Inner Works of Resistances

[myles 2]

(Translation of a German thread by librarian)

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Something need to be said here.

 

I tried to contact the original writer of the article but have not received any response. Many things could have went wrong of course. For one, maybe he doesn't understand English and had no idea what I'm ask him for. Its more likely that he has moved on like Librarian.

 

Still I decided to post it because Librarian has gotten permission for the translation, and I have not modified a single word on this (just some formatting and minor organizing). That said, if anyone has a valid reason for me to remove this, I will do so.

 

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With that out of the way, a little thought from me:

 

I always liked this short but very useful article on resistances, namely the explanation of how mono-elemental is significantly more powerful than multi-elemental. (And how it still makes sense even though I use a crappy translator to help me read the German )

 

As far as I know, this has never laned on the international side of the forum. And well among the things Librarian gave me, there is a translation of the article, which is still valid.

 

As always, questions and comments are welcome. (Just not on German )

 

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Inner works of resistances

 

[Original article in German by Covenant for inSacred.de, translated by Librarian]

 

There's a modest formula in the "official" strategy guide from Ascaron:

 

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Received Damage =

phys.dam*{phys.dam/(phys.dam + phys.res)}

+fire.dam*{...}+mag.dam{...}+pois.dam{...}

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At the first glance it doesn't look promising yet on closer examination can trigger interesting conclusions especially pertaining not to resistances of the player char but of the enemies (from which this formula was derived). Here are several graphs and examples:

 

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Terms

 

inflicted damage - total damage that is inflicted with a weapon blow, shot, spell; it hasn't been decreased by resistances yet

 

received damage - real damage decreased by resistances, indicated by the floating numbers in the game

 

hit - a successful blow, shot

 

one hit - dealing exactly one hit to an opponent

 

multi hit - many combat arts allow hits to be delivered on several opponents and all such arts will be further referred to as multi hit

 

element - type of damage: physical, magic, fire or poison

 

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Character's resistances

 

Here's a very simple example. What effect does the inflicted damage have and how can one protect from it? The graph below details how adequate resistances modify the inflicted damage of 100 points (just any element, doesn't matter which one exactly - only that resistances match damage type).

 

(in the stats screen <I> you can hover over the line of total resistances to get a detailed resists breakdown)

 

Graph 1: 100 damage vs resists (character)

 

It's important to note how effective different resistance ratings are.

 

Clearly with 100 resists countering 100 inflicted damage only 50 received damage scrapes through - that is damage is decreased by 50%. The progression of the curve is interesting here:

 

* 200 res (or twice the inflicted damage) reduces damage by 2/3

* 400 res reduces damage by 80%, although compared to 50% reduction it needs 4 times more res

* 1000 res (10 times the inflicted damage) gives ~91% damage reduction

 

It looks deadly cool but is associated with incredible costs.

 

Now close-combat characters especially those mad about getting sky-high resistances should ask whether its worthwhile using equipment slots for huge resistances. You need more and more resists to lower damage even by a tiny bit. At the same time it's clear that you shouldn't totally rely on resistances cause you can't get totally immune; defense rating is also important.

 

As far as low-res characters goes - mages and rangers such as Wood Elves: Effect on damage reduction is enormous at stages where resistances are low. Resistances half the inflicted damage grant a 33% reduction. It means that players who are normally careless about resistances will receive enormous results paying just a little more attention to resistances.

 

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Enemies' resistances

 

And now to a more splendid aspect of this formula: when applied to foes. It leads to conclusions different from D2 (where there's no difference whether you hit 10 times with 100 damage or once with 1000). Here's a graph:

 

Graph 2: 100 resists vs damage (foe)

 

I assume that the enemy has 100 resistances and look how much damage it will receive at different damage levels.

 

Notes: The dark-green line indicates inflicted damage (f (x) = x). The light-green line is the damage received by a foe. The violet line has been drawn just for help and indicates what the received damage would by if resistances were simply deducted from inflicted damage.

 

It is noticeable that resistances work "similar" to absolute deduction of resists from damage but not completely. When damage is below or equal to resists (damage in range from 0 to 130-150) we see a steady % deduction from damage, yet there's no point where damage is totally nullified. That's how it works in D2. If damage surpasses resistances they are apparently deducted from inflicted damage. To put it more correctly if there were absolute deduction damage would be reduced ever more, as it actually happens with resistances.

 

Conclusion:

 

Against frequent hits with small damage resistances protect by %, against damage higher than resistances the latter protect with absolute damage reduction in the first place. Meaning that resists are very effective when countering small damage, against higher damages their effectiveness gradually decreases.

 

Here's a similar graph detailing relative damage:

 

Graph 3: 100 resists vs damage (foe; relative)

 

Here again we assume that the enemy has only 100 resists but this picture shows how many % of inflicted damage ends up as received damage (light-green curve). And for comparison the amount of reduced damage (violet curve).

 

It clearly works different than D2 - in this third graph drawn for D2 the curve for received damage would be a simple straight line. I.e. no matter how high the damage were it would be reduced by a fixed percentage.

 

The following should be emphasized: many hits for small damage are reduced much greater than a single hit for huge damage. That's very interesting in our hack'n slash.

 

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Implications for damage calculation: One Hit vs Multi Hit

 

All in all a single powerful hit damages more than several multi hits with an equal sum of inflicted damage.

