# [Math, Analysis] Which 3* and 4* troops dominate in damage output and tanking hits (not so intuitive)

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 heroâ€™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 heroâ€™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:

Troops summarized

In general, 3* troops can be categorized based on their attack and defense stat as â€śhigh attack troopsâ€ť, â€ścompromise attack/defense troopsâ€ť, and "high defense troops. 4* troops can be categorized based on their attack and defense stat as â€śhigh attack troopsâ€ť and â€śhigh defense troopsâ€ť, or commonly recognized and described in other posts on this forum as â€śmana troopsâ€ť and â€ścrit troopsâ€ť 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 itâ€™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 heroâ€™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 heroâ€™s total health. The fraction of damage received is thus:

Fraction of Damage received = Constants*(Opponentâ€™s Attack/Heroâ€™s Defense)/Heroâ€™s total health

Fraction of Damage received = ConstantsOpponentâ€™s Attack/(Heroâ€™s DefenseHeroâ€™s total health)

Troop stat boosts once again work to add a certain percentage to a heroâ€™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 opponentâ€™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 heroâ€™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.

Thatâ€™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.

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I use 4* troops, and indeed I have focused on leveling up my crit 4* troops because of analysis done by Revelate and others in a parallel thread that the mana regen was basically worthless until the troops reached a very high level. (The lowest is yellow mana helping Jackal at level 11.) Your work only sharpens that conclusion.

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So if we donâ€™t value the healing boost and the mana boost at all then the crit troops are better. Good to know.

I like the spreadsheet troop comparison, but there is one other thing Iâ€™d like to see compared in it, and cannot without actually recreating the formulas:

How does it work with troops that arenâ€™t maxed? The boost percentages shown are for Level 20 3* troops and Level 30 4* troops.

Iâ€™ve currently got 3* and 4* troops that are Level 5 or 6. Conventional wisdom seems to be that getting 3* troops high enough level to beat a level 1 4* troop is a waste of food and feeder troops, but Iâ€™d love to see what level a 3* attack troop has to be to outmatch either kind of level 1 4* troop.

If you can share the spreadsheet, Iâ€™d be happy to work it out myself and share results.

Ok. The post on top is too long for me.

4* troops. I might be leveling the wrong one or not. Mana troops or Crit troops? All around 10 or 11. I have quite a few of each color.

General wisdom is use 4* crit troops unless your 4* mana troop is able to drop a tile from your cast and partially depending on your special as well.

Very slow = lvl 1 and 23 mana troop (only speed u can drop 2 tiles)
Very fast = lvl 11 mana troop
Slow = lvl 17 mana troop
Average = lvl 23 mana troop
Fast = lvl 29 mana troop

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Sigh I wasted feeders on mana troops then. Most of my crit troops are still level 5 and below.

Does that also apply to defensive raid setups?

Itâ€™s not wasted if you are trying to level it up to the correct level to drop a tile on cast.

Getting to lvl 17 is not that badâ€¦ lvl 23/29 is a pain.

I have 3 fast cast heroâ€™s I use crit troops on and am leveling and 2 average cast heroâ€™s Iâ€™m working on lvling to 23 mana troopsâ€¦those mana troops are only lvl 15/16 right now. And I have a bunch of troops save up as I wait my 3 days until the barracks is leveled up. Itâ€™s going to take a little bit more time but I think itâ€™s worth it to drop a tile off hel and ares.

Ares is a tank and if I can get his heal/buff down to 9 tiles he can trigger more often and hopefully be harder to debuff as quickly, hel is also a great counter to a lot other heroâ€™s. So even though I donâ€™t have them at the level I want yet they are still better then me using lvl1 crit troops.

It applies to any setup where you want your hero to cast 1 tile faster(2 in case of very slow). Maybe you have a center tank hero and prefer the crit/def boost over faster special. It really depends on the individual hero and thier special.
Usually I feel the mana troop is better but it also requires you to level that troop to the correct point.
Standard tile casts for specials are:
Very slow 13.5
Slow 12
Average 10
Fast 8
Very fast 6.5

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Maybe I didnâ€™t explain myself very good, but as far as I know defensive raid setups donâ€™t use titles since the AI controls them. With that in mind, wouldnâ€™t mana troops be better for the higher attack and only the tank use the crit troop for higher defense/health?

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I use the term tiles but in reality mana troops increase the amount of mana you obtain from all sources (usually thatâ€™s tiles). So on raid defense you still increase the rate of charging.

To be fair I donâ€™t know exactly how much mana you get per turn on defense. Itâ€™s provably on the forums somewhere or I can look it up.

I use 4 fast snipers but kashrek in the tank spot.
My ares is still in ascension 2.

So not sure how to go about this. Change all the snipers to using crit troops. Ares in the future using mana troops?

Thatâ€™s the dilemma unless you plan to spend a lot of money itâ€™s a long planned out process leveling troops. And you may get new heroâ€™s later to replace the ones you are using. Which may change what Troops you want. (Heck and some day they may make 5* troops)

But as previously said mana troops do have the highest atk % so itâ€™s not a total wash on snipers. But it takes a lot of \$\$\$\$ to get those mana troops to lvl 29â€¦

Realistically lvl 17 is a reachable goal and lvl 23 will take you opening up your wallet a bit.

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Thanks. So I gotta start upping my crit troops. I always thought mana troops were better.

I think mana troops are better if you get them to the right level. In a world of unlimited funds Iâ€™d be using almost all Mana troops.

You absolutely have not wasted feeders. Mana troops are necessary as well. I seriously need to write a Troops guide. I keep saying that and never get around to it.

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For someone playing this long Iâ€™m gonna ask a stupid question. Does the troops affect defense? I put random troops for my defense since I always think it does not affect although they are 4* troops.

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Yes, they do. Troops can alter the base stats of a hero and therefore affect both offense and defense.

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A lot of people tend to level a crit and mana troop at same time becuase they use both troops when they color stack. It is not wasted. I was just trying to focus on mana troops to get to level 23 for my average cast heroâ€™s. So I left the crit troops at lvl 1. Currently I have my raid defense w 2 green heroâ€™s I have a sniper in corner with the mana troop at lvl 16 and a tank in the center with a lvl 1 crit troop becuase the crit troop gives health and more def. whereas the mana troop in corner has a higher atk and a heal boost but lower shields and no heath. Iâ€™m not getting a whole lot from the mana regen since my caster in corner is fast so it still takes me 8tiles to charge him.

Maybe someone can write a troop guide at some point becuase I think itâ€™s one of the most confusing subjects for people especially the mana % buff.

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