{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Playing with Random Forests in League of Legends\n",
"\n",
"This notebook contains the code to generate the figures found in the [post on my blog](http://www.trailofpapers.net/2015/10/playing-with-random-forests-in-league.html). Functions called by this notebook can be found on [github](http://github.com/map222/lolML). My summoner IDs are lemmingo and Umiy.\n",
"\n",
"### Table of contents\n",
"\n",
"[Querying Riot's API](#query)\n",
"\n",
"[Explore data](#explore)\n",
"\n",
"[Machine learning](#machine)\n",
"\n",
"[Surrendered games](#surrender)\n",
"\n",
"Load libraries and API key"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import requests, json\n",
"import numpy as np\n",
"from src import API_io\n",
"import importlib\n",
"import pandas as pd\n",
"import os\n",
"import pickle\n",
"from src import feature_calc"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"working_dir = 'C:\\\\Users\\\\Me\\\\Documents\\\\GitHub\\\\lolML'\n",
"os.chdir(working_dir)\n",
"with open(working_dir+ '\\\\api_key.txt', 'r') as api_file:\n",
" api_key = api_file.read()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"# Get summoner names, and list of matches\n",
"\n",
"Load featured games, and get a list of summoner_names"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"featured_json = API_io.load_featured_games(api_key) # load json of featured games\n",
"featured_game_ids = [x['gameId'] for x in featured_json ] # use list comprehension to get featured games; don't use this"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Make a list of summoner names and summoner IDs from the featured JSON"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['ÅNTI', 'Fer Pitou', 'Royalx799', 'Xandertrax', 'KimJinHo']"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"summoner_names, summoner_IDs = API_io.get_summoners_IDs_from_featured_games(featured_json, api_key)\n",
"summoner_names[:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Make a list of summoner ID urls to query RITO with, and then query them (this is rate limited to one query / 1.2 seconds to avoid overloading API)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"summoner_urls = [API_io.make_matchlist_url_summoner_ID(x, True, True, api_key) for x in summoner_IDs]\n",
"summoner_urls[:2]\n",
"match_histories = [API_io.get_limited_request(x) for x in summoner_urls ]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Extract the match ID from the match history JSON"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"match_IDs = np.empty(0, dtype=int)\n",
"for cur_matches in match_histories:\n",
" match_IDs = np.append( match_IDs, [x['matchId'] for x in cur_matches['matches']] )\n",
"pd.Series(match_IDs).to_csv('Match IDs.csv')\n",
"match_IDs.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load a csv of match infor if you have it saved from a previous time."
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(27928,)"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"match_df = pd.read_csv('Match IDs.csv', header =None)\n",
"match_IDs = match_df[1]\n",
"match_IDs = match_IDs.unique()\n",
"match_IDs.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Query Riot's API for individual game info\n",
"\n",
"Make a list of match urls, and then use requests to query them; again this is rate limited."
