DSC 80 Project

By Katelyn Abille and Aneesh Pamula

Curated by students of DSC 80, this academic project is intended to demonstrate the process of cleaning and performing exploratory data analysis, assessing missingness, and conducting permutation tests. Our website stands as a holistic report of our findings.

Our predictive modeling on this dataset can be found here:
Model Building: Predicting Champion Class Based on Post-Game Statistics


Table of Contents

  1. Introduction
    a. Description of Raw Data
    b. Description of Columns
  2. Cleaning and EDA
    a. Data Cleaning
    b. Univariate Analysis
    c. Bivariate Analysis
    d. Interesting Aggregates
  3. Assessment of Missingness
    a. NMAR Analysis
    b. Missingness Dependency
      i. Comparing Missingness of 'playerid' to 'league'
      ii. Compare Missingness of 'playerid' to 'side'
  4. Hypothesis Testing
    a. Background Information
    b. Permutation Testing


Introduction

League of Legends is a game with an extremely diverse cast of characters or “champions,” each with their own strengths. Some have very high damage, but lack defenses. Some do not deal as much damage, but are very durable and have a variety of disruption tools. Certain champions have characteristics that make them very strong when played in a coordinated team setting. For example, Jinx can output a massive amount of damage from a long distance, but she often requires her teammates to protect her since she can be killed very quickly. Such champions are picked very often by professional players, who can rely on their teammates to coordinate with them.

Another one of these champions that is picked rather often in professional play is Renekton. With his great early game strength, high mobility, and a reliable immobilization tool, Renekton is a champion that many players have come to think of as a “pro play champion;” that is, one can expect to see Renekton fairly often when watching professional games.

A somewhat popular joke among League players is that such “pro play champions” are often buffed, or made stronger, in the patches leading up to the World Championships in the late fall. This idea stems from the idea that Riot Games (the publishers and developers of League of Legends) would want to buff champions that people are expecting to see at the World Championships, thus leading to a more engaging experience and increased viewership. In this project, we will examine whether this sentiment is true with regards to Renekton in 2022. Thus, we will be answering the question:

Is the champion Renekton “buffed” for World Championships?

Description of Raw Data

In order to answer this question, we will be using data from the 2022 League of Legends competitive matches provided by Oracle’s Elixir. The raw data set includes 123 columns of game statistics ranging from first bloods to kill and death counts, with every 12 rows being data for two teams going head to head in one game. These 12 rows can also be broken down into two groups of 6 rows, each of which consists of individual statistics for the 5 players in a team plus a row for team aggregate statistics over that game, and this goes on for a total of 149,400 rows corresponding to 12,450 different competitive matches!

For the purposes of our analysis, we will not be using a majority of these columns and will focus on a select few:

Description of Columns

The columns in our cleaned data set are:

Cleaning and EDA

Data Cleaning

As mentioned earlier, this dataset contains far more information than what is necessary to answer our core question. For the purposes of this analysis, we removed rows containing aggregate team statistics, as well as the columns 'datacompleteness', 'url', 'participantid', 'year', 'split', 'playoffs', and 'game'. We also ignored the columns that refer to other game statistics, such as gold difference, dragons, towers, etc., since they will also not factor into our analysis. Additionally, we cast the values in the 'result' column, which contained ones and zeroes, to booleans, and renamed that column to 'win' to make its values make more sense.

We removed the unnecessary rows and columns in the raw data, modified the 'result' column, and stored the values we obtained in the DataFrame 'league’, which can be seen below:

