results.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load CSVs\n",
    "csv_names = ['lewis', 'fifty', 'random', 'traditional', 'one']\n",
    "dfs = []\n",
    "for name in csv_names:\n",
    "    df_temp = pd.read_csv(f'data/{name}.csv')\n",
    "    df_temp['distribution_type'] = name\n",
    "    dfs.append(df_temp)\n",
    "df = pd.concat(dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "avg1st_score = df.groupby('distribution_type')['score_1'].mean()\n",
    "avg2nd_score = df.groupby('distribution_type')['score_2'].mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Score variability for different tile value distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What are the scores for each player for each tile value distribution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, '')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=1, ncols=2, figsize = (20, 5))\n",
    "\n",
    "# Dropping \"fifty\" distribution since it's not illustrative\n",
    "df_no_fifty = df[df['distribution_type'] != 'fifty']\n",
    "\n",
    "ax = df_no_fifty.boxplot('score_1', by='distribution_type', showfliers=False, ax=axes[0])\n",
    "ax.set_ylim(0, 900)\n",
    "fig = ax.get_figure()\n",
    "ax.set_title('Distribution of first player values')\n",
    "ax.set_ylabel('score')\n",
    "\n",
    "ax = df_no_fifty.boxplot('score_2', by='distribution_type', showfliers=False, ax=axes[1])\n",
    "ax.set_ylim(0, 900)\n",
    "fig = ax.get_figure()\n",
    "ax.set_title('Distribution of second player values')\n",
    "ax.set_ylabel('score')\n",
    "\n",
    "fig.suptitle('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is the percent difference for each tile value distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'percent difference')"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.boxplot('percent_dif', by='distribution_type', showfliers=False)\n",
    "fig = ax.get_figure()\n",
    "fig.suptitle('')\n",
    "ax.set_title('Percent difference for each tile value distribution')\n",
    "ax.set_ylabel('percent difference')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What percent of the time was the winner the player who went first?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "distribution_type\n",
       "fifty          55.518395\n",
       "lewis          56.212026\n",
       "one            54.456429\n",
       "random         53.826030\n",
       "traditional    56.978992\n",
       "Name: winner, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['winner'] = df['score_1'] > df['score_2']\n",
    "df.groupby('distribution_type')['winner'].apply(lambda series: series.sum() / series.shape[0] * 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Effect of Bingos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What tile value distribution had the highest percentage of equal bingos?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "distribution_type\n",
       "fifty          50.167224\n",
       "lewis          22.952022\n",
       "one            22.097644\n",
       "random         24.133421\n",
       "traditional    23.830391\n",
       "Name: equal_bingos, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['equal_bingos'] = df['bingo_1'] == df['bingo_2']\n",
    "df.groupby('distribution_type')['equal_bingos'].apply(lambda series: series.sum() / series.shape[0] * 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For each tile value distribution, what is the average difference in bingo count?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "distribution_type\n",
       "fifty          0.625418\n",
       "lewis          1.325686\n",
       "one            1.428470\n",
       "random         1.266187\n",
       "traditional    1.305323\n",
       "Name: bingo_difference, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['bingo_difference'] = abs(df['bingo_1'] - df['bingo_2'])\n",
    "df.groupby('distribution_type')['bingo_difference'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is the percent difference in scores when bingos are unequal v. when they are equal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, '')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_equal_bingos = df[df['equal_bingos']]\n",
    "df_unequal_bingos = df[~df['equal_bingos']]\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=2, figsize = (20, 5))\n",
    "\n",
    "ax = df_unequal_bingos.boxplot('percent_dif', by='distribution_type', showfliers=False, ax=axes[0])\n",
    "ax.set_ylim(0, 100)\n",
    "fig = ax.get_figure()\n",
    "ax.set_title('Percent difference when bingos are uneqal')\n",
    "ax.set_ylabel('percent difference')\n",
    "\n",
    "ax = df_equal_bingos.boxplot('percent_dif', by='distribution_type', showfliers=False, ax=axes[1])\n",
    "ax.set_ylim(0, 100)\n",
    "fig = ax.get_figure()\n",
    "ax.set_title('Percent difference when bingos are equal')\n",
    "ax.set_ylabel('percent difference')\n",
    "\n",
    "fig.suptitle('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}