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"['https://na.api.pvp.net/api/lol/na/v2.2/match/1955239698?includeTimeline=true&api_key=0da3703d-7bf5-4e72-96cd-5062b28720d7',\n",
" 'https://na.api.pvp.net/api/lol/na/v2.2/match/1954974642?includeTimeline=true&api_key=0da3703d-7bf5-4e72-96cd-5062b28720d7']"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# make urls for loading\n",
"match_urls = [API_io.make_match_info_url(x, True, api_key) for x in match_IDs] # True flag means we get the timeline\n",
"match_urls[:2]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import time\n",
"import sys\n",
"match_range = np.arange(2000,2010)\n",
"# this for loop is ugly; used list comprehension previously, but rate limit was fluky\n",
"full_match_info = np.empty(0)\n",
"for cur_match in match_range:\n",
" time.sleep(1.2) # RIOT API is throttled to ~0.83 requests / second\n",
" try:\n",
" full_match_info = np.append(full_match_info, requests.get(match_urls[cur_match]).json() )\n",
" except requests.exceptions.HTTPError as e:\n",
" print('Error: ' + e + ' in game ' + str(match_IDs[cur_match]))\n",
" except:\n",
" err = sys.exc_info()[0]\n",
" print('Error: ' + str(err) + ' in game ' + str(match_IDs[cur_match]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Save to a JSON or .pickle so we don't have to query again."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with open('full matchinfo.csv', 'w') as out_file:\n",
" json.dump(full_match_info.tolist(), out_file)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# saving as a pickle file saves ~%40 of the space\n",
"pickle_name = 'full match info.pickle'\n",
"if not os.sys.isfile(pickle_name): # make sure you don't overwrite a file\n",
" with open(pickle_name, 'wb') as pickle_file:\n",
" pickle.dump(full_match_info, pickle_file)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load information from local JSON or pickle\n",
"\n",
"If you already ran the above code and have some data saved, you can load it directly"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# load from JSON\n",
"with open('games 6000-8000.json') as json_file:\n",
" scraped_matches= json.load(json_file)\n",
"scraped_matches = np.array(full_match_info)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# loading the pickle in\n",
"with open('full match info.pickle', 'rb') as pickle_file:\n",
" full_match_info = pickle.load(pickle_file)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analyze game data\n",
"\n",
"## Explore and clean data\n",
"\n",
"First, load some more libraries\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import src.plotting as lol_plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the length of games"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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rw1m8n+6E1z+LT6RRtxfX2NZ07G0/sBa+gJ8mZeSVwJ2ktuu2x1WIsQdYk91W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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"game_lengths = np.array([np.size(x['timeline']['frames']) for x in full_match_info] )\n",
"plt.hist(game_lengths, bins = 50);\n",
"plt.xlabel('Game length (min)', fontsize = 18)\n",
"plt.ylabel('# Games', fontsize = 18)\n",
