Data Mining of Deck Archetypes in Hearthstone? Pablo Garcı́a-Sánchez1[0000−0003−4644−2894] , Antonio Fernández-Ares2[0000−0001−9774−0651] , Alberto P. Tonda3[0000−0001−5895−4809] , and Antonio M. Mora2[0000−0003−1603−9105] 1 Department of Languages and Computer Systems, University of Granada, Spain pablogarcia@ugr.es 2 Department of Signal Theory, Telematics and Communications, University of Granada, Spain {antares,amorag}@ugr.es 3 UMR 518 MIA, INRAE, Paris, France alberto.tonda@inrae.fr Abstract. Computer games have become a very interesting environ- ment or testbed to develop new algorithms in many of the branches of Artificial Intelligence. In fact, collectible card games, such as Hearth- stone, have recently attracted the attention of researchers because of their characteristics: uncertainty, randomness, or the infinite and unpre- dictable interactions that can occur in a game. In this game each player composes decks to face other players from a pool of more than 3,000 cards, each one with its own rules and statistics. This implies a great variability of decks and card combinations with rich effects. This paper proposes the use of clustering techniques to extract information from data provided by Hearthstone players, i.e. a Game Mining approach. To do so, more than 500,000 decks created by game players (both experts and just enthusiasts) have been downloaded from Hearthpwn website. Thus, a descriptive analysis of this dataset, along with Data Mining tech- niques, have been carried out in order to understand which archetypes (or deck types) are the favourites among the community of players, and what relationships can be identified between them. The results show that it is possible to use clustering algorithms such as K-Means to automati- cally detect the archetypes used by the players. Keywords: Game Data Mining · Collectible Card Games · Hearthstone · Archetypes · Clustering Algorithms · K-Means · Agglomerative Hierar- chical Clustering 1 Introduction Although there is a large amount of work devoted to the use of AI in video games, most of it is focused on making agents that play, or allow to generate content. ? This work has been supported in part by projects B-TIC-402-UGR18 (FEDER and Junta de Andalucı́a), RTI2018-102002-A-I00 (Ministerio Español de Ciencia, Inno- vación y Universidades), projects TIN2017-85727-C4-1-2-P (Ministerio Español de Economı́a y Competitividad), and TEC2015-68752 (also funded by FEDER) Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). 2 P. Garcı́a-Sánchez et al. However, a very interesting area of application is the modeling of players. That is, starting from information related to how the human player interacts with the game to obtain useful knowledge. Furthermore, understanding and modelling the interaction between the player and the game can be considered a holy grail for game developers and designers [22]. The interaction between players and games is particularly challenging in the area of Collectible Card Games (CCGs), such as Magic The Gathering. This type of games involves a lot of human interaction not only during the game, but also during the creation of the decks to be used from a pool of thousands of cards. These decks are usually shared and commented on the internet, so many players use them as a basis to create their own versions. In addition, the appearance of new cards and expansions makes players have to adapt their decks to the current meta-game, that is, to the players’ behavior at a given time. One of the most popular Digital CCGs (DCCGs) nowadays is HearthStone, Heroes of Warcraft (HS), with over 40 million players. In addition, this game is becoming a de facto benchmark for researchers in artificial intelligence branches, due to the enormous amount of combinations when creating decks, along with the randomness of the effects of the cards, and the hidden information [9]. In HS, players build a deck of 30 cards from a card pool (that can be expanded buying random packs). To win, players must reduce the health of the opponent’s Hero from 30 to 0, using the two types of cards available: spells, that affect the battleground and are then discarded, and minions, that stay in play and can attack the enemy’s Hero or other minions. There are also, weapons, a sub-set of spells that allow the hero to attack other characters during several turns using special abilities. Each card has an associated cost (in number of mana crystals), that is reduced from the player’s bunch after a card is played. This amount of crystals of each player is replenished at the beginning of the turn and increased in one up to a maximum of 10. In HS, deckbuilding is limited to the neutral card pool and the cards that belong to the class of the Hero chosen for the game: Druid, Mage, Hunter, Paladin, Priest, Rogue, Shaman, Warlock, or Warrior. Every Hero class comes with a different Hero Power (costing 2 crystals to use), that in conjunction with their card set, matches every Hero to different deck archetypes. For example, Priest’s healing abilities are a very powerful choice for decks that attempt to control the board, but not so convenient for aggressive ones, that aim to quickly end the game. Due to its popularity, players share the list of cards they use in their decks publicly on websites such as Hearthpwn4 , where users and game enthusiasts vote for, copy and comment on the most popular decks. Currently, this website has a huge amount of data: over 600,000 decks in total for all Hero classes, and game modes. The data obtained by crowdsourcing, like those on this website, allows for a dynamic, extensive and organic study of user-generated data [16]. The created decks can be entered into archetypes: that is, decks with a specific behavior and use. For example, the Jade Druid archetype is one in which the 4 https://www.hearthpwn.com/ Data Mining of Deck Archetypes in Hearthstone 3 Druid class uses Jade Idols and other cards with the Jade keyword to obtain stronger and stronger effects. Players are familiar with these archetypes and often create other archetypes to counteract them. The aim of this paper is to demonstrate whether it is possible to extract in- formation from large user-created datasets within the scope of the DCCGs, i.e. conduct a Game Data Mining [5] study. Specifically, the application of clustering algorithms will allow us to detect groups of decks with common features, and check if they are included within known archetypes. This can be useful for re- searchers in Artificial Intelligence, for example, since by detecting certain cards in the opponent’s deck, the corresponding archetype can be inferred, and thus the agent could adapt its actions accordingly in order to face the predicted be- haviour. This can also be useful for game developers that want to study how the players are using the game resources and how they adapt to changes such as new expansions or card updates. The process that we are going to follow in this work consists of downloading the dataset and pre-processing to remove unnecessary information. Next, a de- scriptive analysis of the dataset will be performed to obtain relevant information before applying clustering algorithms. An expert player will analyze the different clusters to confirm that they correspond to different decks archetypes. The rest of the paper is structured as follows. After the state of the art in section 2, Section 3 describes the methodology used to obtain the dataset, preprocess and analyze it. In the following section a descriptive analysis of the dataset is made and the results of the clustering method are discussed. Finally, in Section 5 the conclusions and future lines of work are presented. 