League of Legends Exploratory Data Analysis

Creator: Ryan Hung

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Introduction:

Question summary:

This exploratory data analysis employs Oracle Elixir's dataset consisting of player and team data from the 2022 League of Legends competitive season.

The dragon is one of the most pivotal objectives in the game as it provides powerful buffs to the team that claims its souls. Thus, having solid macro and map control to ensure dragon kills is crucial for high level competitive play, where teams can use any sliver of advantage they can get.

This exploratory data analysis focuses on how the value of dragons have shifted by split - is there a variation in dragons killed in different splits? It will also focus on analyzing the overall impact dragons have in a competitive match.

Data summary:

The dataset consists of 149232 rows and 123 columns. The first 10 rows consists of player rows - 5 players from each team. The 11th and 12th columns consists of team rows. Thus, the first 12 rows make up the data for a match. The same pattern follows for the remaining rows.

Relevant columns that we address in our processing and analysis include:

1. split - The season split the match was played in
2. side - The side of map assigned to a team
3. gamelength - Length of game in minutes
4. result - The result of the match for a team
5. firstdragon - Whether or not a team secured the first dragon kill
6. dragons - The total number of dragons killed
7. infernals, mountains, clouds, chemtechs, hextechs, elders - The total number of dragons of each type killed
8. date - The date that the match was played on
9. position - The lane position of a player or simply team for team rows
10. teamname - The name of the team

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Cleaning and EDA:

Data cleaning:

1. First, our analysis focuses on team performance with respect to dragons so we filtered out all rows that consisted of player data
   • For this, we queried all rows that had the value "team" in the position column - this is based on the data generating process that produced this dataset
2. gamelength was originally represented as seconds but League of Legends game duration is measured in minutes by convention so we scaled this feature
3. date was converted into a pd.Timestamp object
4. Many columns that were specific to player row data were removed because we could gain zero information from these columns as we are dealing with team data
   • For this, we went through each column and dropped all columns that were completely missing - again, based on data generating process creating variables that were specific only to players
5. Many columns such as result and firstdragon, to name a few, could be represented as Boolean types

Performing the data cleaning steps above helped streamline our analyses by shrinking our dataframe to consist only of relevant information needed. Here is the head of the cleaned dataframe:

gameid	datacompleteness	url	league	year	split	playoffs	date	game	patch	side	teamname	teamid	ban1	ban2	ban3	ban4	ban5	gamelength	result	kills	deaths	assists	teamkills	teamdeaths	doublekills	triplekills	quadrakills	pentakills	firstblood	team kpm	ckpm	firstdragon	dragons	opp_dragons	elementaldrakes	opp_elementaldrakes	infernals	mountains	clouds	oceans	chemtechs	hextechs	dragons (type unknown)	elders	opp_elders	firstherald	heralds	opp_heralds	firstbaron	barons	opp_barons	firsttower	towers	opp_towers	firstmidtower	firsttothreetowers	turretplates	opp_turretplates	inhibitors	opp_inhibitors	damagetochampions	dpm	damagetakenperminute	damagemitigatedperminute	wardsplaced	wpm	wardskilled	wcpm	controlwardsbought	visionscore	vspm	totalgold	earnedgold	earned gpm	goldspent	gspd	minionkills	monsterkills	monsterkillsownjungle	monsterkillsenemyjungle	cspm	goldat10	xpat10	csat10	opp_goldat10	opp_xpat10	opp_csat10	golddiffat10	xpdiffat10	csdiffat10	killsat10	assistsat10	deathsat10	opp_killsat10	opp_assistsat10	opp_deathsat10	goldat15	xpat15	csat15	opp_goldat15	opp_xpat15	opp_csat15	golddiffat15	xpdiffat15	csdiffat15	killsat15	assistsat15	deathsat15	opp_killsat15	opp_assistsat15	opp_deathsat15
ESPORTSTMNT01_2690210	complete	nan	LCK CL	2022	Spring	False	2022-01-10 07:44:08	1	12.01	Blue	Fredit BRION Challengers	oe:team:68911b3329146587617ab2973106e23	Karma	Caitlyn	Syndra	Thresh	Lulu	28.55	False	9	19	19	9	19	0	0	0	0	True	0.3152	0.9807	False	1	3	1	3	0	0	0	0	0	1	nan	0	0	True	2	0	False	0	0	True	3	6	True	True	5	0	0	1	56560	1981.09	3537.2	2364.73	74	2.5919	51	1.7863	33	197	6.9002	47070	28222	988.511	44570	-0.0283123	680	160	nan	nan	29.4221	16218	18213	322	14695	18076	330	1523	137	-8	3	5	0	0	0	3	24806	28001	487	24699	29618	510	107	-1617	-23	5	10	6	6	18	5
ESPORTSTMNT01_2690210	complete	nan	LCK CL	2022	Spring	False	2022-01-10 07:44:08	1	12.01	Red	Nongshim RedForce Challengers	oe:team:d2dc3681437e2beb2bb4742477108ff	Lee Sin	Twisted Fate	Zoe	Nautilus	Rell	28.55	True	19	9	62	19	9	6	0	0	0	False	0.6655	0.9807	True	3	1	3	1	2	1	0	0	0	0	nan	0	0	False	0	2	False	0	0	False	6	3	False	False	0	5	1	0	79912	2799.02	3009.67	2872.33	93	3.2574	51	1.7863	45	205	7.1804	52617	33769	1182.8	45850	0.0283123	792	184	nan	nan	34.1856	14695	18076	330	16218	18213	322	-1523	-137	8	0	0	3	3	5	0	24699	29618	510	24806	28001	487	-107	1617	23	6	18	5	5	10	6
ESPORTSTMNT01_2690219	complete	nan	LCK CL	2022	Spring	False	2022-01-10 08:38:24	1	12.01	Blue	T1 Challengers	oe:team:6dcacec00a6ba7576c5ab7f30c995cd	Sona	Jarvan IV	Caitlyn	Lulu	Lucian	35.2333	False	3	16	7	3	16	0	0	0	0	False	0.0851	0.5393	False	1	4	1	4	0	1	0	0	0	0	nan	0	0	True	1	1	False	0	2	False	3	11	False	False	2	3	0	2	59579	1690.98	2984.02	3109.61	119	3.3775	55	1.561	47	277	7.8619	57629	34688	984.522	53945	-0.207137	994	215	nan	nan	34.3141	14939	17462	317	16558	19048	344	-1619	-1586	-27	1	1	3	3	3	1	23522	28848	533	25285	29754	555	-1763	-906	-22	1	1	3	3	3	1
ESPORTSTMNT01_2690219	complete	nan	LCK CL	2022	Spring	False	2022-01-10 08:38:24	1	12.01	Red	Liiv SANDBOX Challengers	oe:team:5380cdbc2ad2b8082624f48f99f6672	LeBlanc	Yuumi	Twisted Fate	Karma	Alistar	35.2333	True	16	3	39	16	3	1	0	0	0	True	0.4541	0.5393	True	4	1	4	1	0	2	1	0	0	1	nan	0	0	False	1	1	True	2	0	True	11	3	True	True	3	2	2	0	74855	2124.55	2745.72	2868.42	129	3.6613	70	1.9868	65	346	9.8202	71004	48063	1364.13	66410	0.207137	1013	244	nan	nan	35.6764	16558	19048	344	14939	17462	317	1619	1586	27	3	3	1	1	1	3	25285	29754	555	23522	28848	533	1763	906	22	3	3	1	1	1	3
8401-8401_game_1	partial	https://lpl.qq.com/es/stats.shtml?bmid=8401	LPL	2022	Spring	False	2022-01-10 09:24:26	1	12.01	Blue	Oh My God	oe:team:f4c4528c6981e104a11ea7548630c23	Renekton	Lee Sin	Caitlyn	Jayce	Camille	22.75	True	13	6	35	13	6	nan	nan	nan	nan	False	0.5714	0.8352	False	2	1	nan	nan	nan	nan	nan	nan	nan	nan	2	nan	nan	False	nan	nan	False	1	0	False	8	3	False	False	nan	nan	1	0	40086	1762.02	2263.25	nan	79	3.4725	33	1.4505	32	162	7.1209	45468	30167	1326.02	36908	-0.00586225	nan	172	98	18	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan

Univariate Analysis:

To better understand the importance of the dragon objective, we can graph the number of dragons killed by all teams in 2022. It seems that teams generally kill 2 dragons the most frequently.

<iframe src="assets/fig_univariate_1.html" width=800 height=600 frameBorder=0>s</iframe>

Bivariate Analysis:

To answer our main question, let's see how the value of dragons has shifted over time. Specifically, how has the mean number of dragons killed varied by split over the 2022 competitive season? In the bar plot below, we can see that the Fall split had the lowest mean number of dragons killed by 1.827.

<iframe src="assets/fig_bivariate_1.html" width=800 height=600 frameBorder=0>s</iframe>

Interesting Aggregates:

We wanted to see if getting the first dragon increased a team's chance of winning. The columns False and True denote whether or not a team has killed the first dragon. The index result denote whether or not a team has won the game. The pivot table shown below is actually a concatenation of two pivot table, one for each team side. The proportions inside shown the conditional probability P(Winning | First Dragon).

result	False	True	team
False	0.52774	0.377525	blue
True	0.47226	0.622475	blue
False	0.596116	0.454819	red
True	0.403884	0.545181	red

The trend in this table is that killing first dragon always increases the chances of winning for both team colors - and it also means that not killing the first dragon increases the chances of losing for both team colors. To better visualize this, we provide a bar plot.

