Dominating the Rift: Uncovering the Most Impactful Position in League of Legends

A UCSD DSC80 project analyzing the impact of different roles in League of Legends.

Contributors: Charisse Hao and Nicole Zhang

Table of Contents

Introduction

Welcome to Summoner’s Rift! League of Legends (LoL) is a popular online multiplayer battle arena game, with millions of active players worldwide. The game’s massive player base makes it an excellent source of data for researchers and data scientists interested in exploring various aspects of the game, from player behavior to gameplay mechanics.

League of Legends is a competitive game, so it is natural for players to want to dominate their games and achieve victory. However, what is the best way to obtain this goal? Two teams, consisting of five players each, battle to destroy the opposing team’s center base known as the Nexus. Each team’s players fulfill a specific role on the team—selecting to play one of the five roles: top, jungle, middle, bottom, or support. If players want to carry their team to victory, they might want to pick the best role to do so. Thus, we decided to conduct our data analysis on which role is the most impactful in the overall duration of the game.

* For our purposes, impact will be defined through the statistics of KDA, total gold, and damage to champions.

The dataset we used to conduct this analysis is the 2022 League of Legends Esports Stats dataset provided by Oracle’s Elixir, a website that provides advanced statistics and analysis tools for the game. This dataset contains a comprehensive collection of data from professional League of Legends matches, including detailed information on player and team performance, game events, and match outcomes. The dataset contains information on thousands of matches, covering various tournaments and competitions.

Dataset Statistics and Definitions:

The dataset has a total of 149,232 rows and 123 columns. We cleaned the dataset to only include the data we needed for our analysis, so our dataframe consisted of 124,360 rows and 9 columns. Below are the definitions of the columns we used from this dataset.

Column Name Definition
gameid game ID
datacompleteness indicates if the data for this match was complete or partial
position player’s position (more detail in table below)
kills total kills per player
deaths total deaths per player
assists total assists per player
damagetochampions total damage dealt to other champions
totalgold total gold per player
total cs total creep score per player

* Note: we will be using the terms “role” and “position” interchangeably.

Positions Abbreviation Meaning
top top
jng jungle
mid middle
bot bottom
sup support

Cleaning and EDA (Exploratory Data Analysis)

Data Cleaning

The first step of our data cleaning process was to check for missingness in our dataset. We found that the column damagetochampions had missing values when the value for datacompleteness was “partial”. After dropping the rows which contained “partial” datacompleteness, there were no more missing values in our dataset and we were able to move onto the next step of our data cleaning.

The second step of our data cleaning process was to calculate and add the KDA column to our dataset. We calculated each player’s KDA by using the formula: KDA = (kills + assists) / deaths. However, some of our KDA values were inf (infinity) due to the fact that some players had 0 deaths. Dividing by 0 led to the KDA value to be inf, and we solved this issue by filling in these inf KDA values with an adjusted formula: KDA = kills + assists.

The third step of our data cleaning process was to standardize our statistics in the dataset. We transformed all our data to z-scores for each game. We did this by creating a helper function that calculates the z-score using the z-score formula: Z = (X - µ) / σ

To standardize the statistics accordingly based on each game, we grouped by gameid before applying .transform(z-score). The first five rows of our dataframe are included below:

gameid datacompleteness position damagetochampions totalgold total cs KDA
0 ESPORTSTMNT01_2690210 complete top 0.319151 0.470574 0.587278 -0.947893
1 ESPORTSTMNT01_2690210 complete jng -0.283245 -0.404958 -0.399444 -0.892339
2 ESPORTSTMNT01_2690210 complete mid 0.091917 -0.123676 0.135526 -0.704843
3 ESPORTSTMNT01_2690210 complete bot -0.382416 0.310190 0.527837 -1.017335
4 ESPORTSTMNT01_2690210 complete sup -1.502484 -1.604184 -1.659597 -0.934004

Univariate Analysis

For our univariate analysis, we decided to focus on investigating the distribution of each statistic’s z-scores depending on the position column. In order to generate these plots, we grouped by position before calculating the average z-score for each statistic we were investigating. These included: KDA, total gold, total creep score, and damage to champions.