2 State of the art Game Data Mining [5] is one of the multiple research lines that videogames have brought. This is understood as the application of Data Mining techniques to datasets related to any videogame, such as telemetry measures, user-monitoring data, player-generated information, play recordings, etc. Normally the aim is the extraction of knowledge, mainly focused on getting some conclusions about any of the game factors related with player experience [20], such as: enjoyment, playability, engagement or balance; which could help the designers to improve the game mechanics. Other approaches are centered on modelling the player’s behaviour itself [3], which is very useful in the creation of non-player characters, for instance. Obtaining the dataset is the main bottleneck, thus, even if this research line has been widely studied in several papers, the games analysed are just a few - those for which there are available data -. For instance, Thurau and Bauckhage [18] analysed more than 190 million records (from 4 years) of World of Warcraft game and found different tendencies in the evolution of guilds. Weber and Mateas [19] applied classification techniques in order to forecast enemy behaviour in StarCraft. Also Madden NFL [21] and (Infinite) Super Mario [20] have been studied from this perspective. 4 P. Garcı́a-Sánchez et al. However the most prolific game so far has been Tomb Raider: Underworld, which has been deeply analysed in many papers. Drachen et al. have several works applying different data mining and machine learning techniques to more than 1300 records of players that have finished the game, such as [3], where the authors applied Self-Organizing Maps to identify player models (archetypes), or [15] in which the researchers used classification methods in order to predict the players behaviour with respect to their game finishing time (or their potential withdraw). The objective of the present paper is also to analyze data to find archetypes, but we are considering Hearthstone, which, to our knowledge, has not been analyzed with this purpose yet. This DCCG, anyway, has been one of the most prolific games/environments for research in the last years. The studies have been mainly focused on the creation of competitive agents to play autonomously the game [2, 17, 9], but there are in addition other works centered on the design part, such as the game mechanics analysis or the game balance testing [8]. Data mining has also been applied to HS. Indeed there have been two Data Mining Challenges (AAIA’175 and AAIA’186 ) using this game as a testbed. However, the 2017 Challenge and the derived papers [13, 10] was devoted to help AI to win the game, whereas the 2018 edition and related papers [14, 12] had as aim to predict win-rates for specific decks. Thus, in this study we will apply clustering methods to a big dataset, but instead of trying to model player behaviour as in [4], we aim to discover key features (cards in this case) in predefined decks which could lead us to identify a cluster or set of decks as belonging to an archetype. This would help to (auto- matically) identify game ‘profiles’ in those decks belonging to the same cluster as an already known archetype, which could be useful for developers (to evaluate game mechanics or the impact of an expansion) and also for autonomous agents (to decide the best strategy to face an opponent), as already mentioned in the Introduction. 3 Methodology 3.1 Obtaining the dataset As the objective of this work is to analyze the decks that players create, it is necessary to obtain a large amount of data. In our case we have used the data available on a repository: the HearthPwn website (https://www.hearthpwn. com/). This database contains information about all the cards available in the game, and offers to its users the possibility to create and share decks built from those cards. Currently there are more than 600,000 decks created, allowing filtering by expansion, hero class, or type of game, among others. Users can view other users’ decks and copy them into the game to use against other players. 5 https://knowledgepit.ml/aaia17-data-mining-challenge/ 6 https://knowledgepit.ml/aaia18-data-mining-challenge/ Data Mining of Deck Archetypes in Hearthstone 5 Typically, the most popular and proven powerful decks are copied, or variations are created from them. To download the data we have made a script in Python that allows to iterate by deck id to get the URL of that deck and download the specific deck webpage. That web in HTML format is parsed using the BeautifulSoup 7 library to obtain the list of cards, the date, the class and the game type of deck (Game types in Hearthstone are: Ranked, Tavern Brawl, Arena and Adventures). With the name of the cards it would also be possible to access to more information, such as the cost of making the complete deck with Arcane Dust (the virtual currency of the game), the mana cost of each card, or the card type: Spell, Minion or Weapon. Other information such as the Rarity of cards, can als be extracted. We have limited the decks to those belonging to the “Ranked” category. This game mode is the one where players prepare their decks in order to compete against other players, because it is the most popular game mode. It also is the most common in the whole dataset, with a proportion of 62%. Each sample (row) will be a deck identifier, and each feature (columns) will be a card from the entire collection. A 1 in a position indicates that the deck has that card, a 2 indicates that it has 2 copies (the maximum for non legendary cards) and a 0 indicates that it is not included in the deck. 3.2 Method of analysis Initially we will perform a descriptive analysis of the dataset, to see the number of decks per Hero Class, the date of creation, or the most common cards of each class. This can be useful as an initial