University of Warsaw - Faculty of Economic Sciences

Libraries 

library(knitr)
library(readxl)
library(arules)
library(arulesViz)
library(arulesCBA)
library("FactoMineR")
library("factoextra")
library(magrittr) 
library(ggrepel)

1 Introduction and motivation

Riot’s Teamfight Tactics is a multiplayer game based on chess but much more various. The key rule of this game is you have to choose your team comp among 100 available champions. Every champion has a trait, and the more traits from a certain group of champions you have the stronger bonuses you receive. I’m a huge fan of this game and it’s hard to be up to date in this game (especially during a winter exam session) because it changes every patch and every season. So a new change was uploaded to a live server one week ago and I haven’t adapted yet. I really like to be one of the best players in European server so I will use my degree to help myself.

Association rules are a field in machine learning that finds the relation between data and more precisely will tell us what likes to combine with each other. That algorithm is used by the biggest IT companies like Facebook, Youtube, or NETFLIX to create the best possible recommendations for us. That’s why I find it useful because I will try to analyze games of the best players and by that, I will know what team comps are the best right now, and what champions are played together.

2 Data

2.1 What data?

I used a useful site that shows basic statistics about TFT (team fight tactics) https://lolchess.gg/ to scrap data for 16 polish players that perform in the best polish TFT league called Ultraliga. I will use the last 5 games of every one of them to collect the data. But I will also use only team comps from winning games. That means only from place 1-4 out of 8. Because for that places u gain points. For places 5-8 you lose points. So that will give me a multidimensional approach because every player has a unique preference to play different team comps. So I will eventually accomplish 16 * 4 *5=320 rows of data

Players_of_group_A Players_of_group_B
OGIII ARNOLD
KACPERSKY DV1 SAGE
TKEY ANO VICER
SIMPLYWOJTEK DV1 SHIRCANE
AKI AGO TRAVISCWAT
AGO LELOUCH SPC ARKADY
LEFT KUBIXON
AGO ZBROJSON UNLUCKYHUBI

2.2 Scraped data

I’ve mentioned previously I will use 320 rows of data that will tell what team comps are built in TFT games.

So after finalising database it’s time to inspect it and see if the data is prepared correctly

## transactions as itemMatrix in sparse format with
##  320 rows (elements/itemsets/transactions) and
##  70 columns (items) and a density of 0.1151339 
## 
## most frequent items:
##        Silco           Vi      Sejuani Renata Glasc          Zac      (Other) 
##          196          194          170          127          116         1776 
## 
## element (itemset/transaction) length distribution:
## sizes
##   6   7   8   9 
##  13  44 174  89 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   6.000   8.000   8.000   8.059   9.000   9.000 
## 
## includes extended item information - examples:
##       labels
## 1       Ahri
## 2    Alistar
## 3 Blitzcrank

That’s pretty informative for now. The most popular champion in nearly 61,25% of winner matches is Silco and most winning team comps are composed of 8 champions (the most popular basket size).

But let’s deep into the 10 popular winning champions .

From the point of view of a TFT player, the score has a logical explanation. Sejuani is pretty always combined with Vi because really strong game buffs. Silco and Renata Glasc are juz overpowered champions that will be weakened in next patches. Zac and Reksai creates perfect combo with Sejuani and Vi guaranting your team additional health points. Seraphine and Jayce are guaranting you a strong buff called ‘Innovator’ and are the most powerful champions from this buff area. Ekko and Sivir are just really strong and they do not have a certain connection with other champions. But to judge on that let’s perform a deeper analysis based on association rules

3 Items (champions) frequency

3.1 Two-dimensional tables

An easy and also powerful tool to check the champions frequency is just two-dimensional tables that will show the most popular combination. Cross-tables are also useful to perform correspondence analysis. But for now let’s inspect the 15 most popular champions

Silco Vi Sejuani Renata Glasc Zac Reksai Seraphine Ekko Sivir Jayce Viktor Gnar JarvanIV Lucian Irelia
Silco 196 128 123 99 86 56 41 28 47 41 51 39 40 40 33
Vi 128 194 144 95 98 67 43 34 54 50 68 30 45 39 28
Sejuani 123 144 170 84 90 63 27 8 63 17 58 33 57 51 22
Renata Glasc 99 95 84 127 92 53 23 11 6 27 61 10 5 6 9
Zac 86 98 90 92 116 57 15 7 1 22 63 8 2 3 9
Reksai 56 67 63 53 57 98 15 14 20 14 32 24 10 5 20
Seraphine 41 43 27 23 15 15 81 51 6 36 11 26 7 0 31
Ekko 28 34 8 11 7 14 51 76 8 42 2 24 1 1 34
Sivir 47 54 63 6 1 20 6 8 74 7 1 23 55 50 17
Jayce 41 50 17 27 22 14 36 42 7 71 13 17 2 5 21
Viktor 51 68 58 61 63 32 11 2 1 13 71 3 1 1 3
Gnar 39 30 33 10 8 24 26 24 23 17 3 67 13 14 40
JarvanIV 40 45 57 5 2 10 7 1 55 2 1 13 61 46 11
Lucian 40 39 51 6 3 5 0 1 50 5 1 14 46 60 3
Irelia 33 28 22 9 9 20 31 34 17 21 3 40 11 3 58

3.2 Eclat Algorithm

3.2.1 Description



ECLAT (Equivalence Class Clustering and bottom-up Lattice Traversal) algorithm is a really basic conception based on the support statistic that creates the most frequent item sets. So now it’s important to describe what support in terms of the ECLAT Algorithm means. Basically, support is the relative frequency of a certain item set in the entire basket of items. The Algorithm tells us which items occur together the most, but there are not directly created rules. So the advantage is the method is very fast but in the end we are still out of strong rules, we have just hints.



