This could be useful for the bloody battles where no heals are allowed 
I would always go with defense over health, even because my healing potions would gain a better “damage recovery” value and because unlike health I could further improve them with buffs as Aegir / Vivica / etc
Just one more thing, since players seem to keep wondering how healing does influence the decision between Def or HP:
Healing that is based on max HP (= healing a certain percentage, which most healings in the game do) doesn’t influence the Def vs HP decision at all. Increased max HP means more HP get restored when receiving healing. But this additional HP pool has to be destroyed by the attackers afterwards, which means that the Def value is applied more often.
Imagine the most extreme healing situation: A hero is down to 1 HP and gets 100% healing. Then he is back to were he was at the beginning of the battle. So obviously all calculations regarding Def vs HP are still valid. The attackers just have to essentially kill the same hero twice.
Healing that is not based on max HP (e.g. potions in PvE, life-stealing specials) profits only from Def though.
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There’s not much of a difference imo. Withstanding/jinx is the one we want, not a minionlike health buff.
I tried to increase those, which the hero already had more to make his given stat ability even better. High def already, def up, high hp, hp up.
I hope, the def-att-routes will always be better than any with hearts in it.
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No! That’s exactly what shouldn’t be done.
For Gormek for example, Def is definitely better than HP. The more HP a hero has, the more valuable every point in Def becomes (and vice versa). You should balance the two.
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Thanks for this! It’s been helping me a little bit thus far.
By any chance do you still have the math formula(s) you used in the calculations?
I’ve opted to give fighter emblems to Boldtusk and some of my paladin emblems to Sonya. And having a formula to use could help me a lot with picking which paths they should follow.
BT is very tanky. I feel like I should start him by focusing on ATT&DEF, but I’m having trouble figuring out sure if I should do this throughout the entire grid or if I should eventually switch to focusing to ATT&HP once his DEF hits like >755 or so.
Similar issue with Sonya; super tanky already, I feel like I should start by focusing on ATT&HP but don’t know if I should eventually switch
Yes, I still have file that I used to calculate this stuff. I hardly ever work with Google drive. Hopefully the way I set it up works:
You basically just have to enter the current Def of your hero in the blue field in the top left. Then it will calculate the minimum HP the hero needs to profit more from 18 Def than from 36 HP.
It did the calculation for both attack and defense team (=with and without 20% Def boost). As you can see, both results are always the same. Which isn’t surprising, when looking at the damage formula.
Notice though, that the calculated HP is the HP that is destroyed in a fight by attacks that take Def into account. It will change when damage-ignoring attacks come into play.
Example:
Saying “a hero with 600 Def will need 884 HP to profit more from 18 Def than from 36 HP” isn’t the whole truth. The correct phrase is: “A hero with 600 Def will need to lose 884 HP in a fight by non-Def-ignoring attacks to profit more from 18 Def than from 36 HP”.
If the hero loses 300 HP by DoT attacks in a fight, then he needs 884+300=1184 HP to profit more from Def (since only 884 of his HP are destroyed by taking Def into account). You have to decide for yourself how much DoT damage you expect in an average fight to find the exact threshold between Def and HP.
That’s why the emblems are well balanced in this regard and you should not overthink the Def vs HP decision. However, you should not make the mistake to buff Def on already high Def heroes or HP on already my HP heroes. Def and HP should be balanced. For Gormek it will always be better to increase Def, for Boril HP is the better option. For heroes that are somewhat balanced with Def and HP, it will depend on how much DoT attacks they will suffer in average, which is hard to predict.
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Thanks so much the sheet and all the advice helps me tremendously!
And yup the sheet coding works perfectly for me. All I had to do was open it up in “sheets” and used “share and export —> make a copy” to make my own copy that can be edited!
Does that make such a difference to lever RNG? Probably not…
This statement is wrong, and somewhat inexplicable. A simple test shows that things like troop percentages multiply the fixed boost from emblems too:
| Base Defense | Talent Increas | Total Pre Troop | After Troops | Measured Boost |
|---|---|---|---|---|
| 673 | 56 | 729 | 838 | 15.00% |
If the troop didn’t boost the talent amount, Rigard would have a full defense of 829, not 838.
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Of course the troops (and all other multipliers) multiply the Def from emblems, too. That’s why so many players make the same wrong assumption you did apparently: That the efficiency of the Def boost gets increased by multipliers and that the +18 Def from emblems get more valuable if the Def gets multiplied. That is wrong.
The higher the Def already is, the less you gain from additional Def. The Rigard in your example would gain less from the emblems after the +15% boost is applied. Only the fact that the emblem bonus gets multiplied by 1.15 too, makes the efficiency of the emblems remain the same as without the 15% boost.
