LoL AI Model Part 1: Initial EDA and First MDP

AI in Video Games: Improving Decision Making in League of Legends using Real Match Statistics and Personal Preferences

Part 1: Initial Exploratory Analysis and First Markov Decision Process Model

Motivations and Objectives

League of Legends is a team oriented video game where on two team teams (with 5 players in each) compete for objectives and kills. Gaining an advantage enables the players to become stronger (obtain better items and level up faster) than their opponents and, as their advantage increases, the likelihood of winning the game also increases. We therefore have a sequence of events dependent on previous events that lead to one team destroying the other’s base and winning the game.

Sequences like this being modelled statistically is nothing new; for years now researchers have considered how this is applied in sports, such as basketball (https://arxiv.org/pdf/1507.01816.pdf), where a sequence of passing, dribbling and foul plays lead to a team obtaining or losing points. The aim of research such as this one mentioned is to provide more detailed insight beyond a simple box score (number of points or kill gained by player in basketball or video games respectively) and consider how teams perform when modelled as a sequence of events connected in time.

Modelling the events in this way is even more important in games such as League of Legends as taking objectives and kills lead towards both an item and level advantage. For example, a player obtaining the first kill of the game nets them gold that can be used to purchase more powerful items. With this item they are then strong enough to obtain more kills and so on until they can lead their team to a win. Facilitating a lead like this is often referred to as ‘snowballing’ as the players cumulatively gain advantages but often games are not this one sided and objects and team plays are more important.

The aim of this is project is simple; can we calculate the next best event given what has occurred previously in the game so that the likelihood of eventually leading to a win increases based on real match statistics?

However, there are many factors that lead to a player’s decision making in a game that cannot be easily measured. No how matter how much data collected, the amount of information a player can capture is beyond any that a computer can detect (at least for now!). For example, players may be over or underperforming in this game or may simply have a preference for the way they play (often defined by the types of characters they play). Some players will naturally be more aggressive and look for kills while others will play passively and push for objectives instead. Therefore, we further develop our model to allow the player to adjust the recommended play on their preferences.

Import Packages and Data

In [1]:

import pandas as pd
import numpy as np
import datetime
import matplotlib.pyplot as plt
import seaborn as sns
from IPython.display import Image
import math
from scipy.stats import kendalltau

import timeit

import warnings
warnings.filterwarnings('ignore')

In [2]:

#kills = pd.read_csv('C:\\Users\\Phil\\Documents\\LoL Model\\kills.csv')
#matchinfo = pd.read_csv('C:\\Users\\Phil\\Documents\\LoL Model\\matchinfo.csv')
#monsters = pd.read_csv('C:\\Users\\Phil\\Documents\\LoL Model\\monsters.csv')
#structures = pd.read_csv('C:\\Users\\Phil\\Documents\\LoL Model\\structures.csv')

kills = pd.read_csv('../input/kills.csv')
matchinfo = pd.read_csv('../input/matchinfo.csv')
monsters = pd.read_csv('../input/monsters.csv')
structures = pd.read_csv('../input/structures.csv')

Pre-Processing and Exploratory Analysis

In [3]:

matchinfo.head()

Out[3]:

	League	Year	Season	Type	blueTeamTag	bResult	rResult	redTeamTag	gamelength	blueTop	blueTopChamp	blueJungle	blueJungleChamp	blueMiddle	blueMiddleChamp	blueADC	blueADCChamp	blueSupport	blueSupportChamp	redTop	redTopChamp	redJungle	redJungleChamp	redMiddle	redMiddleChamp	redADC	redADCChamp	redSupport	redSupportChamp	Address
0	NALCS	2015	Spring	Season	TSM	1	0	C9	40	Dyrus	Irelia	Santorin	RekSai	Bjergsen	Ahri	WildTurtle	Jinx	Lustboy	Janna	Balls	Gnar	Meteos	Elise	Hai	Fizz	Sneaky	Sivir	LemonNation	Thresh	http://matchhistory.na.leagueoflegends.com/en/...
1	NALCS	2015	Spring	Season	CST	0	1	DIG	38	Cris	Gnar	Impaler	Rengar	Jesiz	Ahri	Mash	Caitlyn	Sheep	Leona	Gamsu	Irelia	Crumbzz	JarvanIV	Shiphtur	Azir	CoreJJ	Corki	KiWiKiD	Annie	http://matchhistory.na.leagueoflegends.com/en/...
2	NALCS	2015	Spring	Season	WFX	1	0	GV	40	Flaresz	Renekton	ShorterACE	Rengar	Pobelter	Fizz	Altec	Sivir	Gleeb	Annie	Hauntzer	Sion	Saintvicious	LeeSin	Keane	Azir	Cop	Corki	BunnyFuFuu	Janna	http://matchhistory.na.leagueoflegends.com/en/...
3	NALCS	2015	Spring	Season	TIP	0	1	TL	41	Rhux	Irelia	Rush	JarvanIV	XiaoWeiXiao	Leblanc	Apollo	Sivir	Adrian	Thresh	Quas	Gnar	IWDominate	Nunu	Fenix	Lulu	KEITH	KogMaw	Xpecial	Janna	http://matchhistory.na.leagueoflegends.com/en/...
4	NALCS	2015	Spring	Season	CLG	1	0	T8	35	Benny	Gnar	Xmithie	JarvanIV	Link	Lissandra	Doublelift	Tristana	aphromoo	Janna	CaliTrlolz8	Sion	Porpoise8	RekSai	Slooshi8	Lulu	Maplestreet8	Corki	Dodo8	Annie	http://matchhistory.na.leagueoflegends.com/en/...

In [4]:

# Add ID column based on last 16 digits in match address for simpler matching

matchinfo['id'] = matchinfo['Address'].astype(str).str[-16:]
kills['id'] = kills['Address'].astype(str).str[-16:]
monsters['id'] = monsters['Address'].astype(str).str[-16:]
structures['id'] = structures['Address'].astype(str).str[-16:]
matchinfo.head()

Out[4]:

	League	Year	Season	Type	blueTeamTag	bResult	rResult	redTeamTag	gamelength	blueTop	blueTopChamp	blueJungle	blueJungleChamp	blueMiddle	blueMiddleChamp	blueADC	blueADCChamp	blueSupport	blueSupportChamp	redTop	redTopChamp	redJungle	redJungleChamp	redMiddle	redMiddleChamp	redADC	redADCChamp	redSupport	redSupportChamp	Address	id
0	NALCS	2015	Spring	Season	TSM	1	0	C9	40	Dyrus	Irelia	Santorin	RekSai	Bjergsen	Ahri	WildTurtle	Jinx	Lustboy	Janna	Balls	Gnar	Meteos	Elise	Hai	Fizz	Sneaky	Sivir	LemonNation	Thresh	http://matchhistory.na.leagueoflegends.com/en/...	fbb300951ad8327c
1	NALCS	2015	Spring	Season	CST	0	1	DIG	38	Cris	Gnar	Impaler	Rengar	Jesiz	Ahri	Mash	Caitlyn	Sheep	Leona	Gamsu	Irelia	Crumbzz	JarvanIV	Shiphtur	Azir	CoreJJ	Corki	KiWiKiD	Annie	http://matchhistory.na.leagueoflegends.com/en/...	055b17da8456fdc8
2	NALCS	2015	Spring	Season	WFX	1	0	GV	40	Flaresz	Renekton	ShorterACE	Rengar	Pobelter	Fizz	Altec	Sivir	Gleeb	Annie	Hauntzer	Sion	Saintvicious	LeeSin	Keane	Azir	Cop	Corki	BunnyFuFuu	Janna	http://matchhistory.na.leagueoflegends.com/en/...	8e8a9b58df366e2d
3	NALCS	2015	Spring	Season	TIP	0	1	TL	41	Rhux	Irelia	Rush	JarvanIV	XiaoWeiXiao	Leblanc	Apollo	Sivir	Adrian	Thresh	Quas	Gnar	IWDominate	Nunu	Fenix	Lulu	KEITH	KogMaw	Xpecial	Janna	http://matchhistory.na.leagueoflegends.com/en/...	0ed1cd0e0e57329c
4	NALCS	2015	Spring	Season	CLG	1	0	T8	35	Benny	Gnar	Xmithie	JarvanIV	Link	Lissandra	Doublelift	Tristana	aphromoo	Janna	CaliTrlolz8	Sion	Porpoise8	RekSai	Slooshi8	Lulu	Maplestreet8	Corki	Dodo8	Annie	http://matchhistory.na.leagueoflegends.com/en/...	f932becf86175f38

In [5]:

# Dragon became multiple types in patch v6.9 (http://leagueoflegends.wikia.com/wiki/V6.9) 
# so we remove and games before this change occured and only use games with the new dragon system
monsters['Type'].unique()

Out[5]:

array(['DRAGON', 'EARTH_DRAGON', 'WATER_DRAGON', 'AIR_DRAGON',
       'FIRE_DRAGON', 'ELDER_DRAGON', 'BARON_NASHOR', 'RIFT_HERALD'],
      dtype=object)

In [6]:

old_dragon_id = monsters[ monsters['Type']=="DRAGON"]['id'].unique()
old_dragon_id

Out[6]:

array(['fbb300951ad8327c', '055b17da8456fdc8', '8e8a9b58df366e2d', ...,
       'd2eaf13bcbb3c021', '035394afd3bfc218', '94537494cdbc8b4c'],
      dtype=object)

In [7]:

monsters = monsters[ ~monsters['id'].isin(old_dragon_id)]
monsters[monsters['Type']=="DRAGON"]

Out[7]:

In [8]:

# Again remove old games, we have some missing values (probably for other events) so remove this
# Create a column for the minute in which the kill took place
# Reassign the team column to a simpler Red/Blue accordingly for matching with other tables

kills = kills[ ~kills['id'].isin(old_dragon_id)]
kills = kills[ kills['Time']>0]

kills['Minute'] = kills['Time'].astype(int)

kills['Team'] = np.where( kills['Team']=="rKills","Red","Blue")
kills.head()

Out[8]:

	Address	Team	Time	Victim	Killer	Assist_1	Assist_2	Assist_3	Assist_4	x_pos	y_pos	id	Minute
4462	http://matchhistory.na.leagueoflegends.com/en/...	Blue	6.032	CLG Huhi	TSM Svenskeren	TSM Bjergsen	NaN	NaN	NaN	7825	8666	55109b5a7a91ae87	6
4463	http://matchhistory.na.leagueoflegends.com/en/...	Blue	9.428	CLG Huhi	TSM Biofrost	TSM Bjergsen	TSM Doublelift	NaN	NaN	8728	8751	55109b5a7a91ae87	9
4464	http://matchhistory.na.leagueoflegends.com/en/...	Blue	9.780	CLG Xmithie	TSM Bjergsen	TSM Hauntzer	TSM Svenskeren	NaN	NaN	8655	1172	55109b5a7a91ae87	9
4465	http://matchhistory.na.leagueoflegends.com/en/...	Blue	10.252	CLG Stixxay	TSM Doublelift	TSM Biofrost	NaN	NaN	NaN	3621	11607	55109b5a7a91ae87	10
4466	http://matchhistory.na.leagueoflegends.com/en/...	Blue	12.993	CLG Darshan	TSM Doublelift	TSM Biofrost	NaN	NaN	NaN	5674	12903	55109b5a7a91ae87	12

In [9]:

# For the Kills table, we need decided to group by the minute in which the kills took place and averaged 
# the time of the kills which we use later for the order of events

f = {'Time':['mean','count']}

killsGrouped = kills.groupby( ['id','Team','Minute'] ).agg(f).reset_index()
killsGrouped.columns = ['id','Team','Minute','Time Avg','Count']
killsGrouped = killsGrouped.sort_values(by=['id','Minute'])
killsGrouped.head(13)

Out[9]:

	id	Team	Minute	Time Avg	Count
4	0001f4374a03c133	Red	4	4.6350	1
5	0001f4374a03c133	Red	6	6.0640	1
0	0001f4374a03c133	Blue	8	8.1940	1
6	0001f4374a03c133	Red	10	10.4780	1
7	0001f4374a03c133	Red	17	17.3870	2
1	0001f4374a03c133	Blue	18	18.0980	1
8	0001f4374a03c133	Red	18	18.0670	2
9	0001f4374a03c133	Red	21	21.7900	1
2	0001f4374a03c133	Blue	22	22.5125	2
10	0001f4374a03c133	Red	22	22.4578	5
3	0001f4374a03c133	Blue	31	31.1685	2
11	0001f4374a03c133	Red	31	31.3880	1
12	0001f4374a03c133	Red	32	32.7634	5

In [10]:

# Repeat similar steps for the structures table

structures = structures[ ~structures['id'].isin(old_dragon_id)]
structures = structures[ structures['Time']>0]

structures['Minute'] = structures['Time'].astype(int)
structures['Team'] = np.where(structures['Team']=="bTowers","Blue",
                        np.where(structures['Team']=="binhibs","Blue","Red"))
structures2 = structures.sort_values(by=['id','Minute'])
structures2.head(13)

Out[10]:

	Address	Team	Time	Lane	Type	id	Minute
6740	http://matchhistory.na.leagueoflegends.com/en/...	Blue	11.182	TOP_LANE	OUTER_TURRET	0001f4374a03c133	11
57600	http://matchhistory.na.leagueoflegends.com/en/...	Red	11.006	BOT_LANE	OUTER_TURRET	0001f4374a03c133	11
6741	http://matchhistory.na.leagueoflegends.com/en/...	Blue	16.556	BOT_LANE	OUTER_TURRET	0001f4374a03c133	16
57601	http://matchhistory.na.leagueoflegends.com/en/...	Red	16.145	TOP_LANE	OUTER_TURRET	0001f4374a03c133	16
57598	http://matchhistory.na.leagueoflegends.com/en/...	Red	18.378	MID_LANE	OUTER_TURRET	0001f4374a03c133	18
57602	http://matchhistory.na.leagueoflegends.com/en/...	Red	24.943	MID_LANE	INNER_TURRET	0001f4374a03c133	24
57599	http://matchhistory.na.leagueoflegends.com/en/...	Red	25.463	TOP_LANE	INNER_TURRET	0001f4374a03c133	25
57597	http://matchhistory.na.leagueoflegends.com/en/...	Red	26.330	BOT_LANE	INNER_TURRET	0001f4374a03c133	26
57594	http://matchhistory.na.leagueoflegends.com/en/...	Red	33.153	MID_LANE	BASE_TURRET	0001f4374a03c133	33
57595	http://matchhistory.na.leagueoflegends.com/en/...	Red	33.326	MID_LANE	NEXUS_TURRET	0001f4374a03c133	33
57596	http://matchhistory.na.leagueoflegends.com/en/...	Red	33.408	MID_LANE	NEXUS_TURRET	0001f4374a03c133	33
111295	http://matchhistory.na.leagueoflegends.com/en/...	Red	33.222	MID_LANE	INHIBITOR	0001f4374a03c133	33
35900	http://matchhistory.oce.leagueoflegends.com/en...	Blue	12.603	BOT_LANE	OUTER_TURRET	0016710a48fdd46d	12

