Safe

5055417109

86698277

0

3

111474

Alliance

Offlane

5055417109

18180970

0

0

111474

Alliance

Soft support

The sampled database is then joined with the heroes database containing identificators and names for heroes available in the appendices. The result is then filtered (dplyr::select) to leave columns needed for the SNA graph buildup only, which are indicated in the table below.

Table 5

Hero:role joined sampled database for the Alliance team for a single match

Match unique ID	Hero and its concatenated role	Joined from players' database
m_id	hero	role
5055417109	Shadow Demon: Hard support	Hard support
5055417109	Death Prophet: Mid	Mid
5055417109	Dark Seer: Offlane	Offlane
5055417109	Faceless Void: Safe	Safe
5055417109	Mirana: Soft support	Soft support

The rest structural database examples are given in the appendices. Worth to note, the public matches database mostly follows the same principles described above except for different drafting stages. The latter has the so-called, all-at-once banning phase, which eliminates 22 draft picks.

4.2 Results for recommender model

Since the current paper focuses on many methods and algorithms at once, these would span across the following section. Exploratory research in the form of deep descriptive analytics for in-game trends would be a good starting point. Figure 2 depicts the match duration across professional dataset. Game update (from now on - patch) 7.22f is the first recorded for the observed matches, spanned from July 2019 to September 2019. This patch made it through the International 2019 and lasted the most amongst the others in the dataset. The last patch recorded is 7.24, which was introduced in late January 2020, it went offline on February 26, 2020.

The already mentioned figure shows most of the patches' matches became longer, which is displayed by a peak shifting from 27.5 minutes` mark to 33.5 minutes. That was driven by intentional mechanic alterations by game developers, creating the obstacles for adepts of aggressive gameplay and fast games. Professional teams, forced to play the changing rules, have been focusing more and more on late-game-beneficial heroes and resource-demanding playstyles.

Figure 2. Gametime counts by game version in 2019/20 professional season

Ridgeline application is substantial in finding that timings' shift since basic averages and `digit-only' information could not determine the trend. Since the data samples are not normally distributed (appendix 1), standard mean comparisons' results (showing means' equality) could not stand for the truth, whereas all the charts point the opposite in terms of Dota 2 importance of time. The means are generally affected by frequent outliers becoming a wide distribution, which stands for Dota's variability, as well as several patches having a higher number of matches. Moreover, Dota 2 assumes two-three minutes difference, derived from comparison, significant for gameplay and tempo. Ridgeline is free from these deviations since it uses frequency over mean.

Nevertheless, gametime is not the most important thing to determine the drafting process. Game changes, which often focus on hero upgrades and degrades (buffs and nerfs), followingly increase or decrease a team's demand in affected heroes. The graph below depicts overall professional teams' interest in the top ten heroes at each patch. The graph clearly demonstrates that a few heroes stay in trend throughout time and different updates. Most of them are at the top for just several weeks (not considered on the graph) and then replaced by other ones, while others might carry a `strong meta' flag for several consecutive patches. Worth to note, meta also accepts heroes not previously appeared in recent patches, which illustrates the developer's intention to maintain a wide hero choice.

Figure 3. Dynamic top ten heroes in 2019/20 pro season bump graph

Taking the popular draft options by a total number of occurrences of those, one can again try the ridgelines approach. This time to obtain pick and ban separate trends for the most popular heroes (top ten each) in professional matches (figure 4.) The critical changes mostly happened right after patch's 7.22h departure: many heroes got significant changes (mostly buffs), and professional players showed the interest and started using that. Both charts indicate what teams consider acceptable and allow opponents to picks and what scares them and got banned.

Figure 4. Top banned (left) and picked (right) heroes' counts in 2019/20 pro season

For example, Puck's change made the hero very strong at dealing with certain opponents and also amplified combat mobility already outstanding at the time. Unsurprisingly, teams have considered that a very significant gamechanger and preferred to ban Puck, which skyrocketed its' ban rate for the period. The hero has been later changed once again outside of the dataset range, bringing ban rates back to normal. The other example is Treant Protector, which received the new mechanic completely free (not via ability substitution). That change made the hero a bit stronger and versatile, but professionals preferred to play with it rather than a ban. Some heroes remained popular across all the time, like Tiny, who had not received much attention in terms of changes. Figure 5 also proves an increased professional's demand in buffed heroes after patches by depicting the top five by pick rate increase delta on a ten-day timespan. Game updates can always bring back forgotten heroes and do the opposite as well. Significant changes to Vengeful Spirit and heroes it counters the best allowed the hero to once again prove the strengths and take a more significant part of professional matches.

