breakdown_by_play_call.ipynb

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      "name": "breakdown_by_play_call.ipynb",
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      "authorship_tag": "ABX9TyMMJDPCRgPEhCqO13533mVl",
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    "kernelspec": {
      "name": "python3",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/microprediction/firstdown/blob/main/breakdown_by_play_call.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bASjzoIUTneR"
      },
      "source": [
        "import pandas as pd\n",
        "df = pd.read_csv('https://raw.githubusercontent.com/microprediction/nflMarkov/master/inputData/pbp_nfldb_2009_2013.csv')\n",
        "pd.set_option('mode.chained_assignment',None)"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yX9O-ZuIMx7N"
      },
      "source": [
        "## Do you want 2nd and 1-yard or 1st and 10-yards? \n",
        "Thanks Ben Dilday for compiling the down data. \n",
        "\n",
        "This notebook examines 2nd down and close positions, and considers the question of whether 2nd down and 1 is superior to 1st down and 10 (plus one yard)\n",
        "\n",
        "### Step 1: We add the final field position achieved in the drive and a few other things... "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7y-yiSI3NUKI"
      },
      "source": [
        "drive_start = 0\n",
        "drive_starts = list()\n",
        "\n",
        "drive_index = 0\n",
        "drive_indexes = list()\n",
        "down_index = 0\n",
        "down_indexes = list()\n",
        "running_first_yfogs = list()    # Best field position of drive at 1st down\n",
        "running_yfogs = list() # just a check\n",
        "running_yfog = 0 \n",
        "best_first_yfog = 0 \n",
        "prev_team = None \n",
        "is_first_play_of_drive = True \n",
        "is_firsts = list()\n",
        "prev_down = 3 \n",
        "\n",
        "for yfog, dwn, posteam in zip(df['yfog'].values,df['dwn'].values, df['posteam'].values):\n",
        "\n",
        "    is_first_play_of_drive = (prev_team != posteam )\n",
        "    is_firsts.append(dwn==1)\n",
        "\n",
        "    if is_first_play_of_drive:\n",
        "        drive_start = yfog \n",
        "        drive_index += 1 \n",
        "         \n",
        "    # Update best field position for the drive \n",
        "    running_yfog = yfog \n",
        "    if dwn==1:\n",
        "        running_first_yfog = yfog\n",
        "\n",
        "    # Update    \n",
        "    running_first_yfogs.append(running_first_yfog)\n",
        "    running_yfogs.append(running_yfog)\n",
        "    drive_indexes.append(drive_index)\n",
        "    drive_starts.append(drive_start)\n",
        "\n",
        "    if (posteam!=prev_team):\n",
        "       down_index += 1 \n",
        "       down_indexes.append(down_index)\n",
        "    else:\n",
        "       down_indexes.append(down_index)\n",
        "       if dwn==1:\n",
        "          down_index+=1 \n",
        "\n",
        "    prev_team = posteam \n",
        "    prev_down = dwn\n",
        "     \n",
        "df['is_first'] = is_firsts\n",
        "df['running_yfog'] = running_yfogs\n",
        "df['running_first_yfog'] = running_first_yfogs\n",
        "df['drive_index'] = drive_indexes\n",
        "df['drive_start'] = drive_starts\n",
        "df['down_index'] = down_indexes\n",
        "   \n",
        "df['eventual_yfog'] = df[['drive_index','running_yfog']].groupby('drive_index').transform(max)\n",
        "df['eventual_down_yfog_raw'] = df[['down_index','running_yfog']].groupby('down_index').transform(max)\n",
        "df['eventual_down_yfog'] = [ d1 if dwn>1 else d2 for d1, d2, dwn in zip (df['eventual_down_yfog_raw'],df['eventual_down_yfog_raw'].shift(-1),df['dwn']) ]\n",
        "del df['eventual_down_yfog_raw']\n",
        "\n",
        "df['eventual_first_yfog'] = df[['drive_index','running_first_yfog']].groupby('drive_index').transform(max)\n",
        "df['eventual_drive'] = df['eventual_yfog'] - df['drive_start']\n",
        "df['eventual_gain'] = df['eventual_yfog'] - df['yfog']\n",
        "df['eventual_down_gain'] = df['eventual_down_yfog'] - df['yfog']\n",
        "df['will_get_first_down'] = df['eventual_down_gain']>=df['ytg']\n",
        "assert all(df['running_yfog']==df['yfog'])\n",
        "\n",
        "\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
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          "base_uri": "https://localhost:8080/",
          "height": 379
        },
        "id": "QMLGiL60CUp1",
        "outputId": "26c2bfad-815b-49af-d84d-acf75474bf25"
      },
      "source": [
        "df[170:180]"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>game_id</th>\n",
              "      <th>playername</th>\n",
              "      <th>dwn</th>\n",
              "      <th>ytg</th>\n",