In [11]:

# Merge the two together
kills_structures = killsGrouped.merge(structures2[['id','Minute','Team','Time','Lane','Type']],
                                      on=['id','Minute','Team'],how='outer')
kills_structures.head(20)

Out[11]:

	id	Team	Minute	Time Avg	Count	Time	Lane	Type
0	0001f4374a03c133	Red	4	4.6350	1.0	NaN	NaN	NaN
1	0001f4374a03c133	Red	6	6.0640	1.0	NaN	NaN	NaN
2	0001f4374a03c133	Blue	8	8.1940	1.0	NaN	NaN	NaN
3	0001f4374a03c133	Red	10	10.4780	1.0	NaN	NaN	NaN
4	0001f4374a03c133	Red	17	17.3870	2.0	NaN	NaN	NaN
5	0001f4374a03c133	Blue	18	18.0980	1.0	NaN	NaN	NaN
6	0001f4374a03c133	Red	18	18.0670	2.0	18.378	MID_LANE	OUTER_TURRET
7	0001f4374a03c133	Red	21	21.7900	1.0	NaN	NaN	NaN
8	0001f4374a03c133	Blue	22	22.5125	2.0	NaN	NaN	NaN
9	0001f4374a03c133	Red	22	22.4578	5.0	NaN	NaN	NaN
10	0001f4374a03c133	Blue	31	31.1685	2.0	NaN	NaN	NaN
11	0001f4374a03c133	Red	31	31.3880	1.0	NaN	NaN	NaN
12	0001f4374a03c133	Red	32	32.7634	5.0	NaN	NaN	NaN
13	0016710a48fdd46d	Blue	5	5.9710	1.0	NaN	NaN	NaN
14	0016710a48fdd46d	Red	8	8.3750	1.0	NaN	NaN	NaN
15	0016710a48fdd46d	Blue	11	11.9720	1.0	NaN	NaN	NaN
16	0016710a48fdd46d	Red	11	11.9130	1.0	NaN	NaN	NaN
17	0016710a48fdd46d	Red	13	13.1030	1.0	NaN	NaN	NaN
18	0016710a48fdd46d	Blue	17	17.2070	1.0	NaN	NaN	NaN
19	0016710a48fdd46d	Red	17	17.9140	1.0	NaN	NaN	NaN

In [12]:

# Again repeat same steps, we also map the types of dragon to a simpler 'Dragon' label

monsters = monsters[ ~monsters['id'].isin(old_dragon_id)]
monsters['Type2'] = np.where( monsters['Type']=="FIRE_DRAGON", "DRAGON",
                    np.where( monsters['Type']=="EARTH_DRAGON","DRAGON",
                    np.where( monsters['Type']=="WATER_DRAGON","DRAGON",       
                    np.where( monsters['Type']=="AIR_DRAGON","DRAGON",   
                             monsters['Type']))))

monsters = monsters[ monsters['Time']>0]

monsters['Minute'] = monsters['Time'].astype(int)

monsters['Team'] = np.where( monsters['Team']=="bDragons","Blue",
                   np.where( monsters['Team']=="bHeralds","Blue",
                   np.where( monsters['Team']=="bBarons", "Blue", 
                           "Red")))



monsters.head()

Out[12]:

	Address	Team	Time	Type	id	Type2	Minute
696	http://matchhistory.na.leagueoflegends.com/en/...	Blue	23.444	EARTH_DRAGON	55109b5a7a91ae87	DRAGON	23
697	http://matchhistory.na.leagueoflegends.com/en/...	Blue	31.069	WATER_DRAGON	55109b5a7a91ae87	DRAGON	31
698	http://matchhistory.na.leagueoflegends.com/en/...	Blue	16.419	AIR_DRAGON	55109b5a7a91ae87	DRAGON	16
699	http://matchhistory.na.leagueoflegends.com/en/...	Blue	32.022	EARTH_DRAGON	e147296c928da5b4	DRAGON	32
700	http://matchhistory.na.leagueoflegends.com/en/...	Blue	25.304	WATER_DRAGON	e147296c928da5b4	DRAGON	25

In [13]:

# Merge the monsters to our previously merged table
# This provides us with a table that has each event seperated by columns depending on what type of event it was
kills_structures_monsters = kills_structures.merge(monsters[['id','Minute','Team','Time','Type2']], on=['id','Minute'],how='outer')
kills_structures_monsters = kills_structures_monsters.sort_values(by=['id','Minute'])
kills_structures_monsters.head(5)

Out[13]:

	id	Team_x	Minute	Time Avg	Count	Time_x	Lane	Type	Team_y	Time_y	Type2
0	0001f4374a03c133	Red	4	4.635	1.0	NaN	NaN	NaN	NaN	NaN	NaN
1	0001f4374a03c133	Red	6	6.064	1.0	NaN	NaN	NaN	NaN	NaN	NaN
2	0001f4374a03c133	Blue	8	8.194	1.0	NaN	NaN	NaN	NaN	NaN	NaN
3	0001f4374a03c133	Red	10	10.478	1.0	NaN	NaN	NaN	NaN	NaN	NaN
94502	0001f4374a03c133	Blue	11	NaN	NaN	11.182	TOP_LANE	OUTER_TURRET	Red	11.261	DRAGON

In [14]:

# Although this is a good start, information is repeated on the rows if multiple 
# events occured in the same minute.
#
# Therefore, I decided to let each event have its own row by stacking the tables
# on top of one another. We then add a more detailed time column and sort by this 
# so we know exactly which event came first (allowing for some errors with kill time
# being averaged).


stackedData = killsGrouped.append(structures2)
stackedData = stackedData.append(monsters[['id','Address','Team','Minute','Time','Type2']])

stackedData['Time2'] = stackedData['Time'].fillna(stackedData['Time Avg'])

stackedData = stackedData.sort_values(by=['id','Time2'])

stackedData['EventNum'] = stackedData.groupby('id').cumcount()+1

stackedData = stackedData[['id','EventNum','Team','Minute','Time2','Count','Type','Lane','Type2']]

stackedData.columns = ['id','EventNum','Team','Minute','Time','KillCount','StructType','StructLane','Monster']

stackedData.head(5)

Out[14]:

	id	EventNum	Team	Minute	Time	KillCount	StructType	StructLane	Monster
4	0001f4374a03c133	1	Red	4	4.635	1.0	NaN	NaN	NaN
5	0001f4374a03c133	2	Red	6	6.064	1.0	NaN	NaN	NaN
0	0001f4374a03c133	3	Blue	8	8.194	1.0	NaN	NaN	NaN
6	0001f4374a03c133	4	Red	10	10.478	1.0	NaN	NaN	NaN
57600	0001f4374a03c133	5	Red	11	11.006	NaN	OUTER_TURRET	BOT_LANE	NaN

In [15]:

# We then add an 'Event' column to merge the columns into one, where kills are now
# simple labelled as 'KILLS'

stackedData['Event'] = np.where(stackedData['KillCount']>0,"KILLS",None)
stackedData['Event'] = stackedData['Event'].fillna(stackedData['StructType'])
stackedData['Event'] = stackedData['Event'].fillna(stackedData['Monster'])

                        

stackedData.head(10)

Out[15]:

	id	EventNum	Team	Minute	Time	KillCount	StructType	StructLane	Monster	Event
4	0001f4374a03c133	1	Red	4	4.635	1.0	NaN	NaN	NaN	KILLS
5	0001f4374a03c133	2	Red	6	6.064	1.0	NaN	NaN	NaN	KILLS
0	0001f4374a03c133	3	Blue	8	8.194	1.0	NaN	NaN	NaN	KILLS
6	0001f4374a03c133	4	Red	10	10.478	1.0	NaN	NaN	NaN	KILLS
57600	0001f4374a03c133	5	Red	11	11.006	NaN	OUTER_TURRET	BOT_LANE	NaN	OUTER_TURRET
6740	0001f4374a03c133	6	Blue	11	11.182	NaN	OUTER_TURRET	TOP_LANE	NaN	OUTER_TURRET
24027	0001f4374a03c133	7	Red	11	11.261	NaN	NaN	NaN	DRAGON	DRAGON
42565	0001f4374a03c133	8	Red	15	15.777	NaN	NaN	NaN	RIFT_HERALD	RIFT_HERALD
57601	0001f4374a03c133	9	Red	16	16.145	NaN	OUTER_TURRET	TOP_LANE	NaN	OUTER_TURRET
6741	0001f4374a03c133	10	Blue	16	16.556	NaN	OUTER_TURRET	BOT_LANE	NaN	OUTER_TURRET

In [16]:

stackedData['Event'].unique()

Out[16]:

array(['KILLS', 'OUTER_TURRET', 'DRAGON', 'RIFT_HERALD', 'BARON_NASHOR',
       'INNER_TURRET', 'BASE_TURRET', 'INHIBITOR', 'NEXUS_TURRET',
       'ELDER_DRAGON'], dtype=object)

In [17]:

NumEventAnalysis = stackedData[['id','EventNum']].groupby('id').max().reset_index()

NumEventAnalysis2 = NumEventAnalysis.groupby('EventNum').count().reset_index()

NumEventAnalysis2.head()

Out[17]:

	EventNum	id
0	14	1
1	16	3
2	17	4
3	18	7
4	19	12

In [18]:

plt.bar(NumEventAnalysis2['EventNum'],NumEventAnalysis2['id'] ,alpha=0.3)
plt.plot(NumEventAnalysis2['EventNum'],NumEventAnalysis2['id'])
plt.title('Distribution of Number of Events in Each Match (EXACT)')
plt.xlim(0,100)
plt.xlabel("Number of Events")
plt.ylabel("Number of Matches")
plt.show()

In [19]:

sns.distplot(NumEventAnalysis['EventNum'],bins=65)
plt.title('Distribution of Number of Events in Each Match (NORMAL DIST)')
plt.xlim(0,100)
plt.xlabel("Number of Events")
plt.ylabel("Number of Matches")
plt.show()

In [20]:

print("The max number of events for any team in a single game is:",NumEventAnalysis['EventNum'].max())
print("The min number of events for any team in a single game is:",NumEventAnalysis['EventNum'].min())

The max number of events for any team in a single game is: 79
The min number of events for any team in a single game is: 14

In [21]:

# We then create a table with just the unique match ids that we will use to merge our tables to shortly
matchevents = pd.DataFrame(stackedData['id'].unique())
matchevents.columns = ['id']

matchevents.head()

Out[21]:

	id
0	0001f4374a03c133
1	0016710a48fdd46d
2	0016c9df37278448
3	0021b45647424cd5
4	00405293fb859241

In [22]:

# WARNING: Takes a while to run

# This cell has a lot of steps but the idea is to:
#    1) Seperate the the events into each team (Red/Blue)
#    2) For each, go through each match and transpose the list of events into a single row
#    3) Stack a table that has the events for both team of the matches

bluerows = pd.DataFrame()
stackedData_blue = stackedData
stackedData_blue['EventBlue'] = np.where( stackedData_blue['Team']!="Red",stackedData_blue['Event'],np.nan)


redrows = pd.DataFrame()
stackedData_red = stackedData
stackedData_red['EventRed'] = np.where( stackedData_red['Team']=="Red",stackedData_red['Event'],np.nan)


for i in range(0,len(matchevents)):
    
    #Red Team Output
    stackedData_match_red = stackedData_red[stackedData_red['id'] == matchevents.iloc[i,0] ]
    
    redextract = stackedData_match_red.iloc[:,[1,11]]
    redextract.iloc[:,0] = redextract.iloc[:,0]-1
    redextract = redextract.set_index('EventNum')
    
    redrow = pd.DataFrame(redextract.transpose())
    redrow['id'] = (stackedData_match_red['id'].unique())
    
    redrows = redrows.append((redrow))
    redrows = redrows.reset_index(drop=True)
    
    
    
    #Blue Team Output
    stackedData_match_blue = stackedData_blue[stackedData_blue['id'] == matchevents.iloc[i,0] ]
    
    blueextract = stackedData_match_blue.iloc[:,[1,10]]
    blueextract.iloc[:,0] = blueextract.iloc[:,0]-1
    blueextract = blueextract.set_index('EventNum')
    
    bluerow = pd.DataFrame(blueextract.transpose())
    bluerow['id'] = (stackedData_match_blue['id'].unique())
    
    bluerows = bluerows.append((bluerow))
    bluerows = bluerows.reset_index(drop=True)
    
  
    

In [23]:

redrows = redrows.sort_values('id')
redrows.head(5)

Out[23]:

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	id	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78
0	KILLS	KILLS	NaN	KILLS	OUTER_TURRET	NaN	DRAGON	RIFT_HERALD	OUTER_TURRET	NaN	KILLS	DRAGON	KILLS	NaN	OUTER_TURRET	KILLS	KILLS	NaN	BARON_NASHOR	DRAGON	INNER_TURRET	INNER_TURRET	INNER_TURRET	DRAGON	NaN	KILLS	KILLS	BASE_TURRET	INHIBITOR	NEXUS_TURRET	NEXUS_TURRET	0001f4374a03c133	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	NaN	KILLS	DRAGON	KILLS	NaN	NaN	KILLS	NaN	NaN	KILLS	KILLS	NaN	OUTER_TURRET	NaN	NaN	NaN	KILLS	NaN	KILLS	OUTER_TURRET	NaN	KILLS	OUTER_TURRET	NaN	KILLS	NaN	KILLS	NaN	KILLS	BARON_NASHOR	KILLS	0016710a48fdd46d	INNER_TURRET	INNER_TURRET	INNER_TURRET	NaN	KILLS	BASE_TURRET	NaN	INHIBITOR	KILLS	NaN	KILLS	NEXUS_TURRET	NEXUS_TURRET	NaN	NaN	NaN	KILLS	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	OUTER_TURRET	NaN	NaN	KILLS	NaN	NaN	NaN	KILLS	BARON_NASHOR	OUTER_TURRET	DRAGON	KILLS	OUTER_TURRET	INNER_TURRET	INNER_TURRET	BASE_TURRET	INHIBITOR	INNER_TURRET	BASE_TURRET	BASE_TURRET	INHIBITOR	NEXUS_TURRET	0016c9df37278448	NEXUS_TURRET	NaN	KILLS	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
3	NaN	KILLS	KILLS	KILLS	NaN	DRAGON	RIFT_HERALD	NaN	OUTER_TURRET	NaN	OUTER_TURRET	NaN	DRAGON	KILLS	KILLS	OUTER_TURRET	NaN	KILLS	BARON_NASHOR	NaN	DRAGON	INNER_TURRET	KILLS	INNER_TURRET	BASE_TURRET	INHIBITOR	NaN	KILLS	NEXUS_TURRET	BARON_NASHOR	INNER_TURRET	0021b45647424cd5	NaN	DRAGON	INHIBITOR	BASE_TURRET	INHIBITOR	NaN	NaN	KILLS	NaN	KILLS	NEXUS_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
4	KILLS	NaN	NaN	NaN	NaN	OUTER_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	OUTER_TURRET	KILLS	KILLS	NaN	OUTER_TURRET	DRAGON	BARON_NASHOR	KILLS	INNER_TURRET	BASE_TURRET	INHIBITOR	KILLS	INNER_TURRET	KILLS	BASE_TURRET	00405293fb859241	INHIBITOR	NaN	KILLS	INNER_TURRET	NEXUS_TURRET	NEXUS_TURRET	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

In [24]:

bluerows = bluerows.sort_values('id')
bluerows.head(5)

Out[24]:

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	id	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78
0	NaN	NaN	KILLS	NaN	NaN	OUTER_TURRET	NaN	NaN	NaN	OUTER_TURRET	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	0001f4374a03c133	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	KILLS	NaN	NaN	NaN	KILLS	OUTER_TURRET	NaN	DRAGON	KILLS	NaN	NaN	KILLS	NaN	OUTER_TURRET	DRAGON	KILLS	NaN	OUTER_TURRET	NaN	NaN	KILLS	NaN	NaN	KILLS	NaN	KILLS	NaN	DRAGON	NaN	NaN	NaN	0016710a48fdd46d	NaN	NaN	NaN	KILLS	NaN	NaN	KILLS	NaN	NaN	KILLS	NaN	NaN	NaN	KILLS	KILLS	DRAGON	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	KILLS	KILLS	KILLS	OUTER_TURRET	DRAGON	KILLS	NaN	KILLS	RIFT_HERALD	NaN	OUTER_TURRET	DRAGON	NaN	DRAGON	KILLS	OUTER_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0016c9df37278448	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
3	KILLS	NaN	NaN	NaN	KILLS	NaN	NaN	KILLS	NaN	KILLS	NaN	KILLS	NaN	NaN	NaN	NaN	OUTER_TURRET	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	0021b45647424cd5	KILLS	NaN	NaN	NaN	NaN	KILLS	BARON_NASHOR	NaN	KILLS	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
4	NaN	KILLS	KILLS	KILLS	OUTER_TURRET	NaN	DRAGON	KILLS	OUTER_TURRET	KILLS	KILLS	DRAGON	OUTER_TURRET	NaN	KILLS	DRAGON	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	00405293fb859241	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

In [25]:

# We can now merge these two tables for each team's events in the match to
# our table with just the match ids. We also add a column for the result of 
# the red team for the match and change column names according to which team 
# made the event.



matchevents2 = matchevents.merge(redrows,how='left',on='id')
matchevents3 = matchevents2.merge(bluerows,how='left',on='id')
    

    
matchevents4 = matchevents3.merge(matchinfo[['id','rResult','gamelength']], on='id',how='left')


matchevents4.columns = ['id',
'RedEvent1','RedEvent2','RedEvent3',
'RedEvent4','RedEvent5','RedEvent6','RedEvent7',
'RedEvent8','RedEvent9','RedEvent10','RedEvent11',
'RedEvent12','RedEvent13','RedEvent14','RedEvent15',
'RedEvent16','RedEvent17','RedEvent18','RedEvent19',
'RedEvent20','RedEvent21','RedEvent22','RedEvent23',
'RedEvent24','RedEvent25','RedEvent26','RedEvent27',
'RedEvent28','RedEvent29','RedEvent30','RedEvent31',
'RedEvent32','RedEvent33','RedEvent34','RedEvent35',
'RedEvent36','RedEvent37','RedEvent38','RedEvent39',
'RedEvent40','RedEvent41','RedEvent42','RedEvent43',
'RedEvent44','RedEvent45','RedEvent46','RedEvent47',
'RedEvent48','RedEvent49','RedEvent50','RedEvent51',
'RedEvent52','RedEvent53','RedEvent54','RedEvent55',
'RedEvent56','RedEvent57','RedEvent58','RedEvent59',
'RedEvent60','RedEvent61','RedEvent62','RedEvent63',
'RedEvent64','RedEvent65','RedEvent66','RedEvent67',
'RedEvent68','RedEvent69','RedEvent70','RedEvent71',
'RedEvent72','RedEvent73','RedEvent74','RedEvent75',
'RedEvent76','RedEvent77','RedEvent78','RedEvent79',
                        
                        
'BlueEvent1','BlueEvent2','BlueEvent3','BlueEvent4',
'BlueEvent5','BlueEvent6','BlueEvent7','BlueEvent8',
'BlueEvent9','BlueEvent10','BlueEvent11','BlueEvent12',
'BlueEvent13','BlueEvent14','BlueEvent15','BlueEvent16',
'BlueEvent17','BlueEvent18','BlueEvent19','BlueEvent20',
'BlueEvent21','BlueEvent22','BlueEvent23','BlueEvent24',
'BlueEvent25','BlueEvent26','BlueEvent27','BlueEvent28',
'BlueEvent29','BlueEvent30','BlueEvent31','BlueEvent32',
'BlueEvent33','BlueEvent34','BlueEvent35','BlueEvent36',
'BlueEvent37','BlueEvent38','BlueEvent39','BlueEvent40',
'BlueEvent41','BlueEvent42','BlueEvent43','BlueEvent44',
'BlueEvent45','BlueEvent46','BlueEvent47','BlueEvent48',
'BlueEvent49','BlueEvent50','BlueEvent51','BlueEvent52',
'BlueEvent53','BlueEvent54','BlueEvent55','BlueEvent56',
'BlueEvent57','BlueEvent58','BlueEvent59','BlueEvent60',
'BlueEvent61','BlueEvent62','BlueEvent63',
'BlueEvent64','BlueEvent65','BlueEvent66','BlueEvent67',
'BlueEvent68','BlueEvent69','BlueEvent70','BlueEvent71',
'BlueEvent72','BlueEvent73','BlueEvent74','BlueEvent75',
'BlueEvent76','BlueEvent77','BlueEvent78','BlueEvent79',
                        
                        'rResult','gamelength']



matchevents4.head(20)

Out[25]:

	id	RedEvent1	RedEvent2	RedEvent3	RedEvent4	RedEvent5	RedEvent6	RedEvent7	RedEvent8	RedEvent9	RedEvent10	RedEvent11	RedEvent12	RedEvent13	RedEvent14	RedEvent15	RedEvent16	RedEvent17	RedEvent18	RedEvent19	RedEvent20	RedEvent21	RedEvent22	RedEvent23	RedEvent24	RedEvent25	RedEvent26	RedEvent27	RedEvent28	RedEvent29	RedEvent30	RedEvent31	RedEvent32	RedEvent33	RedEvent34	RedEvent35	RedEvent36	RedEvent37	RedEvent38	RedEvent39	...	BlueEvent42	BlueEvent43	BlueEvent44	BlueEvent45	BlueEvent46	BlueEvent47	BlueEvent48	BlueEvent49	BlueEvent50	BlueEvent51	BlueEvent52	BlueEvent53	BlueEvent54	BlueEvent55	BlueEvent56	BlueEvent57	BlueEvent58	BlueEvent59	BlueEvent60	BlueEvent61	BlueEvent62	BlueEvent63	BlueEvent64	BlueEvent65	BlueEvent66	BlueEvent67	BlueEvent68	BlueEvent69	BlueEvent70	BlueEvent71	BlueEvent72	BlueEvent73	BlueEvent74	BlueEvent75	BlueEvent76	BlueEvent77	BlueEvent78	BlueEvent79	rResult	gamelength
0	0001f4374a03c133	KILLS	KILLS	NaN	KILLS	OUTER_TURRET	NaN	DRAGON	RIFT_HERALD	OUTER_TURRET	NaN	KILLS	DRAGON	KILLS	NaN	OUTER_TURRET	KILLS	KILLS	NaN	BARON_NASHOR	DRAGON	INNER_TURRET	INNER_TURRET	INNER_TURRET	DRAGON	NaN	KILLS	KILLS	BASE_TURRET	INHIBITOR	NEXUS_TURRET	NEXUS_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	34
1	0016710a48fdd46d	NaN	KILLS	DRAGON	KILLS	NaN	NaN	KILLS	NaN	NaN	KILLS	KILLS	NaN	OUTER_TURRET	NaN	NaN	NaN	KILLS	NaN	KILLS	OUTER_TURRET	NaN	KILLS	OUTER_TURRET	NaN	KILLS	NaN	KILLS	NaN	KILLS	BARON_NASHOR	KILLS	INNER_TURRET	INNER_TURRET	INNER_TURRET	NaN	KILLS	BASE_TURRET	NaN	INHIBITOR	...	NaN	NaN	NaN	KILLS	KILLS	DRAGON	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	40
2	0016c9df37278448	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	OUTER_TURRET	NaN	NaN	KILLS	NaN	NaN	NaN	KILLS	BARON_NASHOR	OUTER_TURRET	DRAGON	KILLS	OUTER_TURRET	INNER_TURRET	INNER_TURRET	BASE_TURRET	INHIBITOR	INNER_TURRET	BASE_TURRET	BASE_TURRET	INHIBITOR	NEXUS_TURRET	NEXUS_TURRET	NaN	KILLS	INHIBITOR	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	40
3	0021b45647424cd5	NaN	KILLS	KILLS	KILLS	NaN	DRAGON	RIFT_HERALD	NaN	OUTER_TURRET	NaN	OUTER_TURRET	NaN	DRAGON	KILLS	KILLS	OUTER_TURRET	NaN	KILLS	BARON_NASHOR	NaN	DRAGON	INNER_TURRET	KILLS	INNER_TURRET	BASE_TURRET	INHIBITOR	NaN	KILLS	NEXUS_TURRET	BARON_NASHOR	INNER_TURRET	NaN	DRAGON	INHIBITOR	BASE_TURRET	INHIBITOR	NaN	NaN	KILLS	...	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	42
4	00405293fb859241	KILLS	NaN	NaN	NaN	NaN	OUTER_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	OUTER_TURRET	KILLS	KILLS	NaN	OUTER_TURRET	DRAGON	BARON_NASHOR	KILLS	INNER_TURRET	BASE_TURRET	INHIBITOR	KILLS	INNER_TURRET	KILLS	BASE_TURRET	INHIBITOR	NaN	KILLS	INNER_TURRET	NEXUS_TURRET	NEXUS_TURRET	KILLS	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	39
5	00416ed438e29f14	NaN	KILLS	NaN	NaN	NaN	OUTER_TURRET	NaN	KILLS	KILLS	DRAGON	NaN	NaN	OUTER_TURRET	KILLS	KILLS	BARON_NASHOR	NaN	OUTER_TURRET	NaN	INNER_TURRET	INNER_TURRET	NaN	BARON_NASHOR	KILLS	BASE_TURRET	NaN	NaN	NaN	INHIBITOR	KILLS	INNER_TURRET	BASE_TURRET	BASE_TURRET	INHIBITOR	NaN	KILLS	NaN	NEXUS_TURRET	NEXUS_TURRET	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	41
6	007802c051352561	NaN	KILLS	DRAGON	KILLS	KILLS	RIFT_HERALD	NaN	NaN	OUTER_TURRET	OUTER_TURRET	INNER_TURRET	NaN	NaN	NaN	OUTER_TURRET	NaN	KILLS	DRAGON	INNER_TURRET	DRAGON	NaN	NaN	KILLS	BARON_NASHOR	NaN	KILLS	KILLS	ELDER_DRAGON	INNER_TURRET	BASE_TURRET	INHIBITOR	BARON_NASHOR	BASE_TURRET	NaN	KILLS	INHIBITOR	KILLS	NEXUS_TURRET	NEXUS_TURRET	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	44
7	0091705b03924485	NaN	NaN	NaN	NaN	NaN	NaN	DRAGON	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	INHIBITOR	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	27
8	00986b51908a63c3	NaN	KILLS	KILLS	KILLS	KILLS	KILLS	NaN	OUTER_TURRET	DRAGON	OUTER_TURRET	NaN	INNER_TURRET	KILLS	OUTER_TURRET	INNER_TURRET	DRAGON	KILLS	NaN	NaN	DRAGON	NaN	NaN	KILLS	INNER_TURRET	BASE_TURRET	INHIBITOR	NaN	NaN	NaN	KILLS	BASE_TURRET	NaN	NaN	INHIBITOR	NaN	NaN	KILLS	INHIBITOR	BASE_TURRET	...	NaN	NaN	NaN	KILLS	INNER_TURRET	NaN	NaN	NaN	KILLS	NaN	BARON_NASHOR	KILLS	KILLS	ELDER_DRAGON	BASE_TURRET	NaN	NaN	NaN	KILLS	KILLS	NEXUS_TURRET	NEXUS_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	69
9	00b13dbf1bd7aff0	NaN	KILLS	OUTER_TURRET	NaN	DRAGON	NaN	DRAGON	OUTER_TURRET	NaN	OUTER_TURRET	NaN	KILLS	NaN	NaN	KILLS	BARON_NASHOR	NaN	NaN	NaN	NaN	DRAGON	NaN	KILLS	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	36
10	00b2492ce66406e9	KILLS	KILLS	KILLS	NaN	NaN	NaN	NaN	KILLS	KILLS	KILLS	KILLS	KILLS	OUTER_TURRET	OUTER_TURRET	DRAGON	RIFT_HERALD	OUTER_TURRET	BARON_NASHOR	INNER_TURRET	NaN	INNER_TURRET	KILLS	INNER_TURRET	DRAGON	KILLS	BASE_TURRET	BASE_TURRET	BASE_TURRET	INHIBITOR	KILLS	NEXUS_TURRET	INHIBITOR	NEXUS_TURRET	INHIBITOR	NaN	KILLS	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	29
11	00df84280ed2625b	KILLS	NaN	NaN	DRAGON	NaN	KILLS	NaN	KILLS	KILLS	OUTER_TURRET	OUTER_TURRET	KILLS	NaN	BARON_NASHOR	NaN	KILLS	OUTER_TURRET	DRAGON	INNER_TURRET	NaN	KILLS	KILLS	KILLS	BARON_NASHOR	DRAGON	INNER_TURRET	KILLS	NaN	BASE_TURRET	INHIBITOR	NEXUS_TURRET	KILLS	INNER_TURRET	BASE_TURRET	KILLS	NEXUS_TURRET	NaN	KILLS	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	39
12	00e4eb2c47c14065	NaN	OUTER_TURRET	NaN	OUTER_TURRET	NaN	DRAGON	RIFT_HERALD	NaN	NaN	NaN	KILLS	OUTER_TURRET	NaN	NaN	BARON_NASHOR	INNER_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	31
13	00ecc69a0f024ada	NaN	NaN	NaN	NaN	NaN	NaN	OUTER_TURRET	NaN	NaN	OUTER_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	INHIBITOR	NaN	NaN	NaN	INHIBITOR	NaN	NaN	NaN	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	34
14	00fc8c3957193d35	KILLS	KILLS	OUTER_TURRET	NaN	INNER_TURRET	NaN	DRAGON	NaN	KILLS	NaN	OUTER_TURRET	OUTER_TURRET	DRAGON	NaN	KILLS	NaN	NaN	NaN	DRAGON	KILLS	BARON_NASHOR	NaN	KILLS	INNER_TURRET	NaN	KILLS	BASE_TURRET	INHIBITOR	KILLS	INNER_TURRET	KILLS	NaN	DRAGON	NaN	KILLS	NaN	KILLS	NEXUS_TURRET	NEXUS_TURRET	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	32
15	0122e715a37611f0	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	DRAGON	KILLS	KILLS	OUTER_TURRET	KILLS	NaN	NaN	NaN	NaN	OUTER_TURRET	NaN	NaN	NaN	KILLS	NaN	NaN	KILLS	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	INHIBITOR	NaN	INHIBITOR	NaN	INHIBITOR	NaN	...	NEXUS_TURRET	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	36
16	01321351be01672f	OUTER_TURRET	NaN	NaN	OUTER_TURRET	NaN	DRAGON	NaN	NaN	NaN	OUTER_TURRET	NaN	KILLS	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	INHIBITOR	NaN	KILLS	NaN	NaN	KILLS	NaN	INHIBITOR	NaN	KILLS	NaN	INHIBITOR	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	34
17	01360c9cdc07e173	NaN	KILLS	KILLS	NaN	NaN	KILLS	NaN	DRAGON	NaN	NaN	NaN	OUTER_TURRET	NaN	KILLS	NaN	BARON_NASHOR	NaN	DRAGON	OUTER_TURRET	OUTER_TURRET	NaN	INNER_TURRET	KILLS	NaN	BASE_TURRET	INNER_TURRET	NaN	INHIBITOR	KILLS	NaN	DRAGON	NaN	NEXUS_TURRET	NaN	INNER_TURRET	NaN	BASE_TURRET	DRAGON	INHIBITOR	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	1	44
18	01368b5ce8fcef87	NaN	KILLS	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	KILLS	DRAGON	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	INHIBITOR	NaN	INHIBITOR	NaN	NaN	NaN	INHIBITOR	NaN	KILLS	NaN	NaN	NaN	KILLS	INHIBITOR	KILLS	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	34
19	01417eebd0d9ccb3	NaN	NaN	KILLS	NaN	KILLS	NaN	KILLS	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	NaN	NaN	KILLS	NaN	NaN	NaN	NaN	INHIBITOR	NaN	NaN	INHIBITOR	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	31