Figure 5. First days top five heroes of 7.23 patch by a highest pick rate increase

Public matches also received the ridgeline trend treatment for the picked heroes only. The chart below shows trends for the stated kind of matches. Interestingly, several heroes made it here through professional matches' meta: Slark and Puck. Considering the sampled public matches are high-tier, the same professional players might have been practicing the heroes for the upcoming tournaments. Void Spirit's and Snapfire's peaking popularity were backed by the heroes' introduction in patch 7.23. Lastly, most of the heroes remain stable throughout the entire dataset, which points towards them being pillars of matchmaking: Pudge, Legion Commander (LC), Invoker; these were popular anytime.

Figure 6. Top picked heroes in public matches during 2019/20 season

Variability within roles also matters for professional Dota 2 matches since that unveils positions, which may be flexible with a higher hero pool and, thus, still be sound when targetly banned. Table 6 shows team Alliance's top five heroes for each role with respective pick rates.

Table 6

Role distribution and variability, top five picks by roles for team Alliance

Safe	Mid	Offlane
Hero	Count	Rate	Hero	Count	Rate	Hero	Count	Rate
Faceless Void	13	12.87 %	Death Prophet	14	14.29 %	LC	17	15.89 %
Gyrocopter	11	10.89 %	Lina	7	7.14 %	Abaddon	7	6.54 %
Bloodseeker	8	7.92 %	Viper	7	7.14 %	Brewmaster	6	5.61 %
Alchemist	7	6.93 %	Puck	6	6.12 %	Invoker	5	4.67 %
Wraith King	5	4.95 %	Dazzle	5	5.1 %	Bloodseeker	4	3.74 %
Total = 101	44	43.56%	Total = 98	39	39.79%	Total = 107	39	36.44%
Soft Support	Hard Support
Hero	Count	Rate	Hero	Count	Rate
Rubick	12	9.21 %	Ogre Magi	24	27.27 %
Jakiro	10	7.89 %	Jakiro	10	11.36 %
Magnus	7	7.89 %	Lich	10	10.23 %
Doom	6	5.26 %	Undying	9	10.23 %
Leshrac	6	5.26 %	Vengeful Spirit	7	7.95 %
Total = 76	41	53.94%	Total = 88	60	68.18%

Team Alliance role's draft distribution proves the unwritten law of Dota 2: there are fewer support heroes to select from compared to cores. Nevertheless, teams do not find this a problem, since variability is still present. While a certain support hero is banned, it could be substituted with an alternative with a similar game role. I.e., Ogre Magi and Lich are strong laners able to protect weak safelane core (such as Gyrocopter) during the laning phase. Teams prefer to focus on core heroes alternations rather than supports because Mid's contribution towards the win is much higher compared to Hard Support. Overall, higher counts for core positions indicate teams are more willing to find and practice as many cores as possible, to be flexible in cases of meta-bans.

Speaking of the tools of the recommender model itself, the first one, if to consider, is the interactive graph for cooperation analysis done on the SNA basis. It represents heroes in the form of nodes and connections between those in the form of links. These links stand for heroes being both drafted in the same match. To visually understand the recommendations of the model user should understand, the heroes' importance depends on the nodes' size and links thickness. Node size depends on one of the centralities measures - Eigenvector centrality. The value of Eigenvector node sets its size; larger nodes mean more important heroes, that influence the team play. The reason why exactly Eigenvector centrality was chosen for the research is that, unlike degree, it does not only measure the number of connections a hero has but also the strength and importance of these connections. It also allows the algorithm to be more flexible even if the hero played not that many matches. The colorized visual demonstration of Eigenvector centrality compared to others is shown in figure 6.



Figure 7. Centrality measures

Link thickness gives the brief onto the number of matches the linked heroes played together for the selected team. Moreover, with the increasing number of matches played together, the line between heroes becomes thicker. Last indicator that could be taken into account in terms of analyzing graph - the number of links that come out of one node (degree). In terms of Dota 2, this number indicates hero universality; more links mean hero can be combined well by that team.

SNA implementation in the current research has visualizations for both separate pick and ban drafting stages. Team Alliance matches' drafts acts as an example. Graph from figure 7 demonstrates all the picked heroes for that team from the data sample. Colors represent different in-game roles for each hero. Some heroes appear more than once, which means the team uses a hero in different positions.

Figure 8. Alliance's picked heroes SNA graph

Role division in terms of cooperation is important in the drafting stage since the same hero at different roles can form various combinations and, thus, structures within the graph. The bigger nodes represent more crucial points of the draft, which both combine other valuable nodes or form a unique section. Mostly having only one connection to the main graph body, these `outliers' could be denied with the single ban. In that case, the player should also attribute hero-substitutes not earlier played - the ones, which perform nearly the same job during the match, i.e., heavy early fighter or magic damage dealer. Also, one of the extras of the graph is that it is possible to distinguish five-ended heroes subnetworks, allowing them to take a look at the possible structure of a team in a match. The motivation to use the current SNA implementation lies under the interactivity; one can drag and drop heroes highlighting connections with other nodes to make the graph easier to read.