overview of the whole dataset, and will help to understand further analyses. Then, a clustering analysis have been conducted using two techniques: – K-Means [11], a classic method which starts from a set of patterns and tries to separate them into k different groups, according to their features. – Agglomerative Hierarchical Clustering (AHC) analysis [7], an algo- rithm which, starting from samples, pairs two by two similar clusters and builds a binary tree, called dendrogram, representing their similarity. The first technique has been applied because it is very fast but also very effective, as it has been proved in hundreds of studies with all kinds of data. On the other side, Hierarchical clustering offers a very simple visual output, that could be interpreted easily by a human expert, as this is the case in this work. The input of both algorithms is the dataset. While in K-Means we want to detect if we can extract archetypes (clustering decks), in the AHC we want to extract information about how cards are related (clustering cards). That is the reason in the AHC the input is the transpose of the array: now each card is a row, and each feature (column name) is the ID of the deck the card belongs. Since each hero has a subset of specific cards that only that class can use, it does not make sense to do the clustering analysis with all the cards/decks, 7 https://pypi.org/project/beautifulsoup4/ 6 P. Garcı́a-Sánchez et al. as the clusters obtained would be the classes themselves, considering they have disjoint features - their exclusive cards -. In the case of K-Means we have focused on three classes: Druid, Mage and Warrior, as they have a very wide range of archetypes to play. The obtained results of the analysis are presented and discussed in the fol- lowing section. 4 Results 4.1 Descriptive Analysis of the Dataset Figure 1 shows the distribution of dataset decks by hero class. Although they have a similar number, there is a 32% difference between the class with the highest number of decks (Priest) and the one with the least (Warrior). The most common classes (Priest, Mage and Druid) are also more oriented to control and long-term strategy, so it can explain the variability of user-created decks. 70083 65379 66306 60000 62418 57961 57184 53435 54129 52885 Number of decks 40000 20000 0 MAGE WARLOCK PALADIN PRIEST DRUID ROGUE SHAMAN HUNTER WARRIOR Class Fig. 1: Number of decks by hero class. Figure 2 shows the creation of decks over time. The spikes that occur im- mediately after a new expansion emerges can be seen clearly. Therefore, many of these new decks may not adapt to the meta-game during the season of that expansion, but are the basis for more refined decks. Figure 3 is particularly interesting, as it shows that, despite having more than 3000 cards available in the pool, all classes have one particular card with more than 50% chance. Even, the probability of some classes is extremely high, like Backstab in Rogue decks (with 80% chance of appearing). Classes like Mage or Priest have up to 3 cards with a percentage of appearance of more than 70%. The Warlock class is perhaps the least predictable with respect to its top ten, however, there is a minimum of a 30% chance of getting one of the 10 cards right. 4.2 Clustering Analysis K-Means algorithm has been applied to the decks in order to see how they are related. We have set to 10 the number of clusters for each class, a value expected Data Mining of Deck Archetypes in Hearthstone 7 3000 2000 count 1000 0 2014 2015 2016 2017 2018 2019 Date Fig. 2: Number of decks introduced in the data bases analyzed, over time. It is in- teresting to observe how the spikes in the number of decks are in correspondence to the release of a new expansion, that added more cards to the available pool while at the same time often removing some of the previously popular cards. to produce enough variety of archetypes, while delivering a reasonable amount of data to be analyzed. After applying K-Means, we extracted the 15 most common cards from the decks of each cluster. Figure 4 show the percentage of each one for each cluster. One of the authors, a HearthStone player that reached the highest rank (Legend) in the competitive ladder, manually inspected the clusters and provided an expert analysis for three classes, selected because of an anticipated larger variety of deck archetypes: Druid, Mage, and Warrior. In the following, the notation used for clusters is the initial of the hero class, plus the cluster id (e.g. M2 indicates the second cluster for the Mage class). Also, Figure 4 shows the ten most common cards in each cluster. Druid Clusters D1, D5, D7 all present cards that provide advantages in the late game (such as Wild Growth and Nourish); but while D1 and D7 have control cards (such as Starfall ), D5 exploits the late-game advantage to close combos, using potentially one-turn-kills like Malygos or Aviana. Clusters D2 and D6, on the contrary, have none of these cards, but feature weak, cheap creatures such as Arcane Raven and Fire Fly, plus cards that enhance all friendly creatures on the board, such as Savage Roar, thus grouping decisively Aggressive archetypes. D3 and D9 show a preponderance of Jade cards (Jade Idol, Jade Spirit, Jade Behemoth), thus placing these decks in the category of Jade Druid, a special- ized midrange archetype. Cluster D10 presents mostly cards with the C’Thun keyword, identifying the decks belonging to this cluster as variants of the combo C’Thun Druid archetype. Clusters D4 and D8 are harder to categorize, as they seem to either be mid-range variations of aggressive decks, or present poor co- hesion, possibly representing outliers. Mage Clusters M3, M4, M6, and M9 all represent aggressive archetypes, fea- turing cards such as Fireball and Frostbolt. M3 exploits synergies with secrets (Arcanologist, Counterspell, Medivh’s Vallet), M4 relies upon Flamewaker and cheap spells to damage to opponent, M6 shows a strong presence of Mech minions 8 P. Garcı́a-Sánchez et al. Frost Nova 28.62 % Bloodreaver Gul'dan 30.02 % Righteous Protector 23.74 % Blizzard 38.69 % Twisting Nether 31.06 % Spikeridged Steed 24.52 % Ice Block 39.27 % Soulfire 32.65 % Sunkeeper Tarim 25.08 % Sorcerer's Apprentice 39.65 % Power Overwhelming 32.68 % Divine Favor 30.54 % Polymorph 41.7 % Flame Imp 36.72 % Blessing of Kings 34.2 % Mana Wyrm 44.96 % Doomguard 43.17 % Aldor Peacekeeper 45.22 % Flamestrike 57.35 % Siphon Soul 44.69 % Tirion Fordring 50.19 % Fireball 70.1 % Voidwalker 48.36 % Equality 55.19 % Arcane Intellect 71.93 % Mortal Coil 50.49 % Truesilver Champion 67.16 % Frostbolt 76.33 % Hellfire 54.3 % Consecration 69.3 % 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% Percentage of MAGE decks using the card Percentage of WARLOCK