In the bar graphs provided above, each graph corresponds to a different role, with each bar on the x-axis representing a different statistic while the y-axis indicates the average z-score. Upon taking a closer look at these graphs, the first thing we noticed was that roles such as middle and bottom have positive average z-scores for all statistics, while top has a combination of positive and negative, and roles such as support and jungle have average z-scores around or below zero. Based on this observation, the data seems to indicate middle and bottom roles have more impact in games overall than top, support, and jungle.

Bivariate Analysis

In this section, we wanted to continue comparing the statistics’ z-scores across all positions. We combined all positions’ average z-scores into one bar graph to make comparisons easier, as well as creating box plots to perform further analysis on the distribution of z-scores for each statistic.

The graph above contains each positions’ average z-score across all statistics. Along the x-axis, it specifies which position the bars belong to, and the y-axis once again indicates the average z-score. The bins for each position are color coded based on the legend, with blue corresponding to KDA, red to total gold, green to total creep score, and purple to damage to champions. By plotting all positions side-by-side, we were able to deduce that bottom has the overall highest average z-scores for all statistics, while support has the lowest average z-score for all statistics besides KDA.

The following box plots illustrate each position’s distribution of z-scores for KDA and damage to champions respectively. The x-axis specifies which position the box plot corresponds to and the y-axis represents the z-score.

Taking a closer look at this plot, we found that all positions seem to have relatively the same spread in z-scores, with the median ranging from around -0.1 to -0.5. The boxplot for top seems to be slightly lower compared to the others, and top and support are the only roles containing outliers. We also noticed that the variance for top is comparably lower than the rest of the positions. This shows more consistency in KDA for top players, which suggests a less explosive playstyle for top. Once again, we noticed the roles of middle and bottom have higher z-scores, as their box plots are higher than the other positions’.

Unlike the previous boxplot, there is a lot more variance in the distribution of z-scores across each role. Top, middle, and bottom all seem to have similarly wide ranges, while jungle and support have much smaller ranges. Furthermore, jungle and support have the lowest medians at -0.55 and -1.23 respectively, and they also have the most outlying data points. On the other hand, middle and bottom continue to have the highest medians, which further implies that these two roles may be the most impactful overall.

Interesting Aggregates

To further explore the distribution of z-scores and the pattern we noticed of middle and top consistently having higher z-scores, we decided to plot all positions’ z-scores for KDA and total damage to champions in an overlaid histogram. For the following plots, the x-axis represents the z-score, the y-axis represents the number of players that fall within each z-score bin, and each color corresponds to a certain role based on the legend-blue is top, red is jungle, green is middle, purple is bottom, and support is orange.

This overlaid histogram seems to indicate that all roles have a similar spread in z-scores for KDA, contrasting to the plots we analyzed previously. Each bin appears to have a similar count for each role, and this conflicting observation led us to our null hypothesis: Do all roles have the same impact overall?

Unlike the preceding overlaid histogram, this plot supports the observation made in previous sections-support generally has the lowest z-scores while middle, bottom, and top have the highest z-scores.

Assessment of Missingness

NMAR Analysis

We believe that the column ban5 in our dataset is not missing at random (NMAR). Values are missing in this column with no apparent pattern, leading us to consider circumstances where some teams may have either forgotten to ban or did not see the need to ban a fifth champion. This would make the missing data points dependent on the actual value of the missing data point itself, causing the missingness to be NMAR. To make this column missing at random (MAR), we can collect more data on whether or not the total 5 bans for each team were complete and name the new column bancompleteness. With this new column, the ban5 column will no longer be dependent on the actual value itself, but will instead depend on bancompleteness.

Missingness Dependency

When we first began exploring this dataset, we were interested in overall data and data collected at the 15 minute mark. We noticed many of the columns corresponding to data collected at this time mark have missing values, so we decided to investigate the missingness dependency of the column killsat15.

The first column we tested missingness against was the column datacompleteness.