The banning stage graph from figure 7 has only one node color since the ban considers all heroes equal in terms of roles. They do not participate in the match and, thus, do not have any role. The figure depicts what was banned versus team Alliance be it meta heroes, good combinations, or earlier mentioned `respect bans.'

Figure 9. Alliance's banned-against heroes SNA graph

The other tool used in the current research is the Sankey diagram, which example is given in figure 8. It represents the draft ordering of the particular team, i.e., Alliance once again. Named blocks represent heroes appeared in the first drafting phase (bans 1-6) of an analyzed team and every of its opponent. Every match of a team is plotted. Each block is added with a number accordingly to the ban order; that is crucial to be able to put the same heroes into different steps. The connections in the diagram represent the consecutive actions of teams' captains in the first phase of the draft. I.e., hero Mirana ban from Alliance's opponent in the first ban results in a hero Kunkka ban by Alliance in the second ban, and so on. The entire first phase might tell the opposing teams and match observers, what these teams are going to do strategically and which heroes they would prefer to play with. The thickness of the exact connections on the graph describes the number of occurrences of the given sequence. The Sankey diagram helps to look a few steps forward in the draft and to find possible combinations of the fourth or even fifth team's move even if only two stages passed.

Nonetheless, having an entire draft in a Sankey form is pointless, since too wide sequencing often brings unnecessary difficulties; thus, only the first phase is analyzed. One more point on Sankey is that the first phase quite often features `respect bans' for heroes, the team recognized for. I.e., during not analyzed ESL Los-Angeles 2020, Virtus.Pro's opponents used to ban hero Techies because VP.Zayac (player) is a known master of that hero at the professional level.

Figure 10. Sankey diagram for Alliance team ban phase when last-picking

Last but not least, the tool of the recommender model is the association rules algorithm. Based on historical match data, it summarizes head-body (if-then) pairs for any drafting choices. Association rules algorithm considers 8,000 professional matches and does not adjust to any particular team. The typical case of the association rules is presented in table 6, which shows the top five sequential actions for professional matches sorted by confidence. Worth to note, pure mathematics and algorithm's coefficients cannot entirely interpret `rules of the game' and, thus, the rules' output requires player's consideration to verify the eligibility of any suggestion.

Table 7

Association rules results for professional matches', top five (of 438)

LHS	RHS	Support	Confidence	Coverage	Lift	Count
01 Lina, 07 Axe	08 Skywrath Mage	0.001001	1	0.001001	48.19310	7
03 Night Stalker, 07 Centaur Warrunner	08 Rubick	0.001001	0.875	0.001144	16.30533	7
07 Naga Siren	08 Disruptor	0.001574	0.846153	0.001860	39.41948	11
00 Magnus, 01 Alchemist	03 Enchantress	0.001287	0.818181	0.001574	36.65035	9
00 Kunkka, 01 Night Stalker, 03 Keeper of the Light	06 Mirana	0.001287	0.818181	0.001574	13.58065	9

Banned Kunkka (step zero) and Centaur (step two) with the 70% chance will result in Lina being banned at step four; all the steps belong to the same team. The given rule is valid since heroes' abilities combine well at the laning stage, which could be enough to determine the match flow. The given top is ordered by already stated confidence in the decreasing order since its value reflects the reliability of the given association rule. Lift is the second important output here, and as far as it is greater than 1, the correlation between LHS and RHS of the rule is positive. The other two values - support and coverage - are not significant in the case of the current research. These take the overall quantity of matches (association rules' transactions initially) into account, whereas the considered dataset has too many of them. Neglecting that, the small number of matches (count) resulted in decent and logical association rules led by a proper team's preparation and tactics.

The same set of rules sorted by the number of occurrences returns very strong and popular combinations in-game, which is proven by high count and great support given the data size. The latter are amongst the highest in the current research considering all the rules' build attempts. The given sort mostly represents pick sequences opponents often want to stop. Thus, the support level of exact pairs is lower, because heroes might appear in both picking and banning phases separately.



Table 8

Association rules results for professional matches', top five (of 438)

LHS	RHS	Support	Confidence	Lift	Count
08 Morphling	07 Earthshaker	0.0054379	0.716981	40.40535	38
08 Juggernaut	07 Magnus	0.0047224	0.589285	24.80679	33
09 Io	06 Tiny	0.0045793	0.571428	7.367422	32
07 Axe	08 Skywrath Mage	0.0038638	0.509434	24.55120	27
03 Keeper of the Light, 06 Mirana	01 Night Stalker	0.0030052	0.5	6.706334	21

Association rules were also applied to Dota 2 public matches to determine frequent patterns int there. Unexpectedly, the initial dataset of over 150.000 matches did not result in any proper pattern definition. Table 7 depicts the top 5 associative rules obtained after a long process of the algorithm's finetuning to get at least understandable RHS-LHS pairs. Nevertheless, these mostly pair Nyx Assasin and Snapfire because of the algorithm's approach to Snapfire's popularity.

