NelsonMinar/bf4plots.ipynb

## bf4plots.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Battlefield 4 player data exploration\n",
    "### Some tinkering with pandas and scikit-learn\n",
    "\n",
    "Note that the conclusions drawn here are not particularly insightful or accurate; early experiments! See also [blog post notes](https://nelsonslog.wordpress.com/2015/09/16/my-first-ipython-notebook/) and [alternate visualization of this data](http://www.somebits.com/bf4plots/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import cluster, preprocessing\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "numpy.set_printoptions(suppress=True)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load our dataset from a URL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alldata = pd.read_csv('http://www.somebits.com/bf4plots/data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspect the dataset, get a feel for what's there.\n",
    "\n",
    "How big is it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5209, 68)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alldata.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at a few rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>plat</th>\n",
       "      <th>timePlayed</th>\n",
       "      <th>avengerKills</th>\n",
       "      <th>deaths</th>\n",
       "      <th>dogtagsTaken</th>\n",
       "      <th>flagCaptures</th>\n",
       "      <th>flagDefend</th>\n",
       "      <th>headshots</th>\n",
       "      <th>heals</th>\n",
       "      <th>...</th>\n",
       "      <th>weaKpm</th>\n",
       "      <th>vehTimeP</th>\n",
       "      <th>vehKillsP</th>\n",
       "      <th>vehKpm</th>\n",
       "      <th>ribbons</th>\n",
       "      <th>ribbonsUnique</th>\n",
       "      <th>ribpr</th>\n",
       "      <th>medals</th>\n",
       "      <th>medalsUnique</th>\n",
       "      <th>assignments</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-CIA-PsychoKilla</td>\n",
       "      <td>pc</td>\n",
       "      <td>3143760</td>\n",
       "      <td>3479</td>\n",
       "      <td>33335</td>\n",
       "      <td>660</td>\n",
       "      <td>6279</td>\n",
       "      <td>3673</td>\n",
       "      <td>6078</td>\n",
       "      <td>27237</td>\n",
       "      <td>...</td>\n",
       "      <td>1.279</td>\n",
       "      <td>18.611</td>\n",
       "      <td>13.666</td>\n",
       "      <td>0.511</td>\n",
       "      <td>18096</td>\n",
       "      <td>48</td>\n",
       "      <td>6.619</td>\n",
       "      <td>341</td>\n",
       "      <td>27</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-Chian-Dragon</td>\n",
       "      <td>pc</td>\n",
       "      <td>3196470</td>\n",
       "      <td>4957</td>\n",
       "      <td>43579</td>\n",
       "      <td>539</td>\n",
       "      <td>3488</td>\n",
       "      <td>5018</td>\n",
       "      <td>10188</td>\n",
       "      <td>21010</td>\n",
       "      <td>...</td>\n",
       "      <td>1.750</td>\n",
       "      <td>10.485</td>\n",
       "      <td>7.067</td>\n",
       "      <td>0.697</td>\n",
       "      <td>26629</td>\n",
       "      <td>46</td>\n",
       "      <td>10.664</td>\n",
       "      <td>513</td>\n",
       "      <td>34</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-CopKiIIeR-</td>\n",
       "      <td>pc</td>\n",
       "      <td>3720140</td>\n",
       "      <td>2010</td>\n",
       "      <td>27136</td>\n",
       "      <td>839</td>\n",
       "      <td>7351</td>\n",
       "      <td>4246</td>\n",
       "      <td>4533</td>\n",
       "      <td>9400</td>\n",
       "      <td>...</td>\n",
       "      <td>0.903</td>\n",
       "      <td>18.823</td>\n",
       "      <td>16.668</td>\n",
       "      <td>0.375</td>\n",
       "      <td>14951</td>\n",
       "      <td>50</td>\n",
       "      <td>5.786</td>\n",
       "      <td>281</td>\n",
       "      <td>33</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-DJangoooooO-</td>\n",
       "      <td>pc</td>\n",
       "      <td>3410630</td>\n",
       "      <td>2922</td>\n",
       "      <td>17296</td>\n",
       "      <td>329</td>\n",
       "      <td>3277</td>\n",
       "      <td>3910</td>\n",
       "      <td>8556</td>\n",
       "      <td>8864</td>\n",
       "      <td>...</td>\n",
       "      <td>1.509</td>\n",
       "      <td>36.381</td>\n",
       "      <td>43.234</td>\n",
       "      <td>1.010</td>\n",
       "      <td>25540</td>\n",
       "      <td>45</td>\n",
       "      <td>10.175</td>\n",
       "      <td>486</td>\n",
       "      <td>33</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4 rows × 68 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               name plat  timePlayed  avengerKills  deaths  dogtagsTaken  \\\n",
       "0  -CIA-PsychoKilla   pc     3143760          3479   33335           660   \n",
       "1     -Chian-Dragon   pc     3196470          4957   43579           539   \n",
