Human Team Behavior and Predictability in the Massively Multiplayer Online Game WOT Blitz

Advances in information technology and the World Wide Web enable online and real-time communication among users worldwide. One form of such communication is provided by Massively Multiplayer Online Games (MMOGs) [1, 15, 18]. MMOGs allow the connection of players who are locally separated to play a multitude of different games online. Popular examples for MMOGs with millions of active users are World of Warcraft, Guild Wars 2, Lord of the Rings Online, World of Tanks, and The Elder Scrolls [80]. From a scientific perspective, it has been realized that MMOGs allow the addressing of many different questions from a variety of fields because large amounts of data are available for a quantitative analysis [4]. Put simply, one can utilize an MMOG as a representation of a virtual world from which every aspect can be recorded and monitored. That means an MMOG is like a virtual Petri dish that can be studied to learn about social, behavioral, psychological, or economic phenomena [13, 60, 72]. Instances for previously studied questions include the network structure of gold farming or user interactivity networks [44, 70], the scaling behavior of online users (avatars), game servers or behavioral action sequences [41, 76, 78], cooperation and team formation [63, 79], and the psychology of users [8].

In this article, we study the MMOG World of Tanks (WOT) Blitz. WOT Blitz was developed by Wargaming and released in 2014. According to Wargaming, the game is played by 100 million players worldwide. The mobile game is available for tablets, smartphones, and PCs for Windows 10, Android, and iOS. WOT Blitz is a competitive strategy game between two teams, each with seven players. The game has a similar play style as dodgeball, where ‘ball hits’ are exchanged via ‘shots’ causing a certain amount of damage. Different battle types are available (regular, rating, or realistic), as well as a number of different maps that can either be played in encounter or supremacy mode. The goal of the game is essentially either to destroy all vehicles of the opponent or to capture the base(s).

For investigating WOT Blitz, we use a data science [64] and complex adaptive systems [39, 69] approach for analyzing data on the population level to gain insight into the organizational behavior of the system. Specifically, we utilize information about 403 vehicles (tanks) from 10 tiers (corresponding to difficulty levels) for which average summary statistics from 24,015 players and more than 2.62 million matches are available. Importantly, the rules of the game allow only the pairing of vehicles in matches that are either from the same tier or from adjacent tiers (e.g., from tier 4 and tier \(5)\) . That means vehicles from further apart tiers never meet in-game.

There are several reasons for selecting WOT Blitz for our study. First, despite the immense popularity of WOT Blitz, so far there are no studies investigating this game. In fact, the only study based on WOT Blitz we found investigates in-game chat and cyberbullying [58]. In contrast, in our study, we do not use information from the in-game chat at all. Second, the available data in the form of summary statistics of vehicles are quite challenging because they hide many details (e.g., about the performance of individual players or the teams). This is intriguing because it allows us to learn what can still be revealed beyond individual vehicles. Third, the available summary statistics of vehicles are robust. This is due to a feature of the game that limits the duration of a match to 7 minutes; however, a game can end even earlier. In combination with its popularity, this allows us to gather information about the outcome of millions of games upon which the summary statistics of vehicles are based. Fourth, although WOT Blitz is not a sports game itself, it has characteristics thereof because two teams are playing against each other to win. That means the underlying mechanism that drives everything is human team behavior. All these reasons together make our study unique and provide the first steps toward deeper insights into this complex game.

In this article, we investigate the organizational principles of WOT Blitz and its game mechanics. For this, we study three major levels. First, we study the scaling behavior of the population of vehicles. This allows us to identify long-range interactions of system variables. Second, we identify and quantify the predictability of performance measures by classifying the population of vehicles. For this, we will study the hierarchical clustering of vehicles based on averaged vehicle characteristics. That means we define profile vectors of vehicles based on averaged vehicle characteristics estimated from thousands of individual matches. Performing such an analysis in dependence on the tiers allows us to reveal differences and similarities of different tier stages. This translates the abstract finding about the scaling behavior of the population of vehicles into concrete realizations with a focus on output variables. Third, we quantify the importance of covariates on the predictability by a regression framework utilizing the method LMG (Lindeman, Merenda, and Gold) [47]. LMG is a method for decomposing the coefficient of determination, R2, which can be estimated for linear regression models [32]. This will provide information about the probabilistic contribution of individual predictor variables. Hence, this analysis step focuses on the input variables on which an output variable (in our case, a performance measure) depends, and their contribution on the prediction. In general, this decomposition allows us to identify the covariates that are most important in predicting the output variable. For our analysis, we perform such a decomposition in dependence on different tiers allowing us to gain insight on the progression of the game across the offered difficulty levels.