decks using the card Percentage of PALADIN decks using the card Cabal Shadow Priest 26.07 % Ultimate Infestation 20.58 % Vilespine Slayer 29.6 % Auchenai Soulpriest 26.43 % Living Roots 21.17 % Edwin VanCleef 38.1 % Dragonfire Potion 28.53 % Power of the Wild 21.47 % Deadly Poison 39.74 % Circle of Healing 31.63 % Savage Roar 28.94 % Shadowstep 42.41 % Shadow Visions 33.78 % Druid of the Claw 29.1 % SI:7 Agent 55.69 % Holy Nova 49.35 % Nourish 43.35 % Preparation 58.52 % Shadow Word: Pain 62.57 % Wild Growth 51.92 % Sap 59.39 % Northshire Cleric 73.2 % Innervate 53.95 % Fan of Knives 60.48 % Shadow Word: Death 74.81 % Wrath 57.71 % Eviscerate 72.79 % Power Word: Shield 77.54 % Swipe 67.74 % Backstab 82.29 % 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% Percentage of PRIEST decks using the card Percentage of DRUID decks using the card Percentage of ROGUE decks using the card Thing from Below 29.82 % Deadly Shot 30.94 % Ravaging Ghoul 31.14 % Rockbiter Weapon 30.66 % Freezing Trap 38.51 % Whirlwind 32.25 % Maelstrom Portal 34.38 % Hunter's Mark 39.27 % Armorsmith 35.19 % Fire Elemental 36.84 % Explosive Trap 40.86 % Grommash Hellscream 36.69 % Feral Spirit 37.54 % Houndmaster 46.47 % Slam 44.25 % Lightning Bolt 39.83 % Savannah Highmane 56.85 % Shield Slam 49.3 % Mana Tide Totem 48.23 % Unleash the Hounds 58.29 % Brawl 58.77 % Flametongue Totem 54.29 % Eaglehorn Bow 64.12 % Shield Block 59 % Lightning Storm 67.38 % Kill Command 69.56 % Fiery War Axe 72.13 % Hex 71.92 % Animal Companion 75.82 % Execute 73.48 % 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% Percentage of SHAMAN decks using the card Percentage of HUNTER decks using the card Percentage of WARRIOR decks using the card Fig. 3: Most commons cards in decks, by hero class. Interestingly, some of the cards that appear most frequently has been banned or ‘nerfed’ (cost increased and/or effectiveness reduced) over time. Notable examples are Power word: Shield for Priest, Innervate for Druid, Hex for Shaman, and Fiery War Axe for Warrior. (Mechwarper, Snowchugger ), and M9 is based around cheap spells (Ice Lance, Magic Trick ) plus the minion Mana Cyclone to generate new damaging spells. Clusters M2, M5, M7, and M8 all fall under different control archetypes, us- ing either secrets in the case of M2, a large number of board resets (Doom- sayer, Flamestrike) for M5, or a unique late-game finisher (Dragoncaller Alanna, C’Thun) for clusters M7 and M8, respectively. Notably, cluster M7 also includes decks built using only odd-cost cards, exploiting the synergy with Baku, the Mooneater, that provides a powerful effect in exchange for limiting the pos- sibilities of deck construction. Cluster M1 encompasses decks using the syn- ergy between Elemental minions and Jaina, Frost Lich, thus positioning these archetypes in a mid-range position. Finally, cluster M10 includes combo decks, based on the quest Open the Waygate, Archimage Antonidas, and Sorcerer’s Apprentice. Warrior Clusters W1, W2, W3, and W4 all represent variations of Warrior Control archetypes. Decks in W1 rely upon Dead Man’s Hand to try and finish the game through fatigue damage, W2 groups both Mech synergy (Dr. Boom, Mad Genius, Zilliax ) and Odd Warrior (Baku, the Mooneater ), W3 decks seem to exploit older cards (Sylvanas, Justicar Trueheart) possibly representing Wild decks, W3 is a Control version of C’Thun Warrior, with the C’Thun cards and several other synergies. W8 is a set of decisively aggressive decks, with cards Data Mining of Deck Archetypes in Hearthstone 9 such as Leeroy Jenkins, Patches the Pirate, Southsea Deckhand. W6, W7, and W10 all represent combo decks: W6 includes cards that can damage all minions on the board (Whirlwind, Death’s Bite) plus minions that benefit from being damaged (Grim Patron, Frothing Berserker ); W7 and W10 are variations of C’Thun Warrior, with less control elements with respect to W3, and cards such as Brann Bronzebeard to try and finish the game using a colossal amount of damage from C’Thun. Cluster W5 groups together Quest Warrior archetypes based on Fire Plume’s Heart, and more generic mid-range decks still based on Taunt minions (Stonehill Defender, Direhorn Hatchling). Finally, cluster W9 shows relatively few points in common between its decks, with the most common card being Fiery War Axe appearing in only 68% of cases, and might thus represent a collection of outliers, or very different mid-range decks. Once the clusters generated by K-Means have been analyzed, Agglomerative Hierarhical Clustering has been applied. AHC can show also interesting infor- mation about the influence of the cards. We have run the method for the three heroes, but due to space limitations we are showing and analyzing here only the results of the Warrior class, as they are somehow representative and interesting. Figure 5 show the complete generated dendrogram of the Warrior cards, and more detail of the subtrees with height=4 is shown in Figure 6. The height of the fusion, provided on the vertical axis, indicates the similarity/distance between two cards. The higher the height of the fusion, the less similar the cards are. This height is known as the cophenetic distance between the two cards. Most of the cards are in a big cluster (subtree 4), but there exist several relevant cards (single cards) that have enough weight to appear in their own subtree, even at level 1. Several pair of cards shown are usually used in combos, have some kind of synergies or belong to the same expansion. For example: N’Zoth and Bloodsail Cultist. 5 Conclusions Understanding how players play a game is a major concern for developers, as they can adapt elements of the game, such as the rules and content, to facilitate the balance or fun it can provide. In this paper we propose to use Game Data Mining [5], to obtain information about how players create Hearthstone decks. The goal is to demonstrate if using a large set of user-created card lists it is possible to extract deck archetypes automatically. To do this we have extracted a dataset from the HearthPwn website and performed a descriptive analysis plus applied clustering algorithms. After expert analysis of the results, we have provided information on how the cards are related to each other, and how it is possible to detect different archetypes from the data created by the users. However, the proposed auto- matic clustering approach also showed a few limitations: 3 out of the 30 clusters analyzed seems to be composed of mostly outlier decks, identifying no clear archetype (D4, D8, W9); moreover, distinct clusters in the same hero class seem to present very similar archetypes (W7, W10); and finally, it is sometimes pos- 10 P. Garcı́a-Sánchez et al. DRUID − Cluster 1 ( 5340 decks) DRUID − Cluster 2 ( 