              "      <th>yfog</th>\n",
              "      <th>type</th>\n",
              "      <th>posteam</th>\n",
              "      <th>yds</th>\n",
              "      <th>seas</th>\n",
              "      <th>away_team</th>\n",
              "      <th>home_team</th>\n",
              "      <th>is_first</th>\n",
              "      <th>running_yfog</th>\n",
              "      <th>running_first_yfog</th>\n",
              "      <th>drive_index</th>\n",
              "      <th>drive_start</th>\n",
              "      <th>down_index</th>\n",
              "      <th>eventual_yfog</th>\n",
              "      <th>eventual_down_yfog</th>\n",
              "      <th>eventual_first_yfog</th>\n",
              "      <th>eventual_drive</th>\n",
              "      <th>eventual_gain</th>\n",
              "      <th>eventual_down_gain</th>\n",
              "      <th>will_get_first_down</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>170</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>MichaelTurner</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>32</td>\n",
              "      <td>RUSH</td>\n",
              "      <td>ATL</td>\n",
              "      <td>1</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>False</td>\n",
              "      <td>32</td>\n",
              "      <td>24</td>\n",
              "      <td>32</td>\n",
              "      <td>24</td>\n",
              "      <td>78</td>\n",
              "      <td>33</td>\n",
              "      <td>33.0</td>\n",
              "      <td>24</td>\n",
              "      <td>9</td>\n",
              "      <td>1</td>\n",
              "      <td>1.0</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>171</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>MattRyan</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>33</td>\n",
              "      <td>PASS</td>\n",
              "      <td>ATL</td>\n",
              "      <td>0</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>False</td>\n",
              "      <td>33</td>\n",
              "      <td>24</td>\n",
              "      <td>32</td>\n",
              "      <td>24</td>\n",
              "      <td>78</td>\n",
              "      <td>33</td>\n",
              "      <td>33.0</td>\n",
              "      <td>24</td>\n",
              "      <td>9</td>\n",
              "      <td>0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>172</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>RickyWilliams</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>36</td>\n",
              "      <td>RUSH</td>\n",
              "      <td>MIA</td>\n",
              "      <td>7</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>True</td>\n",
              "      <td>36</td>\n",
              "      <td>36</td>\n",
              "      <td>33</td>\n",
              "      <td>36</td>\n",
              "      <td>79</td>\n",
              "      <td>84</td>\n",
              "      <td>58.0</td>\n",
              "      <td>84</td>\n",
              "      <td>48</td>\n",
              "      <td>48</td>\n",
              "      <td>22.0</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>173</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>PatWhite</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>43</td>\n",
              "      <td>PASS</td>\n",
              "      <td>MIA</td>\n",
              "      <td>0</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>False</td>\n",
              "      <td>43</td>\n",
              "      <td>36</td>\n",
              "      <td>33</td>\n",
              "      <td>36</td>\n",
              "      <td>79</td>\n",
              "      <td>84</td>\n",
              "      <td>58.0</td>\n",
              "      <td>84</td>\n",
              "      <td>48</td>\n",
              "      <td>41</td>\n",
              "      <td>15.0</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>174</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>ChadPennington</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>43</td>\n",
              "      <td>PASS</td>\n",
              "      <td>MIA</td>\n",
              "      <td>15</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>False</td>\n",
              "      <td>43</td>\n",
              "      <td>36</td>\n",
              "      <td>33</td>\n",
              "      <td>36</td>\n",
              "      <td>79</td>\n",
              "      <td>84</td>\n",
              "      <td>58.0</td>\n",
              "      <td>84</td>\n",
              "      <td>48</td>\n",
              "      <td>41</td>\n",
              "      <td>15.0</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>175</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>ChadPennington</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>58</td>\n",
