At last, I understand spell damage!

[Uncle Al]

I was trying to finally crack this from the rather patchy (it was translated from Russian some time ago) info pedroelms put in his guide from Silicoid's initial code diving. After a lot of head scratching I've also found the original Russian discussion board, and Google Translate is a LOT better these days, so finally it all makes sense. Thought I'd share what I've deduced.

I've done this as a long explanation rather than using formula notation, as a lot of people don't like reading pure formulas.

There are seven things that affect spell damage reduction:

The caster's level (caster level, so level -4 for hybrids and it varies for multi class characters)
The target's level
The target's resistance to the realm of the spell
The power level the spell is cast at
The inherent strength of the spell (this is derived from mana cost and spell level)
The power cast skill
A random roll


First you calculate a Spell Attack Strength (SAS):

Caster's level, power level and inherent strength are combined together then multiplied by 1 + powercast/100 - so maxed out power cast makes your spells twice as good at overcoming resistances. This total (we're calling it Spell Attack Strength) is:

1/4 of the mana cost per power level of the spell +
1/2 of the level of the spell +
The power level you cast it at +
1/2 of your caster level

Then all of that is increased if you have power cast by a percentage equal to your power cast skill (so double at 100% skill).

So Energy Blast (level 1, 2 mana per power level) cast at power level 1 by a first level mage with no power cast skill has a Spell Attack Strength of:

0.5 + 0.5 + 1 + 0.5 = 2.5

The same Energy Blast (level 1, 2 mana per power level) cast at power level 7 by a 30th level mage with no power cast skill has a Spell Attack Strength of:

0.5 + 0.5 + 7 + 15 = 23

Nuclear Blast (level 7, 18 mana per power level) cast at power level 7 by a 30th level mage with 100 power cast has a Spell Attack Strength of:

4.5 + 3.5 + 7 + 15 = 30 then increase that by 100% for your 100 power cast = 60

KEY POINT - If you're spell attack strength is lower than your target's level, you probably won't achieve much. If it's higher, you'll lower their effective resistances and probably get a decent result.

So, we've got a Spell Attack Strength...



Next you calculate the Effective Resistance (ER) of the target:

Effective Resistance is whatever the monster or character's basic resistance to the realm of the spell is, modified by three times the difference between the target's level and the Spell Attack Strength we just calculated.

So Effective Resistance = (Target Level - SAS) * 3 + Base Resistance

Our first level mage using Energy Blast with an SAS of 2.5 casting at a first level target will reduce their base resistance by 4.5.

The same mage at 30th level casting Energy Blast power level 7 (SAS 23) at a 30th level target would increase the target's base resistance by 21. This is why low level spells get bad against high level targets.

The level 7 Nuclear Blast with maxed out power cast on a level 30 target would reduce their base resistance by 90! Now we're talking.

If Effective Resistance is less than or equal to zero, you take full damage from the spell. You never take extra damage.



Now the random roll:

Effective Resistance gets randomised into a Final Resistance, which is between half and one and half times the Effective Resistance.

The way this is done is you get Final Resistance = (Effective Resistance/2) + (Random Roll between 0 and Effective Resistance/2) + (Random Roll between 0 and Effective Resistance/2)

This means you'll mostly see a Final Resistance round about the Effective Resistance, and very rarely see the really extreme ends of the scale where your resistance is halved or increased to one and a half times.




The actual damage taken is the rolled damage of the spell reduced by a percentage equal to the Final Resistance - so 100 Final Resistance means zero damage, 50 Final Resistance is half damage and so on.

This is why a Base Resistance of 150 is where you almost always see no damage, unless you're using a powerful spell with a high level caster with power cast (which is pushing the Effective Resistance down). 75 + 1-75 + 1-75 is almost never going to give you a Final Resistance of less than 100.

As a side note, I bet that the calculation for whether an effect like paralyse or web actually works uses Spell Attack Strength not just caster level, which is why high level pure casters with power cast can make those effects work even on high level targets. And equally why low level spells like Web and Paralyse stop working on high level targets even if you're a strong caster.

[CeterumCenseo]

Wow! This is extremely valuable information. Thanks a lot for publishing this here. I do not oversee all the consequences of what you describe here yet, but it confirms a lot of assumptions about magic in the discussions here on this board. The value of Powercast, the role of spell level differences, how resistances work, excellent.