Table 9

Association rules results for public matches', length 3, best result, top five (of 506)

LHS	RHS	Support	Confidence	Lift	Count
01 Nyx Assassin, 03 Slardar	00 Snapfire	0.0000639	0.5555556	12.72929	10
01 Nyx Assassin, 06 Morphling	00 Snapfire	0.0000639	0.5555556	12.72929	10
01 Nyx Assassin, 12 Slark	00 Snapfire	0.0000575	0.5	11.45636	9
06 Vengeful Spirit, 10 Phantom Lancer	09 Drow Ranger	0.0000447	0.5	387.3044	7
01 Nyx Assassin, 06 Razor	00 Snapfire	0.0000447	0.7777778	17.82101	7

Low occurrence (count) of exact cases given the total number of input matches is the main problem of the public matches nature. Applied to the professional level, the obtained `public' rules could not provide a decent depth of analysis to base draft decisions on these. It could be explained by the fact that regular players in public matches, unlike the professionals, do not apply high-level tactics to the drafting stage. They tend to just practice specific in-game aspects for specific heroes. Hence, to follow any reliable pattern in public matches, much more data should be collected.

The previous table contains the information for the association rules with a length of 3.

Table 8 presents rules with a max length of 2. The appendices section also contains extra cases with different settings for pair rules determination only. The dimension shortage to only one hero at both LHS and RHS was aimed to acquire higher counts for pairs. Nevertheless, the restriction did not achieve better results; the algorithm favors already mentioned Snapfire's and Void Spirit's introduction for both lengths. Still, these public rules are bad at predictions quality and number of occasions; counts are even lower this time.

Table 10

Association rules results for public matches', best result, length 2, top five (of 55)

LHS	RHS	Support	Confidence	Lift	Count
18 Luna	06 Vengeful Spirit	0.000019	0.75	733.45781	3
18 Enchantress	00 Disruptor	0.000013	1	95.64242	2
19 Rubick	02 Void Spirit	0.000013	1	44.85981	2
21 Crystal Maiden	09 Skywrath Mage	0.000013	1	608.8365	2
21 Luna	02 Kunkka	0.000013	1	206.4261	2

Public matches' rules result in decent predictions when the Captain's Mode used in professional matches becomes the playground. Table 9 depicts relatively higher counts for defined rules, which at the same moment have low confidence. The given pairs return both hero counters picks and based on opponent' choices preventive bans well-known to experienced players.

Table 11

Association rules results for public-CM matches', length 3, top five (of 15)

LHS	RHS	Support	Confidence	Lift	Count
09 Elder Titan	08 Meepo	0.000185	0.3766234	50.111085	29
20 Invoker	19 Broodmother	0.000153	0.2376238	192.64885	24
13 Chen	12 Lycan	0.000147	0.2	19.983525	23
20 Templar Assassin	19 Huskar	0.000147	0.2421053	183.00702	23
19 Pugna	17 Outworld Devourer	0.000134	0.2413793	312.13936	21

Mentioned attempts to get better association rules involve tuning of support and confidence targets, rule lengths, sorting priorities, as well as other arguments. The intermediate results tables are given in the appendices for comparison, as well as the algorithm's settings linked to those.

4.3 Application design

As was stated above, the outcome of this research is the interactive application made on the Shiny package for R. The application looks the following way:

Figure 11. Recommender application beta UI

The UI is split into two main sections: control and outputs. The use scenario starts with the user selecting the team for analysis; the selector includes 89 top-tier Dota 2 teams. The team could be selected from the given list or searched manually with the help of the input field. The total number is limited due to the limitations coming from actual data collection using API.

Just below the team selector, the toggle for draft orientation sits. It allows a user to select what draft stage to analyze - picks or bans. The next selector for the graph visualization stands for hero exclusion. It allows to cross-off heroes from the graph in a case those heroes have already been picked or banned. Such exclusion allows the algorithm to restructure the graph and highlight the remaining heroes to make the tool more flexible. The selector itself shows not only the names of heroes but also the number of matches played by the particular hero for the selected team; also, it gives an opportunity to either select all heroes at once which would make graph empty or deselect all previous choices to look at the clean full graph. The next selectors' section refers to the Sankey diagram. The first set of radio buttons allows the user to switch mode and analyze every team or just the selected one. The next `Draft ordering' pair appears when the `Team-spec' mode is set and defines whether the selected team first- or lastpicks. The Firstpick choice restructures diagram to the situation when the selected team goes first in the drafts and the Lastpick displays the opposite situation - when the opponent has the first pick. Lastly, two final radio buttons related to the Sankey diagram define the faction selection. Once chosen, it filters a diagram only to matches played by the team on one of the sides.

