This DSC80 project of UCSD involves tasks such as cleaning data, performing exploratory data analysis, assessing missingness, and conducting hypothesis tests. The results and insights from these analyses are presented on this website, serving as a comprehensive report of our findings.
Creators: Angelina Zhang and Ziyu Huang
We choose the dataset documenting professional League of Legends games throughout 2023; each game, uniquely identified by a distinct gameid shown in the first column, is represented with ten rows delineating individual player data for competing teams and an additional two rows offering comprehensive team statistics. The dataset boasts 129264 rows and 123 columns with detailed information about each game. With such data, we want to investigate whether there is a correlation between the side of the team and the win rate (question: Would the side of the team affect the win rate?). Furthermore, our investigation extends to exploring potential associations between the identified side-dependent win rate and the nuanced disparities in resource allocation across the game map. The differences involve explicitly scrutinizing the variances in resources, such as those about baron, dragon, and herald objectives, to discern whether inherent map-related distinctions contribute to divergent team performances based on their designated sides. As a result, we added a new column, called natural_resources, dedicated to explicitly recording perceived resources, aiming to encapsulate the nuanced dynamics surrounding resource acquisition.
Our analysis aims to shed light on the intricate dynamics and strategic implications associated with team positioning in the League of Legends competitive landscape by providing a more granular understanding of the impact that map-related differences may exert on team outcomes.
‘side’ is the side of one team in the game, which is Blue or Red
‘result’ is True when the team won the game and False otherwise
‘gamelength’ is the total time taken to finish the game in second
‘league’ is the league to which the game belongs
‘golddiffat15’ is the variance in total gold between teams at the 15-minute mark in a game
‘golddiffat10’ is the variance in total gold between teams at the 10-minute mark in a game
‘totalgold’ is the cumulative total gold accumulated by a team throughout the duration of the game
‘earned gpm’ is the earned gold per minute, offering insights into the team’s gold generation rate
‘barons’ is the number of baron objectives secured by a team in the game
‘dragons’ is the total number of dragon objectives secured by a team
‘heralds’ is the number of herald objectives secured by a team in the game
‘datacompleteness’ is the given completeness of each row in the original dataframe, which contains complete, and partial
‘gamelength_new’ is the length of a game and we convert the original gamelength into hours: minutes format
‘natural_resources’ we add this column after imputation to better showcase the relation between side and resources distribution, it contains the sum of barons, dragons, and heralds
We cleaned the data first by making a copy of the original dataset. Then we keep relevant columns and rows, to be more specific, those columns described before and rows that contain team summary for each game. We change ‘barons’ and ‘dragons’ from float type into int and change ‘result’ into boolean type. After investigation, we found out that the ‘game length’ column contains the total time of a game in minutes, and we chose to keep it to facilitate time comparison but added a new column ‘gamelength_new’ to let it become a readable format. We did not convert ‘golddiffat15’, ‘golddiffat10’, and ‘heralds’ because they contain missing values, and we will address that in a later section. We will also add the ‘natural_resources’ after imputation in a later section.
| side | result | gamelength | league | golddiffat15 | golddiffat10 | totalgold | earned gpm | barons | dragons | heralds | datacompleteness | gamelength_new |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Blue | True | 2612 | LFL2 | -530 | 75 | 72807 | 1028.8 | 1 | 4 | 2 | complete | 43:32 |
| Red | False | 2612 | LFL2 | 530 | -75 | 62745 | 797.665 | 0 | 3 | 0 | complete | 43:32 |
| Blue | False | 2436 | LFL2 | 673 | -361 | 80627 | 1339.95 | 2 | 3 | 2 | complete | 40:36 |
| Red | True | 2436 | LFL2 | -673 | 361 | 77449 | 1261.67 | 1 | 4 | 0 | complete | 40:36 |
| Blue | True | 1980 | LFL2 | -1901 | -1001 | 60938 | 1192.85 | 0 | 4 | 0 | complete | 33:00 |
This histogram provides a visual representation of the distribution of game lengths, allowing one to observe patterns, central tendencies, and variability in the dataset.
