files/2016_primary_prediction/Prediction Check -- 538 2016 Primary.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# Double-checking FiveThirtyEight's 2016 Primary Predictions\n",
    "\n",
    "Here I look at the [predictions that FiveThiryEight made](https://projects.fivethirtyeight.com/election-2016/primary-forecast/) about the 2016 Presidential Primaries.\n",
    "\n",
    "## Loading the data\n",
    "\n",
    "Load the data about their predictions and the actual outcomes into `pandas` dataframes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Load the dataframes from disk\n",
    "import pandas as pd\n",
    "dem = pd.read_csv(\"./2016_dem_primary_dataframe.csv\", index_col=[0,1])\n",
    "gop = pd.read_csv(\"./2016_gop_primary_dataframe.csv\", index_col=[0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# We only care about races where there was a prediction made\n",
    "dem = dem.dropna()\n",
    "gop = gop.dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Looking at the data\n",
    "\n",
    "Let's look at the results for Iowa for the Democrats, just to see what is in the table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
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   "outputs": [
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>80% Lower Bound</th>\n",
       "      <th>80% Upper Bound</th>\n",
       "      <th>Result</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th>Candidate</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">Iowa</th>\n",
       "      <th>Clinton</th>\n",
       "      <td>44.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>49.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>O'Malley</th>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sanders</th>\n",
       "      <td>40.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>49.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "                 80% Lower Bound  80% Upper Bound  Result\n",
       "State Candidate                                          \n",
       "Iowa  Clinton               44.0             54.0    49.9\n",
       "      O'Malley               4.0              8.0     0.6\n",
       "      Sanders               40.0             52.0    49.6"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "dem.ix[[\"Iowa\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 80% confidence intervales are given by the \"`80% Lower Bound`\" and \"`80% Upper Bound`\" columns. The actually result of the election is given in the \"`Result`\" column.\n",
    "\n",
    "Here is the data for Iowa for the Republicans:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>80% Lower Bound</th>\n",
       "      <th>80% Upper Bound</th>\n",
       "      <th>Result</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th>Candidate</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">Iowa</th>\n",
       "      <th>Carson</th>\n",
       "      <td>3.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cruz</th>\n",
       "      <td>14.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>27.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kasich</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rubio</th>\n",
       "      <td>9.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>23.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Trump</th>\n",
       "      <td>15.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>24.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "                 80% Lower Bound  80% Upper Bound  Result\n",
       "State Candidate                                          \n",
       "Iowa  Carson                 3.0             15.0     9.3\n",
       "      Cruz                  14.0             36.0    27.6\n",
       "      Kasich                 1.0              4.0     1.9\n",
       "      Rubio                  9.0             27.0    23.1\n",
       "      Trump                 15.0             38.0    24.3"
      ]
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     "execution_count": 4,
     "metadata": {},
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   "source": [
    "gop.ix[[\"Iowa\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Checking the intervals\n",
    "\n",
    "Now I'll add a set of columns that tells us if the prediction was good or not, that is, if the actual result was within the 80% confidence interval or not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def add_good_predicitons(df, name=\"Prediction Good\"):\n",
    "    cond = (df['80% Lower Bound'] <= df['Result']) & (df[\"Result\"] <= df[\"80% Upper Bound\"])\n",
    "    df[\"Prediction Good\"] = np.where(cond, True, False)\n",
    "    df[\"Prediction Low\"] = np.where(df[\"80% Upper Bound\"] < df[\"Result\"], True, False)\n",
    "    df[\"Prediction High\"] = np.where(df[\"Result\"] < df[\"80% Lower Bound\"], True, False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "add_good_predicitons(dem)\n",
    "add_good_predicitons(gop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": false
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   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>80% Lower Bound</th>\n",
       "      <th>80% Upper Bound</th>\n",
       "      <th>Result</th>\n",
       "      <th>Prediction Good</th>\n",
       "      <th>Prediction Low</th>\n",
       "      <th>Prediction High</th>\n",
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       "    <tr>\n",
       "      <th>State</th>\n",
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       "      <th rowspan=\"3\" valign=\"top\">Iowa</th>\n",
       "      <th>Clinton</th>\n",
       "      <td>44.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>49.9</td>\n",