The outputs section contains the outlined earlier algorithm recommendations in an interactive form. I.e., SNA graph adjusts according to the control inputs: draws different graphs for different teams, eliminates heroes when asked for via the `Heroes' input. Public matches related data preserves the static form since it could not be affected anyhow. Inputs also affect association rules results by filtering the overall rules table with draft-participating heroes. Sankey output changes a lot depending on different inputs too. Building different diagrams for different teams, faction of the team, draft order, and one of the Sankey output also takes into account every team from the dataset, not the selected one. Finally, the various ridgeline charts and other descriptive statistics have only two states depending on input: overall statistics and statistics for one particular selected team.

4.4 Evaluation

It is difficult to assess the recommender model in a purely statistical way, given the fact Dota 2 is extremely difficult to codify into the variables and mathematical world. The algorithms' results are somewhat subjective, and team-dependent; they tend no to predict the exact heroes but to analyze past matches and propose possible ways the drafting stage can emerge. Still, to assess the quality of these results, the current paper uses two ways. Firstly, the tool's suggestions were compared to panel-analysts' predictions, and actual drafts for five randomly picked games' picks from one of the most recent Dota 2 professional tournaments (ESL One Los Angeles 2020 EU + CIS online). The tool was successful in following the analysts' predictions. In terms of Dota 2, all the heroes in table 12's rows create a unique and strong draft. The main advantage of the model is that unlike people, it gives the whole picture nearly immediately with no mistakes. Thus, it saves any team or caster's time and brings an additional scope of deeper momentum analysis to each of the drafting steps. The results of the comparison are in the table below.

Table 12

Recommender model overall suggestions' comparison to casters' predictions on last phases

Phase	Team	Actual pick	Casters suggestions	Model suggestions
18	Secret	Arc Warden	Medusa	Death Prophet
21	Virtus Pro	Death Prophet	Kunkka	Kunkka
21	Alliance	Queen of Pain - Mid	Winter Wyvern - HS	Lina - Mid
22	Spirit	Anti-Mage - Carry	Void/Naga/Lycan - Carry	Invoker/Tiny - Mid
22	Ehome	Huskar	Death Prophet	Invoker/Death Prophet

Then, the mentioned in methodology St.Petersburg's player X also tested the outputs of the algorithms. The aim of such an evaluation method is to verify the viability of the model in real life. Unfortunately, since the player is not a member of any team from the dataset, the results could only be discussed in an indirect manner of feedback based on experience and Dota 2 professional scene understanding. Table 11 depicts the player's most `Fitting results' found out in the outputs.

Table 13

Player X's thoughts on various `worth-to-note' methods used in the recommender model

Method	Result	Evaluation
Ridgeline	Lina pick rate decrease after 7.24 update	Skill nerfs decreased popularity; such charts can depict general trends created by others
SNA graph	Hero triplets+ combinations for any team	Entire five-hero combos prove some potential strange combinations' existence
Roles variability	Specific positions' lack of hero pools	The method unveils not only core/support distinction but weak position performance
Sankey	Sequential approach	Step-by-step ban phase helps against many opponents showing other teams' decisions

The next part of the evaluation involved real match use. During several ranked games, the player X used suggestions of professional matches' association rules. The ones depicted in the table below proved to be sustainable and useful when usual hero pairs are impossible due to bans:

Table 14

Player X's used associative rules from the recommender model during ranked public matches

Usual laning pair-triplet	Banned hero(es)	Suggested and played
Magnus - Juggernaut - Lich	Juggernaut	Magnus - Phantom Assasin - Lich
Axe - Skywrath Mage	Axe	Centaur Warruner - Skywrath Mage
Alchemist (enemy) - Lifestealer	Lifestealer	Alchemist (enemy) - Outworld Devourer
Mirana - Shadow Demon	Shadow Demon, Bane	Mirana - Outworld Devourer - Lich

Conclusion, limitations, and future works

The current paper presents Dota 2 professional players a tool to better predict the in-game drafting stage versus a specific rival through analyzing historical match data. The tool uses an application form that combines social network analysis, association rules, and rich descriptive statistics to distinguish stable hero combinations and patterns. With the initially collected data, the tool fulfills the target expectations and shows promising results of giving the right choices of heroes to pick and to restrict against a team from a certain pool. The tool is ready for more than eighty rival teams to play against by providing deep insight into their strategy and preferences in the form of graphs, draft orders, and meta followings. By default, the tool shows the selected team's network of drafted heroes, sequential first stage choices for both the team and its rivals, and meta descriptions for past season's matches. By simulating a real-game draft sequence, one can find the most probable rival's hero picks in a visual and table forms to be aware of those and ban in-game if needed. Using the input settings, it is possible to clarify the draft stage to actualize information or change prerequisites completely; hence, the tool is interactive and is better when used during the entire drafting stage.

