League of Legends First Blood Statistical Analysis

League of Legends First Blood Statistical Analysis is a comprehensive data science project conducted at UCSD. The project encompasses various stages of analysis, starting from exploratory data analysis to hypothesis testing, creation of baseline models, and concluding with fairness analysis. The primary focus of the project is to investigate the significance of the “first blood” event in League of Legends matches and its impact on match statistics and outcomes.

Authors: Sirui Zhang, Krystal Qiu

Introduction

General Introduction

League of Legends (LOL) is a popular multiplayer online battle arena (MOBA) game developed by Riot Games. With millions of players worldwide, it has become one of the most influential and widely played esports in the gaming industry. The data set we will be working with is a professional data set that’s developed by Oracle’s Elixir. The file records match data from professional LOL esports gaming matches throughout 2022.

This dataset captures key gameplay statistics and outcomes from a collection of LOL matches, offering a rich source of information for understanding player behavior, team dynamics, and match outcomes. It includes a variety of features such as individual player performance, team strategies, in-game statistics, and overall match dynamics.

In the realm of League of Legends (LOL), the concept of “first blood” holds significant weight and serves as an important trajectory of a match. First blood refers to the initial first kill secured by a team during the early stages of a game. Beyond its immediate impact on the scoreboard, first blood sets the tone for the ensuing gameplay, often shaping the general dynamics, strategies, and outcomes of the match.

The central question we are interested in is In what degree of effectiveness does the firstblood status has to other gaming statistics in the data set. We want to use data analysis techniques to testify the impact of first blood on gaming statistics, including individual player performance, team strategies, in-game metrics, and ultimately, match outcomes. And therefore using these statistics to set up a prediction model to predict the positions of the players. This predictive model holds immense potential to enhance strategic decision-making, optimize team compositions, and elevate overall gameplay experience.

Introduction of Columns

The dataset introduces a comprehensive array of columns featuring gameplay metrics and match outcomes from professional League of Legends esports matches. Ther are 148992 rows in this dataset, and here’s an introduction to some of the key columns: In the dataset provided, we encounter various columns that encapsulate essential gameplay statistics and match outcomes from professional League of Legends (LoL) esports matches. Here’s a brief introduction to each of these columns:

Data Cleaning and Exploratory Data Analysis

Data Cleaning

To save time in the further data cleaning steps, we first only keep the relevant columns: gameid, side, result, kills, deaths, assists, firstblood, firstbloodkill, monsterkills, position, minionkills, league. In this dataset, each game has 12 rows, with 10 rows representing each of the players (i.e. player rows), and 2 rows for summarizing the overall team performance and result (i.e. team summary rows). We decide to keep all these rows, as they will be both utilized in the further analysis.

Furthermore, among these columns, we find out that the column minionkills have some missing values, and specifically there is one game that has all minionkills entries as missing. Since there are still many other games in the dataset, we decide to simply drop this specific game. Moreover, the rest of the missing values in minionkills are all coming from team summary rows. We write a helper function to impute these missing values by the total number of minions killed in that team in order to make it consistent with other non-missing values.

Below is the head of our league_clean dataframe.

gameid side result kills deaths assists firstblood firstbloodkill monsterkills position minionkills league
ESPORTSTMNT01_2690210 Blue 0 2 3 2 0 0 11 top 220 LCKC
ESPORTSTMNT01_2690210 Blue 0 2 5 6 1 0 115 jng 33 LCKC
ESPORTSTMNT01_2690210 Blue 0 2 2 3 0 0 16 mid 177 LCKC
ESPORTSTMNT01_2690210 Blue 0 2 4 2 1 0 18 bot 208 LCKC
ESPORTSTMNT01_2690210 Blue 0 1 5 6 1 1 0 sup 42 LCKC

*Note: The cleaned dataset here consists of all the columns we will need for both hypothesis testing and prediction model. When we get into each of the specific parts below, we will adjust this DataFrame further to make it compliant to our necessary steps.