3814 decks) DRUID − Cluster 3 ( 3467 decks) DRUID − Cluster 4 ( 5997 decks) DRUID − Cluster 5 ( 4150 decks) Wrath 70.58% Vicious.Fledgling 48.09% Wrath 85.15% Wrath 54.56% Wrath 97.93% Wild.Growth 75.71% Swipe 37.15% Wild.Growth 93.74% Wild.Growth 30.12% Wild.Growth 93.66% Ultimate.Infestation 52.87% Savage.Roar 96.43% Ultimate.Infestation 95.73% Swipe 64.33% Swipe 97.01% The.Lich.King 35.79% Power.of.the.Wild 95.7% Swipe 90.51% Starfire 21.59% Raven.Idol 80.87% Swipe 67.45% Patches.the.Pirate 64.84% Spreading.Plague 89.24% Starfall 34.75% Nourish 88.22% Spreading.Plague 28.46% Mark.of.Y.Shaarj 84.35% Nourish 95.93% Savage.Roar 21.71% Mulch 40.48% Primordial.Drake 27.27% Mark.of.the.Lotus 95.78% Mire.Keeper 54.43% Nourish 31.45% Moonfire 37.25% Card Card Card Card Card Nourish 76.16% Living.Mana 75.41% Malfurion.the.Pestilent 83.16% Naturalize 40.17% Mire.Keeper 65.76% Mire.Keeper 40.06% Innervate 60.33% Jade.Spirit 65.21% Mark.of.the.Wild 22.04% Living.Roots 87.93% Malfurion.the.Pestilent 46.22% Golakka.Crawler 45.46% Jade.Idol 90.71% Keeper.of.the.Grove 20.98% Innervate 97.88% Jungle.Giants 33.26% Fire.Fly 90.98% Jade.Blossom 99.28% Innervate 45.64% Feral.Rage 64.43% Innervate 67.15% Enchanted.Raven 86.6% Jade.Behemoth 82.92% Healing.Touch 22.76% Fandral.Staghelm 73.71% Fandral.Staghelm 27.38% Druid.of.the.Swarm 43.6% Innervate 47.76% Ferocious.Howl 22.53% Emperor.Thaurissan 50.22% Elder.Longneck 27.9% Crypt.Lord 42% Fandral.Staghelm 68.3% Druid.of.the.Claw 23.9% Azure.Drake 71.9% Earthen.Scales 34.29% Bloodsail.Corsair 66.15% Aya.Blackpaw 75.48% Coldlight.Oracle 21.93% Ancient.of.War 44.41% 100% 100% 100% 100% 100% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 0% 0% 0% 0% 0% Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. DRUID − Cluster 6 ( 5798 decks) DRUID − Cluster 7 ( 8486 decks) DRUID − Cluster 8 ( 9529 decks) DRUID − Cluster 9 ( 4428 decks) DRUID − Cluster 10 ( 3257 decks) Wrath 56.36% Wrath 56.17% Wrath 91.18% Wrath 96.52% Wrath 88.58% Swipe 77.44% Wild.Growth 88.4% Wild.Growth 71.4% Wild.Growth 86.47% Wild.Growth 82.84% Soul.of.the.Forest 40.81% Ultimate.Infestation 75.8% Swipe 98.81% Swipe 96.3% Twin.Emperor.Vek.lor 71.48% Savage.Roar 84.17% The.Lich.King 36.42% Savage.Roar 72.49% Nourish 89.88% Twilight.Elder 79.18% Savage.Combatant 31.1% Swipe 89.68% Piloted.Shredder 42.33% Living.Roots 50.63% Swipe 93.28% Power.of.the.Wild 84.18% Spreading.Plague 69.15% Loatheb 36.68% Jade.Spirit 88.75% Nourish 52.66% Mounted.Raptor 38.38% Oaken.Summons 58.39% Keeper.of.the.Grove 97.04% Jade.Idol 99.53% Klaxxi.Amber.Weaver 71.42% Card Card Card Card Card Menagerie.Warden 22.82% Nourish 90.4% Innervate 97.17% Jade.Blossom 98.92% Innervate 88.18% Mark.of.Y.Shaarj 44.15% Naturalize 56.93% Force.of.Nature 68.95% Jade.Behemoth 94.24% Druid.of.the.Claw 57.75% Living.Roots 52.4% Malfurion.the.Pestilent 70.92% Druid.of.the.Claw 88.4% Innervate 95.19% Disciple.of.C.Thun 90.51% Innervate 58.8% Lesser.Jasper.Spellstone 79.75% Dr..Boom 48.69% Gadgetzan.Auctioneer 71.61% Dark.Arakkoa 98.37% Enchanted.Raven 34.53% Ironwood.Golem 43.98% Big.Game.Hunter 57.81% Feral.Rage 76.76% C.Thun.s.Chosen 76.36% Druid.of.the.Saber 41.41% Hadronox 27.29% Azure.Drake 49.49% Fandral.Staghelm 70.66% C.Thun 99.72% Druid.of.the.Flame 26.79% Ferocious.Howl 48.26% Ancient.of.War 36.98% Azure.Drake 47.06% Beckoner.of.Evil 81.67% Druid.of.the.Claw 48.62% Branching.Paths 85.93% Ancient.of.Lore 86.64% Aya.Blackpaw 77.73% Azure.Drake 53.24% 100% 100% 100% 100% 100% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 0% 0% 0% 0% 0% Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. (a) Druid MAGE − Cluster 1 ( 5511 decks) MAGE − Cluster 2 ( 5713 decks) MAGE − Cluster 3 ( 8109 decks) MAGE − Cluster 4 ( 8232 decks) MAGE − Cluster 5 ( 10555 decks) Water.Elemental 54.85% Sylvanas.Windrunner 38.67% Sorcerer.s.Apprentice 59% Unstable.Portal 46.15% Reno.Jackson 45.77% Tar.Creeper 81.96% Sludge.Belcher 71.64% Primordial.Glyph 78.92% Sorcerer.s.Apprentice 93.78% Polymorph 68.07% Steam.Surger 63.24% Polymorph 73.59% Mirror.Entity 41.73% Mirror.Image 58.67% Kazakus 39.3% Shimmering.Tempest 44.6% Mad.Scientist 84.3% Medivh.s.Valet 73.77% Mirror.Entity 42.57% Ice.Block 59.55% Servant.of.Kalimos 74.69% Ice.Block 53.56% Mana.Wyrm 89.81% Mana.Wyrm 97.66% Frost.Nova 38.97% Pyros 53.37% Frostbolt 85.49% Kirin.Tor.Mage 73.02% Frostbolt 98.31% Frostbolt 65.43% Primordial.Glyph 43.93% Flamestrike 88.41% Kabal.Crystal.Runner 54.59% Flamewaker 95.97% Forgotten.Torch 40.86% Card Card Card Card Card Frost.Lich.Jaina 73.4% Fireball 64.73% Ice.Block 50.24% Flamestrike 56.64% Flamestrike 74.21% Frostbolt 49.14% Emperor.Thaurissan 40.22% Frostbolt 95.38% Flamecannon 40.78% Firelands.Portal 45.76% Flamestrike 37.18% Echo.of.Medivh 37.09% Firelands.Portal 60.77% Fireball 95.32% Fireball 61.29% Fire.Fly 78.52% Duplicate 75.35% Fireball 95.44% Azure.Drake 74.99% Doomsayer 51.37% Fireball 45.44% Dr..Boom 38.54% Explosive.Runes 40.5% Archmage.Antonidas 52.21% Cabalist.s.Tome 42.19% Bonfire.Elemental 42.64% Blizzard 37.51% Counterspell 79.84% Arcane.Missiles 83.93% Blizzard 65.88% Blazecaller 68.39% Arcane.Intellect 57.2% Arcanologist 93.17% Arcane.Intellect 89.64% Babbling.Book 43.17% Arcane.Intellect 54.2% Antique.Healbot 54.86% Arcane.Intellect 88.53% Arcane.Blast 49.21% Arcane.Intellect 65.06% 100% 100% 100% 100% 100% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 0% 0% 0% 0% 0% Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. MAGE − Cluster 6 ( 3308 decks) MAGE − Cluster 7 ( 4195 decks) MAGE − Cluster 8 ( 6079 decks) MAGE − Cluster 9 ( 4025 decks) MAGE − Cluster 10 ( 9652 decks) Unstable.Portal 42.99% Voodoo.Doll 44.17% Water.Elemental 65.57% Stargazer.Luna 29.24% Primordial.Glyph 53.57% Tinkertown.Technician 84.49% Tar.Creeper 53.28% Sorcerer.s.Apprentice 49.56% Sorcerer.s.Apprentice 76.94% Ice.Block 89.23% Spider.Tank 76.39% Stonehill.Defender 39.59% Sen.jin.Shieldmasta 23.67% Ray.of.Frost 23.28% Ice.Barrier 73.41% Snowchugger 93.68% Raven.Familiar 59.17% Polymorph 87.86% Mirror.Image 51.53% Frost.Nova 97.74% Piloted.Shredder 84.43% Polymorph 61.91% Mirror.Image 44.22% Mana.Wyrm 55.68% Frostbolt 75.68% Mechwarper 96.01% Meteor 70.11% Mana.Wyrm 70.49% Mana.Cyclone 24.35% Flamestrike 50.18% Mechanical.Yeti 50.42% Frost.Lich.Jaina 95.4% Frostbolt 95.74% Magic.Trick 24.22% Fireball 58.3% Card Card Card Card Card Goblin.Blastmage 93.86% Flamestrike 94.42% Flamestrike 91.74% Ice.Lance 30.86% Doomsayer 90.3% Frostbolt 90.69% Dragon.s.Fury 92.4% Firelands.Portal 23.36% Frost.Nova 25.47% Bloodmage.Thalnos 49.33% Fireball 89.93% Dragoncaller.Alanna 65.15% Fireball 97.53% Frostbolt 84.07% Blizzard 93.33% Dr..Boom 55.47% Doomsayer 48.56% Faceless.Summoner 24.79% Fireball 70.73% Archmage.Antonidas 54.46% Cogmaster 74% Blizzard 74.14% Azure.Drake 