Cleveland Historic 3PT Game

cle_3pt_shooting.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Read Cleveland game logs (from basketball-reference.com)\n",
    "CLEVELAND = pd.read_csv('/home/jovyan/cle_stats.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5 10  9 10  9  9 13 18  9 13 12 18  5 16 17 11 11  5 10 14 13 11 13 16 11\n",
      " 15  8 15 13 11 10 17  8 17  5 15  8  7  8  9 10 14  9 12 13 12  7 19  7  7\n",
      " 12  6  4 11  9  9 11 12 13  9 16 10 15  6  7 16 12 15  6 19 13  7 14  7 13\n",
      " 11  9 11  8 12  7 11]\n"
     ]
    }
   ],
   "source": [
    "# Use the average made 3pt field goals this season as the 'lambda' in the Poisson model\n",
    "average_3pt_made_field_goals = np.mean(CLEVELAND['3P'])\n",
    "\n",
    "# Model Cleveland made 3pt field goals as a Poisson distribution \n",
    "# https://en.wikipedia.org/wiki/Poisson_distribution\n",
    "fg3m = np.random.poisson(average_3pt_made_field_goals, 82) # one 82-game simulation of the model\n",
    "print(fg3m)"
   ]
  },

  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f81eae07278>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AMAFKIAAAAIAJ+H+Y9eN0xanVXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81ead254a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set figure size\n",
    "plt.figure(figsize=(20,10))\n",
    "\n",
    "# Plot the histogram of the model for a couple of samples and the histogram of Cleveland's actual 3pt makes this season\n",
    "plt.hist(cle_data['3P'], alpha=0.5, label='CLE 2016')\n",
    "plt.hist(np.random.poisson(average_3pt_made_field_goals, 82), alpha=0.25, label='Poisson Model Run 1')\n",
    "plt.hist(np.random.poisson(average_3pt_made_field_goals, 82), alpha=0.25, label='Poisson Model Run 2')\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's pretty clear (and expected, I suppose) that a Poisson model does a fairly good job of modeling this kind of phenomenon. Now let's take the model and simulate thousands of games, say 10,000(!), and see how often we would expect Cleveland to make 25 3pt field goals (according to this simple model, anyway)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f81eaa42048>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RAAAAAE3CEQAAAABNwhEAAAAATcIRAAAAAE3CEQAAAABNwhEAAAAATcIRAAAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81eaa42198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,10))\n",
    "model = np.random.poisson(average_3pt_made_field_goals, 10000)\n",