\(support(X)=\frac{count(X)}{N}\)



Where: X - a certain itemset N - The entire baskter of observations

3.2.2 Performing on data



So let’s perform an apriori algorithm on our data.

I will set the minimum length on 6 because that is the minimum length on the winning team from the previous chapter. The support level should be also high but by the experimental approach I’ve decided to set it on the level 0.10

freq.items<-eclat(trans1, parameter=list(supp=0.10, minlen=6)) 
## Eclat
## 
## parameter specification:
##  tidLists support minlen maxlen            target  ext
##     FALSE     0.1      6     10 frequent itemsets TRUE
## 
## algorithmic control:
##  sparse sort verbose
##       7   -2    TRUE
## 
## Absolute minimum support count: 32 
## 
## create itemset ... 
## set transactions ...[70 item(s), 320 transaction(s)] done [0.00s].
## sorting and recoding items ... [29 item(s)] done [0.00s].
## creating bit matrix ... [29 row(s), 320 column(s)] done [0.00s].
## writing  ... [2 set(s)] done [0.00s].
## Creating S4 object  ... done [0.00s].
inspect(freq.items)
##     items                                           support count
## [1] {Renata Glasc, Sejuani, Silco, Vi, Viktor, Zac} 0.13125 42   
## [2] {Reksai, Renata Glasc, Sejuani, Silco, Vi, Zac} 0.10625 34
freq.rules<-ruleInduction(freq.items, trans1, confidence=0.1) 
inspect(freq.rules)
##      lhs                                            rhs            support
## [1]  {Sejuani, Silco, Vi, Viktor, Zac}           => {Renata Glasc} 0.13125
## [2]  {Renata Glasc, Silco, Vi, Viktor, Zac}      => {Sejuani}      0.13125
## [3]  {Renata Glasc, Sejuani, Vi, Viktor, Zac}    => {Silco}        0.13125
## [4]  {Renata Glasc, Sejuani, Silco, Viktor, Zac} => {Vi}           0.13125
## [5]  {Renata Glasc, Sejuani, Silco, Vi, Zac}     => {Viktor}       0.13125
## [6]  {Renata Glasc, Sejuani, Silco, Vi, Viktor}  => {Zac}          0.13125
## [7]  {Renata Glasc, Sejuani, Silco, Vi, Zac}     => {Reksai}       0.10625
## [8]  {Reksai, Sejuani, Silco, Vi, Zac}           => {Renata Glasc} 0.10625
## [9]  {Reksai, Renata Glasc, Silco, Vi, Zac}      => {Sejuani}      0.10625
## [10] {Reksai, Renata Glasc, Sejuani, Vi, Zac}    => {Silco}        0.10625
## [11] {Reksai, Renata Glasc, Sejuani, Silco, Zac} => {Vi}           0.10625
## [12] {Reksai, Renata Glasc, Sejuani, Silco, Vi}  => {Zac}          0.10625
##      confidence lift     itemset
## [1]  0.9545455  2.405154 1      
## [2]  0.8936170  1.682103 1      
## [3]  0.8235294  1.344538 1      
## [4]  1.0000000  1.649485 1      
## [5]  0.7241379  3.263720 1      
## [6]  1.0000000  2.758621 1      
## [7]  0.5862069  1.914145 2      
## [8]  0.9444444  2.379703 2      
## [9]  0.9444444  1.777778 2      
## [10] 0.7906977  1.290935 2      
## [11] 1.0000000  1.649485 2      
## [12] 0.9444444  2.605364 2

3.2.3 conclusion

Based on the outcomes of the ECLAT algorithm I should say that to win the game I should try to include in my team especially

* {Renata Glasc, Sejuani, Silco, Vi, Viktor, Zac}

* {Reksai, Renata Glasc, Sejuani, Silco, Vi, Zac}

They are really similar. Renata Glasc, Sejuani, Silco, Vi and Zac are the same. The only difference is Vi versus Reksai. Basically the same conclusion comes from frequency based rules. But that’s not the end. Let’s perform different algorithm to check other rules.

3.3 Apriori algorithm

3.3.1 Description

Apriori algorithm in the opposition to ECLAT algorithm is a little bit more complicated but also has a richer outcome. Here we need to take into consideration also a confidence statistic and a lift statistic. That will cause more computation but we will receive in back richer outcome.



\(confidence(X→Y)=\frac{support(X,Y)}{support(X)}\)



-> In the easiest words. Confidence measures how many transactions will occur Y when there is already an X item.