"lol_plt.prettify_axes(plt.gca())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some games don't even last twenty minutes! There is also a large spike of games ending around 20 minutes due to surrenders. When we create features, the feature calculator will have to consider game length."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create features\n",
"\n",
"Create features for the classifier; now just starting with simple stuff like first blood, first tower, and first dragon."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" first_dragon | \n",
" drag_diff | \n",
" total_drag | \n",
" first_baron | \n",
" blue_barons | \n",
" red_barons | \n",
" first_tower | \n",
" tower_diff | \n",
" total_tower | \n",
" first_inhib | \n",
" ... | \n",
" blue_3 | \n",
" blue_4 | \n",
" red_0 | \n",
" red_1 | \n",
" red_2 | \n",
" red_3 | \n",
" red_4 | \n",
" surrender | \n",
" game_length | \n",
" winner | \n",
"
\n",
" \n",
" matchId | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" 1955239698 | \n",
" 1 | \n",
" 1 | \n",
" 3 | \n",
" 1 | \n",
" 1 | \n",
" 0 | \n",
" 1 | \n",
" 1 | \n",
" 9 | \n",
" -1 | \n",
" ... | \n",
" 59 | \n",
" 429 | \n",
" 82 | \n",
" 1 | \n",
" 2 | \n",
" 86 | \n",
" 201 | \n",
" 1 | \n",
" 37 | \n",
" 1 | \n",
"
\n",
" \n",
" 1954974642 | \n",
" 0 | \n",
" -3 | \n",
" 3 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" -7 | \n",
" 9 | \n",
" 0 | \n",
" ... | \n",
" 20 | \n",
" 22 | \n",
" 56 | \n",
" 432 | \n",
" 67 | \n",
" 101 | \n",
" 39 | \n",
" 1 | \n",
" 32 | \n",
" 0 | \n",
"
\n",
" \n",
" 1950969271 | \n",
" 0 | \n",
" 0 | \n",
" 2 | \n",
" 0 | \n",
" 0 | \n",
" 1 | \n",
" 0 | \n",
" 0 | \n",
" 6 | \n",
" -1 | \n",
" ... | \n",
" 60 | \n",
" 267 | \n",
" 201 | \n",
" 238 | \n",
" 223 | \n",
" 119 | \n",
" 150 | \n",
" 0 | \n",
" 44 | \n",
" 0 | \n",
"
\n",
" \n",
"
\n",
"
3 rows × 31 columns
\n",
"
"
],
"text/plain": [
" first_dragon drag_diff total_drag first_baron blue_barons \\\n",
"matchId \n",
"1955239698 1 1 3 1 1 \n",
"1954974642 0 -3 3 0 0 \n",
"1950969271 0 0 2 0 0 \n",
"\n",
" red_barons first_tower tower_diff total_tower first_inhib \\\n",
"matchId \n",
"1955239698 0 1 1 9 -1 \n",
"1954974642 1 0 -7 9 0 \n",
"1950969271 1 0 0 6 -1 \n",
"\n",
" ... blue_3 blue_4 red_0 red_1 red_2 red_3 red_4 \\\n",
"matchId ... \n",
"1955239698 ... 59 429 82 1 2 86 201 \n",
"1954974642 ... 20 22 56 432 67 101 39 \n",
"1950969271 ... 60 267 201 238 223 119 150 \n",
"\n",
" surrender game_length winner \n",
"matchId \n",
"1955239698 1 37 1 \n",
"1954974642 1 32 0 \n",
"1950969271 0 44 0 \n",
"\n",
"[3 rows x 31 columns]"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"importlib.reload(feature_calc)\n",
"games_df = feature_calc.calc_features_all_matches(full_match_info, 20)\n",
"games_df.head(3)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"first_dragon category\n",
"drag_diff float64\n",
"total_drag float64\n",
"first_baron category\n",
"blue_barons float64\n",
"red_barons float64\n",
"first_tower category\n",
"tower_diff float64\n",
"total_tower float64\n",
"first_inhib category\n",
"blue_inhibs float64\n",
"red_inhibs float64\n",
"first_blood category\n",
"gold_diff float64\n",
"kill_diff float64\n",
"total_kill float64\n",
"blue_share float64\n",
"red_share float64\n",
"blue_0 float64\n",
"blue_1 float64\n",
"blue_2 float64\n",
"blue_3 float64\n",
"blue_4 float64\n",
"red_0 float64\n",
"red_1 float64\n",
"red_2 float64\n",
"red_3 float64\n",
"red_4 float64\n",