In [26]:

# We now decided, for the purpose of calculating probabilities, to consider one team's perseperctive.
# Therefore, we make all events either positive or negative for red team but keep their label otherwise.

matchevents5=matchevents4
for j in range(1,len(list(redrows))):
    matchevents5['RedEvent'+str(j)] = '+'+ matchevents5['RedEvent'+str(j)].astype(str)
    matchevents5['BlueEvent'+str(j)] = '-'+ matchevents5['BlueEvent'+str(j)].astype(str)
    
    matchevents5 = matchevents5.replace('+nan',np.nan)
    matchevents5['RedEvent'+str(j)] =  matchevents5['RedEvent'+str(j)].fillna(
                                        (matchevents5['BlueEvent'+str(j)]).astype(str))
    
matchevents5.head()

Out[26]:

	id	RedEvent1	RedEvent2	RedEvent3	RedEvent4	RedEvent5	RedEvent6	RedEvent7	RedEvent8	RedEvent9	RedEvent10	RedEvent11	RedEvent12	RedEvent13	RedEvent14	RedEvent15	RedEvent16	RedEvent17	RedEvent18	RedEvent19	RedEvent20	RedEvent21	RedEvent22	RedEvent23	RedEvent24	RedEvent25	RedEvent26	RedEvent27	RedEvent28	RedEvent29	RedEvent30	RedEvent31	RedEvent32	RedEvent33	RedEvent34	RedEvent35	RedEvent36	RedEvent37	RedEvent38	RedEvent39	...	BlueEvent42	BlueEvent43	BlueEvent44	BlueEvent45	BlueEvent46	BlueEvent47	BlueEvent48	BlueEvent49	BlueEvent50	BlueEvent51	BlueEvent52	BlueEvent53	BlueEvent54	BlueEvent55	BlueEvent56	BlueEvent57	BlueEvent58	BlueEvent59	BlueEvent60	BlueEvent61	BlueEvent62	BlueEvent63	BlueEvent64	BlueEvent65	BlueEvent66	BlueEvent67	BlueEvent68	BlueEvent69	BlueEvent70	BlueEvent71	BlueEvent72	BlueEvent73	BlueEvent74	BlueEvent75	BlueEvent76	BlueEvent77	BlueEvent78	BlueEvent79	rResult	gamelength
0	0001f4374a03c133	+KILLS	+KILLS	-KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+DRAGON	+RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+DRAGON	+KILLS	-KILLS	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+BARON_NASHOR	+DRAGON	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	+DRAGON	-KILLS	+KILLS	+KILLS	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	34
1	0016710a48fdd46d	-KILLS	+KILLS	+DRAGON	+KILLS	-KILLS	-OUTER_TURRET	+KILLS	-DRAGON	-KILLS	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-OUTER_TURRET	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	-KILLS	+KILLS	-DRAGON	+KILLS	+BARON_NASHOR	+KILLS	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	-KILLS	+KILLS	+BASE_TURRET	-KILLS	+INHIBITOR	...	-nan	-nan	-nan	-KILLS	-KILLS	-DRAGON	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	40
2	0016c9df37278448	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-KILLS	-RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	+KILLS	-DRAGON	-KILLS	-OUTER_TURRET	+KILLS	+BARON_NASHOR	+OUTER_TURRET	+DRAGON	+KILLS	+OUTER_TURRET	+INNER_TURRET	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+INNER_TURRET	+BASE_TURRET	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	+KILLS	+INHIBITOR	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	40
3	0021b45647424cd5	-KILLS	+KILLS	+KILLS	+KILLS	-KILLS	+DRAGON	+RIFT_HERALD	-KILLS	+OUTER_TURRET	-KILLS	+OUTER_TURRET	-KILLS	+DRAGON	+KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+BARON_NASHOR	-KILLS	+DRAGON	+INNER_TURRET	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+NEXUS_TURRET	+BARON_NASHOR	+INNER_TURRET	-KILLS	+DRAGON	+INHIBITOR	+BASE_TURRET	+INHIBITOR	-KILLS	-BARON_NASHOR	+KILLS	...	-nan	-KILLS	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	42
4	00405293fb859241	+KILLS	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	+OUTER_TURRET	-DRAGON	-KILLS	-OUTER_TURRET	-KILLS	-KILLS	-DRAGON	-OUTER_TURRET	+KILLS	-KILLS	-DRAGON	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	+DRAGON	+BARON_NASHOR	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+KILLS	+INNER_TURRET	+KILLS	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+INNER_TURRET	+NEXUS_TURRET	+NEXUS_TURRET	+KILLS	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	39

In [27]:

# We take on the red event columns now  and re-add the end result of the game for red team (1=win, 0=loss)

RedMatchEvents = matchevents5.iloc[:,0:80]
RedMatchEvents['RedResult'] = matchevents5['rResult']
RedMatchEvents['MatchLength'] = matchevents5['gamelength']
RedMatchEvents.iloc[0:10]

Out[27]:

	id	RedEvent1	RedEvent2	RedEvent3	RedEvent4	RedEvent5	RedEvent6	RedEvent7	RedEvent8	RedEvent9	RedEvent10	RedEvent11	RedEvent12	RedEvent13	RedEvent14	RedEvent15	RedEvent16	RedEvent17	RedEvent18	RedEvent19	RedEvent20	RedEvent21	RedEvent22	RedEvent23	RedEvent24	RedEvent25	RedEvent26	RedEvent27	RedEvent28	RedEvent29	RedEvent30	RedEvent31	RedEvent32	RedEvent33	RedEvent34	RedEvent35	RedEvent36	RedEvent37	RedEvent38	RedEvent39	...	RedEvent42	RedEvent43	RedEvent44	RedEvent45	RedEvent46	RedEvent47	RedEvent48	RedEvent49	RedEvent50	RedEvent51	RedEvent52	RedEvent53	RedEvent54	RedEvent55	RedEvent56	RedEvent57	RedEvent58	RedEvent59	RedEvent60	RedEvent61	RedEvent62	RedEvent63	RedEvent64	RedEvent65	RedEvent66	RedEvent67	RedEvent68	RedEvent69	RedEvent70	RedEvent71	RedEvent72	RedEvent73	RedEvent74	RedEvent75	RedEvent76	RedEvent77	RedEvent78	RedEvent79	RedResult	MatchLength
0	0001f4374a03c133	+KILLS	+KILLS	-KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+DRAGON	+RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+DRAGON	+KILLS	-KILLS	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+BARON_NASHOR	+DRAGON	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	+DRAGON	-KILLS	+KILLS	+KILLS	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	34
1	0016710a48fdd46d	-KILLS	+KILLS	+DRAGON	+KILLS	-KILLS	-OUTER_TURRET	+KILLS	-DRAGON	-KILLS	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-OUTER_TURRET	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	-KILLS	+KILLS	-DRAGON	+KILLS	+BARON_NASHOR	+KILLS	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	-KILLS	+KILLS	+BASE_TURRET	-KILLS	+INHIBITOR	...	+KILLS	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	-KILLS	-DRAGON	+KILLS	+INHIBITOR	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	40
2	0016c9df37278448	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-KILLS	-RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	+KILLS	-DRAGON	-KILLS	-OUTER_TURRET	+KILLS	+BARON_NASHOR	+OUTER_TURRET	+DRAGON	+KILLS	+OUTER_TURRET	+INNER_TURRET	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+INNER_TURRET	+BASE_TURRET	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	+KILLS	+INHIBITOR	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	40
3	0021b45647424cd5	-KILLS	+KILLS	+KILLS	+KILLS	-KILLS	+DRAGON	+RIFT_HERALD	-KILLS	+OUTER_TURRET	-KILLS	+OUTER_TURRET	-KILLS	+DRAGON	+KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+BARON_NASHOR	-KILLS	+DRAGON	+INNER_TURRET	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+NEXUS_TURRET	+BARON_NASHOR	+INNER_TURRET	-KILLS	+DRAGON	+INHIBITOR	+BASE_TURRET	+INHIBITOR	-KILLS	-BARON_NASHOR	+KILLS	...	+NEXUS_TURRET	-KILLS	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	42
4	00405293fb859241	+KILLS	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	+OUTER_TURRET	-DRAGON	-KILLS	-OUTER_TURRET	-KILLS	-KILLS	-DRAGON	-OUTER_TURRET	+KILLS	-KILLS	-DRAGON	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	+DRAGON	+BARON_NASHOR	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+KILLS	+INNER_TURRET	+KILLS	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+INNER_TURRET	+NEXUS_TURRET	+NEXUS_TURRET	+KILLS	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	39
5	00416ed438e29f14	-KILLS	+KILLS	-KILLS	-DRAGON	-KILLS	+OUTER_TURRET	-KILLS	+KILLS	+KILLS	+DRAGON	-OUTER_TURRET	-OUTER_TURRET	+OUTER_TURRET	+KILLS	+KILLS	+BARON_NASHOR	-DRAGON	+OUTER_TURRET	-KILLS	+INNER_TURRET	+INNER_TURRET	-DRAGON	+BARON_NASHOR	+KILLS	+BASE_TURRET	-KILLS	-KILLS	-INNER_TURRET	+INHIBITOR	+KILLS	+INNER_TURRET	+BASE_TURRET	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	-ELDER_DRAGON	+NEXUS_TURRET	+NEXUS_TURRET	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	41
6	007802c051352561	-KILLS	+KILLS	+DRAGON	+KILLS	+KILLS	+RIFT_HERALD	-OUTER_TURRET	-OUTER_TURRET	+OUTER_TURRET	+OUTER_TURRET	+INNER_TURRET	-INNER_TURRET	-KILLS	-DRAGON	+OUTER_TURRET	-KILLS	+KILLS	+DRAGON	+INNER_TURRET	+DRAGON	-KILLS	-OUTER_TURRET	+KILLS	+BARON_NASHOR	-KILLS	+KILLS	+KILLS	+ELDER_DRAGON	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+BARON_NASHOR	+BASE_TURRET	-KILLS	+KILLS	+INHIBITOR	+KILLS	+NEXUS_TURRET	+NEXUS_TURRET	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	44
7	0091705b03924485	-KILLS	-KILLS	-OUTER_TURRET	-KILLS	-KILLS	-OUTER_TURRET	+DRAGON	-RIFT_HERALD	-OUTER_TURRET	-KILLS	-INNER_TURRET	-DRAGON	-KILLS	-INNER_TURRET	-BARON_NASHOR	-KILLS	-BASE_TURRET	-BASE_TURRET	+INHIBITOR	+INHIBITOR	-KILLS	-NEXUS_TURRET	-NEXUS_TURRET	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	0	27
8	00986b51908a63c3	-KILLS	+KILLS	+KILLS	+KILLS	+KILLS	+KILLS	-OUTER_TURRET	+OUTER_TURRET	+DRAGON	+OUTER_TURRET	-OUTER_TURRET	+INNER_TURRET	+KILLS	+OUTER_TURRET	+INNER_TURRET	+DRAGON	+KILLS	-KILLS	-OUTER_TURRET	+DRAGON	-KILLS	-BARON_NASHOR	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	-KILLS	-KILLS	-ELDER_DRAGON	+KILLS	+BASE_TURRET	-KILLS	-KILLS	+INHIBITOR	-BARON_NASHOR	-INNER_TURRET	+KILLS	+INHIBITOR	+BASE_TURRET	...	+INHIBITOR	+ELDER_DRAGON	+KILLS	-KILLS	-INNER_TURRET	+KILLS	+INHIBITOR	+KILLS	-KILLS	+NEXUS_TURRET	-BARON_NASHOR	-KILLS	-KILLS	-ELDER_DRAGON	-BASE_TURRET	+INHIBITOR	+INHIBITOR	+NEXUS_TURRET	-KILLS	-KILLS	-NEXUS_TURRET	-NEXUS_TURRET	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	0	69
9	00b13dbf1bd7aff0	-KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+DRAGON	-KILLS	+DRAGON	+OUTER_TURRET	-OUTER_TURRET	+OUTER_TURRET	-KILLS	+KILLS	-KILLS	-DRAGON	+KILLS	+BARON_NASHOR	-KILLS	-OUTER_TURRET	-INNER_TURRET	-BASE_TURRET	+DRAGON	-KILLS	+KILLS	+INHIBITOR	-NEXUS_TURRET	-KILLS	-NEXUS_TURRET	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	0	36