Null Hypothesis: Distribution of 'datacompleteness' when 'killsat15' is missing is the same as the distribution of 'datacompleteness' when 'killsat15' is not missing.

Alternative Hypothesis: Distribution of 'datacompleteness' when 'killsat15' is missing is not the same as the distribution of 'datacompleteness' when 'killsat15' is not missing.

Below is the graph portraying the distribution of datacompleteness when killsat15 is and is not missing.

We performed a permutation test to determine whether or not the missingness of killsat15 was dependent on datacompleteness using total variation distance (TVD) as our test statistic. Below is the plot illustrating the empirical distribution of the TVDs, with our observed TVD marked as a red vertical line.

From here, we calculated the p-value by comparing the observed TVD to the TVDs found through permutation testing, and the resulting p-value was 0. Since our p-value is less than the significance level of 0.05, we reject the null hypothesis, and therefore it seems that missingness in killsat15 is dependent on datacompleteness.

The second column we tested missingness against was the column position.

Null Hypothesis: Distribution of 'position' when 'killsat15' is missing is the same as the distribution of 'position' when 'killsat15' is not missing.

Alternative Hypothesis: Distribution of 'position' when 'killsat15' is missing is not the same as the distribution of 'position' when 'killsat15' is not missing.

Following the same steps as above, we plotted the distribution of position when killsat15 is and is not missing. Then, we carried out a permutation test using TVD as the test statistic again.

By comparing the TVDs found through permutation testing to the observed TVD, we found the resulting p-value was 1. Since our p-value is greater than the significance level of 0.05, we fail to reject the null, and therefore it seems that the missingness in killsat15 is not dependent on position.

Hypothesis Testing

After conducting our exploratory data analysis, we chose to answer the general question: do all roles have the same impact overall?

Null hypothesis: All roles have the same impact overall.

Alternative hypothesis: All roles do not have the same impact overall.

We used the total variation distance (TVD) as our test statistic for this test because we are comparing the difference between different positions (top, jungle, middle, bottom, and support), which are categorical distributions. We chose the most commonly used significance level, as a p-value less than 0.05 is considered statistically significant. By using this p-value, it indicates strong evidence against the null hypothesis since there is less than a 5% probability that we see a result as or more extreme than our observed result by chance.

We decided to drop total cs from our hypothesis test since total cs correlates with the total gold a player has. We then did three separate hypothesis tests for each of the three impact variables: KDA, damage to champions, and total gold.

Results for KDA:

Results for Damage to Champions:

Results for Total Gold:

Based on the results presented above, we reject the null hypothesis—all roles do not seem to have the same impact overall. With this knowledge, we then shifted our focus to only one variable: damage to champions. We selected this variable to investigate further because we believe that the KDA statistic may not be as good of a comparison statistic as seen under Interesting Aggregates. Additionally, we considered the fact that an opposing team may target the most impactful player, which would increase that player’s deaths and therefore decrease their KDA ratio. We also did not use total gold because gold obtained by players is used to buy equipment that deals more damage to the opposing team. Hence, we selected damagetochampions as the variable to use.

Looking at the box plot titled: Avg Stat Z-score for All Positions under Bivariate Analysis, we notice that middle and bottom are the only positions that have positive z-scores for all variables (KDA, total gold, total cs, and damage to champions). We then asked a follow-up question: which role has more impact overall for damage to champions—bottom or middle? To answer this, we conducted a one-tailed hypothesis test.

Null hypothesis: Bottom and middle have the same average z-score for damage to champions.

Alternative hypothesis: Bottom has a higher average z-score for damage to champions than middle.

We used the difference in mean as our test statistic because we are comparing quantitative distributions and the mean is not the same for the two distributions. We used the same significance level as stated above.

Results:

Concluding Note

Based on the results of the exploratory data analysis and hypothesis tests conducted in this project, we identified potential key variables that could be used to build a predictive model that predicts a player’s role based on their game statistics in a separate project. To learn more about the predictive modeling process, please refer to our second project: The Summoner’s Oracle: Predicting League of Legends Player Positions.