Can you kindly put this description into a guide so it doesn't get lost and buried under new threads?

The only effect I would have expected, but doesn't seem to exist, is the role of school and realm skill levels. In those equations, they don't occur, so a bishop and a mage would get the same results on a given spell at a given level, excluded the fact that a mage will be 1-2 levels higher with the same XP in the endgame.

Kudos!

[mpnorman10]

Nice work!

Silicoid when doing hit and damage formulas focused on monsters as targets of party characters and did not cover the case of a character in the party being the target if they were wearing a shield. If you happen to come across anything about shields and exactly how they enter the calculations not included in the original google translation of Silicoids work please share. In any case thank you for what you have provided for us.

I have been giving these formulas lots of thought from a programmers perspective and regarding CC's point about no influence from the School and Realm Skill, it seems that neither have any impact. However there is a question if something entering the formula, for example the power level of the spell, might be a composite, i.e. the power level per the spell list multiplied by the School Skill divided by 100, or something like that. There may be no way to tell from the translation of the research Silicoid did, but something to keep in mind in case anything like that shows up.

In the side by side comparison between a Bishop and a Specialist Caster, the latter appears to be slightly more powerful, but that could, as CC points out, be entirely due to the difference in levels compared to the much slower-leveling Bishop.

Tentatively we should accept the formula inputs as raw numbers unless we get strong evidence or direct facts otherwise.

[Uncle Al]

I wasn't particularly surprised that school and realm skill don't factor in, because they both already affect the power level you can cast a spell at, and power level does affect how much you push resistances down significantly. Being able to cast one power level higher is as good as two caster levels!

It's been a while since I've played at a really high level (I confess I've played this game constantly for over ten years and never been to Ascenscion Peak - I always get a new idea for a party or want to try a new mod or something...) but I'm pretty certain being able to green cast level 7 spells requires staggeringly high realm and school skills, which a Bishop won't have compared to the pure casters.

If a Bishop usually has to cast a power level or two lower, and they're a couple of caster levels lower due to their huge exp requirements, and they got power cast later because they have far more stat requirements than a pure caster then you'd expect to see a definite difference in casting effectiveness, even if a pure caster and a Bishop with identical skills actually cast the same.

Equally, though, I take the point that 'Power Level' could be more complex than just the value between 1 and 7 that we click on.

I've never put a guide up on Steam, so I'll have to look at how to do it, but very happy to copy this into the guides section.

[Reality]

My take away is that since spell level matters so much, actually upgrading from Insanity > Pandemonium will let me hit some of those enemies who felt like they were immune.

[peddroelm]

very nice work !

I will link to this post somewhere in my game mechanics guide (and change the link to your new guide if/when you decide to put it up .. )

Anything about music/engineering casting ?

[Uncle Al]

Originally posted by peddroelm:

very nice work !

I will link to this post somewhere in my game mechanics guide (and change the link to your new guide if/when you decide to put it up .. )

Anything about music/engineering casting ?

Great to see you're still active! I'd never have gotten into understanding game mechanics without your guide, so most of the credit for this info really goes to you, and Silicoid of course.

Townltu deserves a mention too because of them testing that if you mod a spell to 240 mana per power level it affects a lvl 100 target as though it had normal resistances and no level based damage reduction. That really brought it all together.

Amazingly Silicoid missed that it was mana cost per level and spell level that were the factors for each spell, but listed a few example spells and what their factors were, and I managed to spot the factors were the same as spell level and power cost.

Sadly haven't been able to dredge up anything on bards and gadgets so far. There's obviously a roll that determines the power level of the spell, as well as fumbles and failures, because the cast levels of instruments in the cosmic forge are quite low (usually lvl 3) but a skilled bard will regularly get power level 5-7 on an actual cast. I assume when you push the spell level up you increase the overall Spell Attack Strength by an extra amount, because high level Bards and Gadgeteers certainly hit like they have a certain amount of power cast.