       "2       -CopKiIIeR-   pc     3720140          2010   27136           839   \n",
       "3     -DJangoooooO-   pc     3410630          2922   17296           329   \n",
       "\n",
       "   flagCaptures  flagDefend  headshots  heals     ...       weaKpm  vehTimeP  \\\n",
       "0          6279        3673       6078  27237     ...        1.279    18.611   \n",
       "1          3488        5018      10188  21010     ...        1.750    10.485   \n",
       "2          7351        4246       4533   9400     ...        0.903    18.823   \n",
       "3          3277        3910       8556   8864     ...        1.509    36.381   \n",
       "\n",
       "   vehKillsP  vehKpm  ribbons  ribbonsUnique   ribpr  medals  medalsUnique  \\\n",
       "0     13.666   0.511    18096             48   6.619     341            27   \n",
       "1      7.067   0.697    26629             46  10.664     513            34   \n",
       "2     16.668   0.375    14951             50   5.786     281            33   \n",
       "3     43.234   1.010    25540             45  10.175     486            33   \n",
       "\n",
       "   assignments  \n",
       "0           60  \n",
       "1           69  \n",
       "2           74  \n",
       "3           67  \n",
       "\n",
       "[4 rows x 68 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alldata[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's a lot of columns; what all are they?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['name', 'plat', 'timePlayed', 'avengerKills', 'deaths',\n",
       "       'dogtagsTaken', 'flagCaptures', 'flagDefend', 'headshots', 'heals',\n",
       "       'killAssists', 'killStreakBonus', 'kills', 'longestHeadshot',\n",
       "       'mcomDefendKills', 'nemesisKills', 'nemesisStreak', 'numLosses',\n",
       "       'numRounds', 'numWins', 'repairs', 'resupplies', 'revives',\n",
       "       'saviorKills', 'shotsFired', 'shotsHit', 'skill',\n",
       "       'suppressionAssists', 'timePlayed.1', 'vehicleDamage',\n",
       "       'vehiclesDestroyed', 'award', 'bonus', 'combatScore', 'general',\n",
       "       'rankScore', 'score', 'squad', 'team', 'totalScore', 'unlock',\n",
       "       'vehicle', 'kdr', 'wlr', 'spm', 'gspm', 'kpm', 'sfpm', 'hkp', 'khp',\n",
       "       'accuracy', 'roundsFinished', 'vehicleTime', 'vehicleKills',\n",
       "       'weaponTime', 'weaponKills', 'weaTimeP', 'weaKillsP', 'weaKpm',\n",
       "       'vehTimeP', 'vehKillsP', 'vehKpm', 'ribbons', 'ribbonsUnique',\n",
       "       'ribpr', 'medals', 'medalsUnique', 'assignments'], dtype=object)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alldata.columns.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boiling the data down.\n",
    "\n",
    "Let's pick out just a few columns to look at. We're going to focus on statistics that are averages for a player over his lifetime; these are not cumulative stats. Also we're going to synthesize a new stat from some cumulative data in the source CSV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>skill</th>\n",
       "      <th>wlr</th>\n",
       "      <th>gspm</th>\n",
       "      <th>kdr</th>\n",
       "      <th>kpm</th>\n",
       "      <th>accuracy</th>\n",
       "      <th>vehKpm</th>\n",
       "      <th>weaKpm</th>\n",
       "      <th>flagsPerMinute</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "      <td>5209.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>307.184296</td>\n",
       "      <td>1.649896</td>\n",
       "      <td>147.834132</td>\n",
       "      <td>1.895097</td>\n",
       "      <td>0.793688</td>\n",
       "      <td>13.353216</td>\n",
       "      <td>0.660907</td>\n",
       "      <td>1.292631</td>\n",
       "      <td>0.203616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>116.208756</td>\n",
       "      <td>1.035978</td>\n",
       "      <td>62.464320</td>\n",
       "      <td>2.503981</td>\n",
       "      <td>0.341581</td>\n",
       "      <td>4.603518</td>\n",
       "      <td>0.564113</td>\n",
       "      <td>0.538782</td>\n",
       "      <td>0.132064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.156000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>225.000000</td>\n",
       "      <td>1.066000</td>\n",
       "      <td>104.223000</td>\n",
       "      <td>1.189000</td>\n",
       "      <td>0.551000</td>\n",
       "      <td>10.486000</td>\n",
       "      <td>0.362000</td>\n",
       "      <td>0.908000</td>\n",
       "      <td>0.104083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>295.000000</td>\n",
       "      <td>1.414000</td>\n",
       "      <td>139.543000</td>\n",
       "      <td>1.609000</td>\n",
       "      <td>0.763000</td>\n",
       "      <td>13.018000</td>\n",
       "      <td>0.574000</td>\n",
       "      <td>1.242000</td>\n",
       "      <td>0.188258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>379.000000</td>\n",
