FinalProjectGroup059-Fa21.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# COGS 108 - Final Project - Analyzing the Correlation Between Gold Lead and Match Outcome Across Different League of Legends Leagues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Permissions\n",
    "\n",
    "Place an `X` in the appropriate bracket below to specify if you would like your group's project to be made available to the public. (Note that student names will be included (but PIDs will be scraped from any groups who include their PIDs).\n",
    "\n",
    "* [X] YES - make available\n",
    "* [  ] NO - keep private"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Names\n",
    "\n",
    "- Justin Chu \n",
    "- John Li\n",
    "- Luke Lloyd\n",
    "- Prathik Malireddy\n",
    "- Dustin Lin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='research_question'></a>\n",
    "# Research Question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the competivite League of Legends video game scene, is there a difference in how well teams across different leagues can close out games when having an advantage (gold lead) at 20 minutes?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='background'></a>\n",
    "\n",
    "## Background & Prior Work"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Background\n",
    "\n",
    "### What is \"League of Legends\"?\n",
    "\n",
    "For anyone blessed enough to not know what League of Legends is, let me ruin that for you. League of Legends is a 5v5 online competitive game where before each match, each player picks a *champion* to play as. The 10 champions interact with each other and other neutral monsters/minions in a large square arena (often called the *map*). Each game usuaslly begins with players spread across the map in what are called *lanes*, gaining gold and experience by killing neutral monsters and minions in order to get stronger. Each game is played between 2 teams (a *blue* team and a *red* team) each consisting of 5 players.\n",
    "\n",
    "\n",
    "Throughout the course of a game the players on each team attempt to gain an advantage over their opponents by gaining gold and experience at a faster rate. With more gold and experience, members of each time can buy items and level up to become stronger than their opponents. With the ultimate goal of destroying the opposing team's base, which is located at the ends of the map/playing field, it is paramount that a team gets an advantage.\n",
    "\n",
    "Gold and experience are gained by getting kills on enemy players, destroying pieces of the enemy’s base (ie: turrets and inhibitors), killing epic monsters that spawn every five minutes as a team (ie: Baron and dragons), and finally by killing creeps (minions that fight for each team and neutral monsters that are distributed around the map). The game is decided when one team reaches the back of the other team’s base and destroys their *Nexus*.\n",
    "\n",
    "### The League of Legends (LoL) competitive scene\n",
    "\n",
    "The League of Legends competitive scene (sometimes called the *professional scene* or *pro scene*) consists of different teams of 5 players each (and typically a coach as well as supporting staff) competing against other teams in a circuit seperated by regions. For example, the north america regional circuit contains around 10 teams with players mostly coming from the US and Canada. Other regions that we will look at include Europe, Korea, and southeast asia. There are often international tournements where teams from different regions come together to compete and decide which region has the best teams and players. *Leagues* refers to the different regional circuits described above. For example, the north american league is referred to as *NALCS*, the european league *EULCS*, the korean's *LCK*, and southeast asia *LMS* just to name a few.\n",
    "\n",
    "\n",
    "As a group, we noticed from our League of Legends playing and watching experience that there is usually a certain point in any specific game where it seems unwinnable for one team. We are interested in how often teams in each region can close out matches that they are already winning. We think that how effective teams are at snowballing their lead and closing out games can be a proxy for their overall skill level.\n",
    "\n",
    "### Choice of parameters for research question\n",
    "\n",
    "We chose to use gold as a proxy for determining which team was \"winning\" at any given point because it both summarizes each team’s performance up until that point and correlates directly with the strength of each team (since individuals can purchase items with their gold which makes their characters stronger), which isn’t something that can be measured on its own.\n",
    "\n",
    "We chose to measure which team was winning at 20 minutes into the match because in our experience, by this time one team usually has a measurable and meaningful lead over the other. In a League of Legends game, 20 minutes is usually when team members leave their *lanes* and begin to group together as 5 team members in order to team up and take down objectives across the map. We affrimed this choice in our EDA section by noticing that a vast majority of obersvations (where each observation is a game) in the dataset last longer than 20 minutes, with the average game time somewhere between 35 and 40 minutes.\n",
    "\n",
    "\n",
    "\n",
    "### Prior Work\n",
    "\n",
    "1) Using the data set, Leonardo Fuchs computed a prediction of which team will win a match when a particular team is playing. They focused on a particular North American team (Cloud9). We consider our work marginally related as we are looking at which teams win certain matches based on their leads. However we are not doing a prediction.\n",