From the description of our analysis follows a number of potential limitations. First, we would like to note that not all studies about MMOGs allow the same level of insights. For instance, in the work of Burt [11], players of the game Everquest were investigated. This allowed them to link observable data in the MMOG via the structure of their collaboration networks as they perform quests, with real-world constructs that are of general importance, including personality. To accomplish such an insightful analysis, the collaboration networks of individual players had to be analysis. In contrast, in our work, we study only data about average game statistics of vehicles that do not allow us to draw conclusions about individual players. Still, the game is played by humans and also our data are the result from human team behavior. Second, despite the generic name massively multiplayer online games, there are considerable differences among MMOGs. For instance, major game types one can distinguish are role-playing, real-time strategy, first-person shooter, or simulations [59], whereas WOT Blitz is of the latter type. It is clear that the game type has an impact on what can be learned, and this is also the case for our study. Third, we are not only limited to data corresponding to summary statistics of vehicles, but these data are obtained from observations, not interventions. That means the data do not result from controlled experiments specifying, for example, well-defined situations or conditions but are obtained from ordinary games.

This article is organized as follows. In Section 2, we discuss our research questions and contributions. In Section 3, we present the methods and data used in this work. In Section 4, we present findings about general characteristics of the data, scaling-behavior of system variables, detection of predictability, and quantifying the importance of predictor variables. This is followed by a discussion and interpretation of our findings in Section 5, which also places these into a broader context. Finally, we present a brief summary and concluding remarks in Section 6.

In this article, we analyze data from the MMOG WOT Blitz. For this, we use summary statistics of vehicles. These data provide information about the average performance of 16 features of vehicles that are used by players in two teams to compete in matches. That means human team behavior is the underlying mechanism that drives everything observable in the summary statistics of vehicles. It is worth highlighting that no information about individual players including their performance is used for our analysis.

The goal of this study is to address the following five research questions based on the available data:

To 1.: The first question aims to establish a connection between WOT Blitz and a class of systems that exhibits self-organizing behavior [3]. This is important because it has been shown that self-organizing systems have a self-tuning property that allows them to reach stable working conditions. Put simply, this is an expression of a functional system. We will establish this connection by identifying power-laws between system variables as a result of local interactions. In our case, this corresponds to the competing vehicles, controlled by human players, in matches.

To 2.: The second question relates to the fact that according to the rules of the game, vehicles of adjacent tiers are selected for a match. Considering that the tiers represent the difficulty levels of the game, this requires a fair balancing among the tiers, as without such a balancing, vehicles of a higher tier would be always stronger and everyone would only want to play the highest tier to guard against sure losses.

To 3.: Since the goal of any game is to win, the win rate of vehicles provides information about the most important aspect of a game, namely the outcome of matches. The third question studies the predictability of the outcome of games by using features of vehicles. Considering the rules of the game that pairs vehicles of adjacent tiers and the need for a balancing of vehicles among tiers, we study this for each tier because the results should also be a reflection of those constraints.

To 4.: For predicting the behavior of a system, typically a high-dimensional representation is needed to achieve good results. In general, the problem with such high-dimensional representations is that they lack interpretability. For this reason, we aim to find a low-dimensional approximation that provides a good representation for outcome variables of the game. For our analysis, we use the LMG method [47], which allows a decomposition of predictor variables for quantifying their importance. From this, we identify the most dominating features of predictions.

Overall, our study makes the following contributions. First, to the best of our knowledge, the game WOT Blitz has not been studied before. Hence, we step on new ground regarding an understanding of essentially any aspect of this complex game, including the predictability of outcome variables, balancing of vehicles among tiers, and the progression through them. Given the popularity of WOT Blitz, which is played by millions of players worldwide, this is surprising because it is not a niche game but a well-known contender for MMOGs.

