Draymond 3pt game.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Read Draymond game logs (from basketball-reference.com)\n",
    "DRAY = pd.read_csv('/home/jovyan/draymond.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 0 1 1 1 1 1 3 1 1 1 2 2 0 1 0 1 2 3 0 2 3 3 1 3 1 2 1 0 2 1 0 0 1 2 1 1\n",
      " 2 1 1 2 1 0 0 3 1 2 1 2 1 0 3 1 2 1 1 0 1 2 4 0 0 1 1 1 0 1 0 1 0 0 0 1 0\n",
      " 2 0 1 0 0 1 1 1]\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(DRAY['3P'])\n",
    "\n",
    "# Model Draymond 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": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.23456790123\n"
     ]
    }
   ],
   "source": [
    "print(average_3pt_made_field_goals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f74a48f4e48>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+Okny5S9/OfX19TnssMMyaNCgdOjQIVdcccVm69pSnRu2devWrVmNG7Ztac7B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\n41ryVq+e69/YVRRF+ySHJ/l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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74b3c53390>"
      ]
     },
     "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 Draymond's actual 3pt makes this season\n",
    "plt.hist(DRAY['3P'], alpha=0.5, label='DRAYMOND 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.hist(np.random.poisson(average_3pt_made_field_goals, 82), alpha=0.25, label='Poisson Model Run 3')\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like a pretty reasonable model to me!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f74a478c828>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KIgAAAABGyiIAAAAARuunDgAAsCc766yLsrS0c+oYa7Zx48HZsuWC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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74a478ccc0>"
      ]
     },
     "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=24)\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's count how many times Draymond made 8+ 3pt shots in this simulation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2908 3582 2211  917  289   71   19    2    1]\n"
     ]
    }
   ],
   "source": [
    "print(np.bincount(model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once! So it's pretty unlikely with lambda=1.2(ish)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, so let's now address the elephant in the room. The \"average\" we used to calculate mostly involves games played with Steph. Using nbawowy.com (at this point long pause, while you cheer), we see that Draymond shoots about 4 3's per 100 possessions when Steph is on the court, but that increases to about 6.5 when Steph is off the court. So, let's just do the simple thing here and increase lambda from the \"with Steph\" scenario to the \"without Steph\" scenario by multiplying it by this ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f74a4594b70>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fWtZrluSHwG+rakeS5cDKqvpH41jq3PB5eh5YX1WHW+dRX5JcCjwI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\nkSRJkiRJksZsFkmSJEmSJGnsvxhoWroWOU/dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74a4594ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,10))\n",
    "model = np.random.poisson(average_3pt_made_field_goals*(6.5/4), 10000)\n",
    "plt.hist(model, alpha=0.55, label='Poisson Model 10K Game Sim',bins=24)\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1399 2686 2714 1787  903  348  124   32    7]\n"
     ]
    }
   ],
   "source": [
    "print(np.bincount(model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, so now it's a bit more likely (7 out of 10K simulations!). Yay statistics! Of course, as I said last time (writing up the CLE game), a Poisson model is about the simplest thing we can do. It likely underestimates the true probabilities in some ways I haven't thought of. But still, it gives you an idea of the game Draymond had."
   ]
  }
 ],
 "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
}