    "\n",
    "2) Chuck Ephron used the data set to compute a heat map of win percentages by gold lead and time for every game in the dataset. They explored a team’s chance of winning based on what gold lead they had at a certain time. We consider our work to be related as we are also looking into how teams are using their gold lead advantage to win the game, but we are doing so across different regions/statistics, not all of the games in the dataset.\n",
    "\n",
    "\n",
    "References (include links):\n",
    "- 1) https://www.kaggle.com/leofuchs/predicting-who-will-win-cloud9-matches-in-lol\n",
    "- 2) https://www.kaggle.com/chuckephron/win-percent-by-gold-lead-and-time-heat-map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hypothesis:** We expect there to be difference across leagues in how well teams can close out games when having a gold lead at 20 minutes.\n",
    "\n",
    "Form our knowledge of the game, we know that there exists different skill levels among teams across the different leagues. One can also analyze the differences in skill level across leagues by looking at which team wins international tournements. Since there are differences in skill across the different leagues, we believe that teams of a certain league are more efficient and skillful when trying to win a game given that they already have a lead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dataset(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Dataset Name: League of Legends\n",
    "- Link to the dataset: https://www.kaggle.com/chuckephron/leagueoflegends?select=LeagueofLegends.csv\n",
    "- Number of observations: 7620 (where each observation is a game between 2 teams)\n",
    "\n",
    "This dataset includes competitive matches between 2015-2018. The leagues in the dataset are LCK, NALCS, EULCS, LMS, TCL, OPL, WC, CBLoL, LCL, LJL, LLN, CLS, IEM, MSI, and RR. Some of the leagues corrospond to international events, which will need to be excluded. The data also contains the gold difference by minute and the winner of each game."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.collections import PolyCollection\n",
    "from scipy.stats import binom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_dataset = pd.read_csv('data/LeagueofLegends.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7620, 57)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_dataset.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = raw_dataset.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Cleaning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Describe your data cleaning steps here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first removed games that ended before 20 minutes. We consdier these games to be outliers since the games ended much quicker than average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = dataset[dataset.gamelength > 20]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we made a new column *golddiff_20min* that contains the gold difference at 20 minutes between each team where the gold difference = blue team - red team."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset['golddiff_20min'] = dataset.golddiff.str[1:-1].str.split(', ').apply(lambda x: int(x[20]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We renamed the column *'bResult'* which contains a boolean indicating if the blue team won the match or not to *'blue_win'* for clairity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LCK      1445\n",
       "NALCS    1269\n",
       "EULCS    1099\n",
       "LMS       777\n",
       "TCL       652\n",
       "OPL       456\n",
       "CBLoL     301\n",
       "LCL       279\n",
       "LJL       258\n",
       "LLN       241\n",
       "CLS       175\n",
       "Name: League, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.rename({'bResult': 'blue_win'}, axis=1, inplace=True)\n",
    "dataset.rename({'rResult': 'red_win'}, axis=1, inplace=True)\n",
    "\n",
    "dataset[['League', 'Year', 'golddiff_20min']].pivot_table(index='League', columns='Year', aggfunc='count')\n",
    "\n",
    "dataset = dataset[dataset.League.isin(['LCK', 'NALCS', 'EULCS', 'LMS', 'TCL', 'OPL', 'CBLoL', 'LCL', 'LJL', 'LLN', 'CLS'])]\n",
    "\n",
    "\n",
    "# The outputed values below represent the observations we have for each region.\n",
    "# Recall that each obervation is a match, which we know lasts for at least 20 minutes.\n",
    "dataset.League.value_counts()\n",
    "\n",
    "\n",
    "# dataset = dataset[['League', 'Year', 'Type', 'blue_win', 'golddiff_20min']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>Season</th>\n",
       "      <th>Type</th>\n",
       "      <th>blueTeamTag</th>\n",
       "      <th>blue_win</th>\n",
       "      <th>red_win</th>\n",
       "      <th>redTeamTag</th>\n",
       "      <th>gamelength</th>\n",
       "      <th>golddiff</th>\n",
       "      <th>...</th>\n",
       "      <th>goldredMiddle</th>\n",
       "      <th>redADC</th>\n",
       "      <th>redADCChamp</th>\n",
       "      <th>goldredADC</th>\n",
       "      <th>redSupport</th>\n",
       "      <th>redSupportChamp</th>\n",
       "      <th>goldredSupport</th>\n",
       "      <th>redBans</th>\n",
       "      <th>Address</th>\n",
       "      <th>golddiff_20min</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Spring</td>\n",
       "      <td>Season</td>\n",
       "      <td>TSM</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>C9</td>\n",