Dota 2 is a highly dynamic game; regular game version updates change teams' preferences, overall meta, in-game mechanics, and economy. Captains might struggle with certain prepared combinations and start exploring new opportunities, turning around an entire competitive season. Every new patch is ready to bring instability and new, unpredicted draft patterns. These cumulative changes complicate the universal analysis approach and require to find loop-holes over the game and its data. Taking a static dataset with a limited team pool appears to be not ideal given the game's high variability and new strategies/drafts' development speed. For example, the current paper uses six starting bans, whereas, during the writing of the work, Dota 2 has entered the eight ban era, which redefines the draft procedure and hero priorities. For the teams, which often struggle to find stable rosters, drafts' analysis might be a problem since the ever-changing line-up brings different active hero pools and combinations' preferences as well. Moreover, Dota 2 is an insanely difficult game to play and to account for all the in-game parameters at once. It is impossible to give a perfect computed tip: hence, the current tool only acts as a helping hand for a player-drafter. Even though it is technically possible to code many parameters, those processing appears to be practically impossible, which creates another strong limitation. Large datasets require either expensive cloud-based services or scientific computation machines because personal workstations could not deal with extreme data arrays. Lastly, the API usage limits the tool with the amount of data available at hand. These two latter limitations combined reasonably impact every part of the research, which requires much more data than the current paper could collect and process. All of the analysis parts would only benefit and result in better predictions once the computational power and data sample are decent.

The key area for the updates and future work is enlarging the dataset for the algorithms with the API delivery optimization and computational power increase. One of the options could be to use the matches history dump files capped at 100+ Gb of records only available to scientific computers for the procession at the moment. Another development might be bringing interactivity up to the next level: create a live match section with automatic updates to it, shift from limited team list to an open form, and API optimizations or new data collection methods, which might take another research paper to write. Moreover, future explorations for Dota 2 hero recommendations could take new arguments and classifications, i.e., hero in-game objectives distinction, to feed to the apriori algorithm or even some others. Social Network Analysis implementation also needs to consider larger professional matches data set and filtering conditions, like win plus lose scenarios for observed teams. Although, future researches can stick to some extra cooperation analysis methods to create an even better approach and study team-building principles in general and multiplayer games in particular.



List of references

Agrawal, R., & Srikant, R. (1994). Fast Algorithms For Mining Association Rules In Datamining. 20th VLDB Conference, 2(12), 13-24.

An, A., Khan, S., & Huang, X. (2006). Hierarchical grouping of association rules and its application to a real-world domain. International Journal of Systems Science, 37(13), 867-878. https://doi.org/10.1080/00207720600891661

Bathurst, E. (2017). Challengermode Raises $1.3M Capital Investment, Zlatan Ibrahimoviж Listed as Investor. The Esports Observer. https://esportsobserver.com/challengermode-investment-ibrahimovic/

Burt, J. (2017, October 15). Why Monaco will continue to be successful despite selling over Ј300m worth of talent. The Telegraph. https://www.telegraph.co.uk/football/2017/10/15/monaco-will-continue-successful-despite-selling-300m-worth-talent/

Chen, C. T., & Hung, W. Z. (2012). Choosing project leader based on interval linguistic TOPSIS and social network technology. 2012 International Conference on Fuzzy Theory and Its Applications, IFUZZY 2012, 310-315. https://doi.org/10.1109/iFUZZY.2012.6409722

Chen, Z., Nguyen, T.-H. D., Xu, Y., Amato, C., Cooper, S., Sun, Y., & El-Nasr, M. S. (2018). The Art of Drafting: A Team-Oriented Hero Recommendation System for Multiplayer Online Battle Arena Games. http://arxiv.org/abs/1806.10130

Cheng, W. Z., & Li Xia, X. (2014). A fast algorithm for mining association rules in images. Proceedings of the IEEE International Conference on Software Engineering and Service Sciences, ICSESS, 513-516. https://doi.org/10.1109/ICSESS.2014.6933618

Conley, K., & Perry, D. (2013). How Does He Saw Me?? A Recommendation Engine for Picking Heroes in Dota 2. Stanford University.

D'Souza, M., Sulakhe, D., Wang, S., Xie, B., Hashemifar, S., Taylor, A., Dubchak, I., Conrad Gilliam, T., & Maltsev, N. (2017). Strategic Integration of Multiple Bioinformatics Resources for System Level Analysis of Biological Networks. In Methods in Molecular Biology (Vol. 1613, pp. 85-99). Humana Press Inc. https://doi.org/10.1007/978-1-4939-7027-8_5

Davids, K., Araujo, D., & Shuttleworth, R. (2005). Applications of Dynamical Systems Theory to Football. Science and Football V: The Proceedings of the Fifth World Congress on Science and Football, i, 537-550.