              "      <td>PASS</td>\n",
              "      <td>MIA</td>\n",
              "      <td>0</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>True</td>\n",
              "      <td>58</td>\n",
              "      <td>58</td>\n",
              "      <td>33</td>\n",
              "      <td>36</td>\n",
              "      <td>79</td>\n",
              "      <td>84</td>\n",
              "      <td>84.0</td>\n",
              "      <td>84</td>\n",
              "      <td>48</td>\n",
              "      <td>26</td>\n",
              "      <td>26.0</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>176</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>ChadPennington</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>63</td>\n",
              "      <td>PASS</td>\n",
              "      <td>MIA</td>\n",
              "      <td>21</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>False</td>\n",
              "      <td>63</td>\n",
              "      <td>58</td>\n",
              "      <td>33</td>\n",
              "      <td>36</td>\n",
              "      <td>80</td>\n",
              "      <td>84</td>\n",
              "      <td>84.0</td>\n",
              "      <td>84</td>\n",
              "      <td>48</td>\n",
              "      <td>21</td>\n",
              "      <td>21.0</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>177</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>ChadPennington</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>84</td>\n",
              "      <td>PASS</td>\n",
              "      <td>MIA</td>\n",
              "      <td>0</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>True</td>\n",
              "      <td>84</td>\n",
              "      <td>84</td>\n",
              "      <td>33</td>\n",
              "      <td>36</td>\n",
              "      <td>80</td>\n",
              "      <td>84</td>\n",
              "      <td>82.0</td>\n",
              "      <td>84</td>\n",
              "      <td>48</td>\n",
              "      <td>0</td>\n",
              "      <td>-2.0</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>178</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>MattRyan</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>69</td>\n",
              "      <td>PASS</td>\n",
              "      <td>ATL</td>\n",
              "      <td>11</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>True</td>\n",
              "      <td>69</td>\n",
              "      <td>69</td>\n",
              "      <td>34</td>\n",
              "      <td>69</td>\n",
              "      <td>82</td>\n",
              "      <td>82</td>\n",
              "      <td>82.0</td>\n",
              "      <td>69</td>\n",
              "      <td>13</td>\n",
              "      <td>13</td>\n",
              "      <td>13.0</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>179</th>\n",
              "      <td>2009091300</td>\n",
              "      <td>MattRyan</td>\n",
              "      <td>2</td>\n",
              "      <td>18</td>\n",
              "      <td>72</td>\n",
              "      <td>PASS</td>\n",
              "      <td>ATL</td>\n",
              "      <td>10</td>\n",
              "      <td>2009</td>\n",
              "      <td>MIA</td>\n",
              "      <td>ATL</td>\n",
              "      <td>False</td>\n",
              "      <td>72</td>\n",
              "      <td>69</td>\n",
              "      <td>34</td>\n",
              "      <td>69</td>\n",
              "      <td>82</td>\n",
              "      <td>82</td>\n",
              "      <td>82.0</td>\n",
              "      <td>69</td>\n",
              "      <td>13</td>\n",
              "      <td>10</td>\n",
              "      <td>10.0</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        game_id      playername  ...  eventual_down_gain  will_get_first_down\n",
              "170  2009091300   MichaelTurner  ...                 1.0                False\n",
              "171  2009091300        MattRyan  ...                 0.0                False\n",
              "172  2009091300   RickyWilliams  ...                22.0                 True\n",
              "173  2009091300        PatWhite  ...                15.0                 True\n",
              "174  2009091300  ChadPennington  ...                15.0                 True\n",
              "175  2009091300  ChadPennington  ...                26.0                 True\n",
              "176  2009091300  ChadPennington  ...                21.0                 True\n",
              "177  2009091300  ChadPennington  ...                -2.0                False\n",
              "178  2009091300        MattRyan  ...                13.0                 True\n",
              "179  2009091300        MattRyan  ...                10.0                False\n",