       "      <td>1.931000</td>\n",
       "      <td>182.682000</td>\n",
       "      <td>2.196000</td>\n",
       "      <td>0.998000</td>\n",
       "      <td>15.783000</td>\n",
       "      <td>0.828000</td>\n",
       "      <td>1.624000</td>\n",
       "      <td>0.283447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>915.000000</td>\n",
       "      <td>21.223000</td>\n",
       "      <td>503.771000</td>\n",
       "      <td>138.345000</td>\n",
       "      <td>2.498000</td>\n",
       "      <td>58.506000</td>\n",
       "      <td>12.865000</td>\n",
       "      <td>3.704000</td>\n",
       "      <td>1.012747</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             skill          wlr         gspm          kdr          kpm  \\\n",
       "count  5209.000000  5209.000000  5209.000000  5209.000000  5209.000000   \n",
       "mean    307.184296     1.649896   147.834132     1.895097     0.793688   \n",
       "std     116.208756     1.035978    62.464320     2.503981     0.341581   \n",
       "min       0.000000     0.156000     0.000000     0.000000     0.000000   \n",
       "25%     225.000000     1.066000   104.223000     1.189000     0.551000   \n",
       "50%     295.000000     1.414000   139.543000     1.609000     0.763000   \n",
       "75%     379.000000     1.931000   182.682000     2.196000     0.998000   \n",
       "max     915.000000    21.223000   503.771000   138.345000     2.498000   \n",
       "\n",
       "          accuracy       vehKpm       weaKpm  flagsPerMinute  \n",
       "count  5209.000000  5209.000000  5209.000000     5209.000000  \n",
       "mean     13.353216     0.660907     1.292631        0.203616  \n",
       "std       4.603518     0.564113     0.538782        0.132064  \n",
       "min       0.000000     0.000000     0.000000        0.000000  \n",
       "25%      10.486000     0.362000     0.908000        0.104083  \n",
       "50%      13.018000     0.574000     1.242000        0.188258  \n",
       "75%      15.783000     0.828000     1.624000        0.283447  \n",
       "max      58.506000    12.865000     3.704000        1.012747  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pick out just a few columns\n",
    "data = alldata.filter(items=('skill', 'wlr', 'gspm', 'kdr', 'kpm', 'accuracy', 'vehKpm', 'weaKpm'))\n",
    "\n",
    "# Create a new column based on some cumulative data\n",
    "data['flagsPerMinute'] = 60 * (alldata.flagCaptures + alldata.flagDefend) / alldata.timePlayed\n",
    "\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do a couple of descriptive plots to see what some of these columns look like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x104ceffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [8, 3]\n",
    "plt.title('Skill distribution')\n",
    "plt.hist(data.skill, bins=40, color='0.5');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Xk5OTQ05ODtXV1U5tHiJNvc888wwnTpzAGMPevXvJysoiPT19WwVKzSoo8uDU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d077a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [8, 8]\n",
    "plt.xlabel('Skill')\n",
    "plt.ylabel('Win/Loss Ratio')\n",
    "plt.xlim(0,1000)\n",
    "plt.title('Win/Loss Ratio vs Skill')\n",
    "plt.scatter(data.skill, data.wlr, c = '0.5', alpha = 0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Principal Component Analysis\n",
    "\n",
    "Let's try smooshing our 8 dimensional dataset down to 2 dimensions using PCA. The projection will lose information, but it's a lot easier to visualize 2 dimensions than 8.\n",
    "\n",
    "First we normalize the data, then do a quicky plot to make sure the scaled data scatterplot looks roughly the same as the original."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CwSCBQIBsNsutW7eYm5vDZrMRCARwuVxUq1VMJhPlchm73U6lUiESidDV1UU+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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d233d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We will hold on to this scaler object so we can use it later to invert the scaling\n",
    "scaler = preprocessing.StandardScaler()\n",
    "scaledData = scaler.fit_transform(data)\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [4, 4]\n",
    "plt.scatter(scaledData[:,0], scaledData[:,1], c='0.5', alpha=0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now apply PCA to the data set to reduce it to two dimensions, then look at the explained variance to see how much information we lost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.49957908,  0.12950954])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca2 = PCA(2)\n",
    "data2d = pca2.fit_transform(scaledData)\n",
    "pca2.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first projected column captures 50% of the variance, and the second captures 13%. We've lost 37% of the variance, which is kind of unacceptable but here we are.\n",
    "\n",
