>\n",
       "      <td>41.7</td>\n",
       "      <td>18.16</td>\n",
       "      <td>3</td>\n",
       "      <td>37.9</td>\n",
       "      <td>30.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3226</th>\n",
       "      <td>5</td>\n",
       "      <td>Eagles D/ST</td>\n",
       "      <td>-16021</td>\n",
       "      <td>PHI</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>35.0</td>\n",
       "      <td>10.39</td>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>30.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9415</th>\n",
       "      <td>15</td>\n",
       "      <td>Kenyan Drake</td>\n",
       "      <td>2979843</td>\n",
       "      <td>ARI</td>\n",
       "      <td>RB</td>\n",
       "      <td>38.6</td>\n",
       "      <td>10.91</td>\n",
       "      <td>3</td>\n",
       "      <td>34.6</td>\n",
       "      <td>29.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3794</th>\n",
       "      <td>6</td>\n",
       "      <td>Stefon Diggs</td>\n",
       "      <td>2976212</td>\n",
       "      <td>MIN</td>\n",
       "      <td>WR</td>\n",
       "      <td>36.5</td>\n",
       "      <td>6.41</td>\n",
       "      <td>1</td>\n",
       "      <td>31.2</td>\n",
       "      <td>28.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>0</td>\n",
       "      <td>Saquon Barkley</td>\n",
       "      <td>3929630</td>\n",
       "      <td>NYG</td>\n",
       "      <td>RB</td>\n",
       "      <td>39.9</td>\n",
       "      <td>15.10</td>\n",
       "      <td>8</td>\n",
       "      <td>23.3</td>\n",
       "      <td>28.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1294</th>\n",
       "      <td>2</td>\n",
       "      <td>Patriots D/ST</td>\n",
       "      <td>-16017</td>\n",
       "      <td>NE</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>35.0</td>\n",
       "      <td>6.35</td>\n",
       "      <td>5</td>\n",
       "      <td>32.0</td>\n",
       "      <td>28.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>632</th>\n",
       "      <td>1</td>\n",
       "      <td>Sammy Watkins</td>\n",
       "      <td>16725</td>\n",
       "      <td>KC</td>\n",
       "      <td>WR</td>\n",
       "      <td>37.8</td>\n",
       "      <td>7.06</td>\n",
       "      <td>9</td>\n",
       "      <td>22.1</td>\n",
       "      <td>27.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4528</th>\n",
       "      <td>7</td>\n",
       "      <td>Chase Edmonds</td>\n",
       "      <td>3119195</td>\n",
       "      <td>ARI</td>\n",
       "      <td>RB</td>\n",
       "      <td>33.0</td>\n",
       "      <td>4.80</td>\n",
       "      <td>5</td>\n",
       "      <td>30.1</td>\n",
       "      <td>26.60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      week               player  player_id proteam position  points  \\\n",
       "3264     5          Aaron Jones    3042519      GB       RB    42.2   \n",
       "3272     5        Will Fuller V    3052876     HOU       WR    39.7   \n",
       "3132     5  Christian McCaffrey    3117251     CAR       RB    41.7   \n",
       "3226     5          Eagles D/ST     -16021     PHI     D/ST    35.0   \n",
       "9415    15         Kenyan Drake    2979843     ARI       RB    38.6   \n",
       "3794     6         Stefon Diggs    2976212     MIN       WR    36.5   \n",
       "112      0       Saquon Barkley    3929630     NYG       RB    39.9   \n",
       "1294     2        Patriots D/ST     -16017      NE     D/ST    35.0   \n",
       "632      1        Sammy Watkins      16725      KC       WR    37.8   \n",
       "4528     7        Chase Edmonds    3119195     ARI       RB    33.0   \n",
       "\n",
       "      proj_points  fteam  vorp   vosp  \n",
       "3264        12.05      9  38.4  31.28  \n",
       "3272         6.89      9  31.1  30.80  \n",
       "3132        18.16      3  37.9  30.78  \n",
       "3226        10.39      1  35.0  30.00  \n",
       "9415        10.91      3  34.6  29.70  \n",
       "3794         6.41      1  31.2  28.90  \n",
       "112         15.10      8  23.3  28.80  \n",
       "1294         6.35      5  32.0  28.00  \n",
       "632          7.06      9  22.1  27.42  \n",
       "4528         4.80      5  30.1  26.60  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vosp_replacement_dict = {}\n",
    "for w, wdf in df.groupby('week'):\n",
    "    vosp_replacement_dict[w] = {}\n",
    "    for p, pdf in wdf.groupby('position'):\n",
    "        if p in ['QB', 'TE', 'D/ST', 'K']:\n",