       "      <td>40</td>\n",
       "      <td>[0, 0, -14, -65, -268, -431, -488, -789, -494,...</td>\n",
       "      <td>...</td>\n",
       "      <td>[475, 475, 552, 842, 1178, 1378, 1635, 1949, 2...</td>\n",
       "      <td>Sneaky</td>\n",
       "      <td>Sivir</td>\n",
       "      <td>[475, 475, 532, 762, 1097, 1469, 1726, 2112, 2...</td>\n",
       "      <td>LemonNation</td>\n",
       "      <td>Thresh</td>\n",
       "      <td>[515, 515, 577, 722, 911, 1042, 1194, 1370, 14...</td>\n",
       "      <td>['Tristana', 'Leblanc', 'Nidalee']</td>\n",
       "      <td>http://matchhistory.na.leagueoflegends.com/en/...</td>\n",
       "      <td>987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Spring</td>\n",
       "      <td>Season</td>\n",
       "      <td>CST</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>DIG</td>\n",
       "      <td>38</td>\n",
       "      <td>[0, 0, -26, -18, 147, 237, -152, 18, 88, -242,...</td>\n",
       "      <td>...</td>\n",
       "      <td>[475, 475, 552, 786, 1097, 1389, 1660, 1955, 2...</td>\n",
       "      <td>CoreJJ</td>\n",
       "      <td>Corki</td>\n",
       "      <td>[475, 475, 532, 868, 1220, 1445, 1732, 1979, 2...</td>\n",
       "      <td>KiWiKiD</td>\n",
       "      <td>Annie</td>\n",
       "      <td>[515, 515, 583, 752, 900, 1066, 1236, 1417, 15...</td>\n",
       "      <td>['RekSai', 'Janna', 'Leblanc']</td>\n",
       "      <td>http://matchhistory.na.leagueoflegends.com/en/...</td>\n",
       "      <td>205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Spring</td>\n",
       "      <td>Season</td>\n",
       "      <td>WFX</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>GV</td>\n",
       "      <td>40</td>\n",
       "      <td>[0, 0, 10, -60, 34, 37, 589, 1064, 1258, 913, ...</td>\n",
       "      <td>...</td>\n",
       "      <td>[475, 475, 533, 801, 1006, 1233, 1385, 1720, 1...</td>\n",
       "      <td>Cop</td>\n",
       "      <td>Corki</td>\n",
       "      <td>[475, 475, 533, 781, 1085, 1398, 1782, 1957, 2...</td>\n",
       "      <td>BunnyFuFuu</td>\n",
       "      <td>Janna</td>\n",
       "      <td>[515, 515, 584, 721, 858, 1002, 1168, 1303, 14...</td>\n",
       "      <td>['Leblanc', 'Zed', 'RekSai']</td>\n",
       "      <td>http://matchhistory.na.leagueoflegends.com/en/...</td>\n",
       "      <td>4597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Spring</td>\n",
       "      <td>Season</td>\n",
       "      <td>TIP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>TL</td>\n",
       "      <td>41</td>\n",
       "      <td>[0, 0, -15, 25, 228, -6, -243, 175, -346, 16, ...</td>\n",
       "      <td>...</td>\n",
       "      <td>[475, 475, 532, 771, 1046, 1288, 1534, 1776, 2...</td>\n",
       "      <td>KEITH</td>\n",
       "      <td>KogMaw</td>\n",
       "      <td>[475, 475, 532, 766, 1161, 1438, 1776, 1936, 2...</td>\n",
       "      <td>Xpecial</td>\n",
       "      <td>Janna</td>\n",
       "      <td>[515, 515, 583, 721, 870, 1059, 1205, 1342, 15...</td>\n",
       "      <td>['RekSai', 'Rumble', 'LeeSin']</td>\n",
       "      <td>http://matchhistory.na.leagueoflegends.com/en/...</td>\n",
       "      <td>2712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Spring</td>\n",
       "      <td>Season</td>\n",
       "      <td>CLG</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>T8</td>\n",
       "      <td>35</td>\n",
       "      <td>[40, 40, 44, -36, 113, 158, -121, -191, 23, 20...</td>\n",
       "      <td>...</td>\n",
       "      <td>[475, 475, 532, 807, 1042, 1338, 1646, 1951, 2...</td>\n",
       "      <td>Maplestreet8</td>\n",
       "      <td>Corki</td>\n",
       "      <td>[475, 475, 532, 792, 1187, 1488, 1832, 2136, 2...</td>\n",
       "      <td>Dodo8</td>\n",
       "      <td>Annie</td>\n",
       "      <td>[475, 475, 538, 671, 817, 948, 1104, 1240, 136...</td>\n",
       "      <td>['Rumble', 'Sivir', 'Rengar']</td>\n",
       "      <td>http://matchhistory.na.leagueoflegends.com/en/...</td>\n",
       "      <td>926</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 58 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  League  Year  Season    Type blueTeamTag  blue_win  red_win redTeamTag  \\\n",
       "0  NALCS  2015  Spring  Season         TSM         1        0         C9   \n",
       "1  NALCS  2015  Spring  Season         CST         0        1        DIG   \n",
       "2  NALCS  2015  Spring  Season         WFX         1        0         GV   \n",
       "3  NALCS  2015  Spring  Season         TIP         0        1         TL   \n",
       "4  NALCS  2015  Spring  Season         CLG         1        0         T8   \n",
       "\n",
       "   gamelength                                           golddiff  ...  \\\n",
       "0          40  [0, 0, -14, -65, -268, -431, -488, -789, -494,...  ...   \n",
       "1          38  [0, 0, -26, -18, 147, 237, -152, 18, 88, -242,...  ...   \n",
       "2          40  [0, 0, 10, -60, 34, 37, 589, 1064, 1258, 913, ...  ...   \n",
       "3          41  [0, 0, -15, 25, 228, -6, -243, 175, -346, 16, ...  ...   \n",
       "4          35  [40, 40, 44, -36, 113, 158, -121, -191, 23, 20...  ...   \n",
       "\n",
       "                                       goldredMiddle        redADC  \\\n",
       "0  [475, 475, 552, 842, 1178, 1378, 1635, 1949, 2...        Sneaky   \n",
       "1  [475, 475, 552, 786, 1097, 1389, 1660, 1955, 2...        CoreJJ   \n",
       "2  [475, 475, 533, 801, 1006, 1233, 1385, 1720, 1...           Cop   \n",
       "3  [475, 475, 532, 771, 1046, 1288, 1534, 1776, 2...         KEITH   \n",