    "plt.hist(model, alpha=0.55, label='Poisson Model 10K Game Sim',bins=25)\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's count how many times Cleveland made 25+ 3pt shots in this simulation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   0    2    8   50  117  265  438  689  979 1176 1274 1174 1070  840  661\n",
      "  481  299  205  131   68   38   19   10    2    2    2]\n"
     ]
    }
   ],
   "source": [
    "print(np.bincount(model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Twice! That's how rare an event we're talking about. Now, sure, this model is very, very simple, and it probably vastly underrates the probability of Cleveland making 25 3pt field goals. But still this should give an appreciation how out of the ordinary that was. Now, just for fun, let's take the team that made the most 3pt shots (13.1) per game (Golden State, of course) and run the same simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f81ea85c8d0>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4A\nAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAA\nAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAA\nAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAA\nqBKOAAAAAKgSjgAAAACo6mj3AADDNWvW/PT3r2v3GJvp7V2RVqvdUwAAAOw44QjY7fX3r0urtbDd\nY2xm6dLp7R4BAABgWNyqBgAAAECVcAQAAABAlXAEAAAAQJVwBAAAAECVcAQAAABAlXAEAAAAQJVw\nBAAAAECVcAQAAABAlXAEAAAAQJVwBAAAAECVcAQAAABAlXAEAAAAQJVwBAAAAECVcAQAAABAlXAE\nAAAAQJVwBAAAAECVcAQAAABAlXAEAAAAQJVwBAAAAECVcAQAAABAlXAEAAAAQJVwBAAAAECVcAQA\nAABAlXAEAAAAQJVwBAAAAECVcAQAAABA1bDDUSllTCnlR6WUmwbed5ZSbi2l3FtKuaWUMn7ItrNL\nKfeXUlaUUqYP99wAAAAAjJydccXRh5MsH/L+oiS3NU1zRJLbk8xOklLKUUnOTHJkklOSfK6UUnbC\n+QEAAAAYAcMKR6WUKUn+OMkXhyyflmTxwOvFSU4feP3uJNc1TfN80zR9Se5P8ubhnB8AAACAkTPc\nK46uSPK/kzRD1iY2TbMmSZqmeTjJgQPrk5OsHLLdqoE1AAAAAEahHQ5HpZT/kWRN0zQ/SfJSt5w1\nL/EZAAAAAKNUxzD2PT7Ju0spf5zkFUleVUr5SpKHSykTm6ZZU0o5KMkjA9uvSnLIkP2nDKxVzZ07\nd/B1d3d3uru7hzEqAAB7qmXLejNjxoXtHqOqq6szixbNafcYAOylenp60tPTM6xj7HA4aprm4iQX\nJ0kp5aQks5qmmVlK+VSSc5N8Msn7ktw4sMtNSa4ppVyRDbeoTU1yz5aOPzQcAQDAlqxfn7RaC9s9\nRlVf3+gMWgDsHTa9EGfevHnbfYzhXHG0JZ9IckMp5bwk/dnwS2ppmmZ5KeWGbPgFtueSnN80jdvY\nAAAAAEapnRKOmqb5bpLvDrxem+RtW9huQZIFO+OcAAAAAIys4f6qGgAAAAB7KOEIAAAAgCrhCAAA\nAIAq4QhkS8/tAAANV0lEQVQAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq\n4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrh\nCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEI\nAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgA\nAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAA\nAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAIAq4QgAAACAKuEIAAAA\ngCrhCAAAAIAq4QgAAACAKuEIAAAAgCrhCAAAAICqjnYPAOweZs2an/7+de0eo6q3d0VarXZPAQAA\nsOcRjoBt0t+/Lq3WwnaPUbV06fR2jwAAVcuW9WbGjAvbPcZmuro6s2jRnHaPAcBuQDgCAIARsn59\nRuX/46Wvb/TFLABGJ884AgAAAKBKOAIAAACgSjgCAAAAoEo4AgAAAKBKOAIAAACgSjgCAAAAoEo4\nAgAAAKBKOAIAAACgSjgCAAAAoEo4AgAAAKBKOAIAAACgSjgCAAAAoEo4AgAAAKBKOAIAAACgSjgC\nAAAAoEo4AgAAAKBKOAIAAACgSjgCAAAAoEo4AgAAAKBKOAIAAACgSjgCAAAAoEo4AgAAAKBKOAIA\nAACgSjgCAAAAoEo4AgAAAKBKOAIAAACgSjgCAAAAoGqHw1EpZUop5fZSys9LKT8tpXxoYL2zlHJr\nKeXeUsotpZTxQ/aZXUq5v5SyopQyfWd8AQAAAABGxnCuOHo+yUeapnltkrckuaCU8v8kuSjJbU3T\nHJHk9iSzk6SUclSSM5McmeSUJJ8rpZThDA8AAADAyNnhcNQ0zcNN0/xk4PXTSVYkmZLktCSLBzZb\nnOT0gdfvTnJd0zTPN03Tl+T+JG/e0fMDAAAAMLJ2yjOOSimtJK9PsjTJxKZp1iQb4lKSAwc2m5xk\n5ZDdVg2sAQAAADAKDTsclVL2TfL1JB8euPKo2WSTTd8DAAAAsBvoGM7OpZSObIhGX2ma5saB5TWl\nlIlN06wppRyU5JGB9VVJDhmy+5SBtaq5c+cOvu7u7k53d/dwRgUAAADYq/T09KSnp2dYxxhWOEry\n/yVZ3jTNp4es3ZTk3CSfTPK+JDcOWb+mlHJFNtyiNjXJPVs68NBwBAAAAMD22fRCnHnz5m33MXY4\nHJVSjk/yniQ/LaX8OBtuSbs4G4LRDaWU85L0Z8MvqaVpmuWllBuSLE/yXJLzm6ZxGxsAAADAKLXD\n4ahpmn9Lss8WPn7bFvZZkGTBjp4TAAAAgF1np/yqGgAAAAB7HuEIAAAAgCrhCAAAAICq4f6qGgAA\nsJtZtqw3M2Zc2O4xqrq6OrNo0Zx2jwHAAOEIAAD2MuvXJ63WwnaPUdXXNzqDFsDeyq1qAAAAAFQJ\nRwAAAABUCUcAAAAAVAlHAAAAAFQJRwAAAABUCUcAAAAAVAlHAAAAAFQJRwAAAABUCUcAAAAAVAlH\nAAAAAFQJRwAAAABUCUcAAAAAVAlHAAAAAFQJRwAAAABUCUcAAAAAVAlHAAAAAFQJRwAAAABUCUcA\nAAAAVAlHAAAAAFQJRwAAAABUdbR7AOB3Zs2an/7+de0eo6q3d0VarXZPAQAAwK4kHMEo0t+/Lq3W\nwnaPUbV06fR2jwAAAMAu5lY1AAAAAKqEIwAAAACqhCMAAAAAqoQjAAAAAKqEIwAAAACqhCMAAAAA\nqoQjAAAAAKqEIwAAAACqOto9AAAAwG8tW9abGTMubPcYVV1dnVm0aE67xwDYpYQjAABg1Fi/Pmm1\nFrZ7jKq+vtEZtABGklvVAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKO\nAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4A\nAAAAqBKOAAAAAKgSjgAAAACo6mj3AAAAALuDZct6M2PGhe0eYzNdXZ1ZtGhOu8cA9lDCEQAAwDZY\nvz5ptRa2e4zN9PWNvpgF7DncqgYAAABAlXAEAAAAQJVwBAAAAECVcAQAAABAlXAEAAAAQJVwBAAA\nAEBVR7sHgHaYNWt++vvXtXuMzfT2rkir1e4pAAAAYAPhiL1Sf/+6tFoL2z3GZpYund7uEQAAAGCQ\nW9UAAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqBKOAAAAAKgSjgAAAACoEo4AAAAAqOpo9wAAAADs\nuGXLejNjxoXtHqOqq6szixbNafcYwDAIRwAAALux9euTVmthu8eo6usbnUEL2HZuVQMAAACgSjgC\nAAAAoEo4AgAAAKBKOAIAAACgysOxGTGzZs1Pf/+6do9R1du7Iq1Wu6cAAACA0U04YsT0968btb/u\nsHTp9HaPAAAAAKOecAQAAMCIWLasNzNmXNjuMTbT1dWZRYvmtHsM2C0IRwAAAIyI9eszKu9C6Osb\nfTELRisPxwYAAACgSjgCAAAAoEo4AgAAAKBql4ejUso7Syn/UUq5r5TyN7v6/AAAAABsm136cOxS\nypgkf5/krUlWJ/lBKeXGpmn+Y1fOAaPBypU9OeSQ7naPASPq/7Z3PyF63HUcx9+frVisQmibtilJ\ndFOEHsQSFYPQHszBELxEFLR6sT2IB2s9pNDiJbkUjFChFy82hSqR+gc0uZmCSFDYJtHGpDVNKjZL\nYv402Ja