BoardGame_Rating_Prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Predict the Rating for Board Games\n",
    "The data set that contains 80000 board games with game informations and their associated review scores.\n",
    "I'm going to predict average_rating using the other columns. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>id</th>\n",
       "      <th>type</th>\n",
       "      <th>name</th>\n",
       "      <th>yearpublished</th>\n",
       "      <th>minplayers</th>\n",
       "      <th>maxplayers</th>\n",
       "      <th>playingtime</th>\n",
       "      <th>minplaytime</th>\n",
       "      <th>maxplaytime</th>\n",
       "      <th>minage</th>\n",
       "      <th>users_rated</th>\n",
       "      <th>average_rating</th>\n",
       "      <th>bayes_average_rating</th>\n",
       "      <th>total_owners</th>\n",
       "      <th>total_traders</th>\n",
       "      <th>total_wanters</th>\n",
       "      <th>total_wishers</th>\n",
       "      <th>total_comments</th>\n",
       "      <th>total_weights</th>\n",
       "      <th>average_weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12333</td>\n",
       "      <td>boardgame</td>\n",
       "      <td>Twilight Struggle</td>\n",
       "      <td>2005.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>20113</td>\n",
       "      <td>8.33774</td>\n",
       "      <td>8.22186</td>\n",
       "      <td>26647</td>\n",
       "      <td>372</td>\n",
       "      <td>1219</td>\n",
       "      <td>5865</td>\n",
       "      <td>5347</td>\n",
       "      <td>2562</td>\n",
       "      <td>3.4785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>120677</td>\n",
       "      <td>boardgame</td>\n",
       "      <td>Terra Mystica</td>\n",
       "      <td>2012.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14383</td>\n",
       "      <td>8.28798</td>\n",
       "      <td>8.14232</td>\n",
       "      <td>16519</td>\n",
       "      <td>132</td>\n",
       "      <td>1586</td>\n",
       "      <td>6277</td>\n",
       "      <td>2526</td>\n",
       "      <td>1423</td>\n",
       "      <td>3.8939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>102794</td>\n",
       "      <td>boardgame</td>\n",
       "      <td>Caverna: The Cave Farmers</td>\n",
       "      <td>2013.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>210.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>210.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>9262</td>\n",
       "      <td>8.28994</td>\n",
       "      <td>8.06886</td>\n",
       "      <td>12230</td>\n",
       "      <td>99</td>\n",
       "      <td>1476</td>\n",
       "      <td>5600</td>\n",
       "      <td>1700</td>\n",
       "      <td>777</td>\n",
       "      <td>3.7761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>25613</td>\n",
       "      <td>boardgame</td>\n",
       "      <td>Through the Ages: A Story of Civilization</td>\n",
       "      <td>2006.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>13294</td>\n",
       "      <td>8.20407</td>\n",
       "      <td>8.05804</td>\n",
       "      <td>14343</td>\n",
       "      <td>362</td>\n",
       "      <td>1084</td>\n",
       "      <td>5075</td>\n",
       "      <td>3378</td>\n",
       "      <td>1642</td>\n",
       "      <td>4.1590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3076</td>\n",
       "      <td>boardgame</td>\n",
       "      <td>Puerto Rico</td>\n",
       "      <td>2002.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>39883</td>\n",
       "      <td>8.14261</td>\n",
       "      <td>8.04524</td>\n",
       "      <td>44362</td>\n",
       "      <td>795</td>\n",
       "      <td>861</td>\n",
       "      <td>5414</td>\n",
       "      <td>9173</td>\n",
       "      <td>5213</td>\n",
       "      <td>3.2943</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       id       type                                       name  \\\n",
       "0   12333  boardgame                          Twilight Struggle   \n",
       "1  120677  boardgame                              Terra Mystica   \n",
       "2  102794  boardgame                  Caverna: The Cave Farmers   \n",
       "3   25613  boardgame  Through the Ages: A Story of Civilization   \n",
       "4    3076  boardgame                                Puerto Rico   \n",
       "\n",
       "   yearpublished  minplayers  maxplayers  playingtime  minplaytime  \\\n",
       "0         2005.0         2.0         2.0        180.0        180.0   \n",
       "1         2012.0         2.0         5.0        150.0         60.0   \n",
       "2         2013.0         1.0         7.0        210.0         30.0   \n",
       "3         2006.0         2.0         4.0        240.0        240.0   \n",
       "4         2002.0         2.0         5.0        150.0         90.0   \n",
       "\n",
       "   maxplaytime  minage  users_rated  average_rating  bayes_average_rating  \\\n",
       "0        180.0    13.0        20113         8.33774               8.22186   \n",
       "1        150.0    12.0        14383         8.28798               8.14232   \n",
       "2        210.0    12.0         9262         8.28994               8.06886   \n",
       "3        240.0    12.0        13294         8.20407               8.05804   \n",
       "4        150.0    12.0        39883         8.14261               8.04524   \n",
       "\n",
       "   total_owners  total_traders  total_wanters  total_wishers  total_comments  \\\n",
       "0         26647            372           1219           5865            5347   \n",
       "1         16519            132           1586           6277            2526   \n",
       "2         12230             99           1476           5600            1700   \n",