    "            best_nonstarter = pdf.sort_values('points', ascending = False).iloc[11]['points']\n",
    "            vosp_replacement_dict[w][p] = best_nonstarter\n",
    "        elif p in ['RB', 'WR']:\n",
    "            best_nonstarter = pdf.sort_values('points', ascending = False).iloc[21]['points']\n",
    "            vosp_replacement_dict[w][p] = best_nonstarter\n",
    "        \n",
    "print(vosp_replacement_dict[6])\n",
    "        \n",
    "df['vosp'] = df.apply(lambda x: x.points - vosp_replacement_dict[x.week][x.position], axis = 1)\n",
    "\n",
    "df.sort_values('vosp', ascending = False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(9.924999999999997, 0.5, 'wins')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x = 'vosp', y = 'outcome', data = team_vorp_df)\n",
    "plt.ylim([0,16])\n",
    "plt.ylabel('wins')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x193a8f6cc08>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.boxplot(x = 'final_standing', y = 'vosp', data = vorp_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Is VORP or VOSP more important?\n",
    "\n",
    "While Vorp is a measure of how good the entire team is, the entire team does not score.  For VOSP, you want your starting lineup to be positive vosp.  VOSP vs VORP is the debate of if you want a shallow high end team (High VOSP) or a balanced deep team (High Vorp).  Obviously you want both but most teams can't get that, so which is better? \n",
    "\n",
    "One way to look at this is to simply run a linear regression and see which is weighted more.  A linear regression will create a multidimensional line that predicts the outcome measures based on the inputs.  In this case, lets use a teams total VORP, VOSP, and Points For over the course of the season, and see well we can predict that teams final standing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       names  coef    se      T  pval    r2  adj_r2  CI[2.5%]  CI[97.5%]  \\\n",
      "0  Intercept  6.92  0.18  38.55  0.00  0.26    0.26      6.57       7.28   \n",
      "1       vorp  0.00  0.00   2.40  0.02  0.26    0.26      0.00       0.00   \n",
      "2       vosp  0.01  0.00   7.62  0.00  0.26    0.26      0.00       0.01   \n",
      "\n",
      "   relimp  relimp_perc  \n",
      "0     NaN          NaN  \n",
      "1    0.08        29.19  \n",
      "2    0.19        70.81  \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\alext\\Anaconda3\\lib\\site-packages\\outdated\\utils.py:18: OutdatedPackageWarning: The package pingouin is out of date. Your version is 0.3.6, the latest is 0.3.8.\n",
      "Set the environment variable OUTDATED_IGNORE=1 to disable these warnings.\n",
      "  **kwargs\n"
     ]
    }
   ],
   "source": [
    "import pingouin as pg\n",
    "\n",
    "pov = pg.linear_regression(team_vorp_df[['vorp', 'vosp']], team_vorp_df.outcome, relimp = True)\n",
    "print(pov.round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that VOSP is more important than VORP.  Now this does not mean that VORP cant predict the number of wins a team has, rather that it does not add value to a prediction when you already have VOSP.  \n",
    "\n",
    "In short, The goal is to have the best starting lineup, depth can help you get there, but end of the day it is the starters that matters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VOBP - Value Over Bench Player\n",
    "\n",
    "VOBP is really useful to assessing the depth of a team, which is necessary for trades.  To calculate a player's VOBP, you take the points that a starting player scores and subtract the points that the best bench player at that position on that fantasy team scores.  This means that a players VOBP changes from fantasy team to fantasy team.\n",
    "\n",
    "As an example we can look at 2 teams in a given week"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'D/ST': 10.0, 'K': 16.0, 'QB': 27.26, 'RB': 8.8, 'TE': 14.0, 'WR': 15.9}\n",
      "Index(['Unnamed: 0', 'week', 'player', 'player_id', 'proteam', 'position',\n",
      "       'points', 'proj_points', 'fteam', 'vorp'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "vobp_replacement_dict = {}\n",
    "ddf = df[df.fteam != 0].copy()\n",
    "for w, wdf in ddf.groupby('week'):\n",
    "    vobp_replacement_dict[w] = {}\n",
    "    for t, tdf in wdf.groupby('fteam'):\n",
    "        vobp_replacement_dict[w][t] = {}\n",
    "        for p, pdf in tdf.groupby('position'):\n",
    "            if p in ['QB', 'TE', 'D/ST', 'K']:\n",