       "4  [475, 475, 532, 807, 1042, 1338, 1646, 1951, 2...  Maplestreet8   \n",
       "\n",
       "  redADCChamp                                         goldredADC   redSupport  \\\n",
       "0       Sivir  [475, 475, 532, 762, 1097, 1469, 1726, 2112, 2...  LemonNation   \n",
       "1       Corki  [475, 475, 532, 868, 1220, 1445, 1732, 1979, 2...      KiWiKiD   \n",
       "2       Corki  [475, 475, 533, 781, 1085, 1398, 1782, 1957, 2...   BunnyFuFuu   \n",
       "3      KogMaw  [475, 475, 532, 766, 1161, 1438, 1776, 1936, 2...      Xpecial   \n",
       "4       Corki  [475, 475, 532, 792, 1187, 1488, 1832, 2136, 2...        Dodo8   \n",
       "\n",
       "  redSupportChamp                                     goldredSupport  \\\n",
       "0          Thresh  [515, 515, 577, 722, 911, 1042, 1194, 1370, 14...   \n",
       "1           Annie  [515, 515, 583, 752, 900, 1066, 1236, 1417, 15...   \n",
       "2           Janna  [515, 515, 584, 721, 858, 1002, 1168, 1303, 14...   \n",
       "3           Janna  [515, 515, 583, 721, 870, 1059, 1205, 1342, 15...   \n",
       "4           Annie  [475, 475, 538, 671, 817, 948, 1104, 1240, 136...   \n",
       "\n",
       "                              redBans  \\\n",
       "0  ['Tristana', 'Leblanc', 'Nidalee']   \n",
       "1      ['RekSai', 'Janna', 'Leblanc']   \n",
       "2        ['Leblanc', 'Zed', 'RekSai']   \n",
       "3      ['RekSai', 'Rumble', 'LeeSin']   \n",
       "4       ['Rumble', 'Sivir', 'Rengar']   \n",
       "\n",
       "                                             Address golddiff_20min  \n",
       "0  http://matchhistory.na.leagueoflegends.com/en/...            987  \n",
       "1  http://matchhistory.na.leagueoflegends.com/en/...            205  \n",
       "2  http://matchhistory.na.leagueoflegends.com/en/...           4597  \n",
       "3  http://matchhistory.na.leagueoflegends.com/en/...           2712  \n",
       "4  http://matchhistory.na.leagueoflegends.com/en/...            926  \n",
       "\n",
       "[5 rows x 58 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = dataset[['League', 'Year', 'Type', 'blue_win', 'golddiff_20min']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the size of the dataset, it's best if we contain the columns to only what's needed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def attribute_win(row):\n",
    "    blue_win = row['blue_win']\n",
    "    blue_diff = int(row['golddiff_20min'] > 0)\n",
    "    \n",
    "    if blue_win == blue_diff:\n",
    "        return 1\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = dataset.assign(diff_win = dataset.apply(attribute_win, axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See if a higher gold difference is associated with the win"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>League</th>\n",
       "      <th>Year</th>\n",
       "      <th>Type</th>\n",
       "      <th>blue_win</th>\n",
       "      <th>golddiff_20min</th>\n",
       "      <th>diff_win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Season</td>\n",
       "      <td>1</td>\n",
       "      <td>987</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Season</td>\n",
       "      <td>0</td>\n",
       "      <td>205</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Season</td>\n",
       "      <td>1</td>\n",
       "      <td>4597</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Season</td>\n",
       "      <td>0</td>\n",
       "      <td>2712</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NALCS</td>\n",
       "      <td>2015</td>\n",
       "      <td>Season</td>\n",
       "      <td>1</td>\n",
       "      <td>926</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  League  Year    Type  blue_win  golddiff_20min  diff_win\n",
       "0  NALCS  2015  Season         1             987         1\n",
       "1  NALCS  2015  Season         0             205         0\n",
       "2  NALCS  2015  Season         1            4597         1\n",
       "3  NALCS  2015  Season         0            2712         0\n",
       "4  NALCS  2015  Season         1             926         1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Analysis & Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "eda_dataset = raw_dataset.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We were interested at looking at the distribution of game lengths for each region. Perhaps some regions played longer or shorter games due to different playstyles. Out of the 4 regions with the most observations, the distribution seems pretty similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Game time in minutes of LMS games')]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## hist grams for each region\n",
    "dataset_LCK = eda_dataset[eda_dataset['League'] == 'LCK']\n",
    "dataset_NALCS = eda_dataset[eda_dataset['League'] == 'NALCS']\n",
    "dataset_EULCS = eda_dataset[eda_dataset['League'] == 'EULCS']\n",
    "dataset_LMS = eda_dataset[eda_dataset['League'] == 'LMS']\n",
    "\n",
    "\n",
    "fig, ((ax1, ax2)) = plt.subplots(ncols=2, sharey=True, figsize=(10,5))\n",
    "\n",
    "# dataset_LCK['gamelength'].plot.hist(xlabel='Game time in minutes')\n",
    "sns.histplot(data=dataset_LCK, x='gamelength', ax=ax1,  color='m',  )\n",
    "\n",
    "sns.histplot(data=dataset_NALCS, x='gamelength', ax=ax2, color='b' )\n",
    "\n",
    "ax1.set(xlabel='Game time in minutes of LCK games')\n",
    "ax2.set(xlabel='Game time in minutes of NALCS games')\n",
    "\n",
    "\n",
    "fig2, (ax1_2, ax2_2) = plt.subplots(ncols=2, sharey=True, figsize=(10,5))\n",
    "\n",
    "# dataset_LCK['gamelength'].plot.hist(xlabel='Game time in minutes')\n",