<iframe src="assets/Winning_Sides_Distribution.html" width=800 height=600 frameBorder=0></iframe>This pie chart shows the distribution of win rates for the red and blue sides, and we calculated them by separating the cleaned data into two sides and computing the win proportion for each. Two numbers add up to 100% because the total number of games for the red or blue side is the same. Based on the observation, we guess that the Red team has a better chance of winning the game.
<iframe src="assets/Side_Resources_Distribution.html" width=800 height=600 frameBorder=0></iframe>This bar chart shows the average resources allocated by the two sides after we imputed the missing data and calculated the data for the amount of natural resources. The bar chart suggests that the Blue Team is likely to acquire more natural resources than the Red Team. We will conduct a hypothesis test to determine the validity of our assumption.
| league | complete | partial |
|---|---|---|
| AL | 346 | 0 |
| CBLOL | 484 | 0 |
| CBLOLA | 496 | 0 |
| CDF | 136 | 0 |
| CT | 86 | 0 |
| DDH | 172 | 0 |
| EBL | 318 | 0 |
| EL | 82 | 0 |
| EM | 542 | 0 |
| EPL | 172 | 0 |
| ESLOL | 604 | 0 |
| GL | 178 | 0 |
| GLL | 328 | 0 |
| HC | 282 | 0 |
| HM | 324 | 0 |
| IC | 134 | 0 |
| LAS | 504 | 0 |
| LCK | 974 | 0 |
| LCKC | 1010 | 0 |
| LCO | 280 | 0 |
| LCS | 528 | 0 |
| LDL | 0 | 1712 |
| LEC | 574 | 0 |
| LFL | 484 | 0 |
| LFL2 | 498 | 0 |
| LHE | 118 | 0 |
| LJL | 516 | 0 |
| LJLA | 184 | 0 |
| LLA | 384 | 0 |
| LMF | 172 | 0 |
| LPL | 0 | 1510 |
| LPLOL | 320 | 0 |
| LRN | 232 | 0 |
| LRS | 238 | 0 |
| LVP SL | 492 | 0 |
| MSI | 152 | 0 |
| NACL | 1734 | 0 |
| NEXO | 338 | 0 |
| NLC | 314 | 0 |
| PCS | 586 | 0 |
| PGN | 402 | 0 |
| PRM | 484 | 0 |
| SL (LATAM) | 180 | 0 |
| TCL | 360 | 0 |
| UL | 490 | 0 |
| VCS | 646 | 0 |
| VL | 176 | 0 |
| WLDs | 242 | 26 |
To gain insights into the missingness patterns, we examine a pivot table of 'datamissingness' grouped by league. The resulting table shows that missing values are present only in the leagues LPL, LDL, and WLDs. This observation suggests that the missingness may follow a pattern known as Not Missing at Random (NMAR).
In the analysis of Interesting Aggregates, we identified the potential occurrence of Not Missing at Random (NMAR). Upon examination of the table, it became apparent that the entries for "LPL" and "LDL" account for the majority of missing data, and both leagues are located in China. Consequently, we proceeded to group the data into two groups: one comprising leagues from China and the other consisting of leagues not from China. The bar chart below shows the result of the grouping:
The graph indicates a notable impact of leagues on the missing data, the majority of which is concentrated in China, and we want to run a permutation test to support this assumption.
The Data is Not Missing At Random, and the missing data is dependent on whether leagues are in China.
The Data is Missing At Random.
We use the Total Variation Distance (TVD) to see the difference between the missing rate of the leagues in China and leagues not in China.
We choose a significance level of α=0.05.
p = 0.3116
With a p-value of 0.3116 obtained from the permutation test for missingness data, we fail to reject the null hypothesis. The evidence does not provide sufficient grounds to conclude that the missing data depends on whether leagues are in China. Therefore, based on the chosen significance level of α=0.05, we do not have statistically significant support for the alternative hypothesis, suggesting that the data is missing at random.
The Total Variation Distance (TVD) was employed as the test statistic to measure the difference in missing rates between leagues in China and leagues not in China. The non-significant p-value suggests that any observed differences in missingness are likely due to random variation rather than a systematic pattern related to the location of leagues.