"surrender category\n",
"game_length float64\n",
"winner category\n",
"dtype: object"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"games_df.dtypes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The gold difference forms a pretty nice normal distribution."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Standard deviation of gold difference: 8019\n"
]
},
{
"data": {
"image/png": 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Z/Ff+f/28/T+Ax0k9B1sB3yUdEU/udNnHULfTgQXALqXv2ORCnl6u3+dzwHgp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\nmZlV4v8Dp+1WINtwNakAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"count, bins, _ = plt.hist(np.array(games_df['gold_diff']) / 1000, bins = 50)\n",
"plt.ylabel('# Games', fontsize = 18)\n",
"plt.xlabel('Gold difference (thousands)', fontsize = 18)\n",
"lol_plt.prettify_axes(plt.gca())\n",
"print('Standard deviation of gold difference: {:.0f}'.format(games_df['gold_diff'].std()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Both teams have similar amounts of kills."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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X9E3gZtKZSs+osROA92dNFgCzJa0mDXPuGX12NUBEbJZ0FTBf0kZ2DWFeCSxppJahpvvS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\nAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bins = np.arange(40)\n",
"kills_fig = plt.figure()\n",
"plt.hist(games_df['blue_kills'] , bins = bins, color = 'blue')\n",
"plt.hist(games_df['red_kills'] , bins = bins, color = 'red', alpha = 0.5)\n",
"plt.ylabel('# Games', fontsize = 18)\n",
"plt.xlabel('Kills', fontsize = 18)\n",
"lol_plt.prettify_axes(plt.gca())\n",
"#plt.gca().set_xticklabels(bins / 1000, rotation = 90)"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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GauXgTLz44h85cWKmqz/+8Y9kdT9pSXGho9/N9uUhG5BWn84WC9nIGJ0tabzs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\nTvgvGemcdRSWdUwAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pd.tools.plotting.scatter_matrix(games_df[['gold_diff', 'kills_diff', 'tower_diff', 'drag_diff']], figsize = [9, 9]);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As one might expect, there is a lot of multicollinearity between all the variables. This would make running linear regression more difficult, but I am going to use a Random Forest, for which that is less problematic.\n",
"\n",
"\n",
"# Run machine learning algorithms: \n",
"## Load libraries, and initialize feature info"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# load sklearn package \n",
"from sklearn.naive_bayes import GaussianNB\n",
"from sklearn.metrics import confusion_matrix\n",
"from sklearn import cross_validation\n",
"from sklearn.ensemble import RandomForestClassifier"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['first_dragon' 'drag_diff' 'total_drag' 'first_baron' 'blue_barons'\n",
" 'red_barons' 'first_tower' 'tower_diff' 'total_tower' 'first_inhib'\n",
" 'blue_inhibs' 'red_inhibs' 'first_blood' 'gold_diff' 'kill_diff'\n",
" 'total_kill' 'blue_share' 'red_share' 'surrender']\n"
]
}
],
"source": [
"# variables for classifiers\n",
"col_names = feature_calc.col_names\n",
"train_col = np.array([x for x in col_names if x not in\n",
" ['winner', 'game_length', 'blue_0', 'blue_1', 'blue_2', 'blue_3', 'blue_4',\n",