    "How do the 9 input columns get weighted when producing the 2 output columns?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.39796309,  0.27666676,  0.42850564,  0.15660183,  0.44397119,\n",
       "         0.32315385,  0.2002008 ,  0.41645569,  0.20465859],\n",
       "       [-0.05025972, -0.27485704,  0.05732599,  0.48264399, -0.00520455,\n",
       "         0.13423469,  0.54215175, -0.07067902, -0.60722813]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca2.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hard to say really, but the first component sort of equally weights all parameters whereas the second favors columns 4 and 7. Column 4 is Kill/Death Ratio, and column 7 is Vehicle kills per minute. Perhaps these characteristics distinguish players?\n",
    "\n",
    "Just for curiosity, what do players look like in this projected space?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pLczMzOB2u6lWq3R3dxONRslkMmuuGn63QLBbqya3wqYECqWUHfgK8CowCbyn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\ndUmgEELU9f8DcuHT7Q9/eTcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d0d4a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data2d[:,0], data2d[:,1], c='0.5', alpha=0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Broadly speaking, the X axis here is \"player goodness\"; the  higher the number, the better the player. The second column is showing more weighted stats. Higher means higher Kill/Death ratio and vehicle kills / minute. Also lower win/loss ratio and flag captures per minute. I'm not sure this smooshed view is really instructive, it's probably a mistake to convolve those four columns into one stat. And our explained variance ratio above told us this PCA is too reductive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering\n",
    "\n",
    "Now let's apply K-Means clustering to the scaled 9 dimensional data to see what we can learn.\n",
    "\n",
    "First let's do the k-means and present the goodness of fit. I've chosen 4 clusters here because that's the smallest number that presents an interesting outlier. A more honest treatment should have a principled reason for choosing K=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inertia is 24517 (lower is better fit)\n"
     ]
    }
   ],
   "source": [
    "kmeans = cluster.KMeans(n_clusters = 4).fit(scaledData)\n",
    "\n",
    "# The cluster centers found for us by KMeans, scaled back to original space\n",
    "centroids = scaler.inverse_transform(kmeans.cluster_centers_)\n",
    "# The cluster centers projected two the 2d space\n",
    "centroids2d = pca2.transform(kmeans.cluster_centers_)\n",
    "\n",
    "print(\"Inertia is %d (lower is better fit)\" % kmeans.inertia_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot the data as before, but with centroids on the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZSeJRg//vwMIAboE/tNa+J3r7fhzKISIismNseIC31r4GDCzykNnoY4uIiOxUm9kH/yVj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QAIEAEPAECACHgAAAJEwAMAECACHgCAABHwAAAEiIAHACBABDwAAAEi4AEACBABDwBAgAh4AAAC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\nX/ClAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e8e6550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Q0LCqx1/OuWFlWd0vvvgi7e3tlJSUsGXLFmKx2G0t880k2a1m4triY124cIGC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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec68090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Same scatterplot of win/loss ratio vs skill, but with centroids\n",
    "plt.rcParams['figure.figsize'] = [8, 8]\n",
    "plt.xlabel('Skill')\n",
    "plt.ylabel('Win/Loss Ratio')\n",
    "plt.xlim(0,1000)\n",
    "plt.title('Win/Loss Ratio vs Skill')\n",
    "plt.scatter(x = data.skill, y = data.wlr, c = '0.5', alpha = 0.3)\n",
    "plt.scatter(y = centroids[:,1], x = centroids[:,0], c='r', marker='o', s = 100);\n",
    "plt.show()\n",
    "\n",
    "# And scatterplot of PCA-smooshed 2d data, with centroids\n",
    "plt.scatter(data2d[:,0], data2d[:,1], c='0.5', alpha=0.3);\n",
    "plt.scatter(centroids2d[:,0], centroids2d[:,1], c='r', marker='o', s = 100)\n",
    "plt.title('2d projection of player stats')\n",
    "plt.ylabel('.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The primary conclusion I draw from this analysis is that the data is not very obviously clustered. It's a broad smear of players across skill levels. I was hoping the data would obviously group up based on various play style, like vehicle players vs. weapon players or else maybe low kill/death ratio vs high. This analysis doesn't demonstrate that, although it doesn't rule it out either.\n",
    "\n",
    "Something is obviously going on with that fourth upper right cluster, the one with the absurdly high Y value. My suspicion is this is jet jockeys, who will have both a very high kill/death ratio (few deaths) and unusually high vehicle kills per minute. Not confident in this result though.\n",
    "\n",