Then again it's possible they don't, but the fact that you usually spam the high level spells with them means they cut through enemy resistances even without power cast. As my example showed, a level 7 nuclear blast rips though enemy resistances even if they're high level. My experience of the very end game is limited, but I get the impression casting the 15-20 mana per level spells at max level actually doesn't happen much from normal casters. Bards and Gadgeteers are the only ones who can really do it.

Did find spell training that was really interesting:

You get skill checks equal to level multiplied by the power level you try and cast at. Nothing else matters. So low mana cost, high level spells are very good for skill training. Success or failure of the cast doesn't matter.

Combat only spells are pretty straightforward, you make the cast and you get the skill checks.

Buffs, heals and utility spells work in three different ways -

1) Cures, heals etc. They earn a skill up if they actually could achieve something, so the target has to be damaged for heal, have a status condition for cure etc. Stamina is special in that the target must be tired but also it only gains skill ups in combat, everything else gains skill in or out of battle. I don't know about rest all, should test that some time.

2) Non combat utilities like Light, X-ray or Chameleon. You can only gain skill checks once every 3 minutes of real time. Casting before 3 minutes are up resets the timer so you get no skill checks but have to wait another 3 minutes. Casting in combat doesn't make a difference. Oh, loading a game clears the timer, as we already know.

3) Long duration buff spells that have a combat effect, like Missile shield and Armour Plate. These follow the 3 minute rule but also can earn skill checks on a cast if you cast the spell in combat and the new spell duration is more than four times the existing spell duration.


Combat spells cast after all enemies are defeated don't earn a skill check - I'm bummed about that one as throwing out a level 7 stamina on the round I know the final enemies are bound to die was a standard trick of mine. Apparently it doesn't work! I'd swear I've had a Valkyrie get a skill up when that was the only cast she did in a fight, but I bet I'm remembering falsely and actually her cast went off before the last enemy died.

[mpnorman10]

Excellent data. FYI, I recommend (for the new player recommendation) a recast of buffs when resting between battles. That definitely puts more than three minutes between those casts (probably an average of 30 minutes), i.e. empirical observation dovetails nicely with your data.

By empirical observation and measurement there is definitely a Power-Cast-like impact of some sort for the Music and Engineering skills.

In a side by side comparison of same level Gadgeteer (with high Engineering Skill) and Alchemist (with high Power Cast Skill) at the same level against the same foes (a Dozen Demons in the particular experiment) casting Tsumani at Power Level Seven in both cases the Gadgeteer does roughly 70% of the damage of the Alchemist, on the average.

That in comparison to a side by side comparison with and without Power Cast where without Power Cast the damage is a much smaller percentage (like 5%, IIRC), consistently. Those experiments were a long time ago and I no longer have the raw data. I did them for my own benefit and curiosity. Pedroelm is right that Silicoids data (unless you or he find a new reference in the old posts) does not yet cover that case as well as many other things. I am not complaining; as far as I know, nobody paid him for his excellent work we are all benefiting from.

Your work also shows why it seems that casting the spells at higher power levels, into the yellow, orange, etc., tends to lead to more increases, by empirical observation that seemed to be right but was too tight to call for certain.

In a Magic Damage Party (MDP) the Bard and Gadgeteer are heavy contributors to the total magic damage per round all the way through the end of the game and still increasing, in almost every respect, as the game ends, contrary to previous, false "common knowledge" that the effectiveness of magic against foes goes away toward the end of the game. It certainly does without Power Cast (for specialist and other casters only, Bards and Gadgeteers get zero benefit from Power Cast). I have had some success against 150 resistance, but that is the upper limit and usually there is a realm with 125 or below even for high level (non-boss) foes on the peak. Effectiveness (of magic damage) is terrible, of course, if they are much higher in level than the party (like, for example, 10 levels... a killer).

A minor note is that you might want to update your vocabulary on Specialist Casters. Many players early on called them Pure Casters but that is a horrible way to develop a Specialist Caster in almost every case (hundreds) I have encountered. Pure Caster (when not referring to a Bishop) is a design choice that unfortunately has led to the Specialist Casters being labeled as weak by some, even influential, players, when the truth, when developed well, they are almost overpowered.