<iframe src="assets/Empirical_Distribution_of_NMAR.html" width=800 height=600 frameBorder=0></iframe>Given that the missing data for "heralds" is considered part of the natural resources category, we will proceed with imputation to facilitate further analysis.
In light of the absence of any available data on "heralds" in the LPL and LDL leagues and recognizing the limitations for imputation, we randomly assign 1 or 0 to the missing values. This approach is designed to minimize the impact of missingness on our subsequent analysis.
The distribution of wins for the red-side teams is the same as the distribution of wins for the blue-side teams.
The distribution of wins for the red-side teams is different from the distribution of wins for the blue-side teams.
We use the Total Variation Distance (TVD) to see the difference between the win rates of the Red and Blue teams since we use categorical data and wonder if two sample distributions come from the same distribution.
We choose a significance level of α=0.05.
p = 0
Given that the p-value is equal to 0, which is less than the chosen significance level of α=0.05, we reject the null hypothesis H0 in favor of the alternative hypothesis H1. This rejection signifies a statistically significant difference in the distribution of wins between the Red and Blue side teams. Therefore, we have substantial evidence to believe that the team side (Red or Blue) is associated with distinct win rates, supporting the alternative hypothesis.
It's crucial to emphasize that while we reject the null hypothesis, the test, which utilizes Total Variation Distance (TVD) as the test statistic for categorical data, does not provide information regarding the specific nature of the observed difference or establish causation. It only serves as evidence that the win rates differ between the Red and Blue teams.
A follow-up hypothesis test is conducted to ascertain which team side is more likely to win the game. This additional analysis will provide deeper insights into the specific dynamics influencing the observed disparity in win rates between the two teams.
<iframe src="assets/Empirical_Distribution_of_the_difference_in_the_Win_Rate.html" width=800 height=600 frameBorder=0></iframe>The win rate of the Red team is equal to 0.5, suggesting no difference from a balanced win rate.
The win rate of the Red team is greater than 0.5, indicating a tendency for the Red team to win more frequently.
We will use the z-value as the test statistic to assess the deviation of the Red team's win rate from the hypothesized value.
We choose a significance level of α=0.05, representing the probability of observing a result as extreme as the one obtained, assuming the null hypothesis is true.
p = 0
The obtained p-value of 0, which is less than the chosen significance level (α=0.05), leads us to reject the null hypothesis that the win rate of the Red team is equal to 0.5. This rejection provides strong statistical evidence in favor of the alternative hypothesis, indicating that the win rate of the Red team is greater than 0.5.
Therefore, based on the hypothesis test results, we have reason to believe that the Red team is more likely to win games than expected by chance. The statistical significance of this finding implies that the observed difference in win rates is unlikely to be due to random variability.
It's important to note that while we have established a statistically significant difference, the test does not provide information on the magnitude of the difference or the specific factors influencing the win rates. Further analysis or investigations may be warranted to explore the practical significance and potential underlying reasons for the observed pattern in team performance.
<iframe src="assets/Standard_Normal_Distribution.html" width=800 height=600 frameBorder=0></iframe>The amount of natural resources of the Red team and the amount of natural resources of the Blue team are drawn from the same distribution.
The amount of natural resources of the blue team and the amount of natural resources of Red are drawn from different distributions.
We use the mean difference to see the difference between the average natural resources of the red and blue teams since it is a valid measure to figure out if a difference in resource allocation exists for both sides.
We choose a significance level of α=0.05.
p = 0
With a p-value of 0 obtained from the second permutation test, we reject the null hypothesis (H0) that the number of natural resources of the Red and Blue teams are drawn from the same distribution. Our p-value suggests strong evidence favoring the alternative hypothesis (H1) that the amount of natural resources for the Red and Blue teams is drawn from different distributions.
Therefore, based on the significance level of α=0.05, we conclude that there is a statistically significant difference in the average natural resources between the Red and Blue teams. This implies that the resource allocation for these two teams is likely to be distinct, and further investigation may be warranted to understand the underlying factors contributing to this difference.
<iframe src="assets/Empirical_Distribution_of_the_difference_in_the_Natural_Resources.html" width=800 height=600 frameBorder=0></iframe>