    "sns.histplot(data=dataset_EULCS, x='gamelength', ax=ax1_2,  color='r',  )\n",
    "\n",
    "sns.histplot(data=dataset_LMS, x='gamelength', ax=ax2_2, color='g' )\n",
    "\n",
    "ax1_2.set(xlabel='Game time in minutes of EULCS games')\n",
    "ax2_2.set(xlabel='Game time in minutes of LMS games')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To help compare the averages, we created a barplot (this time with all the different regions included). This backed our discoverey in the hist-plots above that the average game times acorss all observations is around 35-40 minutes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Average game length in minutes')]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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glecUHYaZDSC/+PBniw6hUI1eM7mflTcTDiK767wrr5eYmVnrNXpmkr9RcAXwTES046ZFMzPrQo3eZ7Io91gGDJO0XruCkrSFpEtSCfrZkq6XtIOkB2r0fbukP0iakUrTT25XXGZmVlujZyZ/JCtp8gJZnazhwFOSngU+FxH39PXkNZHK0E8BLoiIw1LbBGB0nadcAHw0Iu5Ld8zv2KpYzMysMY0mk18BUyLiBgBJ+wH7A5cB/wXs0cKY9gWWR8R/VxoiYoakMXX6b04q7ZJK1s9uYSxmZrx87S3EoiV99jnymtv63D7QKww3mkx2j4gvVFYi4kZJ34uIYyVt0OKYxlNVhr4fPwIekjSNLOldEBGr1ZBepWrwyNpF28zMaolFS4gFfRf+mNPP9oGu0WTyvKSvAZek9Y8BL6RhpVfbElmDIuLbki4C9gM+DhwOTKzRb2XV4LFjXDXYzBqmoRv322erIcP63D7QKww3mkw+DvwbcDXZNZPbU9sg4KMtjmkWMGlNnhARjwJnSDobmCtps4h4rsVxmVmPWv+gffvtc2GP32fS0Le5ImJeRHw5It4cERMi4ksRMTciXo6IR1oc02+ADSR9rtIg6a3A62t1lvRBrZxoZRzwCjC/xTGZmVkfGr1pcRTwVbJpdTestEfEu1sdUESEpEOAUyV9nawE/WNkZe93lPRErvtXyCbT+pGkpWT3wByRLsSbmVmHNDrMdRFwKdnNi18APgnMbVdQEfEktYfPat3bcnm74jAzs8Y0mkw2i4ifSvqniLgVuFXSre0MrJ3GjRjZ83V0zMxaqdFksjz9+5SkDwJPAtu0JyQzM+s2jSaT70jaBPhn4D+BYWTXK8zMzBqez2RqWlxAdod6V3vkhfkceMVVRYdhZgPEdZMOLTqEwjX01eBUZPHmSqFFSbtI8ry3ZmYGNF41+GzgeNK1k4iYCRzWrqAkLa7RNlnScTXaQ9LJufXjXDnYzKyzGk0mgyPizqq2ssxn8hJwqKSRRQdiZtarGk0m8ySNJc22KGkSqVJvCawgq7nlLwSYmRWk0W9zfZHsA/sNkuYAfwWOaFtUa+4nwExJA7e+s5kV5sXrriUWLay7/chrr+53Hy5BD0TEX4D3StoYWCciFkk6Bji1rdE1KCIWSroQOJpsJsjV5EvQbzTSI2Jm1rhYtJBYsKDu9jl9bOsVjZ6ZABAR+dlhjqUkySQ5lWxGyPNqbcyXoB8+dnuXoDezhmlo3+XltxoypN99uAR9feq/S+dExPOSLgM+A5xbdDxmNnBseOBBfW6/0PeZNHwBvpZ2/nU/WNITucexqf2b+fYazzsZ8BiWmVmH9XlmImkRtZOGgI3aEhEQEfWS3OQafYfklp8BBrcpLDMzq6PPZBIRQzsVSCdtP2K4yx+YmbVQM8NcZmZmgJOJmZm1QDPf5upaj76wmEOuvL3oMMysx0z58N5Fh9A2PjMxM7OmOZmYmVnTuiKZ9FeSXtL5qfikmZkVoCuSiZmZlVtPXoA3M2u1JddeSCya32efI685q9/9dGt14Z5JJqtWDR5dcDRmNtDEovm8uuC5PvvMGcDFhXsmmeSrBo8Y+wZXDTazltLQ4f1eN9hyyIb97qdbqwv3TDIxM2unjQ86st8+F/o+EzMzs/q6JZnUKkm/LvBSrs+Zue3TC4rTzKwndcUwV62S9JKmAHek7Ud1OiYzM1upK5JJNUn3A38Gblyb548dMWRA18gxM+u0rkwmEbFz0TGYmdlK3XLNxMzMSqwrz0ya9fj8lzl6yuNFh2FmPeK0Q7YtOoS285mJmZk1rZTJpFaV4NR+pKQHJM2SNNtVg83MyqGUyaQWSe8HjgH2i4idgLcAA7jSjZlZ9+imaybHA8dFxJMAEfEicHaxIZmZGXRXMhkP3FN0EGZm1R675ocsXziv7vYjp/T/UdutpecruimZNCVfgn7oqK0LjsbMBpLlC+fx8oJn6m4fyKXnK7opmcwCdgN+szZPzpegH739Li5Bb2Yts96wkX1uHzWksTOTbtZNyeQE4ERJB0TE05I2AP4hIk4rOjAz621jDv6XPrf3wn0mZU0mgyU9kVs/JSJOkTQa+LUkAQGcm+tzpqRT0/LjEbFnp4I1M+t1pUwmtaoEp/bzgPNqtB/V7pjMzKy+UiaTdtt2+Po9cdppZtYpXXPTopmZlZeTiZmZNa0nh7nmv7CCq66of4ORmVknHDqp768UdxOfmZiZWdOcTMzMrGmlTSaSfiTpmNz6DZLOya2fLOlYSTtIul7SI5IelHRZuh/FzMw6pLTJBLgD2AtA0jrASGCn3Pa9yAo//gI4IyK2j4g3AmcAozocq5lZTyvzBfjfAT9KyzsBDwBbShoBLAXeCOwITI+I6ypPiohbOh2omVm1a6/7LgsXze2zz9XX9v/3fLdUEy5tMomIJyWtkPQ6srOQ6cDWwJ5kk2LNBN5Ag2Xp81WDR47cpi0xm5lVLFw0lwULnuqzz4IBVE24tMkk+R1ZItkLOIUsmexFlkzuANZvdEf5qsHbj53gqsFm1lbDhvY/2j5kSGNnJt2g7Mmkct1kZ7JhrseBfwYWkhV53Bx4V2HRmZnVcdCB3+i3j+8z6ZzfAQcAz0fEKxHxPDCcbKhrOnAxsJekD1aeIGl/STsXEq2ZWY8qezK5n+xbXL+valsQEfMiYhlZsvmypIclzQaOAp7teKRmZj2s1MNcEfEKMKyq7aiq9T8B+3cwLDMzq1LqZNIuw0esO6DGKs3Milb2YS4zM+sCTiZmZta0nhzmWjpvBfee42v0ZtZab/7s5kWHUBifmZiZWdNKmUwkhaSf5dbXlTRX0tS0PlrSVEn3SZot6frUPkbSA0XFbWbWq8o6zLUEGC9po3QvyfuAObnt3wZuiogfA0japYAYzcwsKeWZSfJLoHJn++HAz3PbtgSeqKxExMwOxmVmZlXKemYCcAnwrTS0tQtZLa53pm0/AS6V9CXg18B5EfFkMWGa2UB21i3f4/klfZeSr9jgtkFrtO9uKS/fiNImk4iYKWkM2VnJ9VXbbpC0Hdmd7+8H7pU0vq/95UvQb7GpS9CbWWOeXzKXeYuebqzzovbGUmalTSbJtcBJwERgs/yGVPTxYuDidPayD33MbZIvQf+mMS5Bb2aN2XTjxidu3WDYmp+ZDBRlTybnkhV1vF/SxEqjpHcDv4+IpZKGAmOB/y0oRjMbwD6/77823LeX7zMpdTKJiCeAH9fYtBtwuqQVZF8iOCci7krDYmZm1mGlTCYRMaRG2zRgWlr+IfDDGn0eA/q8dmJmZq1XymTSboNHrtvTp6NmZq1W5vtMzMysSziZmJlZ03pymGv5My/x9EmPFB2GmQ0wWxy3fdEhFMZnJmZm1jQnEzMza1opk4mkxenfMZKWSZqRexyZtj0m6bdVz5vhEvRmZp3XDddMHo2ICXW2DZW0bUQ8LumNHY3KzMxe0w3JpC+XAR8jq99VKVP/94VGZGYDygl3nsq8Zc811HfQzPXWaN+uGtxZYyXNyK1/OSIqw1tXAOeTJZMDgSOok0zyVYO3Hr5V24I1s4Fl3rLneHrps411XtreWMqsG5JJX8NczwMvSDoMeJA+/ivzVYN33XZnVw02s4aM3Giz/jslg0as+ZnJQNENyaQ/l5JNlnVUwXGY2QB0/NuOabhvL99nMhCSyRSyaXxvADx+ZWZWgG5IJtXXTM6NiNMqKxGxCPgBgKROx2ZmZpQ0mVRK0KeS8hvV6TOmRttjuAS9mVnHlTKZtNt6ozfo6bFNM7NWK+Ud8GZm1l2cTMzMrGk9Ocy1/NlFPHPatKLDMLMeNProiUWH0BY+MzEzs6Z1RTKR9EqlIrCk6yQNT+35qsKzJV0oac1uQTUzs6Z1RTIBlkXEhIgYT1ZC5Yu5bZVyKzsD2wAfLSJAM7Ne1i3JJG86sHV1Y0S8AtxZa5uZmbVXV12AlzQIeA/w0xrbNgT2AP6p03GZWW864Y6LmLt0/ho9Z9Dd567x63RDqfpuSSYbpZIqY4B7gJty2yrlVsYBV0TEzFo7yJeg32bE6PZGa2Y9Ye7S+Ty95Pk1e9KS9sRStG5JJssiYoKkTYCpZNdMKvW5Hk3btgSmSTooIq6t3sEqJehft6NL0JtZ00YNHr7Gzxk0vGaFqD51Q6n6bkkmAETEAklHA9dIOqNq21OSvg4cD6yWTMzMWu34vY5Y4+f4PpOSiIh7gfuAw2psvhoYLOmdnY3KzKy3dcWZSaWKcG79wNzq+Fx7ALt2Ki4zM8t0RTJptfU2HzpgTzXNzIrQdcNcZmZWPspGhnqLpEXAQ0XHUcdIYF7RQdTh2NZemeNzbGunF2N7fUSMqrWhJ4e5gIciYveig6hF0t2Obc2VOTYod3yObe04tlV5mMvMzJrmZGJmZk3r1WRyVtEB9MGxrZ0yxwbljs+xrR3HltOTF+DNzKy1evXMxMzMWsjJxMzMmtZzyUTS/pIekvRIKgxZGpIek3R/mob47oJjOVfSs5IeyLVtKukmSQ+nf0eUKLbJkuakYzdD0gcKim1bSbdIelDSLEn/lNoLP3Z9xFb4sZO0oaQ7Jd2XYvv31F6G41YvtsKPWy7GQZLulTQ1rXf8uPXUNZM0udafgfcBTwB3AYdHxOxCA0skPQbsHhGF3wglaR9gMXBhmi4ZSScCz0fE91MiHhERXytJbJOBxRFxUqfjqYptS2DLiPijpKFk8+98CDiKgo9dH7F9lIKPnSQBG0fEYknrAbeTTXR3KMUft3qx7U8JfuYAJB0L7A4Mi4gDivhd7bUzk7cBj0TEXyLiZeAS4OCCYyqliLgNqJ7152DggrR8AdkHUcfVia0UIuKpiPhjWl4EPEg2lXThx66P2AoXmcVpdb30CMpx3OrFVgqStgE+CJyTa+74ceu1ZLI18Hhu/QlK8suUBHCjpHvSzJBlMzoinoLsgwnYvOB4qn1J0sw0DFbIEFyepDHAm4E/ULJjVxUblODYpaGaGcCzwE0RUZrjVic2KMFxA04Fvgq8mmvr+HHrtWSiGm2l+QsDeEdEvAV4P/DFNJxjjTkDGAtMAJ4CTi4yGElDgCuBYyJiYZGxVKsRWymOXUS8EhETgG2At0ka399zOqVObIUfN0kHAM9GxD2dfu1qvZZMngC2za1vAzxZUCyriYgn07/PAlPIhuXK5Jk07l4Zf3+24HheExHPpF/4V4GzKfDYpXH1K4GLIuKq1FyKY1crtjIduxTPfGAa2TWJUhy3inxsJTlu7wAOStdbLwHeLel/KOC49VoyuQsYJ+n/SVqfbLbGUkzxK2njdFEUSRsD+wEP9P2sjrsW+GRa/iRwTYGxrKLyi5McQkHHLl2s/SnwYESckttU+LGrF1sZjp2kUZKGp+WNgPcCf6Icx61mbGU4bhFxfERsExFjyD7PfhMRn6CI4xYRPfUAPkD2ja5HgW8UHU8uru3IpiO+D5hVdGzAz8lO3ZeTndF9BtgMuBl4OP27aYli+xlwPzCT7Bdpy4Ji25ts6HQmMCM9PlCGY9dHbIUfO2AX4N4UwwPAt1J7GY5bvdgKP25VcU4EphZ13Hrqq8FmZtYevTbMZWZmbeBkYmZmTXMyMTOzpjmZmJlZ05xMzMysaU4m1nKSDpEUkt5QdCxllqrOHteG/R4jaXBufXFf/VOfg9SGKtrN7rf6vVh5+avB1nKSLgO2BG6OiMkt2N+giHil6cBKpl2VjqurT0taHBFDWvkanVKmStrWN5+ZWEuluk/vILuR8LDU9v6UYCp9Jkq6Li3vJ2m6pD9Kujw9vzK3y7ck3Q58RNLnJN2V5pS4svLXqqSxkn6ftn07/1e4pH9J7TOV5qCoEe9nJP1Z0jRJZ0s6PbUfKOkPyuaI+LWk0al9sqQLJN2YYjxU0onK5qH5VSpXgqTdJN2ainbeUHW3dK04xqbn3yPpt5WzOknnSzpN0h2S/iJpUmpfR9J/KZtfY6qk6yVNknQ0sBVwi6Rbcvv/bjp2v6+8l6rXPyr33mu+ZlX/MZL+JOkcSQ9IukjSeyX9TtkcGm9rdL/p52Fqbt+np+et9l76+Hn5vqTZ6f+68JLwPanIOzb9GHgP4BPAT9PyHcBbgHWB/yWbEwKyAnmfAEYCt+Xav0ChcxcAAAQfSURBVMbKu4sfA76a2+9mueXvAF9Oy1PJ5qQB+ALZX/qQlaM5i6y45zqp3z5VsW6VXmdTsrLivwVOT9tGsPLM/bPAyWl5Mtl8FusBuwJLgfenbVPISn2vl977qNT+MeDcGsdqMnBcWr4ZGJeW9yAriwFwPnB5eg9vIptCAWAScH1q3wJ4AZiUO3Yjc68TwIFp+UTgmzViOSr33mu+ZlX/McAKYOfU7x7g3HS8DwaubnS/5O7cTuunA0dVvxfq/Lyk/7+Hcv9fw4v+PejFx7qYtdbhZCWxISs8d3hkkzH9CjhQ0hVkcy98FXgX2YfK7yQBrA9Mz+3r0tzyeEnfAYYDQ4AbUvuerJyr4WKg8lfpfulxb1ofAowj+zCqeBtwa0Q8DyDpcmCHtG0b4NJ0RrE+8Nfc834ZEcsl3Q8MAn6V2u8n+5DdERgP3JTe1yCy8i81pb+u9wIuT/0BNsh1uTqyYoKzc2cVewOXp/an82chNbxMlkwh+9B/Xx99+3rNan+NiPvTe5hFNqwZ6biMaWK/9byd2j8vC4EXgXMk/YKV79U6yMnEWkbSZsC7yT74g+xDNCR9lSwxfJFsUqu7ImKRsk+EmyLi8Dq7XJJbPh/4UETcJ+kosr9m+wwHOCEizuynTz3/CZwSEddKmkh2FlHxEkBEvCppeaQ/h8nmk1g37XdWROzZT4wV6wDzIytxXstLNWLuK/Zq+RhfobHf+1qv2VefV3PrlePQ6H5XsOqQ+4Z1nlv35yUNq72HbGj1S2Q/h9ZBvmZirTSJbCrd10fEmIjYluwv+r3Jyna/BfgcK884fg+8Q9L2AJIGS9ph9d0CMBR4Kl2TOCLX/nvgw2n5sFz7DcCnc2PqW0uqniDoTuBdkkZIWje3H4BNgDlp+ZOsmYeAUZL2TK+9nqSd6nWObE6Rv0r6SOovSbv28xq3Ax9O105Gs2pyXUR2vLrF34A3SdpA0iZkSaEi/15q/ryk/+NNIuJ64Biy+UWsw5xMrJUOJ7tukHcl8PHIvo01lWzir6kAETGXbEz955Jmkn1Y1Ps68f8nmxXwJrLS5BXHAMdKupPsG2QL0r5vJBv2mp6GXa6g6gM2IuYA30v7/TUwu/J8sjORyyX9FlijbxJFNiX0JOAHku4jq867Vz9POwL4TOo/i/6nk76SrGLyA8CZ6T1UYj8L+GU/Q1+lERGPA5eRVd+9iJVDk5B7L338vAwFpqa2W4GvdDB8S/zVYOtqyr7VtSyN1R9Gdo2mvw/i/POHRMTidGYyhexCeXVCLKVc7JuRnWW9IyKeLjou602+ZmLdbjfg9HT9ZT7w6TV8/mRJ7yUbp78RuLrF8bXTVGWTNq0P/IcTiRXJZyZmZtY0XzMxM7OmOZmYmVnTnEzMzKxpTiZmZtY0JxMzM2va/wGberx0U7es7gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "avg_game_time = sns.barplot(data = eda_dataset, y = 'League', x = 'gamelength')\n",
    "avg_game_time.set(xlabel='Average game length in minutes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we were curious what the average gold load at 20 mintues (the new column we created), would this be similar acorss the board like the average game time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LCK      1445\n",
       "NALCS    1269\n",
       "EULCS    1099\n",
       "LMS       777\n",
       "TCL       652\n",
       "OPL       456\n",
       "CBLoL     301\n",
       "LCL       279\n",
       "LJL       258\n",
       "LLN       241\n",
       "CLS       175\n",
       "Name: League, dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eda_dataset = eda_dataset[eda_dataset.gamelength > 20]\n",
    "\n",
    "eda_dataset['golddiff_20min'] = eda_dataset.golddiff.str[1:-1].str.split(', ').apply(lambda x: int(x[20]))\n",
    "\n",
    "eda_dataset.rename({'bResult': 'blue_win'}, axis=1, inplace=True)\n",
    "\n",
    "eda_dataset[['League', 'Year', 'golddiff_20min']].pivot_table(index='League', columns='Year', aggfunc='count')\n",
    "\n",
    "eda_dataset = eda_dataset[eda_dataset.League.isin(['LCK', 'NALCS', 'EULCS', 'LMS', 'TCL', 'OPL', 'CBLoL', 'LCL', 'LJL', 'LLN', 'CLS'])]\n",
    "\n",
    "eda_dataset.League.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Average gold lead at 20 min')]"
      ]
     },
     "execution_count": 17,
     "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": [
    "avg_gold_lead_20 = sns.barplot(data = dataset, y = 'League', x = 'golddiff_20min')\n",
    "avg_gold_lead_20.set(xlabel='Average gold lead at 20 min')\n",
    "# this kinda sucks, hard to look at (positive and negative refer to gold leads for the 2 different teams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok we messed up here becuase we forgot to take into account that the \"gold\" lead can be negative or positive depending on which team color (red or blue) is ahead. What we really want to look at is just the gold lead independent of which team is actually ahead. To do this we take the absolute value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Average gold lead of a team at 20 min')]"
      ]
     },
     "execution_count": 18,
     "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": [
    "# want to create a new column that includes the abs value of the gold lead\n",
    "# we are just interested to see how ahead a team is, not caring about which team\n",
    "eda_dataset['golddiff_20min_abs'] = dataset['golddiff_20min'].abs()\n",
    "avg_gold_lead_20 = sns.boxplot(data = eda_dataset, y='League', x='golddiff_20min_abs')\n",
    "avg_gold_lead_20.set(xlabel='Average gold lead of a team at 20 min')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To take one more step closer to answering out research question, we wanted to look at if a team who was ahead 20 minutes in-game, if they actually won the game at the end of it. We wanted to create a boleean for each observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        True\n",
