yi-jiayu/benford.ipynb

## benford.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def benford(b):\n",
    "    return {d: math.log(1 + 1/d, b) for d in range(1, b)}\n",
    "\n",
    "def plot_benford(b):\n",
    "    predicted = benford(b)\n",
    "    xs = list(range(1, b))\n",
    "    ys = [predicted[x] for x in xs]\n",
    "    plt.bar(xs, ys)\n",
    "    plt.xticks(xs)\n",
    "    plt.title('Frequency of leading digits according to Benford\\'s law for base-{}'.format(b))\n",
    "    \n",
    "plot_benford(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "predicted = benford(10)\n",
    "\n",
    "def bars(counts, compact=False, width=0.25):\n",
    "    xs = list(range(1, 10))\n",
    "    ys = [counts[x] for x in xs]\n",
    "    bs = [predicted[x] for x in xs]\n",
    "    percent = [y/sum(ys) for y in ys]\n",
    "\n",
    "    plt.bar(xs, percent, width, label='Actual')\n",
    "    plt.bar([x + width for x in xs], bs, width, label='Benford')\n",
    "\n",
    "    plt.xticks(xs)\n",
    "\n",
    "    if not compact:\n",
    "        plt.xlabel('Digit')\n",
    "        plt.ylabel('Frequency')\n",
    "        plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import praw\n",
    "\n",
    "CLIENT_ID = os.getenv('REDDIT_CLIENT_ID')\n",
    "CLIENT_SECRET = os.getenv('REDDIT_CLIENT_SECRET')\n",
    "REDDIT_USERNAME = os.getenv('REDDIT_USERNAME')\n",
    "\n",
    "reddit = praw.Reddit(client_id=CLIENT_ID, client_secret=CLIENT_SECRET,\n",
    "                     user_agent='Analysing Reddit Submissions for Benfords\\'s Law by /u/' + REDDIT_USERNAME)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hot: 1000\n",
      "new: 679\n",
      "rising: 1000\n",
      "controversial: 909\n",
      "top: 993\n",
      "gilded: 958\n"
     ]
    }
   ],
   "source": [
    "tabs = ('hot', 'new', 'rising', 'controversial', 'top', 'gilded')\n",
    "submissions = {tab: [] for tab in tabs}\n",
    "\n",
    "for tab in tabs:\n",
    "    args = {'limit': 1000}\n",
    "    if tab == 'top':\n",
    "        args['time_filter'] = 'week'\n",
    "        \n",
    "    for submission in getattr(reddit.subreddit('all'), tab)(**args):\n",
    "        submissions[tab].append(submission)\n",
    "        \n",
    "    print(tab, len(submissions[tab]), sep=': ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "\n",
    "scores_first_digits = {}\n",
    "num_comments_first_digits = {}\n",
    "\n",
    "for tab in tabs:\n",
    "    scores = [abs(s.score) for s in submissions[tab] if s.score != 0]\n",
    "    scores_first_digits[tab] = Counter(int(str(sc)[0]) for sc in scores)\n",
    "    \n",