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       "      <td>False</td>\n",
       "      <td>False</td>\n",
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       "    <tr>\n",
       "      <th>O'Malley</th>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
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       "    <tr>\n",
       "      <th>Sanders</th>\n",
       "      <td>40.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>49.6</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
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      "text/plain": [
       "                 80% Lower Bound  80% Upper Bound  Result Prediction Good  \\\n",
       "State Candidate                                                             \n",
       "Iowa  Clinton               44.0             54.0    49.9            True   \n",
       "      O'Malley               4.0              8.0     0.6           False   \n",
       "      Sanders               40.0             52.0    49.6            True   \n",
       "\n",
       "                Prediction Low Prediction High  \n",
       "State Candidate                                 \n",
       "Iowa  Clinton            False           False  \n",
       "      O'Malley           False            True  \n",
       "      Sanders            False           False  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dem.ix[[\"Iowa\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Compute how the results match the predictions\n",
    "def get_low_right_high(df):\n",
    "    r = df[\"Prediction Good\"]\n",
    "    right = float(r.sum()) / r.count()\n",
    "    h = df[\"Prediction High\"]\n",
    "    high = float(h.sum()) / h.count()\n",
    "    l = df[\"Prediction Low\"]\n",
    "    low = float(l.sum()) / l.count()\n",
    "    \n",
    "    return low, right, high"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dem_low, dem_right, dem_high = get_low_right_high(dem)\n",
    "gop_low, gop_right, gop_high = get_low_right_high(gop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Party         Under   Right   Over   Total\n",
      "------------|-------------------------------\n",
      "Democrats   | 3.64%, 80.00%, 16.36%, 100.00%\n",
      "Republicans | 7.14%, 77.68%, 15.18%, 100.00%\n"
     ]
    }
   ],
   "source": [
    "print \"Party         Under   Right   Over   Total\"\n",
    "print \"------------|-------------------------------\"\n",
    "print \"Democrats   | {:.2%}, {:.2%}, {:.2%}, {:.2%}\".format(dem_low, dem_right, dem_high, sum((dem_low, dem_right, dem_high)))\n",
    "print \"Republicans | {:.2%}, {:.2%}, {:.2%}, {:.2%}\".format(gop_low, gop_right, gop_high, sum((gop_low, gop_right, gop_high)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the Results\n",
    "\n",
    "We can make a plot of the actual voting results by scaling the vote share so that the low edge of the confidence interval is +1, the high edge is -1, and the midpoint is 0. Then if a candidate's vote share is within the predicted range their result will be between -1 and 1. If the prediction was 45% to 55% and the candidate actually got 60%, that would show up at -2 on the plot. The minus sign indicates that the prediction was too low."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def add_scaled_result(df):\n",
    "    interval = (df[\"80% Upper Bound\"] - df[\"80% Lower Bound\"]) / 2.\n",
    "    means = df[\"80% Lower Bound\"] + interval\n",
    "    # The - out front makes it so that if the prediction is 1 sigma high, we get a +1\n",
    "    df[\"Scaled Result\"] = -(df[\"Result\"] - means) / interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "add_scaled_result(dem)\n",
    "add_scaled_result(gop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "width = 10\n",
    "height = 6\n",
    "\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "bins = [float(i)/10. for i in range(-44, 46, 2)]\n",
    "ylim = [0, 17]\n",
    "xlim = [min(bins), -min(bins)]\n",
    "\n",
    "\n",
    "ax1 = plt.subplot2grid((1,2),(0,0))\n",
    "ax2 = plt.subplot2grid((1,2),(0,1))\n",
    "\n",
    "dem[\"Scaled Result\"].plot(kind=\"hist\", color='b', ax=ax1, ylim=ylim, xlim=xlim, bins=bins)\n",
    "gop[\"Scaled Result\"].plot(kind=\"hist\", color='r', ax=ax2, ylim=ylim, xlim=xlim, bins=bins)\n",
    "\n",
    "# 80% Confidence intervals\n",
    "color=\"black\"\n",
    "linestyle=\"dotted\"\n",
    "ax1.axvline(-1, color=color, linestyle=linestyle)\n",
    "ax1.axvline(+1, color=color, linestyle=linestyle)\n",
    "ax2.axvline(-1, color=color, linestyle=linestyle)\n",
    "ax2.axvline(+1, color=color, linestyle=linestyle)\n",
    "\n",
    "ax1.set_title(\"Democrats\")\n",
    "ax2.set_title(\"Republicans\")\n",
    "ax2.yaxis.set_visible(False)\n",
    "\n",
    "plt.subplots_adjust(wspace=0)\n",
    "\n",
    "plt.savefig(\"/tmp/538_scaled_results.png\", bbox_inches='tight')\n",
    "plt.savefig(\"/tmp/538_scaled_results.svg\", bbox_inches='tight')\n",
    "\n",
    "plt.show()"
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   "source": [
    "## A (Rough) Estimate of Uncertainties\n",
    "\n",
    "When I read FiveThirtyEight's plots, I only ever pick a whole number (I certainly am not accurate enough to get better precision than that). I estimate that if I say a number is \"34%\", then it is just as likely to be 33 or 35. To estimate what effect this has, I randomly adjust the prediction bounds (up 1, down 1, or leaving it alone with equal probability) and see how the predictions fare. The number I report below is the mean of these trials, and the uncertainties represent two standard deviations."