  gameid league date patch side position playername playerid teamname teamid champion ban1 ban2 ban3 ban4 ban5 gamelength win
0 ESPORTSTMNT01_2690210 LCKC 2022-01-10 07:44:08 12.01 Blue top Soboro oe:player:38e0af7278d6769d0c81d7c4b47ac1e Fredit BRION Challengers oe:team:68911b3329146587617ab2973106e23 Renekton Karma Caitlyn Syndra Thresh Lulu 1713 False
1 ESPORTSTMNT01_2690210 LCKC 2022-01-10 07:44:08 12.01 Blue jng Raptor oe:player:637ed20b1e41be1c51bd1a4cb211357 Fredit BRION Challengers oe:team:68911b3329146587617ab2973106e23 Xin Zhao Karma Caitlyn Syndra Thresh Lulu 1713 False
2 ESPORTSTMNT01_2690210 LCKC 2022-01-10 07:44:08 12.01 Blue mid Feisty oe:player:d1ae0e2f9f3ac1e0e0cdcb86504ca77 Fredit BRION Challengers oe:team:68911b3329146587617ab2973106e23 LeBlanc Karma Caitlyn Syndra Thresh Lulu 1713 False
3 ESPORTSTMNT01_2690210 LCKC 2022-01-10 07:44:08 12.01 Blue bot Gamin oe:player:998b3e49b01ecc41eacc392477a98cf Fredit BRION Challengers oe:team:68911b3329146587617ab2973106e23 Samira Karma Caitlyn Syndra Thresh Lulu 1713 False
4 ESPORTSTMNT01_2690210 LCKC 2022-01-10 07:44:08 12.01 Blue sup Loopy oe:player:e9741b3a238723ea6380ef2113fae63 Fredit BRION Challengers oe:team:68911b3329146587617ab2973106e23 Leona Karma Caitlyn Syndra Thresh Lulu 1713 False
… … … … … … … … … … … … … … … … … …  
149393 9687-9687_game_5 DCup 2022-12-27 12:43:43 12.23 Red top Bin oe:player:fb66ef5885b4be9323905b821dc3a42 Bilibili Gaming oe:team:d356a144644879dabb5f34cd99c886d Jax K’Sante Syndra Lucian Gwen Sylas 1778 True
149394 9687-9687_game_5 DCup 2022-12-27 12:43:43 12.23 Red jng XUN oe:player:814f33b3479f1ebf6cd22cba78f30e0 Bilibili Gaming oe:team:d356a144644879dabb5f34cd99c886d Vi K’Sante Syndra Lucian Gwen Sylas 1778 True
149395 9687-9687_game_5 DCup 2022-12-27 12:43:43 12.23 Red mid Yagao oe:player:4860d1660ce45bd15a600953309135c Bilibili Gaming oe:team:d356a144644879dabb5f34cd99c886d Ahri K’Sante Syndra Lucian Gwen Sylas 1778 True
149396 9687-9687_game_5 DCup 2022-12-27 12:43:43 12.23 Red bot Elk oe:player:a58a0d41103cdc5b58cbb547eeaca2d Bilibili Gaming oe:team:d356a144644879dabb5f34cd99c886d Varus K’Sante Syndra Lucian Gwen Sylas 1778 True
149397 9687-9687_game_5 DCup 2022-12-27 12:43:43 12.23 Red sup ON oe:player:90651ebea9a35ec4e018c8157492e17 Bilibili Gaming oe:team:d356a144644879dabb5f34cd99c886d Ashe K’Sante Syndra Lucian Gwen Sylas 1778 True

Univariate Analysis

We can look at the counts of each value in the 'champions' column to see which champions were picked the most often during the 2022 season. The graph containing all champions can be seen below:

League of Legends has over 160 playable champions, which makes this graph rather difficult to read. To make it simpler, let’s look at only the 15 most and least picked champions.

The graph displaying the 15 most picked champions can be seen here:

And the graph displaying the 15 least picked champions can be seen here:

These graphs shows that champions such as Nautilus and Jinx were picked very often, possibly alluding to their overall strength in pro games. Meanwhile, champions such as Warwick and Teemo are not picked very often. Our main focus, Renekton, sits around the middle of the graph.

However, it must be noted that simply the pick rate of a champion does not on its own correlate to their strength. Many times, popular champions will be “banned” from being chosen, so to examine the overall prescence of any given champion, we can look at a different statistic that takes this into account (but we will get to this later, during the hypothesis testing section).



Next, we can examine how long pro League games usually go on for.

Below is a box plot depicting the distribution of game times (in minutes) of games played during the 2022 season.

As we can see here, many pro League games average to around 30 minutes in length, with a roughly right skewed distribution. This is important to consider because certain champions (like Renekton) are stronger in the earlier stages of the game (i.e. the first 25 or so minutes) than in the later stages of the game. If many games go on for a long time, then it may affect Renekton’s overall strength, and by extension, whether he received buffs before Worlds.

Bivariate Analysis

We can also take a look at the distribution of games played on each patch.

Patches are modifications to champions or systems in the game with the intent of making the game more balanced and fun to play. These patches are released on a (approximately) two week cycle, which makes them an effective method of analyzing the peaks and valleys of the League pro scene.

Below, we can see the number of games played on each patch. From this, we can see that many games were played on the patches at the beginning of the year, then fewer games were played, but then games spiked again around patch 12.12 thus depicting a bimodal distribution.