\(lift(X→Y)=\frac{confidence(X→Y)}{support(Y)}\)



-> Here the case is more complicated because this measure checks how the conditional probability of occurrence of Y when there is an X item. So we are checking if the occurrence of X somehow can higher the probability of occurrence of the Y item.
Based on that, the Apriori algorithm is building frequency rules ### Performing on data

Once again the minimum length of the rule described by the apriori algorithm has to be 6 to be representative to this analysis 

apriori <- apriori(trans1, parameter=list(minlen=6)) 
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.8    0.1    1 none FALSE            TRUE       5     0.1      6
##  maxlen target  ext
##      10  rules TRUE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 32 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[70 item(s), 320 transaction(s)] done [0.00s].
## sorting and recoding items ... [29 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [9 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
inspect(sort(apriori, by = "support"))
##     lhs                                            rhs            support
## [1] {Renata Glasc, Sejuani, Vi, Viktor, Zac}    => {Silco}        0.13125
## [2] {Renata Glasc, Sejuani, Silco, Viktor, Zac} => {Vi}           0.13125
## [3] {Renata Glasc, Silco, Vi, Viktor, Zac}      => {Sejuani}      0.13125
## [4] {Sejuani, Silco, Vi, Viktor, Zac}           => {Renata Glasc} 0.13125
## [5] {Renata Glasc, Sejuani, Silco, Vi, Viktor}  => {Zac}          0.13125
## [6] {Reksai, Renata Glasc, Sejuani, Silco, Zac} => {Vi}           0.10625
## [7] {Reksai, Renata Glasc, Silco, Vi, Zac}      => {Sejuani}      0.10625
## [8] {Reksai, Sejuani, Silco, Vi, Zac}           => {Renata Glasc} 0.10625
## [9] {Reksai, Renata Glasc, Sejuani, Silco, Vi}  => {Zac}          0.10625
##     confidence coverage lift     count
## [1] 0.8235294  0.159375 1.344538 42   
## [2] 1.0000000  0.131250 1.649485 42   
## [3] 0.8936170  0.146875 1.682103 42   
## [4] 0.9545455  0.137500 2.405154 42   
## [5] 1.0000000  0.131250 2.758621 42   
## [6] 1.0000000  0.106250 1.649485 34   
## [7] 0.9444444  0.112500 1.777778 34   
## [8] 0.9444444  0.112500 2.379703 34   
## [9] 0.9444444  0.112500 2.605364 34

3.3.2 Visualisation

plot(apriori, method="graph",  engine="htmlwidget")
plot(apriori, method="paracoord")

3.3.3 Conculusion

Once again I can say that the best team can be composed of Zac, Vi, Sejuani, Renata Glasc, Silco and we can then add Reksai or/and Viktor. Pretty simple but still I don’t think that this is the final answer we can get from this data.

3.4 Correspondence Analysis

3.4.1 Description

As I’ve mentioned previously cross-tables are perfect for Correspondence Analysis. This method is mapping observations close to each other if they occur together really often or if they are correlated. The final answer is a two-dimensional plot which will show the most often occurring together champions. Seems perfect to visualize the whole TFT meta.

3.4.2 Visualisation

ctab<-crossTable(trans1, sort=TRUE) 
res.ca <- CA(ctab, graph = FALSE)
options(ggrepel.max.overlaps = Inf)
fviz_ca_row(res.ca, repel = TRUE)

But this graph will tell something in addition. Because the most often occurring champions are rather in the middle (they are often played with everything so no reason to give them additional meaning). More interesting is the high absolute value of dimension 1 or 2. That will tell us which comps are often played together, but they don’t occur really often at all.

So what I can see: -> top right -> yordle team comp (Veigar, Poppy, Lulu, Ziggs, Vex, Corki) and Gnar which can occur also in other teamcomps. That’s why he is more to the center.. -> Bottom right -> Hex team comp (Lucian, Swain, Nocturne, Alistar, JarvanIV, Sivir). Somehow Silco and Tamh Kench are also related to this group -> Bottom left -> Challenger team comp (Draven, Warwick, Quinn, Tryndamere and Camille) -> Top left -> Innovator team comp (Ekko, Ezreal, Zilean, Jayce, Seraphine) and Jhin which is really often played with them.

So I think that Correspondence Analysis helped to in opposition to basket market analysis distinguish popular teamcomp but more rare and which don’t occur that often in the game. But they are stll strong and winning as the data is only from winning games.

4 Conclusion

I used association rules to help myself win more matches in Teamfight Tactics games by Riot Games. The outcome is pretty helpful because both ECLAT and Apriori algorithms showed that the most often occurring winning team comp is composed of those 7 champions {Renata Glasc, Sejuani, Silco, Vi, Viktor, Zac, Reksai}.

On the other hand correspondence analysis showed also, that pretty strong team comps that are not that popular are yordles, hexs, challengers, and innovators. That analysis is somehow similar to the professional recommendations about team comps in the current 6.5 patch in team fight tactics which can be found on this link https://tftactics.gg/tierlist/team-comps. Because of that, I’m happy that machine learning methods may contribute to a higher winning rate. I hope so at least!