   ]
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   "cell_type": "code",
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   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "def ugly_simulation_hack(df, sigma=1, iterations=10000, std_to_return=2):\n",
    "\n",
    "    sim_good = []\n",
    "    sim_low = []\n",
    "    sim_high = []\n",
    "\n",
    "    # Run many simulations\n",
    "    for _ in xrange(iterations):\n",
    "\n",
    "        pred_good = []\n",
    "        pred_low = []\n",
    "        pred_high = []\n",
    "\n",
    "        # Check every prediction and perturb them\n",
    "        for ((state, candidate), low, high, result, _, _, _, _) in df.itertuples():\n",
    "\n",
    "            # Perturb the bounds I read from 538's plots assuming a Gaussian\n",
    "            # distribution around the value\n",
    "            #new_low = random.gauss(low, sigma)\n",
    "            #new_high = random.gauss(high, sigma)\n",
    "            new_low = random.randint(low-sigma, low+sigma)\n",
    "            new_high = random.randint(high-sigma, high+sigma)\n",
    "\n",
    "            # Check if the perturbed prediction is good or not\n",
    "            pred_good.append(new_low <= result <= new_high)\n",
    "            pred_low.append(new_high < result)\n",
    "            pred_high.append(result < new_low)\n",
    "\n",
    "        # Calculate the number correct accounting for the perturbations\n",
    "        sim_good.append(sum(pred_good)/float(len(pred_good)))\n",
    "        sim_low.append(sum(pred_low)/float(len(pred_low)))\n",
    "        sim_high.append(sum(pred_high)/float(len(pred_high)))\n",
    "\n",
    "    # Calculate outcome of the simulation\n",
    "    good_mean = np.mean(sim_good)\n",
    "    good_std = np.std(sim_good)\n",
    "    low_mean = np.mean(sim_low)\n",
    "    low_std = np.std(sim_low)\n",
    "    high_mean = np.mean(sim_high)\n",
    "    high_std = np.std(sim_high)\n",
    "\n",
    "    return (\n",
    "        good_mean,\n",
    "        good_std * std_to_return,\n",
    "        low_mean,\n",
    "        low_std * std_to_return,\n",
    "        high_mean,\n",
    "        high_std * std_to_return,\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
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   "outputs": [],
   "source": [
    "gop_good, gop_good_std, gop_low, gop_low_std, gop_high, gop_high_std = ugly_simulation_hack(gop)\n",
    "dem_good, dem_good_std, dem_low, dem_low_std, dem_high, dem_high_std = ugly_simulation_hack(dem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Party         Under           Right          Over\n",
      "------------|---------------------------------------------\n",
      "Democrats   | 5.5% +- 3.0%   77.6% +- 4.2%   17.0% +- 3.0%\n",
      "Republicans | 6.5% +- 1.2%   78.6% +- 3.3%   14.9% +- 3.0%\n"
     ]
    }
   ],
   "source": [
    "print \"Party         Under           Right          Over\"\n",
    "print \"------------|---------------------------------------------\"\n",
    "print \"Democrats   | {:.1%} +- {:.1%}   {:.1%} +- {:.1%}   {:.1%} +- {:.1%}\".format(dem_low, dem_low_std, dem_good, dem_good_std, dem_high, dem_high_std)\n",
    "print \"Republicans | {:.1%} +- {:.1%}   {:.1%} +- {:.1%}   {:.1%} +- {:.1%}\".format(gop_low, gop_low_std, gop_good, gop_good_std, gop_high, gop_high_std)"
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