[peddroelm]

I just realized Cosmic Forge shows the dice for the damage spells.
Which means one can edit a damaging spell from CF ( or later from my CE script) to do constant damage per power level. Then , for starter's set the target monster's resist to that element type to 0 ... And see if a N damage spell does N damage in that condition .. Then one can start messing with levels, mana cost, adding resist (problem because of that extra RNG roll) , power level ...

EDIT: yup - managed to edit spell damage dices in-game (actually the damage preview in the spell description changed, yet to test if actual in-game damage to target changes )

https://i.imgur.com/j8ENy23.jpg

[Uncle Al]

Yes indeed! You should still see variation at resistances above 0, because the random resistance roll will start to have an effect, but at zero resistance it should not be applied according to the info we have so far.

[Zergs]

This is excellent work, thanks Uncle AI.

The main implication to me is actually the opposite of what MPN's saying (forgive me buddy!). Bishops are actually much stronger magic damage dealers in the endgame than specialist casters are, because the caster level portion of the formula actually matters a lot less than I thought it did. With 100 power cast, each extra caster level reduces the enemy's magic resistance by only 3 points. That seems like a really small effect to me.

Consider an endgame party with a level 22 bishop and a level 24 mage. The mage only has a 6-point advantage over the bishop in terms of targeting resistances, which is basically nothing against endgame enemies with 100+ resists. The mage can only target air, fire and mental with level 7 spells, and in terms of AOE damage, has only fire. That means the mage can sustain basically only 2 rounds of max-level blasting with fire AOEs.

Compare to the Bishop, who can use Mind Flay, Earthquake, Nuclear Blast and Tsunami, targeting 4 different resistances with level 7 spells. That's probably a solid 8 rounds of max-strength blasting before falling back to level 6 spells. Moreover, for enemies that have any inherently lower resistances (say 110 water, 150 fire), the Bishop opens with his best attacks against the enemy's weakest resistance, which is a much bigger impact than the mage's 6-point advantage for being two levels higher.

Of course, there are downsides to using a bishop:

1) I think caster level does influence the power level you can choose as "green." In my experience, each caster level you have beyond the level when you learn the spell lets you cast 1 circle higher as green, before factoring in realm bonuses. So a level 18 mage will be able to cast Nuclear Blast with 1 green circle at fire skill = 0, and a level 19 mage will cast at 2 green, all the way up to 7 green circles at mage 24. Having high fire realm skill will raise the green circle capacity 1-2 by circles. This means that assuming equal realm skill, the mage will be able to cast 2 power levels higher than the equivalent bishop, at least until the bishop catches up to 7 circle power on level 7 spells. After that the Bishop is a far superior offensive caster.

2) Bishops obviously would require a lot more training and grinding. But even a two-school bishop is going to be a pretty solid offensive caster if you grind up Earth/Mental using knock knock and divine trap. Having both Mind Flay and Earthquake/Falling Stars is already a great start to high-level damage.

3) As MPN points out, building a specialist caster into a pure spellcaster is kind of a waste--it's easy to make them solid physical damage dealers as well, while that's much harder to do with a Bishop

Final point. The Amulet of Nebdar has a pretty huge effect. AFAIK it's the only item in the game that boosts power cast (+15). Using the level 30 mage nuclear blast example above, +15 power cast adds an extra 4.5 to the SAS--the equivalent of being 9 caster levels higher!! That's huge.

There being only 1 Amulet of Nebdar in the game argues for having one dedicated offensive caster in the party, as the rest will be relatively gimped without the PC bonus. After seeing this effect I would definitely not take multiple Bishops anymore.

[Zergs]

edit - one other implication is that Power Cast hybrids should eventually (more or less) catch up to specialist casters in terms of magic damage. Maybe around level 25-26+, so ultra late game, when a hybrid can cast a level 7 spell at PL 7.

At that point, the hybrid is caster level 22, and a specialist caster would be around caster level 28? Specialist caster still has an edge, lowering enemy resistances by about 18 more than the hybrid. But still, the SAS differential is about 3, which comes out to about 10% lower than the specialist.

So at ultra-high levels, assuming equal gear, a fighter has about a 50% advantage in physical damage over a hybrid (100 str on both), and a mage has about a 10% advantage in magical damage over a hybrid. This is assuming 100 power cast on both.

Does this math seem right?