Second, one important aspect of our study is power-law distributions because they allow a connection to self-organizing systems. An example of another study that investigated power-law distributions is that of Chun et al. [17]. In this work, the game Aion was studied, which is a Massively Multi-Player Online Role-Playing Game (MMORPG), and power-law distributions of network features were found. A similar study for various games was conducted by Kirman et al. [46], all revealing power-law distributions of network features. In contrast, in the work of Jiang et al. [41], the MMORRG Legend of Mir was studied, and power-law distributions for the online avatar numbers revealed corresponding to the number of active players. Yet a different power-law was studied by Pittman and GauthierDickey [62]. In their work, it was shown that the spatial distribution of players in World of Warcraft follows a power-law distribution. This shows that also regarding the studied power-laws, our study is different because we investigate them neither for networks nor active players or spatial positions of players but for measured in-game features that characterize the performance of vehicles controlled by the players.

Third, in our study, we propose the combined usage of methods from data science and complex adaptive systems. This combination provides a large arsenal of available methods and allows the exploitation of complementary benefits. Specifically, in our study, we use eight different methods (descriptive statistics, linear regression, nonlinear regression, classification, hierarchical clustering, scaling behavior, resampling, and LMG) to investigate WOT Blitz from several angles. In contrast, most studies utilize only a few methods or even only one method for the analysis. For example, in the work of Chun et al. [17], network analysis was combined with the scaling behavior, and in the work of Jiang et al. [41], only a spectral analysis was used. In a wider context of MMOGs and related publications, the study by Cheng et al. [16] used descriptive statistics, correlation analysis, and classification, Szell and Thurner [74] used network analysis, and Thawonmas et al. [75] applied clustering. It is noteworthy to highlight that in the work of El-Nasr et al. [21], the importance of data science for studying MMOGs has been addressed but without a connection to complex adaptive systems, whereas in the work of Bainbridge [4], the potential of complex systems for investigating MMOGs has been discussed but without a connections to data science. This shows not only that our study is more extensive with respect to the applied methodology than most studies, even in a broader context, but also that the combined usage of data science and complex adaptive systems is so far underestimated.

The latter point is of particular importance for other MMOGs because it allows a method transfer. That means, beyond the results we obtain from analyzing WOT Blitz, our approach itself that combines methods from data science and complex adaptive systems could be of interest for other MOGGs also requiring flexibility in addressing complex problems.

In this section, we discuss the data and the methods used for our analysis.

In the following section, we present our results. First, we are providing a general overview of the characteristics of the data. Then we investigate the scaling behavior and the predictability of system variables.

From our analysis, we found various power-laws (e.g., between the win rate vs kills/deaths ratio). Statistically, a power-law arises when the relation between two variables assumes a functional form with a constant power independent of the initial size and the relative changes. That means regardless of the size of the initial variable, the response of the second variable does not depend on it. Formally, one can derive this behavior from \(y = ax^{\gamma }\) and \(x \rightarrow x^{\prime }=bx\) byFrom this behavior, one can see that regardless of the scale of x, which is controlled by b, the value of the response variable \(y^{\prime }\) changes according to the same power-law exponent \(\gamma\) as for y. For this reason, the power-law behavior between x and y is called called scale-free.

The power-law behavior between the win rate and kdr is quite interesting for the following reasons. First, it reveals long-range interactions of system variables across all tiers. This is remarkable, because in each match, according to the rules of the game, at most two adjacent tiers are involved; however, the power-law involves all tiers. In general, the connection between a power-law behavior and long-range correlations has been studied extensively. Specifically, critical systems are known to exhibit a temporal and spatial scale-invariant behavior in the form of fractals and 1/f noise [5, 40]. This is a reflection of a propagation process resulting in long-range correlations based on local effects. Famously, this has been demonstrated by using a sandpile model [7] but has been subsequently found in many physical systems (e.g., ferromagnets [19], supercondutors [27], and plasma [66]). Importantly, also outside of physics, this effect has been observed for a number of different models, including the evolution of genomic DNA [53], score evolution of the game cricket [67], earthquakes [45, 61], the MMOG Pardus [74], the Minority game [14], and financial markets [50]. For reasons of clarity, we would like to note that the interpretation of our power-law is different from conventional studies because, usually, the scaling is studied over intuitive dimensions of a system (e.g., space or time). For instance, for the sandpile model, the scaling is over the size of avalanches or their durations [7]. However, exceptions to the preceding can be found in the work of Bak and Sneppen [6], where the scaling of punctuated equilibrium has been studied over the distance of mutations changing the fitness of species, or in the work of Lux and Marchesi [50], where the scaling of the financial market has been studied over returns. Similarly, our power-laws are also observed in an abstract space provided by the system variables win rate, kills/deaths ratio, and damage ratio.