    "                if len(pdf) > 1:\n",
    "                    best_bench = pdf.sort_values('points', ascending = False).iloc[1]['points']\n",
    "                    vobp_replacement_dict[w][t][p] = best_bench\n",
    "                else:\n",
    "                    best_bench = df[(df.week == 5) & (df.fteam == 0) & (df.position == p)].points.max()\n",
    "                    vobp_replacement_dict[w][t][p] = best_bench\n",
    "            elif p in ['RB', 'WR']:\n",
    "                if len(pdf) > 2:\n",
    "                    best_bench = pdf.sort_values('points', ascending = False).iloc[2]['points']\n",
    "                    vobp_replacement_dict[w][t][p] = best_bench\n",
    "                else:\n",
    "                    best_bench = df[(df.week == 5) & (df.fteam == 0) & (df.position == p)].points.max()\n",
    "                    vobp_replacement_dict[w][t][p] = best_bench\n",
    "        \n",
    "print(vobp_replacement_dict[3][1])\n",
    "        \n",
    "ddf['vobp'] = ddf.apply(lambda x: x.points - vobp_replacement_dict[x.week][x.fteam][x.position], axis = 1)\n",
    "print(df.columns)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>player</th>\n",
       "      <th>position</th>\n",
       "      <th>vorp</th>\n",
       "      <th>vobp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1881</th>\n",
       "      <td>Panthers D/ST</td>\n",
       "      <td>D/ST</td>\n",
       "      <td>17.00</td>\n",
       "      <td>4.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1911</th>\n",
       "      <td>Robbie Gould</td>\n",
       "      <td>K</td>\n",
       "      <td>-3.00</td>\n",
       "      <td>-10.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974</th>\n",
       "      <td>Deshaun Watson</td>\n",
       "      <td>QB</td>\n",
       "      <td>6.40</td>\n",
       "      <td>4.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975</th>\n",
       "      <td>Carson Wentz</td>\n",
       "      <td>QB</td>\n",
       "      <td>2.22</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2120</th>\n",
       "      <td>Todd Gurley II</td>\n",
       "      <td>RB</td>\n",
       "      <td>-8.60</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2121</th>\n",
       "      <td>Leonard Fournette</td>\n",
       "      <td>RB</td>\n",
       "      <td>-3.70</td>\n",
       "      <td>4.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2122</th>\n",
       "      <td>Mark Ingram II</td>\n",
       "      <td>RB</td>\n",
       "      <td>18.60</td>\n",
       "      <td>27.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2236</th>\n",
       "      <td>Evan Engram</td>\n",
       "      <td>TE</td>\n",
       "      <td>16.30</td>\n",
       "      <td>10.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2237</th>\n",
       "      <td>O.J. Howard</td>\n",
       "      <td>TE</td>\n",
       "      <td>5.60</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2385</th>\n",
       "      <td>Amari Cooper</td>\n",
       "      <td>WR</td>\n",
       "      <td>17.80</td>\n",
       "      <td>8.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2386</th>\n",
       "      <td>Marquise Brown</td>\n",
       "      <td>WR</td>\n",
       "      <td>1.90</td>\n",
       "      <td>-7.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2387</th>\n",
       "      <td>A.J. Green</td>\n",
       "      <td>WR</td>\n",
       "      <td>-3.00</td>\n",
       "      <td>-12.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2388</th>\n",
       "      <td>Alshon Jeffery</td>\n",
       "      <td>WR</td>\n",
       "      <td>-3.00</td>\n",
       "      <td>-12.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2389</th>\n",
       "      <td>Corey Davis</td>\n",
       "      <td>WR</td>\n",
       "      <td>1.40</td>\n",
       "      <td>-8.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2390</th>\n",
       "      <td>DJ Moore</td>\n",
       "      <td>WR</td>\n",
       "      <td>9.40</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2391</th>\n",
       "      <td>Sterling Shepard</td>\n",
       "      <td>WR</td>\n",
       "      <td>17.10</td>\n",
       "      <td>7.70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 player position   vorp   vobp\n",
       "1881      Panthers D/ST     D/ST  17.00   4.00\n",
       "1911       Robbie Gould        K  -3.00 -10.00\n",
       "1974     Deshaun Watson       QB   6.40   4.18\n",