Univariate Analysis

We permformed univariate analysis on the kill statistics in the dataset

The histogram shows that the distribution of team kills is nearly normal, slightly right skewed. This suggests that the data is well-behaved, with team kills being distributed in a manner that is relatively balanced and typical for such gaming scenarios.

We also plot a graph for the dirstribution of monsterkills in the data set.

The histogram shows that the distribution of monsterkills is nearly normal. This suggests that the data is well-behaved, with monsterkills being distributed in a manner that is relatively balanced and serves as good statistics for analysing player behavior.

Bivariate Analysis

We permformed bivariate analysis on the first blood and result statistics in the dataset to visualize among all the winning teams, how many them gets the first blood.

According to the plot, teams with first blood has a win rate about 60%. A 60% win rate implies that the majority of teams that secure the first blood end up winning the match, indicating that securing the first kill provides a strategic advantage that contributes to overall success.

Interesting Aggregates

Here are some intersting aggregates to invest within the data set.

firstblood result kills deaths assists team kpm minionkills
0 4873 159125 201307 360525 5032.85 1.84307e+07
1 7540 200452 158989 441953 6531.28 1.85042e+07

We first groupby the cleaned data set with firstblood status and then calculate the sum of all statistics. By comparing the gaming statistics with and without first blood. We had a better visualization about the difference in statistics for teams with and without firstblood. The team with first blood has a better statistics: more winning, kills assist, team damages, minionkills and less deaths.

Assessment of Missingness

NMAR Analysis

In our data, we believe the columns ban1, ban2, ban3, ban4, ban5 are all Not Missing At Random (NMAR). Looking into the columns, we see that all these 5 columns do not have any specific trends of missing, or any evidence of depending on other columns. In the actual League of Legends game, the players can decide by themselves if they want to ban any champion or not. In this case, we believe this is NMAR because these missing values appear when the players choose not to ban any champion, and this means the missingness of these values actually depends on themselves. An additional data we would obtain to make these columns Missing at Random (MAR) is all_banned, which has 1 indicating all players have banned a champion, and 0 indicating at least 1 player in the team forgetting to ban.

Missingness Dependency

In this part, we are going to test if the missingness of firstblood column depends on other columns. The two other columns that we used are league and result. The significance level we choose for both permutation tests is 0.5, and the test statistic is Total Variance Distance (TVD).

First, we perform the permutation test on firstblood and league, and the missingness of firstblood does depend on league.

Null Hypothesis: Distribution of league when firstblood is missing is the same as the distribution of league when firstblood is not missing.

Alternative Hypothesis: Distribution of league when firstblood is missing is NOT same as the distribution of league when firstblood is not missing.

Below is the observed distribution of league when firstblood is missing and not missing.

league fb_missing = False fb_missing = True
CBLOL 0.0222936 0
CBLOLA 0.0198165 0
CDF 0.00669725 0
CT 0.00238532 0
DCup 0.00117737 0.0423542
DDH 0.0191743 0
EBL 0.0169725 0
EL 0.0123853 0
ESLOL 0.0222018 0
EUM 0.0244954 0
GL 0.0159633 0
GLL 0.0186239 0
HC 0.0148624 0
HM 0.0140367 0
IC 0.00688073 0
LAS 0.0208257 0
LCK 0.042844 0
LCKC 0.0361468 0
LCL 0.00146789 0
LCO 0.0194495 0
LCS 0.0280734 0
LCSA 0.0495413 0
LDL 0.0143884 0.517602
LEC 0.0222936 0
LFL 0.0226606 0
LFL2 0.0221101 0
LHE 0.0222936 0
LJL 0.019633 0
LJLA 0.00348624 0
LLA 0.017156 0
LMF 0.0292661 0
LPL 0.0120183 0.432343
LPLOL 0.0191743 0
LVP SL 0.0224771 0
MSI 0.00733945 0
NEXO 0.0177064 0
NLC 0.0351376 0
PCS 0.0248624 0
PGC 0.0515596 0
PGN 0.0136697 0
PRM 0.0336697 0
SL (LATAM) 0.0151376 0
TAL 0.0188073 0
TCL 0.0202752 0
UL 0.0223853 0
UPL 0.0377982 0
VCS 0.029633 0
VL 0.0155963 0
WLDs 0.0131498 0.00770077

After we performed permutation tests, we found that the observed statistic for this permutation test is: 0.9647151320636651, and the p-value is 0. The plot below shows the empirical distribution of the TVD for the test.