In [28]:

RedMatchEvents[['RedEvent1','id']].groupby('RedEvent1').count()

Out[28]:

	id
RedEvent1
+DRAGON	158
+KILLS	1931
+OUTER_TURRET	263
+RIFT_HERALD	7
-DRAGON	108
-KILLS	2136
-OUTER_TURRET	302
-RIFT_HERALD	10

In [29]:

RedMatchEvents[['RedEvent1','MatchLength']].groupby('RedEvent1').mean()

Out[29]:

	MatchLength
RedEvent1
+DRAGON	38.278481
+KILLS	36.599689
+OUTER_TURRET	37.680608
+RIFT_HERALD	39.428571
-DRAGON	37.750000
-KILLS	36.265918
-OUTER_TURRET	38.049669
-RIFT_HERALD	41.500000

In [30]:

sns.boxplot(RedMatchEvents['RedEvent1'],RedMatchEvents['MatchLength'],RedMatchEvents['RedResult'],
            boxprops=dict(alpha=.7) )
plt.xticks(rotation=45)
plt.title('Distribution of Match Length by First Event and Match Result (Win = 1, Loss = 0)')
plt.ylim(0,100)
plt.xlabel('Event 1')
plt.plot([1.5, 1.5], [0, 100],'k', linewidth=2,alpha=0.8 )
plt.plot([3.5, 3.5], [0, 100],'k', linewidth=2,alpha=0.8 )
plt.plot([5.5, 5.5], [0, 100],'k', linewidth=2,alpha=0.8 )
plt.show()

In [31]:

# We can now use this to calculate some conditional probabilities as shown

TestData = RedMatchEvents

PwinGivenFirstBloodWon = ( (len(TestData[(TestData['RedEvent1']=="+KILLS")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="+KILLS"])/len(TestData)) )
    
PwinGivenFirstBloodLost = ( (len(TestData[(TestData['RedEvent1']=="-KILLS")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="-KILLS"])/len(TestData)) )


PwinGivenFirstTowerWon = ( (len(TestData[(TestData['RedEvent1']=="+OUTER_TURRET")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="+OUTER_TURRET"])/len(TestData)) )
    
PwinGivenFirstTowerLost = ( (len(TestData[(TestData['RedEvent1']=="-OUTER_TURRET")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="-OUTER_TURRET"])/len(TestData)) )


PwinGivenFirstDragonWon = ( (len(TestData[(TestData['RedEvent1']=="+DRAGON")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="+DRAGON"])/len(TestData)) )
    
PwinGivenFirstDragonLost = ( (len(TestData[(TestData['RedEvent1']=="-DRAGON")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="-DRAGON"])/len(TestData)) )


PwinGivenFirstRiftHeraldWon = ( (len(TestData[(TestData['RedEvent1']=="+RIFT_HERALD")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="+RIFT_HERALD"])/len(TestData)) )
    
PwinGivenFirstRiftHeraldLost = ( (len(TestData[(TestData['RedEvent1']=="-RIFT_HERALD")&(TestData['RedResult']==1)])/len(TestData))/
        (len( TestData[TestData['RedEvent1']=="-RIFT_HERALD"])/len(TestData)) )





print("-------FIRST BLOOD--------------------------------")
print("P(Won | First Blood Taken):",PwinGivenFirstBloodWon)
print("P(Won | First Blood Lost):",PwinGivenFirstBloodLost)

print("")
print("-------FIRST TURRET-------------------------------")
print("P(Won | First Tower Won):",PwinGivenFirstTowerWon)
print("P(Won | First Tower Lost):",PwinGivenFirstTowerLost)

print("")
print("-------FIRST DRAGON-------------------------------")
print("P(Won | First Dragon Won):",PwinGivenFirstDragonWon)
print("P(Won | First Dragon Lost):",PwinGivenFirstDragonLost)

print("")
print("-------FIRST RIFT HERALD (NOTE: ONLY 17 GAMES)----")
print("P(Won | First Rift Herald Won):",PwinGivenFirstRiftHeraldWon)
print("P(Won | First Rift Herald Lost):",PwinGivenFirstRiftHeraldLost)

-------FIRST BLOOD--------------------------------
P(Won | First Blood Taken): 0.5535991714137752
P(Won | First Blood Lost): 0.3647003745318352

-------FIRST TURRET-------------------------------
P(Won | First Tower Won): 0.4790874524714828
P(Won | First Tower Lost): 0.4470198675496689

-------FIRST DRAGON-------------------------------
P(Won | First Dragon Won): 0.5189873417721519
P(Won | First Dragon Lost): 0.4351851851851851

-------FIRST RIFT HERALD (NOTE: ONLY 17 GAMES)----
P(Won | First Rift Herald Won): 0.5714285714285714
P(Won | First Rift Herald Lost): 0.1

In [32]:

aggs = {'id':'count','MatchLength':'mean'}

RedMatchTWOEvents = (RedMatchEvents[['RedEvent1','RedEvent2','RedResult','id','MatchLength']].groupby(
        ['RedEvent1','RedEvent2','RedResult']).agg(aggs).reset_index())

RedMatchTWOEvents = RedMatchTWOEvents.sort_values(['RedEvent1','RedEvent2','RedResult'])

RedMatchTWOEventsWINS = RedMatchTWOEvents[RedMatchTWOEvents['RedResult']==1]
RedMatchTWOEventsLOSS = RedMatchTWOEvents[RedMatchTWOEvents['RedResult']==0]

In [33]:

# First merge the RedWin and RedLoss data tables
# Then remove events which only resulted in a win then calculate the total number of games that has these two events
# Use this total to calculate the prob of win and loss respectively 

RedMatchTWOEventsMERGED = RedMatchTWOEventsWINS.merge(RedMatchTWOEventsLOSS, how='left',on=['RedEvent1','RedEvent2'])


RedMatchTWOEventsMERGED = RedMatchTWOEventsMERGED[RedMatchTWOEventsMERGED['id_y']>0]
RedMatchTWOEventsMERGED['Total'] = RedMatchTWOEventsMERGED['id_x']+RedMatchTWOEventsMERGED['id_y']

RedMatchTWOEventsMERGED['ProbWIN'] = RedMatchTWOEventsMERGED['id_x']/RedMatchTWOEventsMERGED['Total'].sum()
RedMatchTWOEventsMERGED['ProbLOSS'] = RedMatchTWOEventsMERGED['id_y']/RedMatchTWOEventsMERGED['Total'].sum()

RedMatchTWOEventsMERGED['ProbE1ANDE2'] = RedMatchTWOEventsMERGED['Total']/(RedMatchTWOEventsMERGED['Total'].sum())

RedMatchTWOEventsMERGED['ProbWINgivenE1ANDE2'] = RedMatchTWOEventsMERGED['ProbWIN']/RedMatchTWOEventsMERGED['ProbE1ANDE2']
RedMatchTWOEventsMERGED['ProbLOSSgivenE1ANDE2'] = RedMatchTWOEventsMERGED['ProbLOSS']/RedMatchTWOEventsMERGED['ProbE1ANDE2']

# Create column to single binary digit for whether the first event is positive or negative

RedMatchTWOEventsMERGED['RedEvent1Gain'] = np.where(
                                (RedMatchTWOEventsMERGED['RedEvent1']=="+KILLS") |
                                (RedMatchTWOEventsMERGED['RedEvent1']=="+OUTER_TURRET") |
                                (RedMatchTWOEventsMERGED['RedEvent1']=="+DRAGON") |
                                (RedMatchTWOEventsMERGED['RedEvent1']=="+RIFT_HERALD") ,1,0
                                                   
                                                   
                                                   )
# Repeat for second event

RedMatchTWOEventsMERGED['RedEvent2Gain'] = np.where(
                                (RedMatchTWOEventsMERGED['RedEvent2']=="+KILLS") |
                                (RedMatchTWOEventsMERGED['RedEvent2']=="+OUTER_TURRET") |
                                (RedMatchTWOEventsMERGED['RedEvent2']=="+DRAGON") |
                                (RedMatchTWOEventsMERGED['RedEvent2']=="+RIFT_HERALD") ,1,0
                                                   
                                                   
                                                   )
# Create another column for combination of first and second event outcomes classification
RedMatchTWOEventsMERGED['Event1AND2Outcome'] = np.where(
    (RedMatchTWOEventsMERGED['RedEvent1Gain']==1)&(RedMatchTWOEventsMERGED['RedEvent2Gain']==1),"Both Positive",
                
    np.where(
        (((RedMatchTWOEventsMERGED['RedEvent1Gain']==1)&(RedMatchTWOEventsMERGED['RedEvent2Gain']==0))|
        ((RedMatchTWOEventsMERGED['RedEvent1Gain']==0)&(RedMatchTWOEventsMERGED['RedEvent2Gain']==1))),"One Positive",
    
    np.where(
        (RedMatchTWOEventsMERGED['RedEvent1Gain']==0)&(RedMatchTWOEventsMERGED['RedEvent2Gain']==0),"Neither Positive",
             "MISSING",)))

# Sort by highest probability of win to lowest
RedMatchTWOEventsMERGED = RedMatchTWOEventsMERGED.sort_values('ProbWINgivenE1ANDE2',ascending=False)

# Remove event combination with less than x number of games to remove possible outliers
RedMatchTWOEventsMERGED = RedMatchTWOEventsMERGED[RedMatchTWOEventsMERGED['Total']>=0]


RedMatchTWOEventsMERGED.head(5)

Out[33]:

	RedEvent1	RedEvent2	RedResult_x	id_x	MatchLength_x	RedResult_y	id_y	MatchLength_y	Total	ProbWIN	ProbLOSS	ProbE1ANDE2	ProbWINgivenE1ANDE2	ProbLOSSgivenE1ANDE2	RedEvent1Gain	RedEvent2Gain	Event1AND2Outcome
16	+OUTER_TURRET	+KILLS	1	11	38.181818	0.0	2.0	34.50	13.0	0.002248	0.000409	0.002656	0.846154	0.153846	1	1	Both Positive
9	+KILLS	+RIFT_HERALD	1	4	31.750000	0.0	1.0	33.00	5.0	0.000817	0.000204	0.001022	0.800000	0.200000	1	1	Both Positive
1	+DRAGON	+OUTER_TURRET	1	11	37.636364	0.0	4.0	41.75	15.0	0.002248	0.000817	0.003065	0.733333	0.266667	1	1	Both Positive
21	+RIFT_HERALD	-DRAGON	1	2	36.500000	0.0	1.0	32.00	3.0	0.000409	0.000204	0.000613	0.666667	0.333333	1	0	One Positive
20	+RIFT_HERALD	+KILLS	1	2	36.000000	0.0	1.0	33.00	3.0	0.000409	0.000204	0.000613	0.666667	0.333333	1	1	Both Positive

In [34]:

sns.pairplot(data = RedMatchTWOEventsMERGED, x_vars='ProbWINgivenE1ANDE2',y_vars='MatchLength_x',
           hue= 'Event1AND2Outcome', size=8)
plt.title('Probability of Winning Given the First Two Events against Average Game Duration, \n Coloured by Event 1 and 2 Outcomes')
plt.xlabel('Probability of Win GIVEN First Two Events')
plt.ylabel('Average Game Length')
plt.xlim([0,1])
plt.xticks(np.arange(0,1.1,0.1))
#plt.ylim([20,50])

plt.show()

Markov Decision Process (MDP)

We could calculate the conditional probabilities for more events but, as had already become a challenge, the calculation process would be increasingly complicated. Therefore, instead of this, we can model our data as an MDP where we create pairwise probabilities between the events. Each event stage is a state and we calculate the probability of going to the next state given we are in the current one at that event stage.