[mpnorman10]

Zergs, you argue and write well. I have a few points for you to consider and would appreciate your thoughts after considering them.

First to compare the specialist caster and the Bishop it should really be done side by side (as I have done). The Specialist Caster tends to be a bit more effective, but it is close. Hybrids with Power Cast, on the other hand are significantly weaker, at least a factor of 2 weaker in my limited direct comparison experience. Also, Power Cast within a Hybrid has a huge opportunity cost, i.e. the Hybrid's fighting skills (melee/range) can be significantly better if those attribute points are used for that (in Str/Dex, for example) instead of maxing Intelligence.

Second, you have argued that the Bishop is better (at least with grinding) due to the variety of level 7 spells the Bishop can learn and apply against various resistances in the enemies.
2a) Sure, enemies are more vulnerable in some realms, so if fire resistant a Bishop casting Earthquake with high Power Cast will be better than a Mage casting Nuclear Blast. However compare that with an Alchemist and it is a different matter.
2b) In addition to the impact of the level difference on magic damage, level has a huge impact upon the power level at which the spell can be cast (on the green, for example), adding approximately one power level per level between level 18 (when the level 7 spells can be first obtained) and level 24 or 25.

Third, Bishops (which are great!!) can be used in a wide variety of parties, but the most common usage I have seen is when the party has Fighters, Rogues and Hybrids plus a Bishop (or 2). In such a party, when not protecting or healing, the Bishop(s) will often seek to disable or thin (spells like Quicksand, etc.) the enemy ranks. However, even with Power Cast the spells individually will tend to be less than if unresisted. If being attacked, a disabling spell that impacts all but one or two is perfect, letting the party deal with foes one or two at a time. If that disabling spell only impacted 2, leaving 5 or 6 unimpacted, the effectiveness of that disabling spell in protecting the party would be much less. In such a party, if there is only one Bishop, that is all you get in that round.

For magic damage and for an MDP later in the game with high Power Cast, yes the resistances that are higher mean that magic damage spells also are reduced in their effectiveness even by resistances that are, on the average, overcome, but with high Power Cast that effectiveness does not go to zero and with 6 magic damage casters in the party (potentially) those partial effective magic damage spells will still add up to a lot per round. Plus, at the same time, the level 7 spells are becoming more and more powerful with every level because of casting at higher power level. It is the latter that keeps the killing of foes with magic damage very fast even later in the game (unless effectively immune or at much higher level).

Fourth, level 6 spells come into play, potentially at level 14, including the Mage's Blizzard spell. This powerful spell in the water realm is actually more powerful (because of casting at higher power level) than level 7 spells when first obtained at level 18 and a couple levels after. Yes Blizzard is a cone spell that may not work well in every battle as well as an "all enemies" spell like Earthquake, but often, even usually, it will be very effective. It is rare (but can happen) that the foe has exceptionally strong resistance in both the fire and water realms.

At higher power level the Mages Nuclear Blast is highly effective against even rank and file Rapax (even though Earthquake is much more effective). So with a variety of casters all casting best magic damage spell the mix is pretty darn effective. The biggest, overwhelming limit on a Bishop that can cast even every spell (if all 4 schools are high) is that he or she can only cast one spell per round of combat. That is not a criticism of the Bishop, even a tiny bit, but an expression of the fact that the effectiveness of spells needs to be most appropriately compared at the entire party level.

[Zergs]

@MPN

I don't actually disagree with any of your points. The hybrid comment from me was just a theorycraft brainstorming--I have no idea if a powercast hybrid is actually a good build or not, but it's something I've been wondering for a long time.

WRT to the Bishop, I totally agree with your point that 6 magic casters using their best AOE for two rounds is all you need--you don't actually need the Bishop to be chain spamming level 7 spells for 8 rounds. Better to have 6 casters cast 2x, wiping the entire enemy party in two rounds. That's more an argument for thoughtful party design, and going all-in on one strategy--melee, ranged, or magic.