45.91% Bloodmage.Thalnos 32.37% Arcanologist 46.02% Clockwork.Gnome 86.85% Baron.Geddon 42.6% Arcane.Missiles 67.84% Archmage.Antonidas 27.48% Arcane.Intellect 96.5% Archmage.Antonidas 45.13% Arcane.Tyrant 41.72% Arcane.Intellect 84.32% Arcane.Missiles 55.18% Alexstrasza 55.78% Annoy.o.Tron 83.16% Arcane.Artificer 88.03% Arcane.Explosion 23.79% Arcane.Intellect 80.67% Acolyte.of.Pain 54.27% 100% 100% 100% 100% 100% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 0% 0% 0% 0% 0% Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. (b) Mage WARRIOR − Cluster 1 ( 5755 decks) WARRIOR − Cluster 2 ( 6134 decks) WARRIOR − Cluster 3 ( 11918 decks) WARRIOR − Cluster 4 ( 947 decks) WARRIOR − Cluster 5 ( 5168 decks) Whirlwind 35.57% Zilliax 59.13% Sylvanas.Windrunner 65.99% Twin.Emperor.Vek.lor 63.36% Tar.Creeper 51.51% Warpath 46.59% Warpath 37.87% Sludge.Belcher 55.19% Twilight.Elder 63.15% Stonehill.Defender 65% The.Lich.King 35.95% Supercollider 35.38% Slam 52.25% Slam 61.46% Sleep.with.the.Fishes 51.76% Sleep.with.the.Fishes 39.06% Stonehill.Defender 44.13% Shield.Slam 94.4% Shield.Block 59.77% Slam 60.6% Slam 59.93% Shield.Slam 78.71% Shield.Block 92.43% Ravaging.Ghoul 68.43% Shield.Block 61.07% Shield.Slam 60.97% Shield.Block 82.1% Justicar.Trueheart 54.82% Fiery.War.Axe 81.1% Ravaging.Ghoul 87.36% Shield.Block 85.02% Reckless.Flurry 42.68% Grommash.Hellscream 73.09% Execute 91.55% Primordial.Drake 62.38% Card Card Card Card Card Scourgelord.Garrosh 49.28% Omega.Assembly 55.9% Fiery.War.Axe 96.69% Doomcaller 55.12% Fire.Plume.s.Heart 76.66% Execute 93.4% Eternium.Rover 44.86% Execute 98.37% Disciple.of.C.Thun 86.48% Fiery.War.Axe 87.75% Drywhisker.Armorer 36.99% Dyn.o.matic 54.94% Death.s.Bite 65.29% C.Thun.s.Chosen 62.72% Execute 92.71% Dead.Man.s.Hand 61.72% Dr..Boom..Mad.Genius 65.19% Cruel.Taskmaster 53.83% C.Thun 99.16% Direhorn.Hatchling 76.66% Brawl 82.69% Direhorn.Hatchling 38.15% Brawl 91.24% Bloodhoof.Brave 58.39% Brawl 88.82% Blood.Razor 89.42% Brawl 87.63% Bash 55.55% Beckoner.of.Evil 79.09% Bloodhoof.Brave 78.77% Battle.Rage 36.28% Baku.the.Mooneater 44.88% Armorsmith 65.27% Ancient.Shieldbearer 84.37% Alley.Armorsmith 83.2% Acolyte.of.Pain 60.5% Acolyte.of.Pain 31.92% Acolyte.of.Pain 74.17% Acolyte.of.Pain 59.03% Acolyte.of.Pain 64.84% 100% 100% 100% 100% 100% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 0% 0% 0% 0% 0% Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. WARRIOR − Cluster 6 ( 7193 decks) WARRIOR − Cluster 7 ( 1214 decks) WARRIOR − Cluster 8 ( 5847 decks) WARRIOR − Cluster 9 ( 7287 decks) WARRIOR − Cluster 10 ( 1380 decks) Whirlwind 80.24% Twin.Emperor.Vek.lor 75.45% Upgrade. 91.28% Slam 29.75% Twin.Emperor.Vek.lor 88.91% Slam 69.04% Twilight.Elder 65.32% Southsea.Deckhand 95.96% Shield.Block 22.77% Slam 71.96% Ravaging.Ghoul 44.49% Slam 61.86% Southsea.Captain 51.94% Ravaging.Ghoul 26.24% Shield.Slam 97.9% Inner.Rage 68.16% Shield.Slam 95.06% Patches.the.Pirate 62.99% Kor.kron.Elite 61.99% Shield.Block 91.81% Grommash.Hellscream 50.56% Shield.Block 86.41% N.Zoth.s.First.Mate 90.68% Heroic.Strike 22.35% Ravaging.Ghoul 95.65% Grim.Patron 47.75% Justicar.Trueheart 74.3% Mortal.Strike 68.36% Grommash.Hellscream 37.45% Justicar.Trueheart 71.67% Frothing.Berserker 72.04% Fiery.War.Axe 90.94% Leeroy.Jenkins 55.09% Frothing.Berserker 55% Fiery.War.Axe 93.7% Card Card Card Card Card Fiery.War.Axe 88.54% Execute 96.46% Kor.kron.Elite 94.15% Fiery.War.Axe 68.79% Execute 99.28% Execute 93.31% Disciple.of.C.Thun 78.75% Heroic.Strike 83.51% Execute 61.44% Disciple.of.C.Thun 98.48% Death.s.Bite 44.49% C.Thun.s.Chosen 81.88% Frothing.Berserker 80.11% Cruel.Taskmaster 24.61% C.Thun.s.Chosen 93.41% Cruel.Taskmaster 57.44% C.Thun 99.01% Fiery.War.Axe 95.67% Blackwing.Corruptor 21.3% C.Thun 98.26% Blood.To.Ichor 34.19% Brawl 92.5% Dread.Corsair 91.94% Battle.Rage 24.74% Brawl 98.48% Battle.Rage 82.9% Beckoner.of.Evil 83.36% Bloodsail.Raider 91.17% Azure.Drake 25.15% Brann.Bronzebeard 70.22% Armorsmith 68.19% Bash 69.69% Bloodsail.Cultist 89.94% Arcanite.Reaper 34.29% Ancient.Shieldbearer 99.35% Acolyte.of.Pain 90.3% Ancient.Shieldbearer 96.95% Arcanite.Reaper 94.72% Alexstrasza.s.Champion 23.99% Acolyte.of.Pain 75.94% 100% 100% 100% 100% 100% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 25% 50% 75% 0% 0% 0% 0% 0% Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. Percentage of decks (in cluster) using that card. (c) Warrior Fig. 4: Ten most common cards of each cluster for Druid (a), Mage (b) and Warrior (c). Height 0 100 200 300 400 Blood.Razor Direhorn.Hatchling Stonehill.Defender Tar.Creeper Alley.Armorsmith Sleep.with.the.Fishes Dirty.Rat Primordial.Drake Bash Warpath Eternium.Rover Dyn.o.matic Omega.Assembly Rabid.Worgen Town.Crier Militia.Commander Darius.Crowley Redband.Wasp Woodcutter.s.Axe Inner.Rage Grim.Patron Unstable.Ghoul Warsong.Commander Emperor.Thaurissan Gnomish.Inventor Beckoner.of.Evil C.Thun.s.Chosen Ancient.Shieldbearer Disciple.of.C.Thun Revenge Gorehowl Justicar.Trueheart Sylvanas.Windrunner Ysera Alexstrasza Big.Game.Hunter Dr..Boom Ragnaros.the.Firelord Baron.Geddon Harrison.Jones Reckless.Flurry Cornered.Sentry Drywhisker.Armorer Coldlight.Oracle Bring.It.On. Dead.Man.s.Hand Fierce.Monkey Drakonid.Crusher Faerie.Dragon Azure.Drake Alexstrasza.s.Champion Blackwing.Corruptor Twilight.GuardianNaga.Corsair Southsea.Captain Loot.Hoarder Commanding.Shout Wild.Pyromancer Rampage Charge Raging.Worgen Small.Time.Buccaneer Sir.Finley.Mrrgglton Leeroy.Jenkins Patches.the.Pirate Piloted.Shredder Omega.Devastator Clockwork.Goblin Wrenchcalibur Augmented.Elekk Blastmaster.Boom Seaforium.Bomber Weapons.Project Dragonmaw.Scorcher Crowd.Roaster Emberscale.Drake Smolderthorn.Lancer Dragon.Roar Firetree.Witchdoctor Scaleworm Supercollider Dr..Boom..Mad.Genius Zilliax Ironbeak.Owl Amani.Berserker Arathi.Weaponsmith Cleave Acidic.Swamp.Ooze Sen.jin.Shieldmasta Spellbreaker Deathlord King.s.Defender Bolster Sparring.Partner Grimy.Gadgeteer I.Know.a.Guy Public.Defender Stolen.Goods Brann.Bronzebeard Doomcaller C.Thun Twin.Emperor.Vek.lor Crazed.Worshipper Twilight.Elder Argent.Horserider Wolfrider Abusive.Sergeant Arcane.Golem Leper.Gnome Blackwing.Technician Saronite.Chain.Gang Fire.Fly Lesser.Mithril.Spellstone Spiteful.Summoner Gurubashi.Berserker Animated.Berserker Val.kyr.Soulclaimer Arcane.Giant Blood.Warriors Iron.Hide Gemstudded.Golem Deathwing Twilight.Drake Book.Wyrm Netherspite.Historian Rotface Sudden.Genesis Molten.Blade Bittertide.Hydra Captain.Greenskin Nightmare.Amalgam Bonemare Cobalt.Scalebane Amani.War.Bear play the game. Spirit.of.the.Rhino Sleepy.Dragon Charged.Devilsaur The.Boomship Bladed.Gauntlet Geosculptor.Yip Woecleaver Skulking.Geist King.Mosh Second.Rate.Bruiser Stubborn.Gastropod Bluegill.Warrior Murloc.Warleader