 

Example:

Combat art A deals one hit for 5000 damage. CA B - 5 hits for 1000 damage each on one and the same monster; both CAs are executed with the same speed. In D2 it is clear that both CAs are equal in terms of real damage. It's different in Sacred:

 

Suggest the enemy has 100 resistances

A: 5000*5000/(5000+100) = 4902 received damage

B: 5*(1000*1000/(1000+100)) = 4545 received damage

 

Suggest the enemy has 1000 resistances

A: 5000*5000/(5000+500) = 4545 received damage

B: 5* (1000*1000/(1000+500)) = 3333 received damage

 

Suggest the enemy has 2500 resistances

A: 5000*5000/(5000+2500) = 3333 received damage

B: 5* (1000*1000/(1000+2500)) = 1428 received damage

 

Suggest the enemy has 10,000 resistances

A: 5000*5000/(5000+10000) = 1666 received damage

B: 5* (1000*1000/(1000+10000)) = 454 received damage

 

I figure the numbers prove it fairly well: against mediocre monsters B is better. But when resistances grow.... against monsters with high resists A beats B.

 

Conclusion:

 

A one-hit CA is superior to a multi-hit CA. The same holds true in terms of time. 1k damage every second is 'worse' than 5k damage dealt in 5 seconds. But one shouldn't forget other advantages of multi-hit CAs - I.e. the ability to attack several opponents at once.

 

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Implications for damage calculation: mono-elemental damage vs multi-elemental

 

As you know resistances affect only certain element. Thus a hit with four elements can count as four hits - one for each element. Although it depends on the exact combination of resists the enemy has, it is generally better to specialize only in one element for damage.

 

Here's an example:

you hit a foe with 500 damage; the opponent has 200 resists in physical; 50 - magic; 50 - fire; 50 - poison.

 

Suggest you deal all 500 damage as physical:

500*500/(500+200) = 357 received damage

 

Suggest you deal 125 damage in all four elements (500 total):

125*125/(125+200) = 48

+ 3* (125*125/(125+50)) = 3* 89 = 267

48 + 267 = 315 received damage

 

357 vs 315

 

And that's even when the foe had much higher resists in physical than other elements. On the other hand if the enemy had for instance 1000, 50, 50, 50 resists or 200, 0, 0, 0 multi-elemental damage would be more effective.

 

Conclusion:

 

Attention, the above example is just that, an example aimed to prove that multi-elemental damage isn't always 'better' than mono-elemental. In Sacred you can strive for decent damage with all four elements (it may be more effective against foes with certain resists combinations) or specialize in one damage type.

 

The findings have certain implications for different character classes: Mages can easily 'change' their element and perform different spells against different enemies. As far as weapons as the primary source of damage goes it is prudent to have different weapons and switch between them when needed. As far as damage from other items goes (armor/jewelry) it's recommended to stick with one element.

 

Important: there are no immunities in Sacred. With huge mono-elemental damage you can defeat enemies that have high resistance against this element.

 

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Implications for damage calculation: effect of damage increase on received damage

 

Another curios feature is enormous growth of real (received) damage from raising your (inflicted) damage.

 

Example:

damage grows by 20%: A is 1000 damage; B is 1200 damage (inflicted)

 

Suggest the enemy has 100 resistances

A: 1000*1000/(1000+100) = 909 received damage

B: 1200*1200/(1200+100) = 1107 received damage

-> ~21.8% gain

 

Suggest the enemy has 500 resistances

A: 1000*1000/(1000+500) = 666 received damage

B: 1200*1200/(1200+500) = 847 received damage

-> ~27% gain

 

Suggest the enemy has 1000 resistances

A: 1000*1000/(1000+1000) = 500 received damage

B: 1200*1200/(1200+1000) = 654 received damage

-> ~30.9% gain

 

Suggest the enemy has 5000 resistances

A: 1000*1000/(1000+5000) = 166 received damage

B: 1200*1200/(1200+5000) = 232 received damage

-> ~39.3%

 

When enemy resistances are equal or below your inflicted damage any increase in this damage will lead to a similar or greater increase in received damage. When enemy resistances are above your damage any increase will result in a much-much higher growth of received damage.

 

Conclusion:

 

Especially for strong enemies with incredible resists it is better to sacrifice everything for damage and raise it as high as possible.

 

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Implications for damage calculation: average damage

 

I won't go deeply into this, the findings aren't nearly as interesting as the previous ones but still noteworthy. There have been long debates whether broad range of elemental damage on weapons (min dam - max dam) is better than the narrow. In Sacred the argument continues: and here broader range basically wins.

 

Example:

enemy has 500 resists, gets hit twice: A for 1000 and 1000, B for 500 and 1500

 

A:

2*(1000*1000/(1000+500)) = 2* 666.7 = 1333 received damage

 

B:

500*500/(500+500) + 1500*1500/(1500+500) = 250 + 1125 = 1375 received damage

 

Well, not much difference here, just to note it and stress that Sacred is different from other games.

 

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Summary

 

* there are no immunities

 

* calculating 'average damage' is not that straight and simple

 

* in terms of real damage one-hit CAs are better than multi-hit CAs (especially against monsters with high resists)

 

* mono-elemental damage is more powerful than multi-elemental

 

* damage growth reflected in the stats screen will lead to a much higher growth of received damage (especially against tough monsters with lots of resists)

 

* it is prudent to go for the type of elemental damage your enemies can't resist, but there's nothing bad in not following this rule - it won't ruin the game

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