    "    num_comments = [abs(s.num_comments) for s in submissions[tab] if s.num_comments != 0]\n",
    "    num_comments_first_digits[tab] = Counter(int(str(nc)[0]) for nc in num_comments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\n",
    "\n",
    "for i, tab in enumerate(tabs):   \n",
    "    plt.subplot(3, 2, i+1)\n",
    "    plt.title(tab)\n",
    "    bars(scores_first_digits[tab], compact=True)\n",
    "    \n",
    "plt.suptitle('Frequency of first digits of submission scores by tab')\n",
    "plt.tight_layout()\n",
    "plt.subplots_adjust(top=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "\n",
    "for i, tab in enumerate(tabs):\n",
    "    plt.subplot(3, 2, i+1)\n",
    "    plt.title(tab)\n",
    "    bars(num_comments_first_digits[tab], compact=True)\n",
    "    \n",
    "plt.suptitle('Frequency of first digits of number of comments\\nper submission by tab')\n",
    "plt.tight_layout()\n",
    "plt.subplots_adjust(top=0.85)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RzaxrZlYT06ZN4zOf+QzPPPMMjY2NLFmyhAEDBtCrVy8mTZrE2rVrAVixYgUAu+yyC6tXr36zfv/+/ZkzZw7AJt1MK1euZK+9sg6VyZMnb6W1aVmRLYvZwEBJA4DnyA5Yf7K0gKSBEbEwDZ4INL+fAdwi6QpgT2Ag8EiBsZrZdmJrn7U4ZcoUxo8fv8m4U045hXnz5jF69Gjq6+vp3LkzJ5xwAt/5znc488wzOe+88+jatSsPPvggEyZM4KyzzuI73/kOw4f/s6f+K1/5CuPGjeOKK67g6KOPLl/sVlfoM7glnQBcSXbq7KSI+LakS4GGiJgh6cfAscB64GXg/IiYm+p+DfhXYANwQUT8vrVl1dfXx5Y8/KiqU2e7fDK3jA9wm21d8+bN44ADDqh1GNuESttK0pyIaP1oOwVfZxERM4GZZeMuKXn/pVbqfhv4dnHRmZlZtXy7DzMzy+VkYWZmuZwszMwsl5OFmZnlcrIwM7NcvkW5mW1fqrmHW5vml386fF1dHQcffDARQV1dHVdddRWHHnroZi1u/vz5jB07FklMmzaNd73rXW2ex+TJk2loaOCqq67arBgqccvCzGwLde3alccff5wnnniC7373u1x00UWbPa/p06czZswYHnvssaoSRUS8ebuQIjlZmJm1o1WrVtGzZ883h3/wgx9wyCGH8N73vpcJEyYA0NjYyAEHHMA555zDgQceyMiRI1m3bh0zZ87kyiuv5LrrruOoo44C4IorruCggw7ioIMO4sorr9yk/uc//3mGDh3KkiVLuOGGG9hvv/340Ic+xAMPPNDu6+VuKDOzLbRu3ToGDx7Mq6++yvPPP88999wDwKxZs1i4cCGPPPIIEcHo0aO577776NevHwsXLmTKlCn8/Oc/5xOf+AS33347Z5xxBueddx49evTgwgsvZM6cOdxwww08/PDDRATDhw/nQx/6ED179mTBggXccMMN/PSnP+X5559nwoQJzJkzh912242jjjqKIUOGtOs6umVhZraFmruh5s+fzx/+8Ac+85nPEBHMmjWLWbNmMWTIEIYOHcr8+fNZuDC7Bd6AAQMYPHgwAO9///tpbGx8y3zvv/9+Pvaxj9G9e3d69OjBySefzJ///GcA9tlnHz7wgQ8A8PDDD3PkkUfSp08fOnfuzGmnndbu6+iWhZlZOxoxYgQvvfQSy5YtIyK46KKL+NznPrdJmcbGRnbeeec3h+vq6li3bt1b5tXavfu6d+++yXA1t0PfEm5ZmJm1o/nz57Nx40Z69+7N8ccfz6RJk1izZg0Azz33HC+++GLV8zriiCOYPn06a9eu5ZVXXuGOO+7g8MMPf0u54cOHc++997J8+XLWr1/Pbbfd1m7r08wtCzPbvtTgzs/Nxywgaw3ceOON1NXVMXLkSObNm8eIESMA6NGjBzfffDN1dXVVzXfo0KGceeaZDBs2DICzzz6bIUOGvKXLao899mDixImMGDGCPfbYg6FDh7Jx48b2W0EKvkX51uRblJvtmHyL8uptyS3K3Q1lZma5nCzMzCyXk4WZbfO2l+70Im3pNnKyMLNtWpcuXVi+fLkTRisiguXLl9OlS5fNnofPhjKzbVrfvn1pampi2bJltQ6lQ+vSpQt9+/bd7PpOFma2Tdtpp50