Shattered.Sun.Cleric Boulderfist.Ogre Chillwind.Yeti Protect.the.King. Obsidian.Destroyer Sunwalker Grimestreet.Pawnbroker Fool.s.Bane Violet.Illusionist Malkorok Golakka.Crawler Chillmaw Nefarian Bone.Drake Flame.Juggler Devastate Improve.Morale Dimensional.Ripper Sweeping.Strikes Akali..the.Rhino Oondasta Safeguard Vicious.Scraphound Archivist.Elysiana Hecklebot Argent.Squire Plated.Beetle Grimestreet.Smuggler Don.Han.Cho Doppelgangster Brass.Knuckles Hobart.Grapplehammer Zombie.Chow Knife.Juggler Dragon.Egg Nerubian.Egg Phantom.Freebooter Blackwater.Pirate Bloodsail.Corsair Festeroot.Hulk Sul.thraze Heavy.Metal. War.Master.Voone Wyrmguard Hench.Clan.Thug Fungalmancer Vicious.Fledgling Bomb.Lobber Chromaggus Hungry.Dragon Soggoth.the.Slitherer Deathwing..Dragonlord Y.Shaarj..Rage.Unbound Yogg.Saron..Hope.s.End Clockwork.Automaton Azalina.Soulthief Zola.the.Gorgon Jeweled.Scarab Siege.Engine Clockwork.Gnome Mechanical.Yeti Haunted.Creeper Hobgoblin Jeeves Micro.Machine Missile.Launcher Skaterbot Mecharoo Replicating.Menace Cursed.Blade Orgrimmar.Aspirant Bloodmage.Thalnos Prince.Malchezaar Barnes Twilight.Summoner Vicious.Scalehide Blackhowl.Gunspire Carnivorous.Cube Dozing.Marksman Overlord.s.Whip Death.Revenant Night.Howler Corridor.Creeper Prince.Keleseth Explosive.Sheep Tentacle.of.N.Zoth Frost.Giant Garrison.Commander Nexus.Champion.Saraad Arcane.Nullifier.X.21 Piloted.Sky.Golem Sneed.s.Old.Shredder Bull.Dozer Damaged.Stegotron Huge.Toad Mechanical.Whelp Weaponized.Piñata Baleful.Banker Arch.Thief.Rafaam Aberrant.Berserker Deadly.Arsenal Earthen.Ring.Farseer Murloc.Tidehunter Murloc.Tidecaller Coldlight.Seer Grimscale.Oracle Stormwind.Champion Bloodfen.Raptor Razorfen.Hunter Dark.Iron.Dwarf Worgen.Infiltrator Ogre.Warmaul Lone.Champion Dragonhatcher Master.Oakheart Rusty.Recycler Mistress.of.Mixtures Frostwolf.Grunt Pompous.Thespian Wax.Elemental Madder.Bomber Stampeding.Kodo Hogger..Doom.of.Elwynn Kezan.Mystic Hench.Clan.Hogsteed Genn.Greymane Witchwood.Piper Hogger Master.Jouster Ancient.Brewmaster Devilsaur.Egg Tinkmaster.Overspark Sea.Giant Cyclopian.Horror Faceless.Shambler Gorillabot.A.3 Dire.Mole Malygos Mecha.thun Dr..Boom.s.Scheme Barista.Lynchen Unseen.Saboteur Spectral.Knight Feugen Stalagg Dancing.Swords Undertaker Refreshment.Vendor Tournament.Medic Mogu.shan.Warden Cult.Master Target.Dummy Tournament.Attendee Swift.Messenger Coppertail.Imposter Fight.Promoter Scaled.Nightmare Ravasaur.Runt Ebon.Dragonsmith Furnacefire.Colossus Injured.Blademaster Frightened.Flunky Tomb.Warden Infested.Goblin Into.the.Fray Restless.Mummy Bloodsworn.Mercenary SN1P.SN4P Captain.s.Parrot Skycap.n.Kragg Eater.of.Secrets Angry.Chicken Ancient.Watcher Ogre.Brute Glacial.Shard Blazecaller Servant.of.Kalimos Tol.vir.Stoneshaper Fire.Plume.Phoenix Igneous.Elemental Rend.Blackhand Volcanic.Drake Arcanosmith Bilefin.Tidehunter Saronite.Taskmaster Rocket.Boots Explodinator Kaboom.Bot Enhance.o.Mechano Evil.Heckler Corrupted.Seer Marsh.Drake Crazed.Alchemist Marin.the.Fox Naga.Sea.Witch Shade.of.Naxxramas Drakkari.Enchanter Silver.Vanguard Tentacles.for.Arms King.Togwaggle Hired.Gun Kobold.Barbarian Worgen.Abomination Echoing.Ooze Gnomeregan.Infantry Onyxia Corpsetaker Demolisher Faithful.Lumi Magnataur.Alpha Sea.Reaver Kodorider Polluted.Hoarder Flesheating.Ghoul Dragonling.Mechanic Murloc.Raider North.Sea.Kraken Lifedrinker Mossy.Horror Alarm.o.Bot Runic.Egg Bright.Eyed.Scout Hemet..Jungle.Hunter Gadgetzan.Jouster Troggzor.the.Earthinator Fen.Creeper Mukla.s.Champion Silverback.Patriarch Frostwolf.Warlord River.Crocolisk Ancient.Harbinger Acherus.Veteran The.Darkness Finja..the.Flying.Star Gentle.Megasaur Rockpool.Hunter Flying.Machine Wisp Blood.of.The.Ancient.One Recombobulator Giant.Mastodon Stegodon Void.Ripper Furious.Ettin Hungry.Ettin Underbelly.Ooze Hungry.Crab Stranglethorn.Tiger Untamed.Beastmaster Omega.Defender Rabble.Bouncer Force.Tank.MAX Foe.Reaper.4000 Junkbot Spring.Rocket Silithid.Swarmer Cult.Apothecary Friendly.Bartender Toxic.Sewer.Ooze Maiden.of.the.Lake Ironforge.Rifleman Chief.Inspector Silver.Hand.Knight Jungle.Panther Thrallmar.Farseer Windfury.Harpy Magma.Rager Loose.Specimen Mojomaster.Zihi Mindbreaker Ticking.Abomination Half.Time.Scavenger Auctionmaster.Beardo therefore 1-2 and 3-4 are also related. Burgly.Bully Mana.Addict Questing.Adventurer Trogg.Gloomeater Grave.Shambler Toxicologist Corrupted.Healbot Ancient.of.Blossoms Piloted.Reaper Injured.Kvaldir Emerald.Hive.Queen Guild.Recruiter Livewire.Lance Hack.the.System Questing.Explorer Belligerent.Gnome Grand.Archivist Tunnel.Blaster Spiritsinger.Umbra Nat.Pagle Shifter.Zerus Emperor.Cobra Nesting.Roc Imp.Master Blingtron.3000 Salty.Dog Lil..Exorcist Shieldbreaker Wrathion Lorewalker.Cho Swamp.Dragon.Egg Witch.s.Cauldron Bolf.Ramshield Boneguard.Lieutenant Kvaldir.Raider Cards Pit.Fighter Anubisath.Sentinel Old.Murk.Eye Puddlestomper Murloc.Tinyfin Snowflipper.Penguin Ticket.Scalper Jepetto.Joybuzz Daring.Reporter Big.Time.Racketeer Burly.Rockjaw.Trogg Stonesplinter.Trogg Deranged.Doctor Gruul Eerie.Statue Icehowl Cluster Dendrogram Midnight.Drake Medivh..the.Guardian Lance.Carrier Sunborne.Val.kyr Steel.Rager Sightless.Ranger Spark.Drill Baron.Rivendare Skelemancer Tomb.Lurker Burly.Shovelfist Venture.Co..Mercenary Volatile.Elemental E.M.P..Operative Sunreaver.Warmage Clockwork.Giant Gazlowe Toshley Mosh.Ogg.Enforcer Bone.Wraith Injured.Tol.vir Khartut.Defender Armagedillo Faceless.Lurker Arena.Fanatic Deathspeaker Ancient.Shade Goblin.Bomb Whirliglider Nerub.ar.Weblord Hoarding.Dragon Ornery.Tortoise Portal.Keeper Portal.Overfiend Frost.Elemental Maexxna Armored.Warhorse Shallow.Gravedigger EVIL.Cable.Rat Magic.Carpet Scorp.o.matic Fungal.Enchanter Violet.Teacher King.Mukla Spawn.of.N.Zoth Plague.of.Wrath Mekgineer.Thermaplugg Mimiron.s.Head Young.Dragonhawk Spellzerker Darkspeaker Blowgill.Sniper Primalfin.Lookout Mayor.Noggenfogger Grand.Crusader Corrosive.Sludge Green.Jelly Corpse.Raiser Giant.Wasp Wobbling.Runts Dragonslayer Bloodworm Wailing.Soul Weasel.Tunneler Summoning.Stone Spiked.Hogrider Nerubian.Unraveler Crowd.Favorite Fencing.Coach Silver.Hand.Regent Core.Hound Ravenholdt.Assassin Nerubian.Prophet Hyldnir.Frostrider Spark.Engine Wretched.Tiller Illidan.Stormrage Am.gam.Rager Ice.Rager Eydis.Darkbane Priestess.of.Elune Ravencaller Zealous.Initiate Arcane.Dynamo Ogre.Magi Mogor.s.Champion Mogor.the.Ogre Stormwatcher Ultrasaur Hench.Clan.Hag Microtech.Controller Lightwarden Coliseum.Manager Secretkeeper Grook.Fu.Master Saboteur Ozruk Thunder.Lizard Moat.Lurker Humongous.Razorleaf Snapjaw.Shellfighter Prince.Taldaram Oasis.Snapjaw Stoneskin.Gargoyle Argent.Watchman Millhouse.Manastorm Nat..the.Darkfisher Tanglefur.Mystic Faceless.Rager Potion.Vendor Gilblin.Stalker Goblin.Sapper