There is also a small spike from 12.17 to 12.18, which corresponds to the patches that were released right before Worlds (the world championships).



Another statistic we could analyze is which champions had the highest win rates. To ensure that we only analyze champions with a decent sample size, we will take the champions with at least 100 picks according to our univariate analysis from earlier (Number of Times Picked for Each Champion). The graph containing these champions can be seen below:

There are still very many champions that fall under this criteria, causing our graph to be dense with bars. Like before, let’s only look at the champions with the highest and lowest fifteen win rates.

The top 15 are here:

And the bottom 15 are here:

Unlike our univariate analysis of champion pick counts, we see that win rates for each champion has a much smaller variance.

Keep in mind that win rate is not the only factor that determines the strength of a champion. Some champions are only played as counters to other champions, and thus naturally have a higher win rate, since players only play those champions into favorable matchups.

For example, the pick rate of Darius, the champion with the highest win rate, is very low–only 181 games. This is because in many cases, Darius is picked only when the player selecting him knows that they will be able to perform well with him based the enemy team’s champion picks and bans.

Interesting Aggregates

Let’s take a look at how many games each team won with and without picking Renekton.

Won With Renekton Count

teamname False True
100 Thieves 40 3
100 Thieves Academy 66 2
100 Thieves Next 58 1
1907 Fenerbahçe Academy 2 0
300 5 0
… … …
paiN Gaming Academy 40 2
piratesports 2 0
unknown team 152 8
İstanbul Wildcats 40 2
İstanbul Wildcats Academy 25 1

From this table, we can see that teams often win more games when not picking Renekton than they do when picking Renekton. This seems inconsistent with our initial impression of Renekton–if he is such a strong champion in pro play, why are teams winning more games when they don not play him?

The answer is simple–teams simply play far more games without picking Renekton than they do when picking Renekton.

Let’s modify our pivot table to instead show the number of games each team played with and without Renekton.

Picked Renekton Count

teamname False True
100 Thieves 71 5
100 Thieves Academy 113 4
100 Thieves Next 76 1
1907 Fenerbahçe Academy 2 1
300 12 0
… … …
paiN Gaming Academy 53 2
piratesports 7 1
unknown team 281 13
İstanbul Wildcats 57 6
İstanbul Wildcats Academy 39 4

There could be numerous reasons for a team playing many games without Renekton. For example, the opposing team may have simply chosen to ban Renekton. If they did not ban Renekton, they likely deliberately chose champions that fared well against Renekton, thus making Renekton a less viable choice.

Indeed, if we divide the values in the first table by the values in the second table:

Renekton Win Rate

teamname False True
100 Thieves 0.56338 0.6
100 Thieves Academy 0.584071 0.5
100 Thieves Next 0.763158 1
1907 Fenerbahçe Academy 1 0
300 0.416667 nan
… … …
paiN Gaming Academy 0.754717 1
piratesports 0.285714 0
unknown team 0.540925 0.615385
İstanbul Wildcats 0.701754 0.333333
İstanbul Wildcats Academy 0.641026 0.25

We can see that in some cases, the teams win a greater percentage of their games when they pick Renekton, and in other cases, they win a greater percentage when they do not pick Renekton.

The NaN values in this case represent situations where teams did not pick Renekton, and thus have an undefined win rate with him.

Assessment of Missingness

Some of the data in our dataset are missing; however, at first glace we do not necessarily know whether there is an explicit pattern to this missingness, or whether these data are missing at random (either completely or conditional on the values in another column).

NMAR Analysis

We can conclude, based on domain knowledge, that the values in the 'teamname' column are likely not missing at random, or NMAR, since their missingness depends on the values themselves. More popular teams, such as T1 or Team Liquid, are less likely to have their team names missing since their games are more likely to be covered and receive more publicity. On the contrary, lesser known teams are less likely to have their games covered, so their team name is more likely to be missing.

Missingness Dependencys

We will examine a few of the columns in our dataset to determine whether the missingness dependent on another column, and therefore missing at random (MAR). In order to do this, we can run permutation tests between a column with missingness and columns with complete data and draw conclusions from the observed total variation distance (TVD) in comparison to the simmulated TVDs. One such column with missingness that we may test this on is 'playerid'. This could be because the player is unregistered, the data were simply not collected, or certain leagues have a higher chance of not recording data for players–we don’t really know what it could be.

