Introduction

Multiplayer Online Battle Arena (MOBA) is a genre of strategy online games that has drawn growing attention and has become extremely popular. MOBA consist of match-based games, where players, divided into two opposing teams, compete against each other. Each player during the match controls a single character (a.k.a., champion), having a specific role and abilities. The main goal in each match is to destroy the enemy team's base, while enhancing the player level, increasing the abilities of the controlled character, and cooperating with one's own teammates.

This genre of games, including Heroes of the Storm, Dota 2, and League of Legends, has attracted researchers from different fields, especially because they provide a unique way to study the influence of role-playing in competitive games, the impact of cooperation versus individual player attitudes, social behaviors, user commitment, etc. The analysis of MOBA games also allows for the discovery of useful information to study the social dynamics of player communities. For example, by extracting players' social activities and relations, researchers addressed issues such as gender gap and improved the user experience.

One advantage of analyzing players' records in online games is the possibility of monitoring how their behaviors evolve over time. The temporal dimension exhibited by such data enables the study of the evolution of player performance, specifically how players learn, adapt, and modify their playing strategies over time.

We propose to study both the temporal and social dynamics of players in MOBA games at once. Here, we will focus on the analysis of League of Legends (LoL), a popular MOBA game. Our goal will be that of identifying different groups of players with common strategies, such as collaborative versus individualist players, and understanding how these groups of players behave in time, i.e., how their strategies evolve over time.

To this aim, we take advantage of Non-negative Tensor Factorization (NTF)  techniques, which derive from multi-linear algebra. Non-negative Tensor Factorization models can be seen as an extension of Matrix Factorization, a method which provides a low-rank approximation of the data that has been widely used to detect hidden structures among data in several contexts, such as face recognition, hyperspectral unmixing, community detection, recommender systems, etc. Analogously to matrix factorization, tensor factorization allows to approximate data in a lower dimensional space. However, due to their multiple dimensions, tensors are suitable objects to represent multimodal data. This allows to identify correlation in the data at different levels: on the one hand, the application of the NTF helps in the identification of hidden topological structures in the data, like groups or communities, which are easy to interpret as they reflect individuals' social dynamics. On the other hand, these topological structures share correlated activity patterns. A major advantage in mining tensors, instead of using more common matrix factorization techniques, is the possibility of extracting these correlations in the data in more than two dimensions, thus avoiding studying data at an aggregated level. Moreover, the use of non-negative constraints eases the interpretation of the patterns provided by the tensor factorization. Our purpose is therefore to leverage NTF to detect groups of players characterized by similar features (i.e., actions they perform during the game) and strategies as well as their temporal trajectories, i.e., their evolution.


Contributions

In this work, we present a framework based on NTF to study players' behavior in online games. The framework, shown in Figure 1, consists of a combination of machine learning and classification methods. In particular, we use Decision Tree to select the features in the data that will become part of the input of the NTF. We then apply the NTF in combination with other methods, such as k-means, to extract meaningful information about users' activity. Through the lens of this framework, we study the gaming history of about 1000 League of Legends players accounting for a total of roughly 100K
matches. Our analysis will:



Figure 1. Framework. Our methodology is divided into several steps. First, we use Decision Trees to find the features of the dataset that are meaningful in predicting users' performance (the outcome is the feature "winner"). Once the features are selected, we create a tensor whose dimensions coincide to users, selected features, and time. We then decompose the tensor by applying NTF and detect the factor matrices A, B, and C, providing the users' and features membership, and temporal activity respectively. Finally, we use this information to analyze the discovered groups of users characterized by similar features and temporal behavior.

  • Highlight the existence of an underlying structure in the data, that allows us to divide players into groups characterized by similar features and having correlated temporal behaviors;
  • Provide an interpretation of the components extracted by the NTF;
  • Validate the interpretation of the NTF results by analyzing the uncovered groups and their evolution over time;
  • Discover, by analyzing the temporal components, that players' playing strategies are consistent over time;
  • Provide and validate an explanation for players behavioral stability, namely that the design of the game strongly impacts team formation in each match, thus manipulating the team's probability of victory.