YMGBArcPY7rkbyszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCxXoclC0ihJCyQtkjS+wvQvS3pK0l8l/bekfUqmbZT0eHrNKDJOMzNrXWGnzkqqA64GjgOagNmSZkTEUyXFHgPqI2KtpH8Dvg80P7VjXUQMLio+MzOrXpEti2HAoohYHBGvA1OBMaUFIuKPEbE2DT4EbP4VI2ZmVpgik8VewJKS4aY0riVnAb8vGe4iqUHSQ5I+WqmCpHNTmQZfvWlmVpwir+Cu9Iy/ijdvkXQGUA98qGR0v4hYKmlf4B5Jf4uIpzeZWcS1wLWQPc+ifcI2M7NyRbYsmoC9S4b7AkvLC0k6FvgaMDoiXmseHxFL09/FwL3AkAJjNTOzVhSZLGYDAyUNkNQZGAtsclaTpCHANWSJ4sWS8T0l7Zze7w58ECg9MG5mZltRYd1QEbFB0vnAnUAdMCki5kq6FGiIiBnAD4AewG2SAJ6NiNHAAcA1kt4gS2iXlZ1FZWZmW1Ghd52NiJnAzLJxl5S8P7aFen8BDi4yNjMzq56v4DYzs1xOFmZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCyXk4WZmeVysjAzs1xOFmZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCyXk4WZmeVysjAzs1xOFmZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCyXk4WZmeVysjAzs1yFJgtJoyQtkLRI0vgK078s6SlJf5X035L2KZk2TtLC9BpXZJxmZta6wpKFpDrgauDDwCDgdEmDyoo9BtRHxHuBacD3U91ewARgODAMmCCpZ1GxmplZ64psWQwDFkXE4oh4HZgKjCktEBF/jIi1afAhoG96fzxwV0SsiIiXgbuAUQXGamZmrSgyWewFLCkZbkrjWnIW8Pu21JV0rqQGSQ3Lli3bwnDNzKwlRSYLVRgXFQtKZwD1wA/aUjciro2I+oio79Onz2YHamZmrSsyWTQBe5cM9wWWlheSdCzwNWB0RLzWlrpmZrZ1VJUsJB20GfOeDQyUNEBSZ2AsMKNsvkOAa8gSxYslk+4ERkrqmQ5sj0zjzMysBjpVWe5n6Qt/MnBLRPwjr0JEbJB0PtmXfB0wKSLmSroUaIiIGWTdTj2A2yQBPBsRoyNihaRvkSUcgEsjYkWb1szMzNpNVckiIg6TNBD4V6BB0iPADRFxV069mcDMsnGXlLw/tpW6k4BJ1cRnZmbFqrZlQUQslPR1oAH4CTBEWXPg4oj4dVEB7oj6j/9dbpnGy07cCpGYmWWqPWbxXkk/AuYBRwMnRcQB6f2PCozPzMw6gGpbFlcBPydrRaxrHhkRS1Nrw8zMtmPVJosTgHURsRFA0tuALhGxNiJuKiw6MzPrEKq9zuJuoGvJcLc0zszMdgDVJosuEbGmeSC971ZMSGZm1tFUmyxekTS0eUDS+4F1rZQ3M7PtSLXHLC4gu3Cu+ZYbewCnFROSmZl1NNVelDdb0v7Ae8hu8jc/ItYXGpmZmXUYVV+UBxwC9E91hkgiIn5RSFRmZtahVJUsJN0EvAt4HNiYRgfgZFErE3eroszK4uMwsx1CtS2LemBQRFR8HoWZmW3fqj0b6kngX4oMxMzMOq5qWxa7A0+lu802P6CIiBhdSFRmZtahVJssJhYZhJmZdWzVnjr7J0n7AAMj4m5J3cgeaGRmZjuAam9Rfg4wjewRqAB7AdOLCsrMzDqWag9wfwH4ILAKsgchAe8oKigzM+tYqk0Wr0XE680DkjqRXWdhZmY7gGqTxZ8kXQx0lXQccBvwm+LCMjOzjqTaZDEeWAb8DfgcMBPwE/LMzHYQ1Z4N9QbZY1V/Xmw4ZmbWEVV7b6i/U+EYRUTs2+4RmZlZh9OWe0M16wJ8HOjV/uGYmVlHVNUxi4hYXvJ6LiKuBI4uODYzM+sgqr0ob2jJq17SecAuVdQbJWmBpEWSxleYfoSkRyVtkHRq2bSNkh5PrxlVr5GZmbW7aruhfljyfgPQCHyitQqS6oCrgeOAJmC2pBkR8VRJsWeBM4ELK8xiXUQMrjI+MzMrULVnQx21GfMeBiyKiMUAkqYCY4A3k0VENKZpb2zG/M3MbCup9myoL7c2PSKuqDB6L2BJyXATMLz60OgiqYGsJXNZRLzlXlSSzgXOBejXr18bZm1mZm3RlrOhDgGajx2cBNzHpsmgnCqMa8stQvpFxFJJ+wL3SPpbRDy9ycwirgWuBaivr/ftR8zMCtKWhx8NjYjVAJImArdFxNmt1GkC9i4Z7gssrTawiFia/i6WdC8wBHi61UpmZlaIam/30Q94vWT4daB/Tp3ZwEBJAyR1Bsbyz5ZJqyT1lLRzer872R1vn2q9lpmZFaXalsVNwCOS7iDrSvoY8IvWKkTEBknnA3eSPShpUkTMlXQp0BARMyQdAtwB9AROkvTNiDgQOAC4Jh34fhvZMQsnCzOzGqn2bKhvS/o9cHga9dmIeKyKejPJbjpYOu6Skvezybqnyuv9BTi4mtjMzKx41XZDAXQDVkXEj4EmSQMKisnMzDqYaq/gngB8FbgojdoJuLmooMzMrGOptmXxMWA08Aq8eaZS7u0+zMxs+1Btsng9IoJ0nYSk7sWFZGZmHU21yeJWSdcAb5d0DnA3fhCSmdkOo9qzoS5Pz95eBbwHuCQi7io0MjMz6zByk0W6e+ydEXEs4ARhZrYDyu2GioiNwFpJu22FeMzMrAOq9gruV4G/SbqLdEYUQER8sZCorEPpP/53uWUaLztxK0RiZrVSbbL4XXqZmdkOqNVkIalfRDwbETdurYDMzKzjyWtZTAeGAki6PSJOKT4k2yZNrOKQ1sSVxcdhZoXIO8Bd+gCjfYsMxMzMOq68ZBEtvDczsx1IXjfU+yStImthdE3vScMREbsWGp2ZmXUIrSaLiKjbWoGYmVnH1ZbnWZiZ2Q7KycLMzHI5WZiZWS4nCzMzy+VkYWZmuZwszMwsl5OFmZnlcrIwM7NcThZmZpar0GQhaZSkBZIWSRpfYfoRkh6VtEHSqWXTxklamF7jiozTzMxaV1iySM/uvhr4MDAIOF3SoLJizwJnAreU1e0FTACGA8OACZJ6FhWrmZm1rsiWxTBgUUQsjojXganAmNICEdEYEX8F3iirezxwV0SsiIiXgbuAUQXGamZmrSgyWewFLCkZbkrj2q2upHMlNUhqWLZs2WYHamZmrSsyWajCuGqfiVFV3Yi4NiLqI6K+T58+bQrOzMyql/c8iy3RBOxdMtwXWNqGukeW1b23XaKyHYMf82rWropsWcwGBkoaIKkzMBaYUWXdO4GRknqmA9sj0zgzM6uBwpJFRGwAzif7kp8H3BoRcyVdKmk0gKRDJDUBHweukTQ31V0BfIss4cwGLk3jzMysBorshiIiZgIzy8ZdUvJ+NlkXU6W6k4BJRcZnZmbV8RXcZmaWy8nCzMxyOVmYmVkuJwszM8vlZGFmZrmcLMzMLFehp86aFaH/+N/llmnsshUCMduBuGVhZma53LIw2xp8ryrbxrllYWZmuZwszMwsl5OFmZnlcrIwM7NcThZmZpbLZ0OZbSFf92E7ArcszMwsl1sWZjsiX/dhbeSWhZmZ5XLLwswKlXdMp/GyE7dSJLYl3LIwM7NcThZmZpbLycLMzHL5mIWZ1ZbPzNomuGVhZma53LIw2874inIrQqEtC0mjJC2QtEjS+ArTd5b0qzT9YUn90/j+ktZJejy9flZknGZm1rrCWhaS6oCrgeOAJmC2pBkR8VRJsbOAlyPi3ZLGAt8DTkvTno6IwUXFZ2ZWa1W1AjvIdShFdkMNAxZFxGIASVOBMUBpshgDTEzvpwFXSVKBMZmZtc4H3CsqshtqL2BJyXBTGlexTERsAFYCvdO0AZIek/QnSYdXWoCkcyU1SGpYtmxZ+0ZvZmZvKrJlUamFEFWWeR7oFxHLJb0fmC7pwIhYtUnBiGuBawHq6+vL521mtgkf/N98RbYsmoC9S4b7AktbKiOpE7AbsCIiXouI5QARMQd4GtivwFjNzKwVRbYsZgMDJQ0AngPGAp8sKzMDGAc8CJwK3BMRIakPWdLYKGlfYCCwuMBYzcw6pg5yDKWwZBERGySdD9wJ1AGTImKupEuBhoiYAVwP3CRpEbCCLKEAHAFcKmkDsBE4LyJWFBWrmZm1rtCL8iJiJjCzbNwlJe9fBT5eod7twO1FxmZmZtXz7T7MzCyXk4WZmeVysjAzs1xOFmZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCyXk4WZmeVysjAzs1xOFmZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCyXk4WZmeVysjAzs1xOFmZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMzCxXoclC0ihJCyQtkjS+wvSdJf0qTX9YUv+SaRel8QskHV9knGZm1rrCkoUbUU7nAAAGbUlEQVSkOuBq4MPAIOB0SYPKip0FvBwR7wZ+BHwv1R0EjAUOBEYBP03zMzOzGiiyZTEMWBQRiyPidWAqMKaszBjgxvR+GnCMJKXxUyPitYj4O7Aozc/MzGpAEVHMjKVTgVERcXYa/jQwPCLOLynzZCrTlIafBoYDE4GHIuLmNP564PcRMa1sGecC56bB9wAL2nEVdgdeasf5bSnH07qOFE9HigUcT54dPZ59IqJPXqFOBQagCuPKM1NLZaqpS0RcC1zb9tDySWqIiPoi5r05HE/rOlI8HSkWcDx5HE91iuyGagL2LhnuCyxtqYykTsBuwIoq65qZ2VZSZLKYDQyUNEBSZ7ID1jPKyswAxqX3pwL3RNYvNgMYm86WGgAMBB4pMFYzM2tFYd1QEbFB0vnAnUAdMCki5kq6FGiIiBnA9cBNkhaRtSjGprpzJd0KPAVsAL4QERuLirUFhXRvbQHH07qOFE9HigUcTx7HU4XCDnCbmdn2w1dwm5lZLicLMzPL5WRRRtIkSS+ma0BqTtLekv4oaZ6kuZK+VMNYukh6RNITKZZv1iqWUpLqJD0m6bcdIJZGSX+T9Likhg4Qz9slTZM0P+1DI2oYy3vSdml+rZJ0QQ3j+fe0Hz8paYqkLrWKJcXzpRTL3Fpul5b4mEUZSUcAa4BfRMRBHSCePYA9IuJRSbsAc4CPRsRTNYhFQPeIWCNpJ+B+4EsR8dDWjqUsri8D9cCuEfGRGsfSCNRHRIe4yEvSjcCfI+K6dFZit4j4RweIqw54juxC3WdqsPy9yPbfQRGxLp1QMzMiJm/tWFI8B5Hd5WIY8DrwB+DfImJhLeKpxC2LMhFxH9mZWR1CRDwfEY+m96uBecBeNYolImJNGtwpvWr6a0NSX+BE4LpaxtERSdoVOILsrEMi4vWOkCiSY4Cna5EoSnQCuqZrvLpR22u5DiC7a8XaiNgA/An4WA3jeQsni21IuivvEODhGsZQJ+lx4EXgroioWSzJlcBXgDdqHEezAGZJmpNuR1NL+wLLgBtSN911krrXOKZmY4EptVp4RDwHXA48CzwPrIyIWbWKB3gSOEJSb0ndgBPY9MLkmnOy2EZI6gHcDlwQEatqFUdEbIyIwWRX1Q9LzeeakPQR4MWImFOrGCr4YEQMJbvb8hdSt2atdAKGAv8vIoYArwBveVTA1pa6w0YDt9Uwhp5kNywdAOwJdJd0Rq3iiYh5ZHfdvousC+oJsmvMOgwni21AOj5wO/DLiPh1reMBSN0Z95LdQr5WPgiMTscJpgJHS7q5hvEQEUvT3xeBO6jt3ZKbgKaS1t80suRRax8GHo2IF2oYw7HA3yNiWUSsB34NHFrDeIiI6yNiaEQcQdYV3mGOV4CTRYeXDipfD8yLiCtqHEsfSW9P77uSfeDm1yqeiLgoIvpGRH+ybo17IqJmvw4ldU8nIZC6e0aSdS/URET8L7BE0nvSqGPI7opQa6dTwy6o5FngA5K6pc/YMWTHA2tG0jvS337AydR+G22iyLvObpMkTQGOBHaX1ARMiIjraxjSB4FPA39LxwoALo6ImTWIZQ/gxnQmy9uAWyOi5qerdiDvBO7IvnvoBNwSEX+obUj8H+CXqetnMfDZWgaT+uOPAz5Xyzgi4mFJ04BHybp7HqP2t9m4XVJvYD3ZLY5ernE8m/Cps2ZmlsvdUGZmlsvJwszMcjlZmJlZLicLMzPL5WRhZma5nCzMNpOkjenuqXPTnXi/LOltaVq9pJ9UMY+/pL/9JX2y6JjNNpdPnTXbTJLWRESP9P4dwC3AAxExYTPmdSRwYa3vmmvWErcszNpBur3HucD5yhzZ/HyNdOX7XZIelXSNpGck7Z6mNd/F9zLg8NRS+ffarIVZy5wszNpJRCwm+0y9o2zSBLJbkQwlu19UvwrVx5M9d2JwRPyo2EjN2s63+zBrX6ow7jDSswki4g+SOtRtHMyq4ZaFWTuRtC+wkexZH5tMqkE4Zu3KycKsHUjqA/wMuCreetbI/cAnUrmRQM8Ks1gN7FJokGZbwMnCbPN1bT51FrgbmAV8s0K5bwIjJT1K9iyH58mSQ6m/AhvSKbg+wG0djk+dNSuYpJ2BjRGxQdIIsifXDa51XGZt4QPcZsXrB9yaLth7HTinxvGYtZlbFmZmlsvHLMzMLJeThZmZ5XKyMDOzXE4WZmaWy8nCzMxy/X8p0JW9mB6C9QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of submission scores in hot')\n",
    "bars(scores_first_digits['hot'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of submission scores in new')\n",
    "bars(scores_first_digits['new'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of submission scores in rising')\n",
    "bars(scores_first_digits['rising'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of submission scores in top')\n",
    "bars(scores_first_digits['top'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of number of comments\\nper submission in hot')\n",
    "bars(num_comments_first_digits['hot'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of number of comments\\nper submission in new')\n",
    "bars(num_comments_first_digits['new'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of number of comments\\nper submission in rising')\n",
    "bars(num_comments_first_digits['rising'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Frequency of first digits of number of comments\\nper submission in gilded')\n",
    "bars(num_comments_first_digits['gilded'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "959"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_time_top_submissions = []\n",