You can see that easily by just looking at the damage formula: (Atk/Def)^1.35
Let’s leave out the ^1.35 for simplicity and easy numbers, and imagine the base damage is just:
100 * (Atk/Def)
If a 600 Atk hero attacks an 300 Def hero it would mean 100 * (600/300) = 200 damage.
What would a 300 Def boost get you? Answer: 100 * (600/600) = 100 damage
What would a second 300 Def boost get you? Answer: 100 * (600/900) = 67 damage
As you can see, the first 300 Def reduced the damage from 200 to 100 (= by 100). Adding another 300 Def only reduced the damage from 100 to 67 (= by 33).
The multipliers from troops, def team bonus etc. increase your Def. At the resulting higher Def the +18 Def boost from emblems would be less efficient. Only because the emblem bonus gets multiplied too, it remains as efficient as without the multipliers. But it does not get more efficient.
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Let’s start by getting our terms right:
You used the word effectiveness, not efficiency. And that assertion is manifestly, demonstrably wrong. The reduction in damage from combining troops with a fixed emblem bonus is literally larger that without that combination.
A really simple example:
300 defense, 300 attack
Emblem boost +18
Troop boost 15%
So, before emblems, total defense with troops would be:
300*1.15 = 345
Adding in emblems would be:
318*1.15 = 365.7 (truncates to 365)
So:
- 300 points of defense are due to base defense
- 18 points of defense are due to the emblem boost
- 15 points of defense are due to the troop boost to the base defense
- 2 points of defense are due to the combination of troops and emblems
Now, to the damage equation.
Damage including all factors:
100*(300/365)^1.35 = 76.7 (truncates to 76)
Leaving out the 2 defense from emblem/troop interactions.
100*(300/363)^1.35 = 77.3 (truncates to 77)
I’m at a loss to find a definition of “effectiveness” of a damage reducer that doesn’t encompass a literal decrease in the amount of damage taken.
3 Likes
Now, let’s discuss “efficiency,” since you apparently wish to switch to that as a metric.
The efficiency of the emblem boost is also increased by combination with the defender boost and troops, because you actually take less damage due to the combination.
Back to our simple example:
300 defense, 300 attack
Emblem boost +18
Troop boost 15%
So, before emblems, total defense with troops would be:
300*1.15 = 345
Adding in emblems would be:
318*1.15 = 365.7 (truncates to 365)
Of which 2 points are due to the emblem/troop interaction.
Damage calculation
Damage with no emblems:
100*(300/345)^1.35 = 82.8 (truncates to 82)
Damage including emblems but excluding the emblem/troop interaction:
100*(300/363)^1.35 = 77.3 (truncates to 77)
Damage including all factors:
100*(300/365)^1.35 = 76.7 (truncates to 76)
Efficiency
Excluding the emblem/troop interactions, the efficiency of those 18 emblems is:
82-77 = 5 damage reduction for +18 points of defense yields a 27.8% efficiency (5/18)
Including emblem/troop interactions:
82-76 = 6 damage reduction for +18 points of defense yields a 33.3% efficiency (6/18).
So combining troops with emblems boosts the emblem efficiency in our example from 27.8% to 33%.
And again, what definition of “value” are you using for a damage reducer that doesn’t equal “takes less damage?”
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Of course the combination of multiplier (troop etc.) and fixed bonus (emblems) reduces the damage further. Thats exactly what I wrote (multiple times already…).
Remember the original question though: Def or HP emblems?
To use your example numbers: At 300 Def each point of HP is worth less than at 345 Def. The HP gets cut down easier, because of the low Def. The higher the Def, the more effective protection you get from each HP.
That’s why the higher the (base) Def, the more valuable HP points are compared to Def points. The +36 HP from an emblem node is worth more at 345 Def than at 300 Def. The additional 1 HP damage reduction in your example from the combination of multiplier and emblem boost exactly makes up for that.
What I’m trying to say is: Your calculations are all correct, but they are only a part of the picture. Of course the emblem Def points get further boosted by Def multipliers but so are the emblem HP points. Both profit from the multipliers by the same amount. So which troops you are using or if you use your heroes in attack or defense teams has no influence on the HP vs. Def emblem decision (and that’s what this whole thread is about).
+18 Def emblem node → profits from Def multiplier because the Def bonus becomes even higher than 18
+36 HP emblem node → profits from Def multiplier because each point of HP becomes worth more
Both effects are equally strong.
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If durability = hp x defense^1.35 (based on the same priciple you use in this guide)
The crossover point is:
defense = 0.675 hp
A talent node give +36 hp or +18 defense, which mean in talent tree, defense point cost twice than hp point.
To determine the crossover point/turning point, I’ll need dummy variable (total point).