       "1       False\n",
       "2        True\n",
       "3       False\n",
       "4        True\n",
       "        ...  \n",
       "7615     True\n",
       "7616     True\n",
       "7617     True\n",
       "7618     True\n",
       "7619    False\n",
       "Length: 6952, dtype: bool"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# want to create a new column of indicators of if the team had a lead at 20 minutes and ended up wining the game\n",
    "win_given_20min_golddiff= (eda_dataset['blue_win'] == 1) == (eda_dataset['golddiff_20min'] > 0)\n",
    "win_given_20min_golddiff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we actually want to display in a barplot is the win percentage, or the mean of all these True/False indicator variables that we created above (seperated by region)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "eda_dataset['win_given_20min_golddiff'] = win_given_20min_golddiff\n",
    "\n",
    "league_winrate_given_lead_20 = eda_dataset.groupby('League')['win_given_20min_golddiff'].mean().to_frame().reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in the plot below, we are mostly interesed in the \"percentage rate\" gained, which would be the win percentage - 50%. We are looking into how more likely are teams to win if they have an advatage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Win percentage of teams given that they have a gold lead at 20 minutes')]"
      ]
     },
     "execution_count": 21,
     "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": [
    "winrate_plot = sns.barplot(data=league_winrate_given_lead_20, y='League', x='win_given_20min_golddiff')\n",
    "winrate_plot.set(xlabel='Win percentage of teams given that they have a gold lead at 20 minutes')\n",
    "\n",
    "# this seems pretty high, lets see about gold leads at different times"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After looking at 20 minutes, we wondered if patterns would be different at 10 minutes. We applied the same techniques to generat the 10 minute graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Win percentage of teams given that they have a gold lead at 10 minutes')]"
      ]
     },
     "execution_count": 22,
     "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": [
    "eda_dataset['golddiff_10min'] = eda_dataset.golddiff.str[1:-1].str.split(', ').apply(lambda x: int(x[10]))\n",
    "eda_dataset['win_given_10min_golddiff'] = (eda_dataset['blue_win'] == 1) == (eda_dataset['golddiff_10min'] > 0)\n",
    "\n",
    "league_winrate_given_lead_10 = eda_dataset.groupby('League')['win_given_10min_golddiff'].mean().to_frame().reset_index()\n",
    "\n",
    "winrate_plot = sns.barplot(data=league_winrate_given_lead_10, y='League', x='win_given_10min_golddiff')\n",
    "winrate_plot.set(xlabel='Win percentage of teams given that they have a gold lead at 10 minutes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance at 10 minutes seems to be higher than at 20 minutes and the winrate is lower, which is expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize distributions of dataset vs wins attributed to gold difference @ 20m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing distributions of wins and losses vs gold difference per league"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 406.875x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# diff_win = did the team with the gold lead at 20 min win\n",
    "sns.displot(dataset, x=\"golddiff_20min\", y=\"League\", palette=\"magma\", hue=\"diff_win\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A visualization of the distributions of wins where the gold difference @ 20m was greater than 0 only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 766.875x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = sns.catplot(x=\"League\", y=\"golddiff_20min\", hue=\"diff_win\", height=5, aspect=2, kind=\"boxen\", data=dataset)\n",
    "v = sns.violinplot(x=\"League\", y=\"golddiff_20min\", hue=\"diff_win\", height=5, aspect=2, inner=None, data=dataset, ax=g.ax, saturation=0)\n",
    "v_children = v.get_children()\n",
    "for i in v_children:\n",
    "    if isinstance(i, PolyCollection):\n",
    "            i.set_alpha(0.6)\n",
    "g.ax.get_legend().remove()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistically Testing for Significant Difference in Winrate Between Regions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The null hypothesis is that each league has the same winrate (the average over the entire dataset) given that they have the gold advantage at 20 minutes.\n",
    "The alternate hypothesis is that there is a difference in the winrate of at least one league. We will choose an alpha value of 0.05 for our test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7745972382048332"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "null_winrate = dataset.diff_win.mean()\n",
    "null_winrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "League\n",
       "CBLoL    0.750831\n",
       "CLS      0.777143\n",
       "EULCS    0.767061\n",
       "LCK      0.775779\n",
       "LCL      0.788530\n",
       "LJL      0.790698\n",
       "LLN      0.784232\n",
       "LMS      0.804376\n",
       "NALCS    0.742317\n",
       "OPL      0.835526\n",
       "TCL      0.763804\n",
       "Name: diff_win, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observations = dataset.groupby('League')['diff_win'].mean()\n",