In [35]:

RedMatchEvents.head()

Out[35]:

	id	RedEvent1	RedEvent2	RedEvent3	RedEvent4	RedEvent5	RedEvent6	RedEvent7	RedEvent8	RedEvent9	RedEvent10	RedEvent11	RedEvent12	RedEvent13	RedEvent14	RedEvent15	RedEvent16	RedEvent17	RedEvent18	RedEvent19	RedEvent20	RedEvent21	RedEvent22	RedEvent23	RedEvent24	RedEvent25	RedEvent26	RedEvent27	RedEvent28	RedEvent29	RedEvent30	RedEvent31	RedEvent32	RedEvent33	RedEvent34	RedEvent35	RedEvent36	RedEvent37	RedEvent38	RedEvent39	...	RedEvent42	RedEvent43	RedEvent44	RedEvent45	RedEvent46	RedEvent47	RedEvent48	RedEvent49	RedEvent50	RedEvent51	RedEvent52	RedEvent53	RedEvent54	RedEvent55	RedEvent56	RedEvent57	RedEvent58	RedEvent59	RedEvent60	RedEvent61	RedEvent62	RedEvent63	RedEvent64	RedEvent65	RedEvent66	RedEvent67	RedEvent68	RedEvent69	RedEvent70	RedEvent71	RedEvent72	RedEvent73	RedEvent74	RedEvent75	RedEvent76	RedEvent77	RedEvent78	RedEvent79	RedResult	MatchLength
0	0001f4374a03c133	+KILLS	+KILLS	-KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+DRAGON	+RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+DRAGON	+KILLS	-KILLS	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+BARON_NASHOR	+DRAGON	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	+DRAGON	-KILLS	+KILLS	+KILLS	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	34
1	0016710a48fdd46d	-KILLS	+KILLS	+DRAGON	+KILLS	-KILLS	-OUTER_TURRET	+KILLS	-DRAGON	-KILLS	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-OUTER_TURRET	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	-KILLS	+KILLS	-DRAGON	+KILLS	+BARON_NASHOR	+KILLS	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	-KILLS	+KILLS	+BASE_TURRET	-KILLS	+INHIBITOR	...	+KILLS	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	-KILLS	-DRAGON	+KILLS	+INHIBITOR	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	40
2	0016c9df37278448	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-KILLS	-RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	+KILLS	-DRAGON	-KILLS	-OUTER_TURRET	+KILLS	+BARON_NASHOR	+OUTER_TURRET	+DRAGON	+KILLS	+OUTER_TURRET	+INNER_TURRET	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+INNER_TURRET	+BASE_TURRET	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	+KILLS	+INHIBITOR	-nan	-nan	-nan	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	40
3	0021b45647424cd5	-KILLS	+KILLS	+KILLS	+KILLS	-KILLS	+DRAGON	+RIFT_HERALD	-KILLS	+OUTER_TURRET	-KILLS	+OUTER_TURRET	-KILLS	+DRAGON	+KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+BARON_NASHOR	-KILLS	+DRAGON	+INNER_TURRET	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+NEXUS_TURRET	+BARON_NASHOR	+INNER_TURRET	-KILLS	+DRAGON	+INHIBITOR	+BASE_TURRET	+INHIBITOR	-KILLS	-BARON_NASHOR	+KILLS	...	+NEXUS_TURRET	-KILLS	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	42
4	00405293fb859241	+KILLS	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	+OUTER_TURRET	-DRAGON	-KILLS	-OUTER_TURRET	-KILLS	-KILLS	-DRAGON	-OUTER_TURRET	+KILLS	-KILLS	-DRAGON	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	+DRAGON	+BARON_NASHOR	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+KILLS	+INNER_TURRET	+KILLS	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+INNER_TURRET	+NEXUS_TURRET	+NEXUS_TURRET	+KILLS	-nan	...	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	1	39

In [36]:

# WARNING: Takes a while to run
# Replace all N/As with the match outcome so that our final state is either a Win or Loss
for i in range(1,80):
    RedMatchEvents['RedEvent'+str(i)] = RedMatchEvents['RedEvent'+str(i)].replace('-nan',RedMatchEvents['RedResult'].astype(str))
    RedMatchEvents['RedEvent'+str(i)] = RedMatchEvents['RedEvent'+str(i)].replace('+nan',RedMatchEvents['RedResult'].astype(str))
    #Print i for progress tracking
    #print(i)
RedMatchEvents.head()

Out[36]:

	id	RedEvent1	RedEvent2	RedEvent3	RedEvent4	RedEvent5	RedEvent6	RedEvent7	RedEvent8	RedEvent9	RedEvent10	RedEvent11	RedEvent12	RedEvent13	RedEvent14	RedEvent15	RedEvent16	RedEvent17	RedEvent18	RedEvent19	RedEvent20	RedEvent21	RedEvent22	RedEvent23	RedEvent24	RedEvent25	RedEvent26	RedEvent27	RedEvent28	RedEvent29	RedEvent30	RedEvent31	RedEvent32	RedEvent33	RedEvent34	RedEvent35	RedEvent36	RedEvent37	RedEvent38	RedEvent39	...	RedEvent42	RedEvent43	RedEvent44	RedEvent45	RedEvent46	RedEvent47	RedEvent48	RedEvent49	RedEvent50	RedEvent51	RedEvent52	RedEvent53	RedEvent54	RedEvent55	RedEvent56	RedEvent57	RedEvent58	RedEvent59	RedEvent60	RedEvent61	RedEvent62	RedEvent63	RedEvent64	RedEvent65	RedEvent66	RedEvent67	RedEvent68	RedEvent69	RedEvent70	RedEvent71	RedEvent72	RedEvent73	RedEvent74	RedEvent75	RedEvent76	RedEvent77	RedEvent78	RedEvent79	RedResult	MatchLength
0	0001f4374a03c133	+KILLS	+KILLS	-KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+DRAGON	+RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+DRAGON	+KILLS	-KILLS	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+BARON_NASHOR	+DRAGON	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	+DRAGON	-KILLS	+KILLS	+KILLS	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	1	1	1	1	1	1	1	1	...	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	34
1	0016710a48fdd46d	-KILLS	+KILLS	+DRAGON	+KILLS	-KILLS	-OUTER_TURRET	+KILLS	-DRAGON	-KILLS	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-OUTER_TURRET	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	+OUTER_TURRET	-KILLS	+KILLS	-KILLS	+KILLS	-DRAGON	+KILLS	+BARON_NASHOR	+KILLS	+INNER_TURRET	+INNER_TURRET	+INNER_TURRET	-KILLS	+KILLS	+BASE_TURRET	-KILLS	+INHIBITOR	...	+KILLS	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	-KILLS	-DRAGON	+KILLS	+INHIBITOR	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	40
2	0016c9df37278448	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	-DRAGON	-KILLS	+KILLS	-KILLS	-RIFT_HERALD	+OUTER_TURRET	-OUTER_TURRET	-DRAGON	+KILLS	-DRAGON	-KILLS	-OUTER_TURRET	+KILLS	+BARON_NASHOR	+OUTER_TURRET	+DRAGON	+KILLS	+OUTER_TURRET	+INNER_TURRET	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+INNER_TURRET	+BASE_TURRET	+BASE_TURRET	+INHIBITOR	+NEXUS_TURRET	+NEXUS_TURRET	-KILLS	+KILLS	+INHIBITOR	1	1	1	1	...	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	40
3	0021b45647424cd5	-KILLS	+KILLS	+KILLS	+KILLS	-KILLS	+DRAGON	+RIFT_HERALD	-KILLS	+OUTER_TURRET	-KILLS	+OUTER_TURRET	-KILLS	+DRAGON	+KILLS	+KILLS	+OUTER_TURRET	-OUTER_TURRET	+KILLS	+BARON_NASHOR	-KILLS	+DRAGON	+INNER_TURRET	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+NEXUS_TURRET	+BARON_NASHOR	+INNER_TURRET	-KILLS	+DRAGON	+INHIBITOR	+BASE_TURRET	+INHIBITOR	-KILLS	-BARON_NASHOR	+KILLS	...	+NEXUS_TURRET	-KILLS	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	42
4	00405293fb859241	+KILLS	-KILLS	-KILLS	-KILLS	-OUTER_TURRET	+OUTER_TURRET	-DRAGON	-KILLS	-OUTER_TURRET	-KILLS	-KILLS	-DRAGON	-OUTER_TURRET	+KILLS	-KILLS	-DRAGON	+OUTER_TURRET	+KILLS	+KILLS	-KILLS	+OUTER_TURRET	+DRAGON	+BARON_NASHOR	+KILLS	+INNER_TURRET	+BASE_TURRET	+INHIBITOR	+KILLS	+INNER_TURRET	+KILLS	+BASE_TURRET	+INHIBITOR	-KILLS	+KILLS	+INNER_TURRET	+NEXUS_TURRET	+NEXUS_TURRET	+KILLS	1	...	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	39

In [37]:

RedMatchEvents[['RedEvent60','id']].groupby('RedEvent60').count()

Out[37]:

	id
RedEvent60
+BARON_NASHOR	4
+BASE_TURRET	2
+ELDER_DRAGON	1
+INHIBITOR	12
+INNER_TURRET	2
+KILLS	7
+NEXUS_TURRET	5
-BARON_NASHOR	1
-BASE_TURRET	3
-ELDER_DRAGON	2
-KILLS	19
-NEXUS_TURRET	12
0	2629
1	2216

In [38]:

RedMatchEvents2 = RedMatchEvents

In [39]:

# WARNING: Takes a little while to run

EventList = [
    #Positive Events
       '+KILLS', '+OUTER_TURRET', '+DRAGON', '+RIFT_HERALD', '+BARON_NASHOR',
       '+INNER_TURRET', '+BASE_TURRET', '+INHIBITOR', '+NEXUS_TURRET',
       '+ELDER_DRAGON',
    #Negative Events
       '-KILLS', '-OUTER_TURRET', '-DRAGON', '-RIFT_HERALD', '-BARON_NASHOR',
       '-INNER_TURRET', '-BASE_TURRET', '-INHIBITOR', '-NEXUS_TURRET',
       '-ELDER_DRAGON',
    #Game Win or Loss Events        
       '1','0']

RedMatchMDP = pd.DataFrame()

for i in range(1,79):
                              
    Event = i
    for j1 in range(0,len(EventList)):
        Event1 = EventList[j1]
        for j2 in range(0,len(EventList)):
            
            Event2 = EventList[j2]
            
            
            if  len(RedMatchEvents2[(RedMatchEvents2['RedEvent'+str(Event)]==Event1)])==0:
                continue
            #elif len(RedMatchEvents2[(RedMatchEvents2['RedEvent'+str(Event)]==Event1)&
            #                   (RedMatchEvents2['RedEvent'+str(Event+1)]==Event2) ])==0:
                continue
                
            else:
                TransProb = (
                    len(RedMatchEvents2[(RedMatchEvents2['RedEvent'+str(Event)]==Event1)&
                               (RedMatchEvents2['RedEvent'+str(Event+1)]==Event2) ])/

                    len(RedMatchEvents2[(RedMatchEvents2['RedEvent'+str(Event)]==Event1)])
                    )


            RedMatchMDP2 = pd.DataFrame({'StartState':Event,'EndState':Event+1,'Event1':Event1,'Event2':Event2,'Probability':TransProb},
                                  index=[0])
            RedMatchMDP = RedMatchMDP.append(RedMatchMDP2)
   
    #Print i for tracking progress
    #print(i)
    

In [40]:

RedMatchMDP = RedMatchMDP[['StartState','EndState','Event1','Event2','Probability']]
RedMatchMDP[(RedMatchMDP['StartState']==61)&(RedMatchMDP['Event1']=="+INHIBITOR")]

Out[40]:

	StartState	EndState	Event1	Event2	Probability
0	61	62	+INHIBITOR	+KILLS	0.076923
0	61	62	+INHIBITOR	+OUTER_TURRET	0.000000
0	61	62	+INHIBITOR	+DRAGON	0.000000
0	61	62	+INHIBITOR	+RIFT_HERALD	0.000000
0	61	62	+INHIBITOR	+BARON_NASHOR	0.153846
0	61	62	+INHIBITOR	+INNER_TURRET	0.076923
0	61	62	+INHIBITOR	+BASE_TURRET	0.000000
0	61	62	+INHIBITOR	+INHIBITOR	0.076923
0	61	62	+INHIBITOR	+NEXUS_TURRET	0.153846
0	61	62	+INHIBITOR	+ELDER_DRAGON	0.000000
0	61	62	+INHIBITOR	-KILLS	0.076923
0	61	62	+INHIBITOR	-OUTER_TURRET	0.000000
0	61	62	+INHIBITOR	-DRAGON	0.000000
0	61	62	+INHIBITOR	-RIFT_HERALD	0.000000
0	61	62	+INHIBITOR	-BARON_NASHOR	0.153846
0	61	62	+INHIBITOR	-INNER_TURRET	0.000000
0	61	62	+INHIBITOR	-BASE_TURRET	0.000000
0	61	62	+INHIBITOR	-INHIBITOR	0.000000
0	61	62	+INHIBITOR	-NEXUS_TURRET	0.230769
0	61	62	+INHIBITOR	-ELDER_DRAGON	0.000000
0	61	62	+INHIBITOR	1	0.000000
0	61	62	+INHIBITOR	0	0.000000

In [41]:

EndCondition = RedMatchMDP[
    ((RedMatchMDP['Event1']!="1")&(RedMatchMDP['Event2']=="1") )|
    ((RedMatchMDP['Event1']!="0")&(RedMatchMDP['Event2']=="0"))]

EndCondition = EndCondition.sort_values('Probability',ascending=False)

EndConditionGrouped = EndCondition[['StartState','Probability']].groupby('StartState').mean().reset_index()
EndConditionGrouped['CumProb'] = EndConditionGrouped['Probability'].cumsum()