" 'red_0', 'red_1', 'red_2', 'red_3', 'red_4', 'matchId'] ])\n",
"num_features = np.size(train_col)\n",
"print(train_col, )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Naive Bayes:\n",
"\n",
"First let's see how good prediction is with each feature individually"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[('first_dragon', 0.61394410832613078),\n",
" ('drag_diff', 0.69288389513108617),\n",
" ('total_drag', 0.52607317775857099),\n",
" ('first_baron', 0.66580236243157587),\n",
" ('blue_barons', 0.66810717372515127),\n",
" ('red_barons', 0.6698357821953328),\n",
" ('first_tower', 0.58081244598098536),\n",
" ('tower_diff', 0.75569000288101407),\n",
" ('total_tower', 0.52434456928838946),\n",
" ('first_inhib', 0.66493805819648522),\n",
" ('blue_inhibs', 0.66493805819648522),\n",
" ('red_inhibs', 0.62057044079515988),\n",
" ('first_blood', 0.54335926246038602),\n",
" ('gold_diff', 0.82541054451166807),\n",
" ('kill_diff', 0.76692595793719387),\n",
" ('total_kill', 0.52607317775857099),\n",
" ('blue_share', 0.52607317775857099),\n",
" ('red_share', 0.53673292999135691)]"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gnb = GaussianNB()\n",
"def quick_score(games_df, col_index):\n",
" gnb.fit(games_df[[col_index]], games_df['winner'])\n",
" return gnb.score(games_df[[col_index]], games_df['winner'])\n",
"\n",
"scores = [quick_score(games_df, x) for x in np.arange(num_features-1)]\n",
"[x for x in list(zip(train_col, scores))]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, we can already see some features like gold_diff and kills_diff are important, while others like first_blood are less informative. We can put them all together if we design the Naive Bayes classifier correctly, but let's skip ahead to random forests.\n",
"\n",
"## Random Forest Feature Importance\n",
"\n",
"Let's first start by figuring out which features are important with a large random forest. First, let's get a dataframe for each timepoint"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[5995, 5991, 5948, 5800, 4684, 3471, 2019, 912, 294]\n"
]
}
],
"source": [
"timeline_end = 50\n",
"time_indices = np.arange(5, timeline_end, 5)\n",
"timelines_df = [feature_calc.calc_features_all_matches(full_match_info, x) for x in time_indices]\n",
"print([x.shape[0] for x in timelines_df])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create a large forest so we can better identify important features"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"big_forest = RandomForestClassifier(n_jobs = 3, n_estimators = 100, max_features = 'sqrt')"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"importances = std = np.zeros([len(timelines_df), np.size(train_col)])\n",
"for i, cur_df in enumerate(timelines_df):\n",
" big_forest.fit(cur_df[train_col], cur_df['winner'])\n",
" importances[i] = big_forest.feature_importances_\n",
" std[i] = np.std([tree.feature_importances_ for tree in big_forest.estimators_],\n",
" axis=0)\n",
"indices_at_20 = np.argsort(importances[3])[::-1]\n",
"indices_at_35 = np.argsort(importances[6])[::-1]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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fyY2Lz5rqkOnOnhQj7rcx8EjggMw8MyIOA94EvH3UA/QqIX37TsP/H815zUM+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\nMrXy/wHjXbvaq/ymJAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"feature_fig = plt.figure(figsize = [12,9])\n",