    "observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total variation distance, or TVD is a way to calculate how different two catagorical distributions are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def total_variation_distance(dist1, dist2):\n",
    "    return np.sum(np.abs(dist1 - dist2))/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will be using the TVD between a distribution of winrates across the league given that they have the gold advantage at 20 minutes and the uniform distribution consisting of the null winrate as our test statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10424015988563679"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observed_tvd = total_variation_distance(observations, [null_winrate]*len(observations))\n",
    "observed_tvd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Emperically finding distribution of TVDs by permuting the League column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_repetitions = 10000\n",
    "\n",
    "shuffled = dataset.copy()\n",
    "shuffled_leagues = shuffled['League'].values\n",
    "\n",
    "tvds = []\n",
    "for _ in range(n_repetitions):\n",
    "    \n",
    "    # shuffle leagues\n",
    "    shuffled_leagues = np.random.permutation(shuffled_leagues)\n",
    "    \n",
    "    # put them in a DataFrame\n",
    "    shuffled['Shuffled League'] = shuffled_leagues\n",
    "    \n",
    "    # compute group winrate\n",
    "    obs = shuffled.groupby('Shuffled League')['diff_win'].mean()\n",
    "    tvd = total_variation_distance(obs, [null_winrate]*len(obs))\n",
    "    \n",
    "    # add it to the list of tvds\n",
    "    tvds.append(tvd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observed TVD overlayed on top of the distribution of TVDs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "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": [
    "plt.hist(tvds, bins=100)\n",
    "plt.scatter(x=observed_tvd, y=0, zorder=2, color='red', s=50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating the p-value using the emperical distribution of TVDs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1688"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value = (tvds > observed_tvd).mean()\n",
    "p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given that our observed p-value is less extreme than our alpha value, we cannot reject the null hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ethics & Privacy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our project identifies the performance trends of teams based on various in-game statistics. All data used is publicly available on Kaggle and players must accept Riot's privacy policy which allows for data collection. As the dataset includes metrics on all aspects of the game, it inherently includes performance data of each individual player, however we will not be using this information in this study since we are analyzing performance on a team-by-team basis.\n",
    "\n",
    "There may be some implied biases in the dataset due to the difference in number of observations (games) recorded in each league. This bias cannot be outright removed from the dataset without introducing some loss of data fidelity and has a negligible impact on the end result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion & Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From our results in the Data Analysis and Results section, we have determined that there is not a statistically significant difference between the leagues in the ability for their teams to close out games in their own home region. Looking more at other intangibles, it makes more sense that this is the case. In each league, there are top teams and bottom teams and the round robin format of the league makes it so that it is not always a foregone conclusion for a team to gain a lead and win. Comparatively, in international play, teams from better regions are more than likely able to close out their games because there is more of a skill gap, especially between major regions (regions that have large player bases and have historically done well at international events) like the LCK and minor regions (regions with smaller player bases and have historically not done as well) like the CBLoL.\n",
    "\n",
    "What other factors could go into this result that was found? In the game of League of Legends, there are comeback mechanics for teams to be able to recover from a fumbled early game and allow themselves to claw their way back into the game and thus win the game. Super objectives like the Baron Nashor and Elder Dragon give opportunities for teams to win a fight and proceed to win the game, all while not having regained a gold lead.\n",
    "\n",
    "Thus, we can deduce that even though a gold lead at 20 minutes is a contributing factor to a team's success, it is not the only factor. We can also see that skill in a region does not necessarily equate to better quality of games in terms of how cleanly executed a team with a lead plays. Therefore, the quality of region a game is in does not determine whether or not a team with a gold lead will be able to win or not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Team Contributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Specify who in your group worked on which parts of the project.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Justin Chu: Conclusion and Dicussion\n",
    "- John Li: Ethics and Privacy\n",
    "- Luke Lloyd: Data Analysis and Results\n",
    "- Prathik Malireddy: Data Analysis and Results\n",
    "- Dustin Lin: Background and Prior work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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