To further extend the understanding for the observed power-law behavior and its interpretation, we would like to mention that such a behavior is typical for self-organizing systems. In a general context, a “system” is a purposeful collection of inter-related components that work together to achieve an objective. A more dedicated definition of self-organization has been provided by Camazine et al. [12]:

In our case, the “components” are the individual players who work together in teams of seven with the “objective” to win against other teams. Furthermore, the “interrelation” between the components corresponds to the team play because if every player plays egoistically, the chances to win a game are decreased. Finally, the game is self-organizing [3, 12, 38] because there is no external “coach” who would influence or even determine the game, but the individual players make independent decisions in a way that increases the likelihood of winning. We would like to re-emphasize that the game is played by humans, not algorithms. Hence, a team play is a form of social cooperation because for each game, seven humans play against seven other humans. These observations may be obvious to some readers, but due to the technology-mediated form of the game, which masks the underlying setting abstractly, others may not see these connections immediately. To make this even more clear, we would like to add that the game is different from cyber-physical systems (CPS) [31, 56], which are systems of collaborating computational entities that interact with the surrounding physical world and its ongoing processes. Instead, WOT Blitz is in some sense an ordinary team-based game similar to soccer or basketball but with the difference that all interactions among the players, including the generation of the environment itself in which the game takes place, are computer generated and purely virtual. We believe it is interesting to note that this should allow investigations of, for example, social behavior, cooperation, and even psychological phenomena similar to other team-based games [20, 43, 51, 68].

It is also interesting to note that the scaling behavior is only observed in a double logarithmic representation of win rate and kdr. That means the inverse transformation back to the original variables (i.e., win rate and kdr) is an exponentialization. However, this means that in the original scales of win rate and kdr, the interactions are along exponential steps (not linear ones). The latter observation may provide an explanation for the highly nonlinear progression of the game moving toward higher tiers. Put simply, it is a known problem that good players on lower tiers struggle to compete on higher tiers in the sense that their performance drops considerably. The following average statistics for an individual player with a win rate of \(80.1\%, 73.3\%, 65.0\%, 57.0\%, 50.9\%, 53.2\%, 45.1\%,\ \textrm {and}\ 43.9\%\) for tiers 3 through 10, respectively, exemplifies this.

An indirect effect of this may be related to abusive language and toxicity observed from analyzing in-game chats [58]. Unfortunately, this study analyzes this issue only across all tiers for World of Tanks (which is similar to WOT Blitz) and is not tier specific. For this reason, it is unclear if, for example, the use of abusive language increases toward higher tiers. However, individual players are not obligated to play on the highest tier accessible to them but can play low tier vehicles, even when they have vehicles on higher tiers. As a side note, we hypothesize that the jumping of players between tiers might spread toxicity, similar to an infection, even if toxicity would be dominating on one particular tier.