Deloitte Corporate Finance LLC, & The Esports Observer. (2019). The rise of esports investments (Issue April). Deloitte Development LLC. https://www2.deloitte.com/us/en/pages/advisory/articles/the-rise-of-esports-investments.html

Eggert, C., Herrlich, M., Smeddinck, J., & Malaka, R. (2015). Classification of player roles in the team-based multi-player game dota 2. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 9353, 112-125. https://doi.org/10.1007/978-3-319-24589-8_9

Gerrard, B. (2019). Book review: Data Analytics in Football: Positional Data Collection, Modelling and Analysis. Sport Management Review, 22(4), 568-569. https://doi.org/10.1016/j.smr.2019.01.002

Hanke, L., & Chaimowicz, L. (2017). A recommender system for hero line-ups in MOBA games. Proceedings of the 13th AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, AIIDE 2017, 43-49.

Johansson, F., & Wikstrцm, J. (2015). Result Prediction by Mining Replays in Dota 2. http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A829556&dswid=5771

Kinkade, N., Jolla, L., & Lim, K. (2015). DOTA 2 Win Prediction. University of California, 1-13.

Korte, F., & Lames, M. (2019). Passing Network Analysis of Positional Attack Formations in Handball. Journal of Human Kinetics, 70(1), 209-221. https://doi.org/10.2478/hukin-2019-0044

Laporta, L., Afonso, J., & Mesquita, I. (2018). Interaction network analysis of the six game complexes in high-level volleyball through the use of Eigenvector Centrality. PLoS ONE, 13(9), 1-15. https://doi.org/10.1371/journal.pone.0203348

Lйvi-Strauss, C. (1947). Les Structures Йlйmentaires de la Parentй. Mouton et Co.

Link, D. (2018). Data Analytics in Professional Soccer. In Data Analytics in Professional Soccer. https://doi.org/10.1007/978-3-658-21177-6

Logitech International. (2017). Logitech to Acquire ASTRO Gaming, Adding Console Gaming Headsets to its Position as the #1 Maker of PC Gaming Gear. Logitech International. https://ir.logitech.com/press-releases/press-release-details/2017/Logitech-to-Acquire-ASTRO-Gaming-Adding-Console-Gaming-Headsets-to-its-Position-as-the-1-Maker-of-PC-Gaming-Gear/default.aspx

Maincast. (2019). epileptick1d - on Ramzes, new patch, and transfer to VP. https://www.youtube.com/watch?v=B9g79GaYJKY

Manuel, F., Fernando, C., Lourenзo, M., Rui, M., & Mendes, S. (2016). Social Network Analysis Applied to Team Sports Analysis. In SpringerBriefs in Applied Sciences and Technology. Springer International Publishing. https://doi.org/10.1007/978-3-319-25855-3

Methot, J. R., Rosado-Solomon, E. H., & Allen, D. (2018). The network architecture of human captial: A relational identity perspective. Academy of Management Review, 43(4), 723-748. https://doi.org/10.5465/amr.2016.0338

Moreno, J. L. (1934). Who Shall Survive? A New Approach to the Problem of Human Interrelations. Nervous and Mental Disease Publishing Co.

Morschheuser, B., Hamari, J., & Maedche, A. (2019). Cooperation or competition - When do people contribute more? A field experiment on gamification of crowdsourcing. International Journal of Human Computer Studies, 127(October 2018), 7-24. https://doi.org/10.1016/j.ijhcs.2018.10.001

Nunes, M., & Abreu, A. (2020). Managing Open Innovation Project Risks Based on a Social Network Analysis Perspective. Sustainability, 12(8), 3132. https://doi.org/10.3390/su12083132

Park, R. E. (1928). Human Migration and the Marginal Man. American Journal of Sociology, 33(6), 881-893. https://doi.org/10.1086/214592

Radcliffe-Brown, A. (1923). Notes on the Social Organization of Australian Tribes. The Journal of the Royal Anthropological Institute of Great Britain and Ireland, 53(May), 424-446.

Silva, M. P., Silva, V. do N., & Chaimowicz, L. (2017). Dynamic difficulty adjustment on MOBA games. Entertainment Computing, 18, 103-123. https://doi.org/10.1016/j.entcom.2016.10.002

Simmel, G. (1902). The Number of Members as Determining the Sociological form of the Group. American Journal of Sociology, 8(2), 158-196. https://www.jstor.org/stable/2761932

Soltis, S. M., Brass, D. J., & Lepak, D. P. (2018). Social resource management: Integrating social network theory and human resource management. Academy of Management Annals, 12(2), 537-573. https://doi.org/10.5465/annals.2016.0094

Summerville, A., Cook, M., & Steenhuisen, B. (2016). Draft-Analysis of the ancients: Predicting draft picks in DotA 2 using machine learning. AAAI Workshop - Technical Report, WS-16-21-(Godec), 100-106.