       "1975       Carson Wentz       QB   2.22   0.00\n",
       "2120     Todd Gurley II       RB  -8.60   0.00\n",
       "2121  Leonard Fournette       RB  -3.70   4.90\n",
       "2122     Mark Ingram II       RB  18.60  27.20\n",
       "2236        Evan Engram       TE  16.30  10.70\n",
       "2237        O.J. Howard       TE   5.60   0.00\n",
       "2385       Amari Cooper       WR  17.80   8.40\n",
       "2386     Marquise Brown       WR   1.90  -7.50\n",
       "2387         A.J. Green       WR  -3.00 -12.40\n",
       "2388     Alshon Jeffery       WR  -3.00 -12.40\n",
       "2389        Corey Davis       WR   1.40  -8.00\n",
       "2390           DJ Moore       WR   9.40   0.00\n",
       "2391   Sterling Shepard       WR  17.10   7.70"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ddf[(ddf.week == 3) & (ddf.fteam == 2)][['player', 'position', 'vorp', 'vobp']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    team             player position   vorp   vobp\n",
      "0      1      Steelers D/ST     D/ST -22.00   0.00\n",
      "1      1        Mike Nugent        K   3.00 -28.00\n",
      "2      1      Lamar Jackson       QB  51.04  -3.10\n",
      "3      1         Josh Allen       QB  -5.16 -14.80\n",
      "4      1    Ezekiel Elliott       RB  63.60  45.80\n",
      "5      1         Nick Chubb       RB  55.40  37.60\n",
      "6      1        Sony Michel       RB  31.60  13.80\n",
      "7      1        Matt Breida       RB   3.90  -8.40\n",
      "8      1   Devin Singletary       RB -27.70 -45.50\n",
      "9      1       Tony Pollard       RB -13.60 -36.70\n",
      "10     1       Mark Andrews       TE  57.00 -17.90\n",
      "11     1        Julio Jones       WR  43.00  24.70\n",
      "12     1      Brandin Cooks       WR  -0.30  -4.40\n",
      "13     1       Stefon Diggs       WR  36.10  17.80\n",
      "14     2      Seahawks D/ST     D/ST -14.00  -4.00\n",
      "15     2      Zane Gonzalez        K  11.00 -36.00\n",
      "16     2     Deshaun Watson       QB  22.36  57.10\n",
      "17     2       Carson Wentz       QB -12.06  12.78\n",
      "18     2     Todd Gurley II       RB  33.40  35.00\n",
      "19     2  Leonard Fournette       RB  49.70  51.30\n",
      "20     2     Mark Ingram II       RB  57.10  58.70\n",
      "21     2    Adrian Peterson       RB -10.50 -16.70\n",
      "22     2        Evan Engram       TE  25.20  38.30\n",
      "23     2        O.J. Howard       TE  -5.00   3.50\n",
      "24     2       Amari Cooper       WR  40.80  34.70\n",
      "25     2     Marquise Brown       WR  -2.50  -8.60\n",
      "26     2         A.J. Green       WR -53.70 -59.80\n",
      "27     2     Alshon Jeffery       WR  -4.20 -10.30\n",
      "28     2           DJ Moore       WR  -4.60 -10.70\n",
      "29     2   Sterling Shepard       WR  -1.20  -7.30\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "for t in [1,2]:\n",
    "    for pid in ddf[(ddf.fteam == t) & (ddf.week == 8)].player_id:\n",
    "        \n",
    "        pdf = ddf[(ddf.player_id == pid) & (ddf.week < 8)]\n",
    "        try:\n",
    "            row = [t, pdf.iloc[0].player, pdf.iloc[0].position, pdf.vorp.sum(), pdf.vobp.sum()]\n",
    "            data.append(row)\n",
    "        except:\n",
    "            continue\n",
    "        \n",
    "trade_df = pd.DataFrame(data = data, columns = ['team', 'player', 'position', 'vorp', 'vobp'])\n",
    "\n",
    "print(trade_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Value over Replacement - Team Addition\n",
    "\n",
    "We can use the same logic to determine how strong a fantasy team is based on how it performs vs a replacement level team.\n",
    "\n",
    "but what is a replacement level team?\n",
    "\n",
    "In most weeks, we define a replacement level team as the median score of all teams across the league, so a team that is above replacement scored more than at least half of the other teams in the league, while a team that is below replacement scores less than half the other teams in the league."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Unnamed: 0', 'lid', 'week', 'tid', 'real_score', 'espn_lineup_score',\n",
       "       'best_score', 'proj_score', 'opp_score', 'opp_proj_score', 'zero_count',\n",
       "       'reg_standing', 'final_standing', 'real_vs_proj', 'real_vs_espn',\n",
       "       'real_vs_best', 'espn_vs_best', 'coach_win', 'bad_lineup',\n",
       "       'lucky_score', 'unlucky_score', 'above_median', 'score_vs_median',\n",