The hierarchical clusterings shown in Figures 5 through 7 allowed us to study the similarity of performance characteristics of vehicles from different tiers. Intuitively, one would expect that vehicles of the same tier perform similarly. Ideally, this would result in two branches in a dendrogram, each containing only vehicles from the same tier corresponding to all blue and all red branches. When using the dendrogram for a binary classification by splitting it along its two main branches, this would result in a Matthews correlation coefficient of \(\pm 1.0\) (a relabeling of all class labels changes the sign) and an AUROC of 1.0. This case would allow for an error-free prediction of the class to which a vehicle belongs. However, from the summary statistics shown in Figure 8 and Table 3, one can see that all tier pairs are far away from such a perfect classification, implying that there is a considerable mixing of vehicles from different tiers in the main branches of the dendrograms. This means there are many vehicles of tier \(i+1\) that are more similar to vehicles from tier i with respect to their performance. Considering the MM of the game, which allows either vehicles of the same tier or of adjacent tier pairs, this seems to be desirable to avoid the situation where low tier vehicles are always disadvantaged. Another observation one can make from the Matthews correlation coefficients in Figure 8 is that vehicles can be in two regimes. The first region is within one standard deviation of a zero Matthews correlation coefficient, whereas the second region is outside of this interval. This indicates a heterogeneous transition between the tiers because some tier pairs provide vehicles with quite similar performance characteristics (e.g., tier 2-3 or 5-6), whereas others are more different (e.g., tier 1-2 or 7-8).

From analyzing the importance of predictor variables (see Figure 9), we found that the quality of the linear regression models deteriorates toward higher tiers (i.e., R2 is declining). A possible explanation for this decline in predictability could be the underlying skill level of the players. An indirect measure of the latter is given by the hit rate, shown in Figure 2, which indeed is highest for tier 9 and tier 10. Hence, the predictability of the models could decline because the skill level of players increases making the outcome of games less predictable (skills are more important than characteristics of vehicles). Other interesting results we obtained from studying predictability are the fluctuating values of \(p(\mbox{dr})\) and \(p(\mbox{dpm})\) (see Figure 9). This indicates that the progression between tiers is quite heterogeneous and not steady (see also the Matthews correlation coefficients in Figure 8) and that the importance of system variables even changes between the tiers (see \(p(\mbox{dr})\) and \(p(\mbox{dpm})\) ). All these observations point to a heterogeneous progression through the tiers and to nonlinear effects.

For investigating that latter point, we also performed a nonlinear regression by using a MARS model where we used up to seven predictor variables. From a comparison between a nonlinear MARS models and a linear regression model, we found an improvement in R2 by \(80.7\%\) for tier 10 and \(24.2\%\) for tier 9 (also see Figure 10). Importantly, this was only achieved when using seven predictors, whereas lower-dimensional models still obtained an improvement, although much worse than the best ones. Overall, this demonstrates that higher tiers in WOT Blitz require a nonlinear and high-dimensional description to obtain a predictability similar to lower tiers.

When analyzing WOT Blitz, we noticed from the beginning the unconventional choice for the MM pairing vehicles of adjacent tiers together in matches (see Section 3). From our preceding discussion, one may wonder if this is not the cause for the majority of observed issues and specifically for the heterogeneous progression through the tiers. Given the fact that vehicles from tier \(i+1\) are (on average) stronger than vehicles from tier \(i,\) this introduces a bias in the form of a competitive disadvantage. A confirmation of this may be obtained by analyzing eSports events of WOT Blitz (e.g., the Twister Cup). From this, one finds that only vehicles of tier 10 are used despite the fact that tier 9 vehicles would also be permissible. That means, voluntarily, that teams are only formed by vehicles of the same tier. Hence, neither rational scientific arguments (see the preceding) nor the behavior of the community during eSports events provide sensible arguments in favor of tier mixing in matches. However, given the fact that WOT Blitz is a commercial endeavor, one could speculate if mixed MM is supported from a marketing perspective. An argument in this favor is that players using a vehicle of tier i see in matches a vehicle of tier \(i+1\) that is (in average) better, and hence they want this vehicle to become more successful. However, this requires a progression to the next tier. Metaphorically, this corresponds to a ‘carrot on a stick’ strategy that seemingly leads the players through the tiers without applying force.

An important general point to emphasize is that the data upon which we based our analysis are the consequence of human team behavior. That means neither the characteristics of the vehicles nor the rules of the game alone result in an observable action but the combination of all three components. However, detailed characteristics of the human players are entirely hidden from us and only indirectly observable. One of these is the skill level of players, which can be associated with the hit rate (see Figure 2). Furthermore, this also means that technology alone is not sufficient to create a game like WOT Blitz, but there needs to be a concerted synchronization with the human actors to establish a “functional” system. Although the presence of power-laws is a good indicator of such a functioning, we also found issues for transitioning through the tiers. In fact, this progression is heterogeneous (see Figure 8). Additionally, the need for a high-dimensional, nonlinear description for predicting the win rate revealed the complexity of the game toward higher tiers (see Figure 10).