"plt.imshow(importances[:,indices_at_20], interpolation = 'none', extent = [0, num_features*4, 47.5, 2.5])\n",
"plt.ylabel('Time (min)', fontsize = 18)\n",
"plt.xticks(np.arange(0, num_features*4, 4)+2, indices_at_20)\n",
"x_tick_labels = [str(x) for x in train_col[indices_at_20]]\n",
"plt.gca().set_xticklabels(x_tick_labels, rotation = 90)\n",
"lol_plt.prettify_axes(plt.gca())\n",
"plt.gca().yaxis.set_ticks(time_indices);\n",
"plt.colorbar();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gold differential is the most important feature at all timepoints, followed by kill differential, and tower differential. Dragon differential comes in late, behind the total number of towers, at #6. Barons and inhibitors are not particularly informative at later timepoints, probably because they are a reflection of gold and kill differentials."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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SokJER0XTqUknAFamBt7TLK8+faB3b9i71xtgLSIiIpWHEqIASrpidV7+VqJ/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KoLcuMrANeq/zj4UjQqXMZivaPAwgEre7YFlsyZFQ3sBFypqne7hPVZAex5EU9rFpc8/RdVPa8w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\n/wdgag0qcVtANwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = [9, 6])\n",
"plt.plot(importances[3,indices_at_20], label = 'Importance at 20', linewidth = 2)\n",
"plt.plot(importances[6,indices_at_20], label = 'Importance at 35', linewidth = 2)\n",
"plt.ylabel('Importance', fontsize = 18)\n",
"plt.xticks(np.arange(num_features))\n",
"x_tick_labels = [str(x) for x in train_col[indices_at_20]]\n",
"plt.gca().set_xticklabels(x_tick_labels, rotation = 90)\n",
"plt.legend(frameon = False, fontsize = 16)\n",
"lol_plt.prettify_axes(plt.gca())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's extract the important columns for future analyses"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array(['blue_barons', 'blue_inhibs', 'drag_diff', 'first_dragon',\n",
" 'first_inhib', 'first_tower', 'gold_diff', 'kill_diff',\n",
" 'red_barons', 'red_inhibs', 'red_share', 'tower_diff'], \n",
" dtype='"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(time_indices, np.mean(scores_list, 1))\n",
"plt.ylim( 0.5, 1)\n",
"plt.xlabel('Time (min)', fontsize = 18)\n",
"plt.ylabel('Prediction accuracy', fontsize = 18)\n",
"plt.xticks(time_indices)\n",
"lol_plt.prettify_axes(plt.gca())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The game does get more easily predicted with time, as more information is gathered by the model. However, once you reach 30 minutes, the model loses accuracy. This is probably because as the game enters the late phase, gold matters less, and objectives more, and a single decisive teamfight can decide the game either way."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"\n",
"## Are surrendered games winnable?\n",
"\n",
"First, separate games into surrendered early, and those that were semi-close."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" surrender | \n",
" game_length | \n",
"
\n",
" \n",
" matchId | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" 1947508622 | \n",
" 1 | \n",
" 22 | \n",
"
\n",
" \n",
" 1947379227 | \n",
" 1 | \n",
" 25 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" surrender game_length\n",
"matchId \n",