    "for submission in reddit.subreddit('all').top(limit=1000):\n",
    "    all_time_top_submissions.append(submission)\n",
    "len(all_time_top_submissions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weekly top score range:   [21954, 182957]\n",
      "All-time top score range: [59670, 283485]\n"
     ]
    }
   ],
   "source": [
    "weekly_top_min = min(s.score for s in submissions['top'])\n",
    "weekly_top_max = max(s.score for s in submissions['top'])\n",
    "\n",
    "all_time_top_min = min(s.score for s in all_time_top_submissions)\n",
    "all_time_top_max = max(s.score for s in all_time_top_submissions)\n",
    "\n",
    "print('Weekly top score range:  ', '[{}, {}]'.format(weekly_top_min, weekly_top_max))\n",
    "print('All-time top score range:', '[{}, {}]'.format(all_time_top_min, all_time_top_max))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scores = [abs(s.score) for s in all_time_top_submissions if s.score != 0]\n",
    "all_time_top_scores_first_digits = Counter(int(str(sc)[0]) for sc in scores)\n",
    "\n",
    "plt.title('Frequency of first digits of submission scores in top (all-time)')\n",
    "bars(all_time_top_scores_first_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weekly_top_scores = [s.score for s in submissions['top']]\n",
    "all_time_top_scores = [s.score for s in all_time_top_submissions]\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.suptitle('Score distribution')\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.hist(weekly_top_scores)\n",
    "_ = plt.title('Weekly')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.hist(all_time_top_scores)\n",
    "_ = plt.title('All time')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "\n",
    "def dump_data(outfile='submissions.csv'):\n",
    "    with open(outfile, 'w', newline='') as f:\n",
    "        writer = csv.writer(f)\n",
    "        writer.writerow(['tab', 'subreddit', 'id', 'score', 'num_comments'])\n",
    "        \n",
    "        for tab, ss in submissions.items():\n",
    "            for s in ss:\n",
    "                row = [tab, s.subreddit.display_name, s.id, s.score, s.num_comments]\n",
    "                writer.writerow(row)\n",
    "                \n",
    "        for s in all_time_top_submissions:\n",
    "            tab = 'top (all time)'\n",
    "            row = [tab, s.subreddit.display_name, s.id, s.score, s.num_comments]\n",
    "            writer.writerow(row)\n",
    "\n",
    "dump_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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