We would like to mention that there are studies that showed the impact of team composition on performance [57]. However, in our study, we neither use information about individual players nor have information about their participation in common teams in previous games. In contrast, we only use summary statistics of vehicles used by players. Furthermore, the composition of the teams is automatically provided by the MM system of the game. Hence, a player has no influence on the composition of teams at all but is automatically assigned by undisclosed rules.

Based on our findings, there are a number of future studies one could conduct. First, since most issues are more severe on higher tiers, to address these one needs to work its way down. That means starting from tier 10, characteristics of vehicles could be changed by monitoring the coefficient of determination (R2), the dimensionality, and the nonlinearity. Together, these factors need to be optimized without destroying the scaling behavior. At the moment, it is unclear if a homogeneous progression through the tiers is possible given the rules of the game allowing mixed pairing of tiers, and this analysis could bring clarity. Second, one could create special game modes that reflect particular sociological conditions. For instance, one could allow players to select their teammates potentially from a set of preferred players rather than on the individual player level. This way, the formation of teams could be studied. Furthermore, one could allow the players to determine the characteristics of vehicles, within certain boundaries and constraints and by potentially acquiring a penalty. This allows would us to study preferences of the players and resulting consequences. It is important to emphasize that all of these studies require interventions—either changes of the characteristics of the vehicles or the rules of the game. Hence, such studies could be only conducted in collaboration with Wargaming.

Finally, we would like to highlight that we analyzed WOT Blitz by utilizing methods from data science [24, 35, 64] and complex adaptive systems [39, 69], and also other MMOGs may benefit from such an approach. Interestingly, other MMOGs received very little attention from this perspective with notable exceptions of other works [30, 42, 74]. In general, the interdisciplinary nature of such studies may be a contributing factor to the challenge of developing a common language, knowledge, and values that enable equal participation and contribution from various fields. This has been extensively documented and can pose significant obstacles to collaboration and progress [9, 52]. However, real-world systems, such as the economy or society, for which games like WOT Blitz provide a virtual Petri dish, are unlikely to be fully understood through the lens of a single subject. Furthermore, the complexity of economy and human behavior necessitates the establishment of laws that can explain the observed activities. In this regard, the principles of self-organization may offer a potential framework for obtaining basic insights into these complex systems.

MMOGs such as WOT Blitz present wonderful opportunities for investigating virtual societies as their digital nature enables the comprehensive recording and analysis of every aspect of these communities. However, a challenge with this is to distinguish noise from information. In this article, we studied WOT Blitz with population data that combine myriad details into summary statistics.

Specifically, we studied three major levels of WOT Blitz. First, we studied the scaling behavior of the population of vehicles. This allowed us to identify long-range interactions among system variables (win rate vs kills/deaths ratio and win rate vs damage ratio). Second, we identified and quantified the predictability of system variables by classifying the population of vehicles. This translated the abstract finding about the scaling behavior of the population of vehicles into a concrete, observable behavior by assessing the predictability of the system. Third, we quantified the predictability of a performance measure of the system by a multiple regression framework utilizing LMG [47]. From this, we found a heterogeneous progression through the tiers and identified a single system variable (kills/deaths ratio) as the key driver for the win rate. Furthermore, we found that the game becomes more nonlinear for higher tiers rendering linear models suboptimal. Interestingly, this could be compensated by increasing the dimensionality of the model.

Overall, we studied WOT Blitz by combining methods from data science [24, 35, 64] and complex adaptive systems [39, 69]. We believe that, in general, such an interdisciplinary approach can be instructive also for other MMOGs beyond WOT Blitz because these virtual worlds enable different and creative views on social, behavioral, or economic problems that require flexible and powerful analysis methods [17, 18, 36, 65, 71, 73]. As we navigate the ongoing digital revolution [37], this may present an opportunity to receive the vital feedback necessary for effectively adapting to a rapidly changing world within our economy and society.