In the following, we will work with a significance level of 0.01, or 1%.

Comparing Missingness of 'playerid' to 'league'

Because certain players are more likely to play in specific leagues, it is possible that the missingness of the ‘playerid’ column will have a connection to 'league’.

For this test, we will operate on the following hypotheses:

To start off, let’s take a look at the distribution of 'league' when 'playerid' is missing versus when it is not missing:

league playerid_missing = False playerid_missing = True
CBLOL 0.0198641 0.0179541
CBLOLA 0.017657 0.0159592
CDF 0.00579575 0.00616942
CT 0.00197824 0.00258598
DCup 0.00473306 0.0127452
… … …
UL 0.0227252 0.0205401
UPL 0.0327554 0.0346152
VCS 0.0261749 0.0248993
VL 0.0128504 0.0172891
WLDs 0.0126705 0.0114522

At first glance, we see a large variety of differences between missing and non-missing 'playid' distrubutions of 'league' data, holding an observed TVD of 0.056972941528464466.
And after performing our permutation test:

We observe a p-value of 0.0, and so we reject the null.
The distribution of 'league' when 'playerid' data is missing is not the same as the distribution of 'league' when 'playerid' is not missing, and therefore the missingness of 'playerid' may be dependent on 'league'.

Compare missingness of 'playerid' to 'side'

When playing a game of League of Legends, the side of the map that each team plays on (commonly referred to as ‘red side’ or ‘blue side’) is decided before the game by a coin toss. Theoretically, this should not impact the missingness of the ‘playerid’ column, since the side is chosen randomly right before the game starts.

For this test, we will operate on the following hypotheses:

side playerid_missing = False playerid_missing = True
Blue 0.499931 0.500314
Red 0.500069 0.499686

From the start, we see a that the distrubutions of 'league' data based on the missingness of 'playerid' is almost completely even with an observed TVD of 0.00038349595296663375.
And following our permutation test:

We observe a p-value of 0.916, and so we fail to reject the null.
The distribution of 'side' when 'playerid' data is missing is the same as the distribution of 'side' when 'playerid' is not missing, and therefore the missingness of 'playerid' may not be dependent on 'side'.



From these permutation tests, we can now conclude that 'playerid' is MAR, or missing at random, from the dataset.

Hypothesis Testing

Now, let’s begin answering our core question: Is it true that Renekton was buffed for Worlds in 2022?

To do this, we will attempt to quantify the overall presence of Renekton during the first half of the year and compare it to the second half of the year. Since the World Championships take place at the end of the year, if Renekton was really buffed in the patches leading up to Worlds then he should have a greater presence during the second half of the year than the first half of the year.

Background Information

As mentioned earlier, to measure the overall presence of a champion, we must look at a statistic other than pick rates and win rates. A common statistic used in the League community to measure the prescence of a champion is the pick/ban rate, which is calculated as the proportion of games in which the champion was either picked or banned. Champions with high pick/ban rates are often very dominant, since teams will want to either utilize the champion’s strength or prevent their enemy from doing so. We will use the pick/ban rate as the test statistic for our analysis.

In summary, we want to find whether Renekton’s pick/ban rate is significantly greater during the second half of the year (that is, patches 12.13 through 12.23) than in the first half of the year (12.01 through 12.12). We choose to separate this way because patch 12.12 was released at the very end of June.

Permutation Testing

Our null and alternate hypotheses are:

We will continue to work with a significance level of 0.01, or 1%, for this permutation test.



Our observed statistic–the overall difference in the pick/ban rates across the entire dataset–is 0.038313788572777535.
After shuffling the 'patch' column of the dataset and recording the test statistic on each shuffled DataFrame 500 times, we obtained the following distribution of test statistics:

When we compare our observed statistic to the ones we obtained through permutation testing:

We can see that our observed statistic is extremely significant–that is, it is highly unlikely that our data was obtained from a distribution in which Renekton’s pick/ban rate was the same throughout the year.

Our p-value of 0.0 confirms this, since it is lower than our significance level of 0.01.


With this data, we have enough evidence to reject the null hypothesis that Renekton’s pick/ban rate does not change over the year. Through doing this permutation test, we have cast doubt on the claim that Renekton’s presence in the League of Legends professional scene does not increase in the second half of the year.


However, it is important to note that this test does not necessarily prove that Renekton was “buffed for worlds”. We have simply obtained evidence that supports this hypothesis.