"1947508622 1 22\n",
"1947379227 1 25"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"surrender_at_20_df = timelines_df[3].query('(surrender == 1) & (game_length <=25)')\n",
"good_games_df = timelines_df[3].query('(surrender == 0) | (game_length >25)')\n",
"surrender_at_20_df[['surrender', 'game_length']].head(2)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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7AWtGxJfGeanvHp5Yx/snIs6V9Fvgs8Dfd79I/ckBpEZ5DKefApuThuL4ImmQ\ntdVJQ5u8jzTB1EsioheDr2mK1rt7k3WPkILEhyLi+uUFSIFlI+DwiDhtisozLD5KGkrm26X0/YCX\nkuZ9sM5V/R58CThL0pYRcVM3C9SvHEBqImlV0uB/GwFvi4hzm+R5HvChXpet24pnxwWNAd0ebjN9\n0iStHhGPd3u9dZA0E/gH4MsRsbRJFl9l9N5/AKeTBs38QM1l6Qm3gdTnANLEMp9rFjwAIuKpiPhs\n+epD0oaSvqU0TeYSSX+Q9JkclFqS9BJJ35O0KD/Ok/RXnRRe0ixJX1aafvdxSfMkvWqcvGPq3XMd\n82h+Oj+3c8zP7S+X5vSvFyaN2iC/TpIOlvRLSU9IekzSJZJGmuyfZZKOkfSunH8xcEohz+skXSTp\nYUlP5raYg5qU/Y783jaXdL6kRyU9Iun7kspzfSBpZv4sbs7rfUDSf0t6VynfepJOl/TnXHd+l6Qz\n1P50p3sAzyfNgzOmvMAuQGMfjDcB23pK09c+lPflBZI2oUTSOpLmSrozl/PPkk5VGqG5mG+0+Fk1\n24eltD0lXaY0BfFiSX+S9MNiGfI+P03SjXm/PyHpF5L2b7KNxvY3lXSspAX5u3G9pDc2yT9Dadrj\nu/P2r5E0p9mOlvTy/Hnfldd5Tz7u9ijmi4gngP8mVUdPC74Cqc/epLPEr3TyIkkvBa4lDWF/Gqmt\nZDfgY8DfSvq7cc5IG69fizTX8f8inS3dRKpOuoQ0jHc7ZXgucCGwHWkk3qtJVW4XM/78HcUz4vcC\nbwfeRrrCegB4nNT2cwVwFGmI+P/O+R/If78FvJs0YuxXSaOd/gNwsaS3R8RPStvcC9iAtJ9OAx7N\n5T+QNKT6laQpRp8gzYVwuqS/iojijJZBmr9hHukM81zSPC0HkeaWXj5lbt63/0MaTv77wFxSNd22\npBnovpvzbUAaefk5+X38kTQk+MHAbpK2i4hHx9mPDbvmv+WJxj5IGjJ8HcZevd5c+H910jFwFem4\n2Ti/7lxJr4g8HbSkNfM++qtczl/l93Iw8FpJf9PmFd2YNjBJu5KGkP8NcCypnWt94O/ythrTAuwK\nvCbnnU+ac+adwJclvTAijm+yrbOAp4ETgMYV/I8lbRoRfyrkOwd4a173haQJnhpTzxbLujbpu7GM\ndMz8iTSh2nbA31AK4KTvwuslbdbDtsv61D1s83R9kH5oH26SvhLpy198zCgs/3+kg/kNpdedkNPf\nV0jbL6c+fvmoAAAH90lEQVQVh7Y/NqftW3r9iTn9kjbKfmDOe0wp/YM5/fZS+qVN0kZz3g1K6SMU\nhrkvpL8tp+9fSl+Z9CN6eyFtw5z3KWCzUv71SEOrf7vJ+zoJeAbYqJB2R17X3qW8p+b0TQtpp+W0\nA5qsW4X/zyXND/HiUp5XAX8p79dxPoPLgAfGWbbC/i4tWwYcUUo/IqfPKaR9Jqf9cynvITn9k60+\nz8I+vKTw/Is57zot3uPzm+1HUjB/BHhOk+2fV8q/XU4/tpA2h9LQ8Dn9rTl9aSHtLc0+/wnKvE/O\n/7Z28g/6w1VY9ZlJPiMu2ZI0mX3xcSiApJVIB/SvIuKC0uuOIx+4Lba7F+nHqzxV7Gc7KPtepB/a\nL5TSTydNQjMV9snrPi9Xq6wjaR1gFqkjwoZNqmDOjxXPAvcGVgG+VlxPXtdPSQH8daXX3BURPyil\nNapkXgbLP5t3AzdFxApXldH49Utn9W8infk+Xdr+n0hXI02rUkpeSJqwqIqlwMmltDHvJ3sb6fg7\ns5T3DOB+Wh9r43kk/91bE3Q/jsLsornKaW1gbdKV7kxSFXDZmI4DEfEL0tVt8X3tlf9+rpT3XKA8\nW1+jrHvo2cnqJtK4An9RG3kHnquw6vMo6UtQdjvP/oBtDXyeZy+pX0i6jL+x/KJIsxreS2qUn8jG\nwDWNH7TC6++VtKjNsm8M3BOl6otI07jeDqzZ5no6sQWp2u6+cZYH6UtbnBWx/GPQWA/Az1qsp+j2\nJvkaPxRr57/rkLpgl6s0yjYjnUUfkB/N/LHFOiCVs2pvobsj4ulSWvn9QDqWro1cpbV8wxFLJd3G\ns1Mud+pU0tn+acBnJf0PaeKlcyKiUV2JpNVJVxbvJFW5ls1qktbss3qIse9rY1IQbXZ83MyzMwwS\nEZdL+ibpav4fJF1HOna+GxE3N3l94zOZFp0YHEDq8zvgNZI2jMIE9/ms6xJY3thsiUhnvf97gjzl\nwLq4SZ7GF/y9jD8vdflGu3HblOj8R7yR/1uMP23sk22s537glR1uu6Gb76dhoh/MMb8zEfGQpO1J\n7Ru7kxr9TwT+XdIeEXF1zno2qe3oDFKbzYO57HsCH6Z5J6Dx3lvlLuoRsZ+kzwFvzGX+F+DfJH0o\nIuaWsjc6F9xfdXuDxAGkPt8nHYwHkG6Ya8f9pGqcl5cXSJpFqt//VYt13A5sKmml4pmlpPVo/8rh\ndmB3SWtExPIqK6VuxxszfkP6ZNxG6nl0TaTeLlU1zjofjIhLJl+s5R4gdT1udVb+B9KP7fMmuf3f\nAbtIekFElKuyunX2ezuwuaSVo9AxI1c7bcrYs/1GGV4A/LmQdwbpuBxztp+PvcvyA0lbAb8kfRfe\nlDskvAk4KyIOKb52vN5SHb6vOaSrwfL9GlusmB0i4kbSCcrnczXkNcDxpI4SRY2qst9NsowDwW0g\n9fkKcAvwEUl7jZNnzFlT/tL9BNhW0utLeT+a8/+oxXZ/DMwG/rGUfmQ7hS6sY2XSmVjRwaRqpqlw\nFul4Pa7ZQjXpUjuO75Ea1/89/7iV17OmpFU6LVz+bM4BtpT0vgnyPUiq5nq7pFc32b5ye0grjTaL\nHZsse5xnz4Qn40ekatNyVdv7SVV2xWOt0da0eynvhykdx7kto+xWUueGRrXUUlIgHPMblU90DmBy\nQfLH+e9HSuveixQYi2mzcvvWchGxiNQxYNV80lS0A3BvRNzGNOArkJpExBJJe5Iabv9D0qWkxsF7\nSW0jmwPvIjVW31l46VGkL+mPJZ1Gqi/fhVRPfBnjV4s0nAC8h9QV8lU82413B9JZdDuX+l8n9cT6\nhNJwGo1uvHvn8jQ7riZ1l3tE/FDS14HDJG1LugnzAVLd+I6k7p8t72WJiLskHUwK4DdL+hbpjPmF\nwFakuvktKJxFd+Bo4LXAV/JZ8hWk970NsHJENIL2waTuvo369etJP5QbkzpJnAV8ssW2LiBdje5B\n2hdFVwF7Sjo1/78U+HlENKpV2v0sTgDeAczN+/x6nh0h4Za8vOFnpCDwyRwg7gB2Bl7NisfVVySt\nD1xE2s+rko711cidOyLiMUkXAftIehL4Benu+gNJVxDbtfkeVhARF0n6CbCv0v0sF5KOnQNJVw6v\nKGTfF/iwpP8gHdt/IXUvnkNqB3mqkTG32byGDrvmD7S6u4FN9wfpXoZDSO0e95P6sD9MutfjeGCT\nJq/ZkPRFu490Nv0H0v0MM0r59iP9eOxSSn8JqQptUX6cS/rxmk8b3XjzOmaRviiNezguId0jMI8V\nu+w2Szsml61ZN96llLrxFpbvQ6oPX0RqK7gd+AHwjtL+WQZ8YoLy70S6r6OxD+8Cfk46Y35eIV/T\nfTJeOUnVgJ8lVbk9lffPZazYDXht0g/wrfl9PAzcQGoL2LzNz2BuXv9zS+mr5s/mXtIJyPJjoNln\nMdE+I11pzCWdxDxN+sE/BXhBk3VsAvwX6b6ah4HvAC8u70NS761z8zqXkHp6zaPU9TXvoy/nz+bJ\nvH/2J/2ojzmuxzuexvsMSd+7z5PawRaTToJeRzo5Knbj/WvgG/nzfDwfd7/Ox0l5v++b9+GWdf+u\n9Oqh/MbNbMDkm0pvAQ6LiK/WXZ7pTtKvSMF52tyJ7gBiNsAkHUeq/tk0mo85Zj2Q20++A7w8Itrp\nhj0UHEDMzKwS98IyM7NKHEDMzKwSBxAzM6vEAcTMzCpxADEzs0ocQMzMrBIHEDMzq8QBxMzMKvn/\nfzOT9A2jdvoAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gold_bins = np.arange(-20, 20)\n",
"plt.hist(np.array(surrender_at_20_df['gold_diff']) / 1000, bins=gold_bins)\n",
"plt.xlabel('Gold difference (thousands)', fontsize = 18)\n",
"plt.ylabel('# Games', fontsize = 18)\n",
"lol_plt.prettify_axes(plt.gca())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since these are stomps, the gold difference is bimodal towards large leads. However, there are a few games with small gold leads. First, let's see how accurate the random forest is for these stomps. (It should be high!)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Forest mean accuracy for surrendered games: 0.99\n"
]
}
],
"source": [
"surrender_forest = RandomForestClassifier(n_jobs = 2, n_estimators = 10, max_features = 'sqrt')\n",
"surrender_scores = cross_validation.cross_val_score(surrender_forest, surrender_at_20_df[important_col], surrender_at_20_df['winner'], cv=10)\n",
"print('Forest mean accuracy for surrendered games: {:.2f}'.format(np.mean(surrender_scores)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pretty damn good! Ok, what happens if we train the model on the \"close\" games, and use it to predict the probability of winning surrendered ones?"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A forest trained on non-surrender games predicts the team that won would do so with 0.94 probability\n"
]
}
],
"source": [
"close_forest = RandomForestClassifier(n_jobs = 3, n_estimators = 20, max_features = 'sqrt')\n",
"close_forest.fit(good_games_df[important_col], good_games_df['winner'])\n",
"cross_score = np.mean(np.max(close_forest.predict_proba(surrender_at_20_df[important_col]), axis = 1))\n",
"print('A forest trained on non-surrender games predicts the team that won would do so with {:.2f} probability'.format(cross_score))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The random forest trained on close games actually gives games surrendered at 20 a 6% chance of winning!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"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": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}