              "\n",
              "[10 rows x 24 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CJUnhSqX-Hra"
      },
      "source": [
        "## Empirical analysis of stopping shy strategies\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6JnM4FVrc2iy"
      },
      "source": [
        "We compare stopping shy 1-yard, 2-yards or 3-yards to go versus making the first down with 0, 1, 2 or 3 extra yards. \n",
        "\n",
        "We'll report the implied value of possession, measured on yards, which is to say the value of possession in yards that makes the decision to get the first down a wash. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "onMDP0pqdozJ"
      },
      "source": [
        "# Parameters for stopping shy strategy\n",
        "FIRST_PLAY = 'PASS'\n",
        "SECOND_PLAY = 'PASS' # on 2nd and whatever 'RUSH' or 'PASS'\n",
        "# Parameter for alternative scenario where we reach first down \n",
        "EXTRA_YARDS = 0      # 0 means we get 10 yards on 1st down to complete the first down \n",
        "                     # 1 means we get 11 yards on 1st down to complete the first down one yard further down the field\n",
        "\n",
        " \n",
        "\n",
        "def strategy_implied_yards_per_possession(first_play:str, second_play:str, yards_to_go_on_second:int, extra_yards:int):\n",
        "  \"\"\"\n",
        "      Compute implied value of possession in yards when stretching for the first down, as \n",
        "      compared to a strategy of stopping shy\n",
        "\n",
        "          first_play: 'RUSH' or 'PASS'\n",
        "          second_play: 'RUSH' or 'PASS'\n",
        "  \"\"\"\n",
        "  from collections import Counter \n",
        "  the_2_data = df[(df['dwn']==2) & (df['ytg']==yards_to_go_on_second) & (df['type']==first_play) & (df['yfog']<70) & (df['yfog']>20)]\n",
        "  the_2_outcomes = Counter(the_2_data['yds'].values)\n",
        "  denom2 = 1.0* sum(the_2_outcomes.values()) \n",
        "  total_count = 0\n",
        "  probs = list()\n",
        "  yards = list() # Net yards compared to alternative strategy of taking first down \n",
        "  completed = list()\n",
        "  for yd2,ct2 in the_2_outcomes.items():\n",
        "    p2 = (1.0*ct2)/denom2 \n",
        "    if yd2<yards_to_go_on_second:\n",
        "        ytg3 = yards_to_go_on_second-yd2 \n",
        "        the_3_data = df[(df['dwn']==3) & (df['ytg']==ytg3) & (df['type']==second_play) & (df['yfog']<70) & (df['yfog']>20)]\n",
        "        rush_3_outcomes = Counter(the_3_data['yds'].values)\n",
        "        denom3 = 1.0*sum(rush_3_outcomes.values())\n",
        "        sum_p3 = 0\n",
        "        for yd3,ct3 in rush_3_outcomes.items():\n",
        "          p3 = ct3/denom3\n",
        "          sum_p3+=p3\n",
        "          probs.append(p2*p3)\n",
        "          if yd3>=ytg3:\n",
        "              completed.append(1.0)\n",
        "              yards.append(yd3+yd2-yards_to_go_on_second)\n",
        "          else:\n",
        "              completed.append(0.0)\n",
        "              yards.append(yd3+yd2-yards_to_go_on_second)\n",
        "    else:\n",
        "        probs.append(p2)\n",
        "        yards.append(yd2-yards_to_go_on_second)\n",
        "        completed.append(1.0)\n",
        "\n",
        "  sum_prob = sum(probs)\n",
        "  assert abs(sum_prob-1)<0.0001\n",
        "  mean_yards = sum([ w*y for w,y in zip(probs,yards)])\n",
        "  completion_prob = sum([ w*c for w,c in zip(probs,completed)])\n",
        "  cond_mean_yards = sum([ w*y for w,y,c in zip(probs,yards,completed) if c])/completion_prob\n",
        "  cond_mean_loss = sum([ w*y for w,y,c in zip(probs,yards,completed) if c<0.5])/(1-completion_prob)\n",
        "\n",
        "  def implied_poss_yards(p,cy,cl,x,t=2/160.):\n",
        "      \"\"\" Implied value of possession in yards. \n",
        "\n",
        "          Both turnovers and touchdowns are ambiguous. We are conservative, and assume\n",
        "          that with probability t a turnover occurs. \n",
        "\n",
        "          Assuming no turnover, we use the empirical yardages in the database. We complete the\n",
        "          first down with probability p and conditional *relative* gain cy-x \n",
        "\n",
        "          Set  \n",
        "                 rel gain      -   rel loss  - turnover = 0 \n",
        "              (1-t)*p * (cy-x) - (1-t)*(1-p)*(cl+v+x) - t*T = 0  \n",
        "           =>   (1-t)*(1-p)*(cl+v+x) = (1-t)*p * (cy-x) - t*T \n",
        "           =>   v =  p/(1-p)* (cy-x) - t/((1-t)(1-p)) T - x - cl\n",
        "                \n",
        "          where \n",
        "              v  = value of possession in yards \n",
        "              p  = first down completion probability\n",
