As many of you might already be aware, there are 3 general categories of 3* troops and 2 general categories of 4* troops that provide unique boosts to a wide assortment of stats. The most important properties of a hero that determine the outcome of a fight is its ability to deal large amounts of damage and its ability to tank hits from other enemies/receive damage with as little an effect on its lifespan during the fight as possible. Multiple stats determine these parameters. In the case of damage dealt, this is determined by the hero’s attack stat and the base critical hit rate (the rate at which a strike does double the damage as it would otherwise do in normal circumstances). In the case of the ability of a hero to tank/survive a larger number of hits during a fight, this is determined by the hero’s defense stat and the total health stat. The purpose of this post is to analyze the effectiveness of each 3* and 4* troop in each of these respective areas by using math to provide a proper comparison between all of the troop stats.
General Categories of 3 and 4 troops**
This link contains a summary of all of the 3* and 4* troops in the game:
In general, 3* troops can be categorized based on their attack and defense stat as “high attack troops”, “compromise attack/defense troops”, and "high defense troops. 4* troops can be categorized based on their attack and defense stat as “high attack troops” and “high defense troops”, or commonly recognized and described in other posts on this forum as “mana troops” and “crit troops” respectively.
Measuring hero attack and tanking effectiveness enhancements from troop boosts
The amount of damage dealt by a hero under a specific circumstance is determined by a combination of it’s attack stat and the opponents defense stat. In mathematical form:
Damage dealt = Constants* (Hero attack stat/Target Defense stat)
Circumstances can vary depending on whether or not the hit is determined to be a critical strike or not. In that case, the damage dealt from those strikes is double that of a normal strike. Over a large number of hits, the average damage from a strike is, thus:
Average damage dealt = damage from critical hits + damage from regular hits
Average damage dealt = Constants*(Hero attack stat/Target Defense stat)2Critical Strike Rate +Constants*(Hero attack stat/Target Defense stat)*(1-Critical Strike Rate)
Average damage dealt =Constants*(Hero Attack Stat/Target Defense Stat)*(1+Critical Strike Rate)
In the case of troop stat boosts, a certain percentage is added to a hero’s base attack and the critical strike boost is (most likely; correct me if I am wrong here) representative of the actual critical strike rate. The product of attack boost*(1+crit rate) is, thus, a measure of how much a troop enhances a heroes ability to do damage to a target.
When the hero that receives stat boosts from a troop ends up on the receiving end of the damage, boosts that impact how many hits the hero can take before dying become important to consider. The number of hits a hero can take before dying increases as a hit received takes off a smaller fraction of the hero’s total health. The fraction of damage received is thus:
Fraction of Damage received = Damage received/Hero’s total health
Fraction of Damage received = Constants*(Opponent’s Attack/Hero’s Defense)/Hero’s total health
Fraction of Damage received = ConstantsOpponent’s Attack/(Hero’s DefenseHero’s total health)
Troop stat boosts once again work to add a certain percentage to a hero’s existing defense and health stats. The product of defense boost*health boost as seen in the above formula, is thus, an approximate measure of how many more hits of the same type a hero can endure before certain death.
Results:
At the 3* troop level, the abilities of the troops to tank hits and deal out damage are more balanced. The 3* defense troops are the worst troops out of the 3* options to use if the aim is to increase the total damage done by the hero, but also the best troops to use if the aim is to tank more hits; the 3* compromise troops are the worst troops to use if the aim is to tank more hits. Admittedly, 26% extra tankiness from the defense troops is equivalent to permanently decreasing the opponent’s attack stat by only 20.6%, so comparing that to the 28.4% attack boost supplemented by the 3* attack troops severely undermines the general usefulness of tankiness and makes the ability to deal more damage more important. Thus, the most useful general purpose 3* troops are undoubtedly the 3* attack troops.
At the 4* troop level, the balance between the ability to tank hits and the ability to deal hits is very skewed. Overwhelmingly, the 4* crit troops dominate in both of these aspects by margins of at least 12%.
One limitation of this discussion is the exclusion of the %healing and the %mana generation increase troop boost stats. The effect these will have on the usefulness of certain troops will depend on the hero’s mana speed and special ability as well as the mana speed and special abilities of any teammates it has that heal a certain % of its health. I suspect these stats become less important as a normal non-healing hero on a defense team that receives the bulk of the hits and a hero on an attack team that has a random chance of being hit, which is typical of most raid situations. The minimized importance of these stats, in my opinion, for these typical situations, merited their exclusion from the discussion.
That’s all I have to say about that. Would you stop levelling your 4* mana troops to start replacing them with crit troops? Would you feed all your 3* defense and compromise troops to extra 3* attack troops? Let me know this and your other thoughts in the comments below. Thanks for reading through this long post.