<iframe src="assets/aggregate.html" width=800 height=600 frameBorder=0>s</iframe>

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Assessment of Missingness:

NMAR Analysis:

We can argue that teamname is NMAR. This is because the missingness of teamname is dependent on the value of teamname itself. The likely reason for this missingness can be attributed to the fact that perhaps new teams simply do not have an established name, and so the missingness of their name depends on them not having a name. To make teamname MAR, we can perhaps add a new column of data called teamage which shows how long a team has been together. Thus, if teamname is missing, the distribution of teamage would be less than that of teamage if teamname exists.

Missingness Dependency:

Dependent testing

The elder dragon only spawns after one team has killed all four elemental dragons. Thus, the elder dragon typically only appears in games that are longer. Because of this assumption, we can check if elders is MAR dependent on gamelength using a permutation test.

Null: The distribution of gamelength is the same when elders is missing and when elders is not missing

Alternative: The distribution of gamelength is different when elders is missing and when elders is not missing

Test statistic: Absolute difference of group means

Significance level: 0.05

<iframe src="assets/MAR.html" width=800 height=600 frameBorder=0>s</iframe> <iframe src="assets/MAR_ts.html" width=800 height=600 frameBorder=0>s</iframe>

Our p-value is 0.0 so we reject the null. Since we reject the null hypothesis that the two distributions are similar, we show statistical evidence that elder is, potentially, MAR dependent on gamelength. However, this isn't an absolute conclusion!

Not dependent testing

Now, we can perform another permutation test on elders missingness and side because we can follow the reasoning that elders is not MAR dependent on side. This is because, in our data, every pair of rows consists of a match between two teams. These two teams are separated into a blue and red side and so the distribution of side will always be 50/50 regardless of whether elders is missing. However, we can still run a permutation test to have stronger statistical evidence for this logic.

Null: The distribution of side is the same when elders is missing and when elders is not missing

Alternative: The distribution of side is different when elders is missing and when elders is not missing

Test statistic: Total variation distance

Significance level: 0.05

<iframe src="assets/NOT_MAR.html" width=800 height=600 frameBorder=0>s</iframe> <iframe src="assets/NOT_MAR_TS.html" width=800 height=600 frameBorder=0>s</iframe>

Our p-value is 1.0 so we fail to reject the null. Since we fail to reject the null hypothesis that the two distributions are similar, we have statistical evidence that elder, potentially, isn't MAR dependent on side. However, this conclusion isn't absolute!

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Hypothesis testing:

Answering the question:

Our specific question was: is there a variation in dragons killed in split? We can gain more insight into this question by looking at the mean number of dragons killed per split, and seeing if any variations occurred. Per our bivariate analysis above, we can see that the Fall split had the lowest mean number of dragons killed by 1.827.

<iframe src="assets/fig_bivariate_1.html" width=800 height=600 frameBorder=0>s</iframe>

Let's conduct a hypothesis test to see if the mean number of dragons killed during the Fall split was lower than the other averages due to lower chance. That is, dragons and split aren't related - and thus the importance of dragons is potentially not related to the split.

Null hypothesis: dragons and split are not related - the low average number of dragons killed during the Fall is due to random chance

Alternative hypothesis: dragons and split are related - the low average number of dragons killed during the Fall is not due to random chance

Test statistic: Average dragons killed

Significance level: 0.05

Let's go justify each individual decision we made for our hypothesis test:

• For null hypothesis, we state that dragons and split aren't related and that the low number of dragons killed during the Fall split was random. If dragons and split are potentially unrelated, then we can assume that teams value killing dragons the same in other splits
• For alternative hypothesis, we state that dragons and split are related. If dragons and split are potentially related, then we can assume that teams value killing dragons differently in different splits
• For the test statistic, we use the average dragons killed. We obtain this statistc by sampling from our parent dataset under the null. Small values of this statistic will point in the direction of the alternative because we our question is phrased in such a way that we are checking for smaller quantities
• For significance level, we chose the standard 0.05 confidence level

<iframe src="assets/hypoth.html" width=800 height=600 frameBorder=0>s</iframe>

Our p-value was 0.0, so we reject the null. Since we reject the null hypothesis that the low mean value of dragons for the Fall split was due to random chance, we show significant statistical evidence that dragons and split are potentially related. This potential connection could show that team's value dragons differently in a certain split. The variation could have underlying confounding factors such as meta shifts, game durations, buffs/nerfs, and map updates.