    "Let's look a little closer at what these clusters are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>skill</th>\n",
       "      <td>323.798476</td>\n",
       "      <td>454.976602</td>\n",
       "      <td>207.900054</td>\n",
       "      <td>389.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wlr</th>\n",
       "      <td>1.646585</td>\n",
       "      <td>2.663742</td>\n",
       "      <td>1.117635</td>\n",
       "      <td>2.232333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gspm</th>\n",
       "      <td>156.106819</td>\n",
       "      <td>234.792948</td>\n",
       "      <td>91.328184</td>\n",
       "      <td>193.488667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kdr</th>\n",
       "      <td>1.887963</td>\n",
       "      <td>2.954057</td>\n",
       "      <td>1.208011</td>\n",
       "      <td>86.748000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kpm</th>\n",
       "      <td>0.846838</td>\n",
       "      <td>1.279210</td>\n",
       "      <td>0.469544</td>\n",
       "      <td>0.934667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>accuracy</th>\n",
       "      <td>14.135079</td>\n",
       "      <td>17.847537</td>\n",
       "      <td>9.969729</td>\n",
       "      <td>24.017333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vehKpm</th>\n",
       "      <td>0.690271</td>\n",
       "      <td>1.049103</td>\n",
       "      <td>0.416841</td>\n",
       "      <td>1.744333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weaKpm</th>\n",
       "      <td>1.388321</td>\n",
       "      <td>1.998377</td>\n",
       "      <td>0.799584</td>\n",
       "      <td>0.556667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>flagsPerMinute</th>\n",
       "      <td>0.213075</td>\n",
       "      <td>0.290306</td>\n",
       "      <td>0.146043</td>\n",
       "      <td>0.064319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>size</th>\n",
       "      <td>2362.000000</td>\n",
       "      <td>983.000000</td>\n",
       "      <td>1861.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          0           1            2           3\n",
       "skill            323.798476  454.976602   207.900054  389.000000\n",
       "wlr                1.646585    2.663742     1.117635    2.232333\n",
       "gspm             156.106819  234.792948    91.328184  193.488667\n",
       "kdr                1.887963    2.954057     1.208011   86.748000\n",
       "kpm                0.846838    1.279210     0.469544    0.934667\n",
       "accuracy          14.135079   17.847537     9.969729   24.017333\n",
       "vehKpm             0.690271    1.049103     0.416841    1.744333\n",
       "weaKpm             1.388321    1.998377     0.799584    0.556667\n",
       "flagsPerMinute     0.213075    0.290306     0.146043    0.064319\n",
       "cluster            0.000000    1.000000     2.000000    3.000000\n",
       "size            2362.000000  983.000000  1861.000000    3.000000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add cluster labels to our dataset\n",
    "labeledData = data.copy()\n",
    "labeledData['cluster'] = kmeans.labels_\n",
    "\n",
    "# Iterate through all the clusters and print some stats\n",
    "displayData = pd.DataFrame()\n",
    "for i in range(0, kmeans.n_clusters):\n",
    "    c = labeledData[labeledData['cluster'] == i]\n",
    "    thisCluster = c.mean()\n",
    "    thisCluster[\"size\"] = len(c)\n",
    "    displayData[\"%d\" % i] = thisCluster\n",
    "displayData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we have a single cluster with only 3 members in it. They do have an unusually high vehicle KPM and a super high kill/death ratio. Interesting outlier! It's not clear though how _right_ it is to arbitrarily pick 4 clusters. This group disappears with only 3 clusters; is it a real grouping? Why not the other outliers?\n",
    "\n",
    "One last thing, let's see how the number of clusters affects goodness of fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "46881 32091 27913 24518 22636 20528 19013 18093 16895 16270 15420 14762 14241 13812\n"
     ]
    },
    {
     "data": {
      "image/png": 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ky9P2N0m6IcX+Dng78HVJf99jlT8ne+btu92BiPhBRDxC7sFRSW2SWnPvH5Z0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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d215e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kValues = range(1,15)\n",
    "inertias = []\n",
    "for k in kValues:\n",
    "    testKMeans = cluster.KMeans(n_clusters = k).fit(scaledData)\n",
    "    inertias.append(testKMeans.inertia_)\n",
    "    print '%d' % testKMeans.inertia_,\n",
    "print\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [4, 4]\n",
    "plt.xlabel('Number of Clusters')\n",
    "plt.ylabel('Inertia')\n",
    "plt.scatter(x = kValues, y = inertias, c = '0.0')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}