Which card combinations are successful in the high Elo range?

Clustering of Decks

There are 110 different cards to play with in Clash Royale. To examine the different cards used by the top players, we have rated all cards with 52 categories. These categories classify the cards into broader categories, such as ground troops or air troops, and into more specific categories, such as the ability of a card to heal other cards. To play with the cards, the player chooses 8 of these 110 cards and builds a deck with them.

The values of the individual categories of the cards in a deck are used to calculate the category values for the deck. The resulting 52-dimensional category vector that describes the deck is then normalized so that there is an equal relationship between all values. We can use these category vectors to determine the similarity of different decks. To visualize this, we reduce the vector to two dimensions using PCA.

Next, we divide the dimension-reduced category vectors of the individual decks into 10 different clusters using the k-Means algorithm.The decks that are similar to each other are located within these clusters.

In the following scatter plot, the different decks are shown as so-called 'bubbles'. A bubble is larger the more battles occur in our data with this deck. The plot also provides the option of filtering by the number of battles fought. In the opinion of the investigators, a deck can only be rated well if it has at least 100 battles. By hovering over the bubbles, you can display the deck, the win conditions used, the evolutions used and the support card. It also shows the win rate, which is seen as decisive for the value of a deck.

Win Rates of Clusters

To find out which deck types, i.e. which cluster contains the most promising decks, we examine the correlation between the individual clusters and the win rate of the decks in them. To compare the win rate of the clusters we compare the median of the win rates of all decks in a cluster. If we look at all decks with at least 100 battles, we get the information that cluster 4 contains the most promising decks with a median win rate of 62.47%. If we restrict this further to decks with at least 1000 battles, cluster 9 is now the cluster with the best win rate. However, in this case there is also only one deck in cluster 9. Cluster 4 now has the second best median win rate, but with eight different decks.

Specific Decks

We now know which decks are similar to each other and which clusters are the most promising depending on the minimum battle count. To be able to take a look at the specific decks of the clusters, we display this using a treemap. This includes the decks of all battles of a certain selected minimum number of battles. The treemap is structured in such a way that the meta, i.e. all decks in the filter setting, forms the root. However, since the distinction does not only consist of 8 different cards, but also of a support card and the possibility that up to two cards of the 8 deck cards are an evolution, we have to differentiate further. The meta splits down into the 10 clusters. Within the 10 clusters it is then divided according to the win conditions. Win conditions are cards that are particularly responsible for destroying enemy towers and thus for victory. At the next level, we subdivide according to the support card. This is the card that stands on your own towers and defends them. Here you can choose between the tower princess and the cannoneer. The last level before the actual decks is the differentiation between the evolutions used. The explanation of what evolutions are can be found here. Finally, the specific decks remain as leaves. These leaves contain information about the deck, the evolutions used, the support card used and the win conditions used. They also contain the number of recorded battles that were carried out with this combination of cards and the associated win rate.

Based on the information when hovering over the meta area, we can see that a total of 219,134 battles were recorded from decks with over 100 battles. If we compare this with the 445,974 different battles mentioned on the data page of the cleaned data, we see that almost 226,840 battles were played by decks that had less than 100 battles. For performance reasons, we unfortunately had to remove the filter setting of the Treemap to view the data with all recorded decks without restriction by a minimum number of battles. The size of the leaves and nodes of the treemap are based on the number of fights added up at the node. The treemap now allows us to see, for example, that in cluster 4, the most promising cluster, the Hog Rider is the most played win condition. This is then most often played with the Tower Princess as a support card and most often uses the Knight and Firecracker as evolutions. With this restriction, there are still 19 different decks played in the cluster, all of which have win rates of at least 50%.

Order of the nodes: Meta -> Cluster -> Win Condition -> Support Card -> Evolutions -> Deck

Cards, Combinations, and their Win Rates

In addition to the decks of the various clusters, it is of course also interesting to look at the cards and combinations of these in general. For this purpose, we looked at the average win rates of the individual cards in all recorded decks with at least 100 battles. This is shown in the following bar charts for win conditions, support cards and individual cards, as well as for two-, three-, four-, five-, six-, seven- and eight-card combinations. As there are far more than 100 different possible combinations, we only look at the best and worst 100 for all categories except win conditions, support cards and individual cards.

This resulted in, for example, the Graveyard being the best win condition, closely followed by the Hog Rider and the Three Musketeers. However, it is important to note that the Graveyard was played more than 22,000 times, while the Three Musketeers was only played just under 2,000 times. It is also interesting to see that the Heal Spirit is the card with the highest win rate, although this should come as a relative surprise to those in the know. If you look at the number of battles, you can see that the Heal Spirit has only been played just under 1000 times. If we add to this the fact that we are only looking at the best players in Germany, then it is quite possible that a card achieves a very good win rate in relatively few games, even though the card may not be that good in general.

It should also be mentioned that the three-, four-, five-, six- and seven-card combinations often have the same number of battles and the same win rate in succession. This is due to the fact that these decks have been played less, but have often won in these few games. As previously mentioned, this results in a distortion due to the exclusive consideration of the top players in Germany. All combinations of the eight deck cards from this deck are then displayed in the respective diagrams. This means that for such a deck there can be up to eight different combinations with the same number of battles and the same win rate for the seven-card combinations. However, there can also be fewer if certain combinations also occur in other decks. However, the win rate then tends to decrease.