Since the p-value is less than the 0.5 significance level, we reject the null hypothesis. Thus, the missingness of firstblood depends on the league column.

The second permutation test that we are performing is on firstblood and result, and the missingness of firstblood does not depend on result.

Null Hypothesis: Distribution of result when firstblood is missing is the same as the distribution of result when firstblood is not missing.

Alternative Hypothesis: Distribution of result when firstblood is missing is NOT same as the distribution of result when firstblood is not missing.

Below is the observed distribution of result when firstblood is missing and not missing.

result fb_missing = False fb_missing = True
0 0.500092 0.5
1 0.499908 0.5

After we performed permutation tests, we found that the observed statistic for this permutation test is: 9.174311926607448e-05, and the p-value is 0.98 . The plot below shows the empirical distribution of the TVD for the test.

Since the p-value is greater than the 0.5 significance level, we fail to reject the null hypothesis. Thus, the missingness of firstblood does not depend on the result column.

Hypothesis Testing

In the hypothesis test, we aim to assess whether there is a significant difference in the distribution of kills for winning games between the team that secures the first blood and the team that does not. This investigation is crucial for understanding the relationship between securing the first blood in a League of Legends match and the subsequent gameplay dynamics, particularly in terms of kill distribution among winning teams.

Null: The distribution of kills for winning games for the team that gets the first blood is the same as the team that does not get the first blood.

Alternative: The distribution of kills for winning games for the team that gets the first blood is NOT the same as the team that does not get the first blood.

Test Statistics: Absolute mean difference between teams in kills with and without first kills,

Significance Level: 5%

Here is a histogram containing the distribution of our test statistics during the hypothesis test:

Based on the hypothesis test performed, with a p-value of 0.0009990, we reject the null hypothesis. This suggests that the distribution of kills for winning games for the team that secures the first blood is NOT the same as the team that does not get the first blood. This finding leads us to consider that securing the first blood may indeed have a significant impact on the gameplay dynamics and overall success of the team in League of Legends matches.

Framing a Prediction Problem

From the last section, we found out that getting first blood may have a significant impact on the team kills. Since the statistics for each team could be so different, are there any specific characteristics for each position in terms of in-game statistics? In other words, is it possible to predict a player’s position solely by analyzing their in-game statistics, such as first blood kills, deaths, assists, and other relevant features?

To address this question, we can employ machine learning techniques such as classification algorithms. For our prediction model, we will focus on the jungle position only. Thus, at here, the model that we built are based on the following prediction problem: Are we able to predict if a player’s position is jungle or not based on their other game statistics?

In this part, we will need to one-hot encode the original position column, and this will give us 5 binary columns representing each position: position_top, position_jng, position_mid, position_bot, position_sup. Since we are predicting based on individual performance, we decide to drop all the team summary rows, and keep only the player rows. Thus, this is a binary classfication model, and our responsive variable is position_jng. As we are only predicting if the given player is jungle or not, we can drop all other binary columns for position. Below is the head of DataFrame we are using in this section:

index kills deaths assists firstbloodkill team kpm minionkills position_jng
0 2 3 2 0 0.3152 220 0
1 2 5 6 0 0.3152 33 1
2 2 2 3 0 0.3152 177 0
3 2 4 2 0 0.3152 208 0
4 1 5 6 1 0.3152 42 0

To prevent overfitting, the data will be split into two parts: 75% training data, and 25% test data. In terms of model’evaluation, we will use both accuracy and F1-score. The reason we are using F1-score on top of accuracy is because the data we are working on is unbalanced. In the DataFrame, 20% of the player’s positions are jungle, and 80% of players are some other positions; the accuracy score alone won’t give us a representative evaluation of the model.