       "       'opp_vs_median', 'luck_score', 'lucky_win', 'unluck_loss', 'standing',\n",
       "       'league_size'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "team_vor_df = pd.read_csv('team_vor.csv')\n",
    "team_vor_df.head()\n",
    "team_vor_df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determining Matchup Luck\n",
    "\n",
    "One way that team value over replacement is useful is to explore the role of luck.  You can think of one version of luck as matchup luck, specifically who you have to play in a given week.  There is no defense in fantasy football, there is nothing you can do to prevent your opponent from scoring points.  So while scoring above the median should be enough to win that week, we all remember when we had the second highest score of the week, but lost because we faced the highest scoring team.\n",
    "\n",
    "We can look across a league to see how many lucky wins or unlucky losses occured"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-85, 85)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "league_df = team_vor_df[team_vor_df.lid == 38726555].copy()\n",
    "league_df.head()\n",
    "\n",
    "plt.figure()\n",
    "plt.fill([0,85,85, 0], [0,0,85,85], 'r', alpha=0.1, edgecolor='r')\n",
    "plt.fill([-85,0,0, -85], [-85,-85,0, 0], 'g', alpha=0.1, edgecolor='g')\n",
    "sns.scatterplot(x = 'opp_vs_median',y = 'score_vs_median', hue = 'tid', style ='coach_win', data = league_df, \n",
    "                style_order = [True, False], legend=False,\n",
    "                 s = 100)\n",
    "plt.axhline(0)\n",
    "plt.axvline(0)\n",
    "plt.xlim([-85, 85])\n",
    "plt.ylim([-85, 85])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Luck vs final standing\n",
    "\n",
    "We can begin to explore how important luck is by comparing how many lucky wins a team gets vs where they finish"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x20d097c0f88>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "season_luck_df = pd.read_csv('season_luck.csv')\n",
    "\n",
    "plt.figure()\n",
    "sns.pointplot(x = 'standing', y = 'lucky_win', data = season_luck_df[season_luck_df.standing <= 10], color = 'g')\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "sns.pointplot(x = 'standing', y = 'unluck_loss', data = season_luck_df[season_luck_df.standing <= 10], color = 'r')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Breaking down luck even further\n",
    "\n",
    "One way we can break matchup luck down more is thinking about how lucky a win or how unlucky a loss is.  Specifically, how many teams would you have beaten or lost to.  For example, if a team is the team is the top scoring team, there is no luck involved, they are going to win.  Whereas if they were the 3rd highest scoring team, they should win, but there are 2 teams that would have beaten them so we can give them a luck score of 2.  We can do the same with losses, ust how many teams you could beaten given your score.\n",
    "\n",
    "We can even consolidate this as to total season long luck is by combining the luckiness of your wins and subtracting the unluckiness your losses. (this is what the luck score in the season luck file is)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x20d099249c8>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.figure()\n",
    "sns.pointplot(x = 'standing', y = 'luck_score', data = season_luck_df[season_luck_df.standing <= 10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "1. Try to think in terms of value above replacement when assessing the value of players and of teams. \n",
    "\n",
    "2. Both depth and starting lineup strength are important, but depth seems to be a better predictor\n",
    "\n",
    "3. luck matters, but not a ton\n",
    "\n",
    "# What to do Next?\n",
    "\n",
    "* If interested in learning python to enable you to create these sorts of investigations, check out https://www.fantasyfootballdatapros.com/blog/beginner/1\n",
    "\n",
    "* If you know python or want to just explore this without following a blog, The package I use to gather data from my and other fantasy football leagues can be found at https://github.com/cwendt94/espn-api\n",
    "\n",
    "* Finally, if you just want to read more about explorations into fantasy football with data science, check out these blogs\n",
    "    - https://stmorse.github.io/blog.html\n",
    "    - https://www.alexcates.com/blog (this one is mine)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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