EndConditionGrouped2 = EndCondition[['StartState','Probability']].groupby('StartState').sum().reset_index()
EndConditionGrouped2['CumProb'] = EndConditionGrouped2['Probability'].cumsum()

fig, axes = plt.subplots(nrows=2, ncols=2)

axes[0,0].bar(EndConditionGrouped['StartState'],EndConditionGrouped['Probability'] ,alpha=0.3)
axes[0,0].plot(EndConditionGrouped['StartState'],EndConditionGrouped['Probability'])
axes[0,0].set_title('Mean Probability Dist')
axes[0,0].set_xlabel("State")
axes[0,0].set_ylabel("Probability of Ending")
axes[0,0].set_xticks([],[])
axes[0,0].set_xlabel("")
axes[0,0].set_xlim([0,80])
axes[0,0].grid(False)

axes[0,1].bar(EndConditionGrouped['StartState'],EndConditionGrouped['CumProb'] ,alpha=0.3)
axes[0,1].plot(EndConditionGrouped['StartState'],EndConditionGrouped['CumProb'])
axes[0,1].set_title('Mean Cumulative Probability Dist')
axes[0,1].set_xlabel("State")
axes[0,1].set_ylabel("Cumlative Probability of Ending")
axes[0,1].set_xticks([])
axes[0,1].set_xlabel("")
axes[0,1].set_xlim([0,80])
axes[0,1].grid(False)

axes[1,0].bar(EndConditionGrouped2['StartState'],EndConditionGrouped2['Probability'] ,alpha=0.3)
axes[1,0].plot(EndConditionGrouped2['StartState'],EndConditionGrouped2['Probability'])
axes[1,0].set_title('Sum Probability Dist')
axes[1,0].set_xlabel("State")
axes[1,0].set_ylabel("Probability of Ending")
axes[1,0].set_xlim([0,80])
axes[1,0].grid(False)

axes[1,1].bar(EndConditionGrouped2['StartState'],EndConditionGrouped2['CumProb'] ,alpha=0.3)
axes[1,1].plot(EndConditionGrouped2['StartState'],EndConditionGrouped2['CumProb'])
axes[1,1].set_title('Sum Cumulative Probability Dist')
axes[1,1].set_xlabel("State")
axes[1,1].set_ylabel("Cumlative Probability of Ending")
axes[1,1].set_xlim([0,80])
axes[1,1].grid(False)

fig.suptitle("Probability of Game Ending in Each State Averaged and Summed over Varying Start Events")

fig.set_figheight(15)
fig.set_figwidth(15)
plt.show()

In [42]:

RedMatchMDP['Reward'] = 0

RedMatchMDP.head()

Out[42]:

	StartState	EndState	Event1	Event2	Probability	Reward
0	1	2	+KILLS	+KILLS	0.350596	0
0	1	2	+KILLS	+OUTER_TURRET	0.058519	0
0	1	2	+KILLS	+DRAGON	0.076126	0
0	1	2	+KILLS	+RIFT_HERALD	0.002589	0
0	1	2	+KILLS	+BARON_NASHOR	0.000000	0

In [43]:

len(RedMatchMDP)

Out[43]:

25564

In [44]:

RedMatchMDP[(RedMatchMDP['StartState']==15)&(RedMatchMDP['Event1']=="+ELDER_DRAGON")]

Out[44]:

	StartState	EndState	Event1	Event2	Probability	Reward
0	15	16	+ELDER_DRAGON	+KILLS	0.5	0
0	15	16	+ELDER_DRAGON	+OUTER_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	+DRAGON	0.0	0
0	15	16	+ELDER_DRAGON	+RIFT_HERALD	0.0	0
0	15	16	+ELDER_DRAGON	+BARON_NASHOR	0.0	0
0	15	16	+ELDER_DRAGON	+INNER_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	+BASE_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	+INHIBITOR	0.0	0
0	15	16	+ELDER_DRAGON	+NEXUS_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	+ELDER_DRAGON	0.0	0
0	15	16	+ELDER_DRAGON	-KILLS	0.5	0
0	15	16	+ELDER_DRAGON	-OUTER_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	-DRAGON	0.0	0
0	15	16	+ELDER_DRAGON	-RIFT_HERALD	0.0	0
0	15	16	+ELDER_DRAGON	-BARON_NASHOR	0.0	0
0	15	16	+ELDER_DRAGON	-INNER_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	-BASE_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	-INHIBITOR	0.0	0
0	15	16	+ELDER_DRAGON	-NEXUS_TURRET	0.0	0
0	15	16	+ELDER_DRAGON	-ELDER_DRAGON	0.0	0
0	15	16	+ELDER_DRAGON	1	0.0	0
0	15	16	+ELDER_DRAGON	0	0.0	0

Reinforcement Learning AI Model

Now that we have our data modelled as an MDP, we can apply Reinforcement Learning. In short, this applied a model that simulates thousands of games and learns how good or bad each decision is towards reaching a win given the team’s current position.

What makes this AI is its ability to learn from its own trial and error experience. It starts with zero knowledge about the game but, as it is rewarded for reaching a win and punished for reaching a loss, it begins to recognise and remember which decisions are better than others. Our first models start with no knowledge but I later demonstrate the impact initial information about decisions can be fed into the model to represent a person’s preferences.

So how is the model learning? In short, we use Monte Carlo learning whereby each episode is a simulation of a game based on our MDP probabilities and depending on the outcome for the team, our return will vary (+1 terminal reward for win and -1 terminal reward for loss). The value of each action taken in this episode is then updated accordingly based on whether the outcome was a win or loss.

In Monte Carlo learning, we have a parameter 'gamma' that discounts the rewards and will give a higher value to immediate steps than later one. In our model, this can be understood by the fact that as we reach later stages of the games, the decisions we make will have a much larger impact on the final outcome than those made in the first few minutes. For example, losing a team fight in minute 50 is much more likely to lead to a loss than losing a team fight in the first 5 minutes.

In [45]:

alpha = 0.1
gamma = 0.9
num_episodes = 100
epsilon = 0.1

reward = RedMatchMDP['Reward']

StartState = 1
StartEvent = '+KILLS'
StartAction = '+OUTER_TURRET'

In [46]:

def MCModelv1(data, alpha, gamma, epsilon, reward, StartState, StartEvent, StartAction, num_episodes):
    
    # Initiatise variables appropiately
    
    data['V'] = 0
 
    
    outcomes = pd.DataFrame()
    episode_return = pd.DataFrame()
    actions_output = pd.DataFrame()
    
    for e in range(0,num_episodes):
        
        action = []

        current_state = StartState
        current_action = StartEvent
        next_action = StartAction 
   
        actions = pd.DataFrame()
 
        for a in range(0,100):
            
            action_table = pd.DataFrame()

            
            if (current_action=="1") | (current_action=="0") | (current_state==79):
                continue
            else:
                
                data_e = data[(data['StartState']==current_state)&(data['Event1']==current_action)]

                data_e = data_e.sort_values('Probability')
                data_e['CumProb'] = data_e['Probability'].cumsum()
                data_e['CumProb'] = np.round(data_e['CumProb'],4)

                
                rng = np.round(np.random.random()*data_e['CumProb'].max(),4)
                action_table = data_e[ data_e['CumProb'] >= rng]
                action_table = action_table[ action_table['CumProb'] == action_table['CumProb'].min()]
                action_table = action_table.reset_index()
                
                action = action_table['Event2'][0]
                
                if action == "1":
                    step_reward = 10*(gamma**a)
                elif action == "0":
                    step_reward = -10*(gamma**a)
                else:
                    step_reward = -0.005*(gamma**a)
                
                action_table['StepReward'] = step_reward
                

                action_table['Episode'] = e
                action_table['Action'] = a
                
                current_action = action
                current_state = current_state+1
                
                
                actions = actions.append(action_table)

        actions_output = actions_output.append(actions)
                
        episode_return = actions['StepReward'].sum()

                
        actions['Return']= episode_return
                
        data = data.merge(actions[['StartState','EndState','Event1','Event2','Return']], how='left',on =['StartState','EndState','Event1','Event2'])
        data['Return'] = data['Return'].fillna(0)    
             
        data['V'] = data['V'] + alpha*(data['Return']-data['V'])
        data = data.drop('Return', 1)
        
        
                
        if current_action=="1":
            outcome = "WIN"
        elif current_action=="0":
            outcome = "LOSS"
        else:
            outcome = "INCOMPLETE"
        outcome = pd.DataFrame({'Epsiode':[e],'Outcome':[outcome]})
        outcomes = outcomes.append(outcome)

        
        

        
   
        
    
        
    optimal_policy_table = data[ ( data['StartState']==StartState) & (data['Event1']==StartEvent)&(data['Event2']==StartAction)]
     
    for i in range(2,79):
        optimal_V = data[data['StartState']==i]['V'].max()
        optimal_policy = data[ ( data['V']==optimal_V) & (data['StartState']==i)]      
        optimal_policy_table = optimal_policy_table.append(optimal_policy)
                
    return(outcomes,actions_output,data,optimal_policy_table)
    

In [47]:

start_time = timeit.default_timer()


Mdl = MCModelv1(data=RedMatchMDP, alpha = alpha, gamma=gamma, epsilon = epsilon, reward = reward,
                StartState=StartState, StartEvent=StartEvent,StartAction=StartAction,
                num_episodes = num_episodes)

elapsed = timeit.default_timer() - start_time

print("Time taken to run model:",np.round(elapsed/60,2),"mins")

Time taken to run model: 0.65 mins

In [48]:

Mdl[3].head()

Out[48]:

	StartState	EndState	Event1	Event2	Probability	Reward	V
1	1	2	+KILLS	+OUTER_TURRET	0.058519	0	-0.000142
286	2	3	-KILLS	+KILLS	0.405299	0	0.055403
406	3	4	+KILLS	-KILLS	0.380066	0	0.027542
748	4	5	-KILLS	+KILLS	0.345982	0	0.062849
861	5	6	+KILLS	+RIFT_HERALD	0.012048	0	0.038553

RL Model V2

This is a good start but our first model requires the first action to be provided. Instead, we now repeat the process but enable it to calculate the optimal first action when none is given.

In [49]:

def MCModelv2(data, alpha, gamma, epsilon, reward, StartState, StartEvent, StartAction, num_episodes):
    
    # Initiatise variables appropiately
    
    data['V'] = 0
 
    
    outcomes = pd.DataFrame()
    episode_return = pd.DataFrame()
    actions_output = pd.DataFrame()
    
    for e in range(0,num_episodes):
        action = []

        current_state = StartState
        current_action = StartEvent
         
        
      
            
            
        actions = pd.DataFrame()
 
        for a in range(0,100):
            
            action_table = pd.DataFrame()

            
            if (current_action=="1") | (current_action=="0") | (current_state==79):
                continue
            else:
                
                data_e = data[(data['StartState']==current_state)&(data['Event1']==current_action)]

                data_e = data_e[data_e['Probability']>0]

                
                if (StartAction is None)&(a==0):
                    random_first_action = data_e.sample()
                    action_table = random_first_action
                    action_table = action_table.reset_index()
                    action = action_table['Event2'][0]
                elif (a==0):
                    action_table = data_e[ data_e['Event2'] ==StartAction]
                    action = StartAction
                else:
                    data_e = data_e.sort_values('Probability')
                    data_e['CumProb'] = data_e['Probability'].cumsum()
                    data_e['CumProb'] = np.round(data_e['CumProb'],4)
                    rng = np.round(np.random.random()*data_e['CumProb'].max(),4)
                    action_table = data_e[ data_e['CumProb'] >= rng]
                    action_table = action_table[ action_table['CumProb'] == action_table['CumProb'].min()]
                    action_table = action_table.reset_index()

                    action = action_table['Event2'][0]
                if action == "1":
                    step_reward = 10*(gamma**a)
                elif action == "0":
                    step_reward = -10*(gamma**a)
                else:
                    step_reward = -0.005*(gamma**a)

                action_table['StepReward'] = step_reward


                action_table['Episode'] = e
                action_table['Action'] = a

                current_action = action
                current_state = current_state+1


                actions = actions.append(action_table)

        actions_output = actions_output.append(actions)
                
        episode_return = actions['StepReward'].sum()

                
        actions['Return']= episode_return
                
        data = data.merge(actions[['StartState','EndState','Event1','Event2','Return']], how='left',on =['StartState','EndState','Event1','Event2'])
        data['Return'] = data['Return'].fillna(0)    
             
        data['V'] = data['V'] + alpha*(data['Return']-data['V'])
        data = data.drop('Return', 1)
        
        
                
        if current_action=="1":
            outcome = "WIN"
        elif current_action=="0":
            outcome = "LOSS"
        else:
            outcome = "INCOMPLETE"
        outcome = pd.DataFrame({'Epsiode':[e],'Outcome':[outcome]})
        outcomes = outcomes.append(outcome)

        
        

        
   
        
    
        if StartAction is None:
            optimal_policy_table = pd.DataFrame()
            for i in range(1,79):
                optimal_V = data[data['StartState']==i]['V'].max()
                optimal_policy = data[ ( data['V']==optimal_V) & (data['StartState']==i)]      
                optimal_policy_table = optimal_policy_table.append(optimal_policy)        
        else:
            optimal_policy_table = data[ ( data['StartState']==StartState) & (data['Event1']==StartEvent)&(data['Event2']==StartAction)]
            for i in range(2,79):
                optimal_V = data[data['StartState']==i]['V'].max()
                optimal_policy = data[ ( data['V']==optimal_V) & (data['StartState']==i)]      
                optimal_policy_table = optimal_policy_table.append(optimal_policy)

    return(outcomes,actions_output,data,optimal_policy_table)
    

In [50]:

alpha = 0.1
gamma = 0.9
num_episodes = 100
epsilon = 0.1

reward = RedMatchMDP['Reward']

StartState = 1
StartEvent = '+KILLS'
StartAction = None


start_time = timeit.default_timer()


Mdl2 = MCModelv2(data=RedMatchMDP, alpha = alpha, gamma=gamma, epsilon = epsilon, reward = reward,
                StartState=StartState, StartEvent=StartEvent,StartAction=None,
                num_episodes = num_episodes)

elapsed = timeit.default_timer() - start_time

print("Time taken to run model:",np.round(elapsed/60,2),"mins")

Time taken to run model: 1.24 mins

In [51]:

Mdl2[3].head(30)

Out[51]:

	StartState	EndState	Event1	Event2	Probability	Reward	V
11	1	2	+KILLS	-OUTER_TURRET	0.034697	0	0.059365
309	2	3	-OUTER_TURRET	+OUTER_TURRET	0.300847	0	0.056334
430	3	4	+OUTER_TURRET	-DRAGON	0.074447	0	0.055783
793	4	5	-DRAGON	+OUTER_TURRET	0.152104	0	0.055781
891	5	6	+OUTER_TURRET	-OUTER_TURRET	0.261941	0	0.055770
1288	6	7	-OUTER_TURRET	-DRAGON	0.110092	0	0.055765
1606	7	8	-DRAGON	+KILLS	0.265672	0	0.056417
1720	8	9	+KILLS	+BARON_NASHOR	0.005859	0	0.055783
2144	9	10	+BARON_NASHOR	-KILLS	0.312500	0	0.055783
2398	10	11	+OUTER_TURRET	+KILLS	0.185980	0	0.059142
2706	11	12	+KILLS	+KILLS	0.118577	0	0.058965
3244	12	13	-OUTER_TURRET	-KILLS	0.227920	0	0.055783
3596	13	14	-KILLS	-KILLS	0.121409	0	0.054589
3975	14	15	-KILLS	-INNER_TURRET	0.138376	0	0.074098
4168	15	16	+KILLS	-KILLS	0.297481	0	0.056211
4877	16	17	-DRAGON	-INNER_TURRET	0.158576	0	0.055783
5356	17	18	-INNER_TURRET	-KILLS	0.236324	0	0.055783
5698	18	19	-KILLS	+KILLS	0.266546	0	0.057560
5940	19	20	+KILLS	+KILLS	0.128205	0	0.058518
6414	20	21	+KILLS	-DRAGON	0.037569	0	0.055783
7128	21	22	-DRAGON	+KILLS	0.235741	0	0.056081
7346	22	23	+KILLS	1	0.002304	0	0.056324
7795	23	24	+KILLS	+INHIBITOR	0.049818	0	0.033658
8384	24	25	+INHIBITOR	+DRAGON	0.037037	0	0.035062
8717	25	26	+DRAGON	+INNER_TURRET	0.254777	0	0.035054
9196	26	27	+INNER_TURRET	+KILLS	0.230303	0	0.035203
9534	27	28	+KILLS	+NEXUS_TURRET	0.071124	0	0.035062
10162	28	29	+NEXUS_TURRET	1	0.280612	0	0.035062
10721	29	30	-BASE_TURRET	+INHIBITOR	0.576923	0	0.024197
10965	30	31	+INHIBITOR	+ELDER_DRAGON	0.016129	0	0.023902

RL Model V3

It quickly became apparent that our model was not following the structure of the game correctly because we had set no limitations on the number of turrets available to destroy on either team.

Therefore, it was taking more objectives than possible and so we now introduce a rule that removes the turrets, rift heralds and inhibitors after so many are taken by one team.

In [52]:

def MCModelv3(data, alpha, gamma, epsilon, reward, StartState, StartEvent, StartAction, num_episodes):
    
    # Initiatise variables appropiately
    
    data['V'] = 0
    data_output = data
    
    outcomes = pd.DataFrame()
    episode_return = pd.DataFrame()
    actions_output = pd.DataFrame()
    
    for e in range(0,num_episodes):
        action = []

        current_state = StartState
        current_action = StartEvent
        
        
        data_e1 = data
    
    
        actions = pd.DataFrame()

        for a in range(0,100):
            
            action_table = pd.DataFrame()
       
           
            if (current_action=="1") | (current_action=="0") | (current_state==79):
                continue
            else:
                if a==0:
                    data_e1=data_e1
                    
                elif (len(individual_actions_count[individual_actions_count['Event2']=="+RIFT_HERALD"])==1):
                    data_e1_e1 = data_e1[(data_e1['Event2']!='+RIFT_HERALD')|(data_e1['Event2']!='-RIFT_HERALD')]
                    
                elif (len(individual_actions_count[individual_actions_count['Event2']=="-RIFT_HERALD"])==1):
                    data_e1 = data_e1[(data_e1['Event2']!='+RIFT_HERALD')|(data_e1['Event2']!='-RIFT_HERALD')]
                
                elif (len(individual_actions_count[individual_actions_count['Event2']=="+OUTER_TURRET"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='+OUTER_TURRET']
                elif (len(individual_actions_count[individual_actions_count['Event2']=="-OUTER_TURRET"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='-OUTER_TURRET']
                    
                elif (len(individual_actions_count[individual_actions_count['Event2']=="+INNER_TURRET"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='+INNER_TURRET']
                elif (len(individual_actions_count[individual_actions_count['Event2']=="-INNER_TURRET"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='-INNER_TURRET']
                    
                elif (len(individual_actions_count[individual_actions_count['Event2']=="+BASE_TURRET"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='+BASE_TURRET']
                elif (len(individual_actions_count[individual_actions_count['Event2']=="-BASE_TURRET"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='-BASE_TURRET']
                    
                elif (len(individual_actions_count[individual_actions_count['Event2']=="+INHIBITOR"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='+INHIBITOR']
                elif (len(individual_actions_count[individual_actions_count['Event2']=="-INHIBITOR"])==3):
                    data_e1 = data_e1[data_e1['Event2']!='-INHIBITOR']
                    
                elif (len(individual_actions_count[individual_actions_count['Event2']=="+NEXUS_TURRET"])==2):
                    data_e1 = data_e1[data_e1['Event2']!='+NEXUS_TURRET']
                elif (len(individual_actions_count[individual_actions_count['Event2']=="-NEXUS_TURRET"])==2):
                    data_e1 = data_e1[data_e1['Event2']!='-NEXUS_TURRET']
                
                       
                else:
                    data_e1 = data_e1

                
                data_e = data_e1[(data_e1['StartState']==current_state)&(data_e1['Event1']==current_action)]
                
                data_e = data_e[data_e['Probability']>0]
                
                if (StartAction is None)&(a==0):
                    random_first_action = data_e.sample()
                    action_table = random_first_action
                    action_table = action_table.reset_index()
                    action = action_table['Event2'][0]
                elif (a==0):
                    action_table = data_e[ data_e['Event2'] ==StartAction]
                    action = StartAction
                else:
                    data_e = data_e.sort_values('Probability')
                    data_e['CumProb'] = data_e['Probability'].cumsum()
                    data_e['CumProb'] = np.round(data_e['CumProb'],4)
                    

                    rng = np.round(np.random.random()*data_e['CumProb'].max(),4)
                    action_table = data_e[ data_e['CumProb'] >= rng]
                    action_table = action_table[ action_table['CumProb'] == action_table['CumProb'].min()]
                    action_table = action_table.reset_index()

                    action = action_table['Event2'][0]
                if action == "1":
                    step_reward = 10*(gamma**a)
                elif action == "0":
                    step_reward = -10*(gamma**a)
                else:
                    step_reward = -0.005*(gamma**a)

                action_table['StepReward'] = step_reward


                action_table['Episode'] = e
                action_table['Action'] = a

                current_action = action
                current_state = current_state+1

                
                actions = actions.append(action_table)
                
                individual_actions_count = actions
            

        actions_output = actions_output.append(actions)
                
        episode_return = actions['StepReward'].sum()

                
        actions['Return']= episode_return
                
        data_output = data_output.merge(actions[['StartState','EndState','Event1','Event2','Return']], how='left',on =['StartState','EndState','Event1','Event2'])
        data_output['Return'] = data_output['Return'].fillna(0)    
             
        data_output['V'] = data_output['V'] + alpha*(data_output['Return']-data_output['V'])
        data_output = data_output.drop('Return', 1)
        
        
                
        if current_action=="1":
            outcome = "WIN"
        elif current_action=="0":
            outcome = "LOSS"
        else:
            outcome = "INCOMPLETE"
        outcome = pd.DataFrame({'Epsiode':[e],'Outcome':[outcome]})
        outcomes = outcomes.append(outcome)

        
        

        optimal_policy_table = pd.DataFrame()
   
        
        if (StartAction is None):
            
            optimal_policy_table =    data_output[ (data_output['StartState']==StartState)&(data_output['Event1']==StartEvent) &
                (data_output['V']==(data_output[(data_output['StartState']==StartState)&(data_output['Event1']==StartEvent)]['V'].max()))  ]
            for i in range(2,79):
                optimal_V = data_output[(data_output['StartState']==i)]['V'].max()
                optimal_policy = data_output[ ( data_output['V']==optimal_V) & (data_output['StartState']==i)]      
                optimal_policy_table = optimal_policy_table.append(optimal_policy)        
        else:
            optimal_policy_table = data_output[ ( data_output['StartState']==StartState) & (data_output['Event1']==StartEvent)&(data_output['Event2']==StartAction)]
            for i in range(2,79):
                optimal_V = data_output[data_output['StartState']==i]['V'].max()
                optimal_policy = data_output[ ( data_output['V']==optimal_V) & (data_output['StartState']==i)]      
                optimal_policy_table = optimal_policy_table.append(optimal_policy)
                
        if (StartAction is None):
            currentpath_action = StartEvent
            optimal_path = pd.DataFrame()

            for i in range(1,79):
                StartPathState = i
                nextpath_action = data_output [ (data_output['V'] == data_output[ (data_output['StartState']==StartPathState) & (data_output['Event1']==currentpath_action) ]['V'].max()) & 
                                               (data_output['StartState']==StartPathState) & (data_output['Event1']==currentpath_action)  ]
                if (nextpath_action['V'].max()==0):
                    break
                else:
                    nextpath_action = nextpath_action.reset_index(drop=True)
                    currentpath_action = nextpath_action['Event2'][0]
                    optimal_path = optimal_path.append(nextpath_action)
                    
        else:
            currentpath_action = StartEvent
            optimal_path = data_output[(data_output['StartState']==StartPathState) & (data_output['Event1']==currentpath_action) & (data_output['Event2']==StartAction) ]
            for i in range(2,79):
                StartPathState = i
                nextpath_action = data_output [ (data_output['V'] == data_output[ (data_output['StartState']==StartPathState) & (data_output['Event1']==currentpath_action) ]['V'].max()) & 
                                               (data_output['StartState']==StartPathState) & (data_output['Event1']==currentpath_action)  ]
                if (nextpath_action['V'].max()==0):
                    break
                else:

                    nextpath_action = nextpath_action.reset_index(drop=True)
                    currentpath_action = nextpath_action['Event2'][0]
                    optimal_path = optimal_path.append(nextpath_action)


                
                
                
    

        



    return(outcomes,actions_output,data_output,optimal_policy_table,optimal_path)
    

In [53]:

alpha = 0.1
gamma = 0.9
num_episodes = 100
epsilon = 0.1

reward = RedMatchMDP['Reward']

StartState = 1
StartEvent = '+KILLS'
StartAction = None


start_time = timeit.default_timer()


Mdl3 = MCModelv3(data=RedMatchMDP, alpha = alpha, gamma=gamma, epsilon = epsilon, reward = reward,
                StartState=StartState, StartEvent=StartEvent,StartAction=StartAction,
                num_episodes = num_episodes)

elapsed = timeit.default_timer() - start_time

print("Time taken to run model:",np.round(elapsed/60,2),"mins")
print("Avg Time taken per episode:", np.round(elapsed/num_episodes,2),"secs")

Time taken to run model: 1.93 mins
Avg Time taken per episode: 1.16 secs

In [54]:

Mdl3[3].head()

Out[54]:

	StartState	EndState	Event1	Event2	Probability	Reward	V
12	1	2	+KILLS	-DRAGON	0.031590	0	0.094938
341	2	3	-DRAGON	-OUTER_TURRET	0.142857	0	0.094465
529	3	4	-OUTER_TURRET	+OUTER_TURRET	0.368852	0	0.084538
648	4	5	+OUTER_TURRET	-KILLS	0.146843	0	0.094469
978	5	6	-KILLS	-KILLS	0.160743	0	0.087776

In [55]:

Mdl3[4]

Out[55]:

	StartState	EndState	Event1	Event2	Probability	Reward	V
0	1	2	+KILLS	-DRAGON	0.031590	0	0.094938
0	2	3	-DRAGON	-OUTER_TURRET	0.142857	0	0.094465
0	3	4	-OUTER_TURRET	+OUTER_TURRET	0.368852	0	0.084538
0	4	5	+OUTER_TURRET	-KILLS	0.146843	0	0.094469
0	5	6	-KILLS	-KILLS	0.160743	0	0.087776
0	6	7	-KILLS	-OUTER_TURRET	0.271478	0	0.096109
0	7	8	-OUTER_TURRET	+OUTER_TURRET	0.186101	0	0.093135
0	8	9	+OUTER_TURRET	+KILLS	0.194960	0	0.074443
0	9	10	+KILLS	+OUTER_TURRET	0.216617	0	0.072786
0	10	11	+OUTER_TURRET	+DRAGON	0.124464	0	0.082719
0	11	12	+DRAGON	-KILLS	0.250000	0	0.073039
0	12	13	-KILLS	+KILLS	0.266995	0	0.095967
0	13	14	+KILLS	+DRAGON	0.072690	0	0.091666
0	14	15	+DRAGON	+KILLS	0.314985	0	0.094469
0	15	16	+KILLS	-KILLS	0.297481	0	0.073666
0	16	17	-KILLS	-INNER_TURRET	0.124319	0	0.093982
0	17	18	-INNER_TURRET	+KILLS	0.181619	0	0.093859
0	18	19	+KILLS	+BASE_TURRET	0.029692	0	0.094469
0	19	20	+BASE_TURRET	+DRAGON	0.055556	0	0.094469
0	20	21	+DRAGON	-KILLS	0.195745	0	0.095296
0	21	22	-KILLS	-KILLS	0.108607	0	0.107893
0	22	23	-KILLS	1	0.003209	0	0.094469

Part 1 Conclusion

So we have performed some interesting exploratory analysis, modelled the environment as an MDP and even created a RL model, however, there are still many challenges to overcome.

The biggest issue right now is our output doesn't account for cumulative success or failures.

In other words, our model thinks we are just as likely to take good objectives in later stages irrespective of whether we have lost each one before and would likely be behind.

We can see this emphasised by our output getting us to a win from 20+ minutes by simply taking objective after objective even though we had lost the majority of objectives before it. There is no accountability for being in a losing position in our model.

To fix this, we must re-asses our MDP and consider features that would account for the long term success or failure of taking or losing objectives.

This is a good start, in our next part we will redesign our MDP to account for this and fix some other issues.