Takahashi, D. (2017, August 2). Smash.gg raises $11 million for esports tournament platform | VentureBeat. https://venturebeat.com/2017/08/02/smash-gg-raises-11-million-for-esports-tournament-platform/

Tummel, C., Jeschke, S., & Pyttel, T. (2013). Line-Based Optimization of LTL-shipments using a Multi-Step Genetic Algorithm. 2013 IEEE Symposium on Computational Intelligence in Production and Logistics Systems, 70-77.

Uddin, S. (2017). SOCIAL NETWORK ANALYSIS in Project Management. Journal of Modern Project Management, 107, 106-113.

Wang, H., Lu, W., Sцderlund, J., & Chen, K. (2018). The Interplay Between Formal and Informal Institutions in Projects: A Social Network Analysis. Project Management Journal, 49(4), 20-35. https://doi.org/10.1177/8756972818781629

Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.

Wood, M. M. (1934). The Stranger: A Study in Social Relationships. Columbia University Press, 285-290.

Woodsmith, J., Stelzl, U., & Vinayagam, A. (2017). Bioinformatics Analysis of PTM-Modified Protein Interaction Networks and Complexes. In C. H. Wu, C. N. Arighi, & K. E. Ross (Eds.), Protein Bioinformatics (pp. 321-332). Humana Press Inc.

Yang, P., Harrison, B., & Roberts, D. L. (2014). Identifying Patterns in Combat that are Predictive of Success in MOBA Games. Proceedings of Foundations of Digital Games 2014, 1-8.

Zuccolotto, P., Sandri, M., & Manisera, M. (2019). Spatial Performance Indicators and Graphs in Basketball. Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, 1-14.



Appendices

Appendix 1

Figure 1. Normal distribution correlation test for patches' match duration

Figure 2. Mean plot 95% CI for patches' match duration

Appendix 2

Gametime summary by game version in 2019/20 professional season

Patch	Min.	Q1	Median	Mean	Q3	Max.	Count
7.22f	14.25	26.02	31.7	33.23	38.93	95.07	426
7.22g	10.82	26.67	32.72	34.45	41	86.4	1047
7.22h	6.583	27.833	34.725	35.985	42.85	113.167	2590
7.23	15.48	26.62	33.85	37.86	46.93	85.38	94
7.23a	11.48	25.42	33.31	34.56	40.62	82.8	98
7.23b	7.933	24.967	32.033	33.301	39.667	72.167	651
7.23c	17.58	25.98	32.17	34.16	40.03	63	129
7.23d	15.23	26.67	32.5	34	41.02	67.05	180
7.23e	13.72	28.47	34.25	35.7	41.82	76.35	929
7.23f	9.033	28.883	34.817	36.184	42	86.583	591
7.24	11.17	28.23	33.75	34.67	38.92	72	253

Public matches dataset, head(5)

m_id	duration	start_time	account_id	hero_id	kills	deaths	assists	date	hero
5354919011	1984	1586857716	89427480	17	13	3	14	14-04-20	Storm Spirit
5354919011	1984	1586857716	159044938	87	3	2	27	14-04-20	Disruptor
5354919011	1984	1586857716	178980417	15	5	4	15	14-04-20	Razor
5354919011	1984	1586857716	400565176	21	11	7	14	14-04-20	Windranger
5354919011	1984	1586857716	176872896	13	16	2	9	14-04-20	Puck

Sankey graph object, head(5)

Source	Target	Value	IDsource	IDtarget
1 Abaddon	2 Kunkka	1	0	24
1 Abaddon	2 Naga Siren	1	0	28
1 Chen	2 Earthshaker	1	1	22
1 Chen	2 Night Stalker	1	1	30
1 Enchantress	2 Lone Druid	1	2	26

Heroes data base, head(5)

Hero ID	Hero name	Is carry	Is support	Is offlane
1	Anti-Mage	Carry	NA	NA
2	Axe	NA	NA	Offlane
3	Bane	NA	Support	NA
4	Bloodseeker	Carry	NA	NA
5	Crystal Maiden	NA	Support	NA

Appendix 3

Social Network Analysis buildup and call:

SNA object matrix example

...

	Abaddon	Alchemist	Ancient Apparition	Anti-Mage	Arc Warden	Batrider	Beast-master	Blood-seeker	Brew-master
Abaddon	0	0	4	0	0	0	0	0	0
Alchemist	0	0	0	0	0	0	0	0	7
Ancient Apparition	4	0	0	0	3	0	0	0	0

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