I'm just saying that in the endgame, once Bishops are able to cast 7th level spells at PL7 (say level 22 or 23), they are in fact superior magic damage dealers to any single specialist caster because they can always surgically target the enemy's weakest resistance with a 7th level spell. That's all I'm saying--and this was an unexpected realization for me, and it depends on the relatively minor influence of caster level in the SAS formula that Uncle AI just discovered. I'm NOT saying that this makes the Bishop a better character over the entirety of the game. A mage gets to Power Cast faster, meaning he has more points in it and a longer use of it, over the whole game, and will get to 100 faster than a Bishop will. Until level 22 or 23, the mage actually gets to cast his spells at higher PL on top of that (your point 2b, which is the same point I made in my "cons" to bishop 1) above--so I agree with you), so he probably does more magic damage than the Bishop for much of the game. The Bishop only shines in the midgame in cases where the mage has no good spells to target an enemy weakness--i.e., the Bishop can make excellent use of Ego Whip against mental-weak enemies.

On top of all that, he doesn't waste points in Piety, so he can push str/dex, making him a capable physical attacker when needed. All points that you made, that I agree with.

My comment is purely based on the endgame, and the fact that there's only one Amulet of Nebdar.

[mpnorman10]

Okay, that is right. Once the Bishop has all the level 7 spells he or she will be able to choose a more effective spell in some cases. There are times when this might have a bigger impact than the fact the specialist is a level or 2 higher and so can cast their level 7 damage spell at a higher power level by one or two levels. The latter factor goes away somewhere in the level 26 to 28 range, once the Bishop can cast all of those spells (or the relevant ones for that case) at PL7.

For a 2 school Bishop developed without grinding that can still theoretically happen, but less often.

So point conceded.

[HOK1970]

From my point of view, it doesn't matter which individual character deals more damage with a nuke spell, unless it's a solo game. The decisive factor is the amount of damage points the party with its nuke spells comes to in one combat round. This sum of Magic Damage should be sufficient to triumph against the monsters at each stage of the game (Beginning, Midgame, Endgame).

1. The possibilities of each character to use strong nuke spells during the total duration of the game are derived from the magic books (Wizardry, Alchemy, Divinity, Psionics). Wizardry clearly offers the best opportunities here, followed by Alchemy, then Psionics and finally Divinity. Psionics unfortunately falls back from the middle game, because the spells are mainly in the realm Mind Magic and in the further course of the game the opponents have insurmountable resistences here.

2. It is also important when the spells are available. The Fireball from the Wizardry Spell Book is available from level 5 and is available in level 11 on SPL 7. Comparable spell Fire Bomb from the Spell Book Alchemy is available from Level 8 and in Level 14 on SPL 7. In level 14, however, you are often already in Rapax territory, where the spell is of little use.

3. The realm skills are also the ammunition of each caster, and should be sufficient in the respective game situation to break the resistence of the monsters with the appropriate spells. Especially at the beginning of the game, where the teleport magic to the magic source to Tryton is not yet available and you can't get to enough magic stones, a high value in the decisive realms is of great importance. In my opinion, the Fire realm is of the utmost importance at the beginning until the mid game, since most monsters have little resistance to it. Equally important is the rapid expansion of the Divine realm, which is the length of the game strong.
In the Rapax area Water magic is important, while in the Sea Caves the Earth magic is needed.

4. The level of the caster is crucial and therefore a deduction of 2 levels must be taken into account in the Bishop due to the high number of experience points.

5. There are enemies in the game who, due to their height of life points and magical resistences, cannot be defeated quickly enough by magic alone. Here, physical damage is more effective, unless you want to rely solely on the use of elementals. Maces have a big advantage here compared to wands, as they usually have a high status effect of beating an opponent unconscious. It is also possible to wear a shield.

If I were to rank after the 5 points, then the Bishop would be my first choice and this is from my point of view the character class that benefits most from the MDP guide of MPNorman. The Bishop is usually surpassed in its effectiveness in the individual points by a different character class, but in sum it is the strongest and most versatile character for me.

My experience in a 6 Bishop party in relation to the magic damage was very positive. 90% to 95 % of the fights were finished in at least 2, but often in one combat round in my favor. It is the remaining 5% to 10% that is only a challenge in the game. But here, too, the bishop of all pure casters with spells like Guardian Angel, Body of Stone, Superman and the use of a Disruptor Mace (25% KO) has the best arguments.

But that's the good thing about Wizardry 8. There are a wide variety of experiences and associated opinions among the players.