Felsoul.Inquisitor Dollmaster.Dorian Backstreet.Leper Hozen.Healer Arcane.Anomaly Blubber.Baron Mukla..Tyrant.of.the.Vale Star.Aligner Lowly.Squire Pint.Sized.Summoner The.Skeleton.Knight Silvermoon.Guardian Lost.Spirit Mad.Hatter Kobold.Geomancer Kooky.Chemist Gnomish.Experimenter Tortollan.Primalist Banana.Buffoon Gurubashi.Offering Arcane.Tyrant Validated.Doomsayer Keening.Banshee The.Beast Mana.Wraith Grim.Necromancer Necrotic.Geist Moroes Armored.Goon Fallen.Sun.Cleric Linecracker Shroom.Brewer Kobold.Monk Cursed.Disciple Kobold.Apprentice Sated.Threshadon Faceless.Behemoth Backroom.Bouncer Emerald.Reaver Arena.Treasure.Chest Scarab.Egg Twisted.Worgen Helpless.Hatchling Hemet.Nesingwary Gadgetzan.Socialite The.Boogeymonster Eggnapper Vryghoul Toxfin Stoneskin.Basilisk Dragonhawk.Rider Captured.Jormungar Pantry.Spider Archmage Dalaran.Mage Anubisath.Warbringer Heroic.Innkeeper Living.Monument Elite.Tauren.Chieftain Lost.Tallstrider Defias.Cleaner Sergeant.Sally Night.Prowler Mosh.Ogg.Announcer Arena.Patron Silent.Knight Gelbin.Mekkatorque Shrieking.Shroom Mogu.Cultist Madam.Goya Feral.Gibberer Eldritch.Horror Duskboar Deadscale.Knight Red.Mana.Wyrm Regeneratin..Thug Street.Trickster Worgen.Greaser Leatherclad.Hogleader Tanaris.Hogchopper Gormok.the.Impaler Siamat Rattling.Rascal Evolved.Kobold Griftah Former.Champ Drakkari.Trickster Rumbletusk.Shaker Boisterous.Bard Wind.up.Burglebot Tainted.Zealot Splitting.Festeroot Fjola.Lightbane Deathaxe.Punisher Shimmering.Courser Conjured.Mirage Phalanx.Commander Bomb.Squad Booty.Bay.Bookie Walnut.Sprite Traveling.Healer Swamp.Leech Soldier.of.Fortune Sideshow.Spelleater Recruiter Pterrordax.Hatchling Murloc.Tastyfin Mana.Reservoir History.Buff Octosari Serpent.Egg Electrowright Avian.Watcher Violet.Warden Sneaky.Devil Sabretooth.Stalker Exotic.Mountseller Ancient.Mage Wicked.Skeleton Sewer.Crawler The.Voraxx Subject.9 Harbinger.Celestia Holomancer Fossilized.Devilsaur Wrapped.Golem Temple.Berserker Sunstruck.Henchman Streetwise.Investigator Recurring.Villain Neferset.Ritualist Ice.Cream.Peddler Gurubashi.Chicken Furbolg.Mossbinder Flight.Master Eccentric.Scribe Cheaty.Anklebiter Murmy Beaming.Sidekick Jar.Dealer Arcane.Watcher Dalaran.Librarian Fel.Orc.Soulfiend Spellward.Jeweler Mad.Summoner Mad.Scientist High.Inquisitor.Whitemane Happy.Ghoul Zephrys.the.Great Brightwing Colossus.of.the.Moon Kazakus Brainstormer Toothy.Chest Waterboy Unpowered.Mauler Sandbinder Light.s.Champion King.Phaoris Illuminator Golden.Scarab Dalaran.Crusader Frigid.Snobold Frozen.Crusher Spellweaver Chef.Nomi Da.Undatakah Genzo..the.Shark visually using the dendrogram generated by the AHC algorithm Nozdormu Meat.Wagon Unpowered.Steambot Prince.Valanar Gravelsnout.Knight Violet.Wurm Volcanosaur Majordomo.Executus Tomb.Spider Menagerie.Magician Zoobot Squirming.Tentacle Master.Swordsmith Young.Priestess Arfus Blood.Knight Scarlet.Crusader Grotesque.Dragonhawk Djinni.of.Zephyrs Dragonkin.Sorcerer Hakkar..the.Soulflayer Gilnean.Royal.Guard Pumpkin.Peasant Rummaging.Kobold Sharkfin.Fan Proud.Defender Batterhead Archmage.Vargoth Big.Bad.Archmage The.Boom.Reaver Stormwind.Knight Clockwork.Knight Fel.Reaver Dire.Wolf.Alpha Gadgetzan.Auctioneer Crystallizer Grimestreet.Informant Bog.Creeper Psych.o.Tron Fig. 5: Global AHC for all cards used by Warrior class. Goldshire.Footman Shieldbearer Nightblade Lord.of.the.Arena Voodoo.Doctor Booty.Bay.Bodyguard Darkscale.Healer Stormpike.Commando War.Golem Ironfur.Grizzly Raid.Leader Stonetusk.Boar Kel.Thuzad Molten.Giant Mountain.Giant Sunfury.Protector Explore.Un.Goro Skeram.Cultist Twilight.Geomancer Mad.Bomber Spiteful.Smith Tauren.Warrior Novice.Engineer Elven.Archer Reckless.Rocketeer Abomination Voodoo.Doll Countess.Ashmore Muck.Hunter Defender.of.Argus Mind.Control.Tech Reno.Jackson Bouncing.Blade Crush Iron.Juggernaut Antique.Healbot Youthful.Brewmaster Axe.Flinger Varian.Wrynn Ship.s.Cannon Giggling.Inventor Galvanizer Upgradeable.Framebot Beryllium.Nullifier Security.Rover Bronze.Gatekeeper Wargear Loatheb The.Black.Knight Annoy.o.Tron Warbot Cogmaster Mechwarper Screwjank.Clunker Spider.Tank Tinkertown.Technician Argent.Commander Harvest.Golem Data Mining of Deck Archetypes in Hearthstone Cairne.Bloodhoof Infested.Tauren N.Zoth..the.Corruptor Faceless.Manipulator Elise.the.Trailblazer Baku.the.Mooneater Gluttonous.Ooze Ironforge.Portal Doomsayer Elise.Starseeker Mountainfire.Armor Unidentified.Shield Scourgelord.Garrosh Forge.of.Souls Gather.Your.Party The.Lich.King Phantom.Militia Rotten.Applebaum Blackwald.Pixie Witchwood.Grizzly Tar.Lord Ornery.Direhorn Fire.Plume.s.Heart The.Curator Blood.To.Ichor Grommash.Hellscream Battle.Rage Whirlwind Armorsmith Cruel.Taskmaster Death.s.Bite Shieldmaiden Sludge.Belcher Frothing.Berserker Kor.kron.Elite Mortal.Strike Arcanite.Reaper Heroic.Strike Dread.Corsair Bloodsail.Cultist N.Zoth.s.First.Mate Upgrade. Bloodsail.Raider Southsea.Deckhand Slam Bloodhoof.Brave Ravaging.Ghoul Fiery.War.Axe Shield.Block Brawl Shield.Slam Acolyte.of.Pain Execute features related to the decks, such as summarizing of the number of minions in A feature extraction method could be also applied, in order to ‘generate’ decks along the time and expansion releases may help to understand how users techniques, such as visualizing the cards networks, or studying the changes in transversal, specialized or emerging/disappearing categories. Other visualization nities can be plotted in a strategic diagram to see what decks belong to motor, detected [1], and from using their centrality and density measures, these commu- clustering algorithms, such as the Leiden Algorithm, card communities can be cell is the number of decks that share that particular pair of cards. Using other As future work, a card co-appearance matrix can be made, in which each to be defined a priori by the user. Also, relationships between cards can be seen is no ground truth, and parameters such as an arbitrary number of clusters have issues are typical of clustering, an unsupervised learning problem for which there sible to detect two distinct archetypes inside the same cluster (M7, W2). These right) of a binary tree of 4 levels. So 1 is more related to 2, and 3 to 4, and Fig. 6: Subtrees of the AHC cluster. Each id correspond to a leaf (from left to 11 12 P. Garcı́a-Sánchez et al. the set, or the amount of beast cards, weapon cards, or combo cards, to cite some examples. This information could better describe the decks for their analysis. Moreover, other clustering algorithms such as Density-Based Spatial Clus- tering of Applications with Noise [6] can partially solve the issue of deciding a priori the number of clusters; nevertheless, they feature different parameters to be tuned. References 1. 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