29CL262EmZps8W7u7T56ZnX2/4GFnfjsPfA/f+TLzfeb3G/NcK4F5rpXAPNfQjHrb28WL\np7nllvUdRXSZb3xT30z6rWqbgJeqahYgydPANsDG0RJs3/4os7OvdR3GVY4ePc70dNdR9JcXYFoJ\nzHOtBOa5VgLzXEMz6m1vZ8/uZHp6ZzcBzbF375Ze3t8BvPzyCTZsuLPrMK5is+3amnTjaC1wes7+\nGZpmUq+dPPl3Dhw43HUYI61evYrZ2VeZnn6s61CuMjOzpesQJEmSJGlZGdXU6ouZmS1s3ty/2E6d\neuj/H6RFm3TjaFk6fPgoe/b0s3F0++2hqroOQ5IkSZIkDVAm2XRI8jlgZ1VtbfcfAaqqdl1xnJ0Q\nSZIkSZKkMauqLOT4STeOrgNO0CyOfQ44CHy9qo5PLAhJkiRJkiS9LxOdqlZV/0nyALAfmAJ22zSS\nJEmSJEnqp4k+cSRJkiRJkqTlY6rrAOZKsjXJi0lOJnm463ikayHJqSR/TfJckoNdxyONQ5LdSS4k\nOTpn7MYk+5OcSPK7JKu6jFFaqnnyfEeSM0n+0n62dhmjtFRJ1iX5fZIXkhxL8mA7bk3XYIzI8++2\n49Z0DUaS65M82953Hkuyox1fcD3vzRNHSaaAkzTrH50FDgH3VtWLnQYmjVmSfwCfqarXuo5FGpck\n9wBvAT+tqrvasV3Av6rqh+2PATdW1SNdxiktxTx5vgN4s6p+1Glw0pgkWQOsqaojST4C/BnYBtyP\nNV0D8R55/jWs6RqQJDdU1dvtetN/Ah4EvsIC63mfnjjaBLxUVbNV9W/gaZqTVxqa0K9zT1qyqvoj\ncGUzdBvwVLv9FPCliQYljdk8eQ5NXZcGoarOV9WRdvst4DiwDmu6BmSePF/b/tuarsGoqrfbzetp\n1rguFlHP+3TzuhY4PWf/DJdPXmlICngmyaEk3+o6GOkaurWqLkBzgQbc2nE80rXyQJIjSZ5w+o6G\nJMk0sBGYAW6zpmuI5uT5s+2QNV2DkWQqyXPAeeCZqjrEIup5nxpH0kpxd1V9Gvgi8J126oO0EvRj\nbrQ0Xj8G7qiqjTQXZU5v0CC003d+DXyvfSLjyhpuTdeyNyLPrekalKp6p6o+RfPk6KYkn2AR9bxP\njaN/Ah+ds7+uHZMGparOtX8vAr+hmaYpDdGFJLfB/9YSeKXjeKSxq6qLdXnByJ8An+0yHmkcknyA\n5mb6Z1W1tx22pmtQRuW5NV1DVVVvAH8AtrKIet6nxtEh4ONJPpbkg8C9wL6OY5LGKskN7S8bJPkw\nsAV4vtuopLEJ714XYB9wX7v9TWDvlV+QlqF35Xl7wXXJl7GmaxieBP5WVY/PGbOma2iuynNruoYk\nyepL0y2TfAj4As16Xguu5715qxpA+7rDx2kaWrur6gcdhySNVZINNE8ZFc3iZHvMcw1Bkp8Dnwdu\nBi4AO4DfAr8C1gOzwFer6vWuYpSWap4830yzNsY7wCng25fWDZCWoyR3AweAYzTXKwV8HzgI/BJr\nugbgPfL8G1jTNRBJPkmz+PVU+/lFVT2a5CYWWM971TiSJEmSJElSf/RpqpokSZIkSZJ6xMaRJEmS\nJEmSRrJxJEmSJEmSpJFsHEmSJEmSJGkkG0eSJEmSJEkaycaRJEmSJEmSRrJxJEmSJEmSpJFsHEmS\nJEmSJGmk/wKe+/9qe94J2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81ea991a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,10))\n",
    "model = np.random.poisson(13.1, 10000)\n",
    "plt.hist(model, alpha=0.55, label='Poisson Model for GSW', bins=26)\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   0    1    1    6   25   57  137  274  470  643  909 1000 1110 1087 1006\n",
      "  886  707  554  399  273  185  116   75   38   21    9    5    3    3]\n"
     ]
    }
   ],
   "source": [
    "print(np.bincount(model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still only a few games with 25+ 3PTM even for the best team in the league at shooting 3's. And note that the most 3's GSW made in one game this season was 22 (they did that twice)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}