At the time of prediction, we only know the following information for each player: kills, deaths, assists, firstbloodkill, monsterkills, and minionkills. These are all the statistics collected during the game. We will train our model based on the above features.

Baseline Model

For the baseline model, we used a Random Forest Classifier, with the following four features: kills, deaths, assists, and firstbloodkill. Among these four features, three of them are quantitative: kills, deaths, and assists. We utilized StandardScaler Transformer to transform them into standard scale, becasue each match has different time length, and therefore the statistics could seem really different without being standardized. The last one firstbloodkill is a nominal categorical variable, and it is already in binary form, thus we do not need to perform more encodings.

After fitting the model, our accuracy score on the training data is 0.7910. This means that our model is able to correctly predict 79.10% of data. This accuracy score may sound really high, but it is quite misleading since our data is unbalanced. The F-1 score of this model is 7.68% which is extremely low. Such a low F-1 score is due to a low Recall of 0.043, as our model has many false negatives. Our model still has large improvement space, and we will improve it through adding more features, and tuning hyperparameters in the next section.

Final Model

In our final model, we added two more features: monsterkills and minionkills. We are adding these two features into our model because we believe in the LOL game, the champions in jungle positions usually have higher damage, so they are able to kill more minions compared to other positions at the same amount of time. Moreover, the main job of the jungle position in the game is to kill the monsters, so we believe jungle positions should have a relatively high monsterkills number. Additionally, minion kills reflect a player’s ability to efficiently farm gold and experience, which are crucial for scaling and gaining advantages in the game. Therefore, we expect that both monsterkills and minionkills will provide valuable predictive power in our final model, allowing us to better understand the factors influencing victory in League of Legends matches.

Our final model also uses a Random Forest Classifier in alignment with the baseline model. The two additional features we added (monsterkills and minionkills) are both quantitative features, so we used StandardScaler Transformer to perform encodings of these two columns. In terms of tuning hyperparameters, the two hyperparameters we chose are: max depth and the number of estimators for the random forest classifier. We are testing max depth of 2 through 200, with each of 20 steps. For the number of estimators, we are testing from 2 to 100, with each of 10 steps. Using the technique of grid search to find the best hyperparameters, we found out that the best max depth is 22 and the best number of estimators is 42.

The accuracy score is now 0.9993, meaning our model is able to correctly predict 99.93% of our data. This score is super high! If we now take a look into the F-1 score, it is 99.84%, meaning both of our precision and recall are close to 1. We have achieved huge improvement in both evaluation metrics, and this improvement suggests that our adjustment to the model is effective in terms of prediction power.

Fairness Analysis

In this section, we are going to assess if our model is fair among different groups. The question we are trying to answer here is: “does my model perform worse for individuals who have monsterkills less than or equal to 100 than it does for individuals who have monster kills greater than 100?” To answer this question, we performed a permutation test and examined the result of the difference in accuracy between the two groups.

The group X represents the players who have monsterkills less than or equal to 100, and group Y represents those who have monster kills greater than 100. Our evaluation metric is accuracy, and the significance level is 0.05.

The followings are our hypothesis:

Null hypothesis: Our model is fair. Its accuracy for players who have less than or equal to 100 monsterkills is same as the accuracy for players who have greater than 100 monsterkills.

Alternative hypothesis: Our model is unfair. Its accuracy for players who have less than or equal to 100 monsterkills is NOT same as the accuracy for players who have greater than 100 monsterkills.

Test statistics: difference in accuracy between individuals who have monsterkills less than or greater than 100.

After performing the permutation test, the result p-value we got is 0.896, which is larger than the 0.05 significance level. Consequently, we fail to reject the null hypothesis. This outcome implies that our model predicts players from both groups with statistically similar accuracy levels. Consequently, our model appears to be fair, exhibiting no discernible bias towards one group over the other based on the specified criteria.