        "              t  = turnover probability, conditional on loss\n",
        "              cy = mean yards gained versus the \"10-yard 1st down\", assuming completion\n",
        "              cl = mean yards lost versus the \"10-yard 1st down\", assuming no completion\n",
        "              x  = extra yards when making first down \n",
        "              t  = probability of turnover \n",
        "              T  = yardage value of turnover, assumed 80 yards\n",
        "        \n",
        "          assuming a turnover is a loss of T=80 yards\n",
        "      \"\"\"\n",
        "      T = 80\n",
        "      v =  (p/(1-p))*(cy-x) - t/((1-t)*(1-p))*T - x - cl\n",
        "      return v\n",
        "\n",
        "  imp = implied_poss_yards(p=completion_prob,cy=cond_mean_yards, cl=cond_mean_loss,x=extra_yards)\n",
        "  return imp \n",
        "      \n",
        "strategies = list()\n",
        "for x in [0,1,2,3]:\n",
        "  for ytgo2 in [1,2,3]:\n",
        "    for first_play in ['RUSH','PASS']:\n",
        "      for second_play in ['RUSH','PASS']:\n",
        "          strategies.append( (x,ytgo2, first_play,second_play,strategy_implied_yards_per_possession(first_play,second_play,ytgo2,x)))\n",
        "from pprint import pprint\n",
        "pprint(strategies)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qMyk0Q_n4Hff"
      },
      "source": [
        "# Print viable alternatives to first down "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lCxxlvGSBAzF",
        "outputId": "7c672b8a-f0ea-4645-9add-d665880b6ec2"
      },
      "source": [
        "print(\"\"\" \\\\begin{table}\n",
        "        \\\\begin{centering}\n",
        "        \\\\begin{tabular}{|c|c|c|c|c|}\n",
        "        \\\\hline\n",
        "          Extra yards & Yards to go & On second & On third & Implied \\\\\\\\\n",
        "          \\\\hline \"\"\")\n",
        "\n",
        "for x,ytg,p1,p2,imp in strategies:\n",
        "  if (imp>30) and (x>0):\n",
        "     print(str(x)+' & ' + str(ytg) + ' & ' + p1.lower() + ' & ' + p2.lower() + ' & '+str(round(imp)) + ' \\\\\\\\ ')\n",
        "    \n",
        "\n",
        "print(\"\"\"    \\\\hline \n",
        "      \\\\end{tabular}\n",
        "\n",
        "\n",
        "      \\\\caption{A team given the opportunity to gain a first down and extra yards in the\n",
        "              process might nonetheless choose to stop shy with $1$, $2$, or even $3$ yards to go. \n",
        "              The decision is expressed in terms of an implied belief in the value of a possession, measured in yards. \n",
        "              For example if possession is believed to be worth less than $45$ yards, then a team might ``decline'' a $12$-yard \n",
        "              first down completion by stopping one yard shy instead, assuming they plan to pass on second down and rush on third}\n",
        "      \\\\label{tab:viable}\n",
        "      \\\\end{centering}\n",
        "      \\\\end{table}\"\"\") "
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " \\begin{table}\n",
            "        \\begin{centering}\n",
            "        \\begin{tabular}{|c|c|c|c|c|}\n",
            "        \\hline\n",
            "          Extra yards & Yards to go & On second & On third & Implied \\\\\n",
            "          \\hline \n",
            "1 & 1 & rush & rush & 43 \\\\ \n",
            "1 & 1 & rush & pass & 43 \\\\ \n",
            "1 & 1 & pass & rush & 44 \\\\ \n",
            "1 & 1 & pass & pass & 43 \\\\ \n",
            "1 & 2 & pass & rush & 39 \\\\ \n",
            "1 & 2 & pass & pass & 37 \\\\ \n",
            "1 & 3 & pass & pass & 32 \\\\ \n",
            "2 & 1 & rush & pass & 31 \\\\ \n",
            "2 & 1 & pass & rush & 36 \\\\ \n",
            "2 & 1 & pass & pass & 37 \\\\ \n",
            "2 & 2 & pass & rush & 32 \\\\ \n",
            "2 & 2 & pass & pass & 31 \\\\ \n",
            "3 & 1 & pass & pass & 31 \\\\ \n",
            "    \\hline \n",
            "      \\end{tabular}\n",
            "\n",
            "\n",
            "      \\caption{A team given the opportunity to gain a first down and extra yards in the\n",
            "              process might nonetheless choose to stop shy with $1$, $2$, or even $3$ yards to go. \n",
            "              The decision is expressed in terms of an implied belief in the value of a possession, measured in yards. \n",
            "              For example if possession is believed to be worth less than $45$ yards, then a team might ``decline'' a $12$-yard \n",
            "              first down completion by stopping one yard shy instead, assuming they plan to pass on second down and rush on third}\n",
            "      \\label{tab:viable}\n",
            "      \\end{centering}\n",
            "      \\end{table}\n"
          ]
        }
      ]
    }
  ]
}