       "3         14343            362           1084           5075            3378   \n",
       "4         44362            795            861           5414            9173   \n",
       "\n",
       "   total_weights  average_weight  \n",
       "0           2562          3.4785  \n",
       "1           1423          3.8939  \n",
       "2            777          3.7761  \n",
       "3           1642          4.1590  \n",
       "4           5213          3.2943  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "board_games = pd.read_csv(\"board_games.csv\")\n",
    "board_games.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "board_games.dropna(axis=0, inplace = True)\n",
    "board_games = board_games[board_games['users_rated'] > 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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7VV1drXXr1umll17S119/rcHBQdntdkmSw+HQ0NCQJCkcDsvtdkf7O51OhcNhhcNhuVyu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\nAACwIBwAABaEAwDA4v8BnNhYP754P7IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ecca70978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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t4dLXXldWVua2MKCfPLVHqqur1dLS4lctQNZ9+OGH2rlzZ+fP27ZtkySdPXuW9giM4Hmd\ndktLixYsWKDjx4+nH4C1sAgovpsIMs4eAXT1xmPXG5HxeFySurVMgCAblJk2AGDgsjLTTqVSff4T\nk39+AoB/PK0eWbJkiWbNmqUTJ05o4sSJ2rp1q191AQDSyPqBUQAA/3D2CCKHTWEwGaGNyGFTGExG\naCNyqqurVVRUlOsyAFcIbQAwCKENAAYhtAHAIIQ2IinTpjAgqAhtRA6bwmAyNtcAgEGYaQOAQQht\nADAIoQ0ABiG0AcAghDYAGITQBgCDENoAYBBCGwAM8l8NlF8JG2TecgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ed0391f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.57882993483\n",
      "6.01611284933\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.hist(board_games['average_rating'])\n",
    "plt.show()\n",
    "plt.boxplot(board_games['average_rating'])\n",
    "plt.show()\n",
    "\n",
    "std = board_games['average_rating'].std()\n",
    "mean = board_games['average_rating'].mean()\n",
    "\n",
    "print(std)\n",
    "print(mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error Metric\n",
    "The distribution follow a normal distribution, so we can use mean squared error as an error metric"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FEWPh3n9pd/mtLIGXfLSQqa6EaXvgrRgYuxY+eZrQltUc+Xa/s7sqRIMmzzMR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ec78b3dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "kmeans_model = KMeans(n_clusters = 5, random_state=1)\n",
    "numeric_columns = board_games.iloc[:,3:]\n",
    "kmeans_model.fit(numeric_columns)\n",
    "labels = kmeans_model.labels_\n",
    "\n",
    "import numpy\n",
    "game_mean = numeric_columns.apply(numpy.mean, axis=1)\n",
    "game_std = numeric_columns.apply(numpy.std, axis=1)\n",
    "    \n",
    "plt.scatter(x = game_mean, y = game_std, c = labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like most of the games are similar, 4 clusters are between mean = 0 and and mean = 4000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding Correlations\n",
    "Remove columns that don't add predictive power to the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "id                      0.304201\n",
      "yearpublished           0.108461\n",
      "minplayers             -0.032701\n",
      "maxplayers             -0.008335\n",
      "playingtime             0.048994\n",
      "minplaytime             0.043985\n",
      "maxplaytime             0.048994\n",
      "minage                  0.210049\n",
      "users_rated             0.112564\n",
      "average_rating          1.000000\n",
      "bayes_average_rating    0.231563\n",
      "total_owners            0.137478\n",
      "total_traders           0.119452\n",
      "total_wanters           0.196566\n",
      "total_wishers           0.171375\n",
      "total_comments          0.123714\n",
      "total_weights           0.109691\n",
      "average_weight          0.351081\n",
      "Name: average_rating, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "correlations = board_games.corr()\n",
    "print(correlations['average_rating'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The 'yearpublished' column is surprisingly positively correlated with average_rating. So most recent games tend to be rated more highly. \n",
    "- The more 'minage' is high, the more highly is the score.\n",
    "- The more \"weighty\" a game is (complexity rating of a game), the more highly it tends to be rated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cols = list(board_games.columns)\n",
    "cols.remove(\"average_rating\")\n",
    "cols.remove(\"bayes_average_rating\")\n",
    "cols.remove(\"minplayers\")\n",
    "cols.remove(\"maxplayers\")\n",
    "# not numeric values\n",
    "cols.remove(\"name\")\n",
    "cols.remove(\"id\")\n",
    "cols.remove(\"type\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I removed useless columns, like 'bayes_average_rating' derivated from 'average_rating'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4479383303003244\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Training\n",
    "lr = LinearRegression()\n",
    "lr.fit(board_games[cols], board_games[\"average_rating\"])\n",
    "\n",
    "# Prediction\n",
    "predictions = lr.predict(board_games[cols])\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "import math\n",
    "\n",
    "mse = mean_squared_error(board_games['average_rating'], predictions)\n",
    "rmse = math.sqrt(mse)\n",
    "\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The error rate is close to the standard deviation (1.57) of all board game ratings.\n",
    "This indicates that our model may not have high predictive power."
   ]
  }
 ],
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