Is 108 years really a long time?.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Cubs ended their famous 108-year World Series championship drought one month ago. But is 108 years really a long time? Suppose there were a league of 30 teams with a winner chosen uniformly at random every year. Each time the team that hasn’t won in the longest time does win, the length of that drought makes the headlines. (You can assume when the league starts that each team has a zero-year drought.) What are the lengths of these headline-making droughts, on average?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_teams = 30\n",
    "num_trials = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run_experiment():\n",
    "    champ_counter = Counter()\n",
    "    while len(champ_counter.keys()) < num_teams:\n",
    "        champ_counter[np.random.randint(num_teams)] += 1\n",
    "    return np.sum(champ_counter.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.33 s, sys: 3.03 ms, total: 2.33 s\n",
      "Wall time: 2.33 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "drought_tracker = np.empty(num_trials)\n",
    "for i in range(num_trials):\n",
    "    drought_tracker[i] = run_experiment()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def print_stats(drought_tracker):\n",
    "    print(\n",
    "        np.min(drought_tracker), \n",
    "        np.median(drought_tracker), \n",
    "        np.mean(drought_tracker), \n",
    "        np.max(drought_tracker)\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42.0, 113.0, 119.6435, 418.0)\n"
     ]
    }
   ],
   "source": [
    "print_stats(drought_tracker)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_drought_dist(drought_tracker):\n",
    "    bins = np.linspace(0, 500, 101)\n",
    "    plt.hist(drought_tracker, bins=bins, color='dodgerblue', alpha=0.5, \n",
    "             histtype='stepfilled', normed=True)\n",
    "    plt.axvline(108, lw=2, color='orange', label='Cubs')\n",
    "    plt.axvline(np.median(drought_tracker), lw=2, color='blue', ls='--', label='median')\n",
    "    plt.axvline(np.mean(drought_tracker), lw=2, color='blue', label='mean')\n",
    "    plt.title('Is 108 years really a long time?')\n",
    "    plt.ylabel('Probability Density')\n",
    "    plt.xlabel('Length of Drought')\n",
    "    plt.ylim(0, 0.0175)\n",
    "    plt.legend()\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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u6VJJl4Q6TwHvS5oD3Alcnnbs+4EpwH6S5ku6OKy6EThJ0kzgROBH+bapXPkY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\nxOKccy5Rnlicc84l6v8Dok3xK4Pm9FMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1084b56d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 4.5))\n",
    "plot_drought_dist(drought_tracker)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectorized Approx."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([         1,          3,          7,         15,         31,\n",
       "               63,        127,        255,        511,       1023,\n",
       "             2047,       4095,       8191,      16383,      32767,\n",
       "            65535,     131071,     262143,     524287,    1048575,\n",
       "          2097151,    4194303,    8388607,   16777215,   33554431,\n",
       "         67108863,  134217727,  268435455,  536870911, 1073741823])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.bitwise_or.accumulate(1 << np.arange(num_teams))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max_drought = 500\n",
    "full_club_value = 1073741823"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run_trials_parallel(num_trials):\n",
    "    winners_club = np.bitwise_or.accumulate(1 << np.random.randint(num_teams, size=(num_trials, max_drought)), axis=1)\n",
    "    return np.argmax(full_club_value == winners_club, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 854 ms, sys: 396 ms, total: 1.25 s\n",
      "Wall time: 1.25 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "drought_tracker2 = run_trials_parallel(num_trials * 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(39, 112.0, 118.8105, 425)\n"
     ]
    }
   ],
   "source": [
    "print_stats(drought_tracker2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yUDXq0At7H/6lClIVJqXUbfzRq4pdJuecy9RixSLpQGAi8DawqBWVCmbWIOl8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\nFYtzzrlEecXinHMuUV6xOOecS9T/B+6eOh/x6Nh5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10856bd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 4.5))\n",
    "plot_drought_dist(drought_tracker2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}