Let just say we are tasked with giving a hero its defense and hp stat but we are limited in points to be allocated:
Adding 1 defense will cost 2.
Adding 1 hp will cost 1.
If all points are used, then:
2 × defense + 1 × hp = total point
Hp = total point - 2 × defense
Durability = hp x defense^1.35
= (total point - 2 × defense) x defense^1.35
To make it simpler, let just say:
a = defense
b = hp
c = durability
d = total point
c = (d - 2a) × a^1.35
c = (d x a^1.35) - (2 × a^2.35)
We have c as a function of a, to find what a result in maximum c, we use derivative:
1.35d x a^(1.350-1) - (2.35 × 2) × a^(2.35-1) = 0
1.35d × a^0.35 - 4.7 × a^1.35 = 0
1.35d × a^0.35 = 4.7 × a^1.35
(1.35d × a^0.35) / 4.7 = a^1.35
a^1.35 / a^0.35 = (1.35d x a^0.35) / (4.7 × a^0.35
a = (1.35/4.7) × d
b = d - 2a
b = d - (2 × 1.35 / 4.7) × d
b = (2/4.7) × d
a /b = (1.35/4.7) × d / (2/4.7) × d = 0.675
Maximum durability is reached when defense is 0.675x hp
If defense is lower than 0.675x hp, adding defense is better
If defense is higher than 0.675x hp, adding hp is better.
Now, lets prove and compare it with @Kerridoc durability formula, which is measured with SonyaD.
Lets say we have 3 heroes:
- Hero A with 675 defense and 1000 hp.
- Hero B with 693 defense and 964 hp (+18 defense but -36 hp compared to hero A)
- Hero C with 657 defense and 1036 hp (+36 defense but +18 hp compared to hero A)
Their durability and SonyaD will be:
| Hero | Defense | HP | Durability (×10^4) | Durability(Def) (×10^4) | SonyaD | SonyaD(Def) |
|---|---|---|---|---|---|---|
| A | 675 | 1000 | 660.02456 | 844.21833 | 2.16891 | 2.77419 |
| B | 693 | 964 | 659.27545 | 843.26016 | 2.16645 | 2.77104 |
| C | 657 | 1036 | 659.28471 | 843.27201 | 2.16648 | 2.77108 |
As we can see, hero A with def/hp ratio of 0.675 have better durability compared to the hero who trade 18 def for 36 hp and vice versa.
As the durability formula is based on the same formula as SonyaD, their result is similiar.
I the table above, I calculate durability and SonyaD with and without +20% defense bonus, it show that the turning point is still reached at defense/hp = 0.675. I have also try using my method with revised formula (c = (1.2 × a)^1.35 x b) and its result is also a/b = 0.675. Afterall, in those formula, +20% defense become a constant with value of 1.2^1.35 = 1.279. High defense or low defense hero will both gain the same 27.9% durability caused by +20% defense. (It also work the same way for % bonus in talent tree, they are treated as constant thus shall not be included in calculating def/hp ratio)
Most of the heroes have def/hp ratio below 0.675 thus chosing defense node is more beneficial, however there are also hero such as Boldtusk who have high def/hp ratio:
There are 2 crossroad in fighter talent tree which have choices between attack-health or attack-defense. If we take the path that contain health% and def% (already included in the calculation of the table below), there are 3 possibilities of how Boldtusk stat could end up:
| Node | Def/HP | Defense | HP | Durability (×10^4) | Durability(Def) (×10^4) | SonyaD | SonyaD(Def) |
|---|---|---|---|---|---|---|---|
| 5 Def + 4 HP | 0.640 | 801 | 1251 | 1115.14 | 1417.00 | 3.66446 | 4.65642 |
| 6 Def + 3 HP | 0.674 | 819 | 1215 | 1116.03 | 1418.14 | 3.66740 | 4.66015 |
| 7 Def + 2 HP | 0.710 | 837 | 1179 | 1115.22 | 1417.11 | 3.66473 | 4.65676 |
As giving 6 Def and 3 HP will make the def/hp ratio closer to 0.675, it result in highest durability.
Judging on how close the durability between them, I have to give SG 
for equating +18 def with +36 hp.
NB: the 0.675 crossover point only apply if hp node give twice as much point as defense node.
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Based on your calculations, would I be right in going Attack & Def for Node 5 & 6?
And then Def for node 11? And then Attack & Def for Node 13 &14?
I think that would result in a def/hp ratio of like 0.56. But going Attack & HP instead of Attack & Def would yield an even lower ratio…
Yes, attack and defense for Drake Fong.
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Well said!!! Make them better not mediocre. I like that. Makes sense.
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Thanks for the like. Never imagined someone would read what I wrote 2 years ago. 
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Lol, he just stating facts
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