Direct damage spell analysis

AENARlON

Here are some key stats for direct damage spells:


EXPLANATION

Max damage is the theoretical maximum damage a spell can cause to a single unit. As damage_chance is rolled for each entity in the unit, max damage is similar to the damage a multi-entity spell will achieve against a large infantry unit, and is a primary basis for appraising multi-entity spells. More formally, max damage=ticks*damage per tick*max damaged entities

SE damage is the expected damage against a single entity, accounting for the probability of a failed damage_chance roll. It is a primary basis for assessing single entity spells. More formally, SE damage=ticks*damage per tick*damage chance

For radius spells, you simply multiply max damage or SE damage by the number of units in the radius to arrive at the max or SE damage across all units. All damage numbers are for large unit size.

ANALYSIS

Some thoughts on each of the four DD spell categories:

SINGLE TARGET SINGLE ENTITY
These seem well balanced, with arcane unforging trading some damage/WoM for its ability cooldown increase.

30m RADIUS SINGLE ENTITY
Soul stealer is weakest in damage/WoM terms but well balanced given the hp absorption. Flensing ruin outperforms final transmutation - it has almost identical damage/WoM so the -30 armour in a 30m radius is essentially a free bonus.

SINGLE TARGET MULTI-ENTITY
Melkoth's outperforms Usirian's incantation with more damage per WoM and more seconds of speed reduction per WoM. Fate of Bjuna may look underpowered in max damage/WoM terms but it has half as many max damaged entities as the other spells in this category so doesn't lose as much of its performance against mid-sized units such as cavalry.

30m RADIUS MULTI-ENTITY
Flock of doom outperforms devolve in damage/WoM terms but this is compensated by the latter's leadership debuff. Like Bjuna, traitor-kin is something of an outlier, and while it is not strong against infantry or SEs, it has effective performance against cavalry and monstrous infantry.

In summary, while most DD spells seem balanced, Usirian's incantation underperforms while flensing ruin overperforms.

(Plug for doktarr's spirit leech/Bjuna thread which got me thinking about this topic - https://forums.totalwar.com/discussion/257293/numbers-on-spirit-leech-fate-of-bjuna)

Reym#7442

Interesting analysis, I just think one spell is a bit miss judge and that is traitor kin. The spell is a weird hybrid between the two main categories. It works better on multi-entities yet damages them like a single entity spell (by killing model one by one or in its case two by two). Which makes it very deadly on overcast vs 45 model units for exemple. So I wouldn't say the spell underperform more that it is more niche ?

AENARlON

Reym said:

Interesting analysis, I just think one spell is a bit miss judge and that is traitor kin. The spell is a weird hybrid between the two main categories. It works better on multi-entities yet damages them like a single entity spell (by killing model one by one or in its case two by two). Which makes it very deadly on overcast vs 45 model units for exemple. So I wouldn't say the spell underperform more that it is more niche ?

I think you're right actually. Traitor-kin and Bjuna are the two 'inbetweener' spells in the table (2 entities and 9 entities rather than the usual 1 or 18) and they aren't as well assessed by the maximum damage and SE damage stats, which are optimised for anti-infantry and anti-SE performance respectively. These two spells work well as anti-cavalry, and TK even does nicely on low model count monstrous infantry. I'd accounted for the special case of Bjuna but not TK.

While testing TK I also noticed a limitation of my mathematics, which is that it assumes that the number of ticks =duration/hp_change_frequency, so for instance TK gets 12/2=6 ticks. TK actually gets an extra tick (7 total), because it has a tick at the first instant and last instant of duration. Some other spells are treated as having fractions of ticks (e.g. spirit leech has 13/2=6.5 ticks), which obviously isn't possible.

Later on I'll make a major edit to the OP to fix this stuff. Cheers for the feedback!

Witchblade

I think it's best to test damage on Large unit size, as damage scales with the unit size setting and I'm not sure if it's the same scaling percentage for all spells.

rambotop1playa

lul soul stealer is only good on malekith since 500 hp isnt the same on morathi/sorc. Flensing ruin is OP cos its newesty dlc so yeah P2W confirmed lmao :DDDDDDD

sonofabhorash

Thanks for this

TlaxtlanSoothsayer

It's an interesting summary.

I'm not sure if I agree with some of these conclusions though.

rymeintrinseca said:

In summary, Usirian's, devolve and traitor-kin appear to underperform relative to other spells in their classes, while flensing ruin overperforms.

Flock of Doom and Devolve:
These spells are really similar, their efficiency is almost the same as they deal exactly the same amount of damage per second. You're right, that Flock of Doom is a little bit more cost efficient per wind of magic spent:

- Upgraded Flock of Doom: 1,17 seconds of damage per WoM

- Upgraded Devolve: 1,10 seconds of damage per WoM

The difference in terms of damage output is quite small. Devolve also reduces the leadership of enemy units by 8 which is more useful than increased range. So it's no surprise that it deals a little bit less damage than Flock of Doom.


Traitorkin:
The main issue of this spell is that CA's description is wrong. In theory the UI tells the player that Traitorkin is supposed to be "Strong vs. a single combatant". Although it deals next to no damage when hitting single entities. Traitorkin is an anti cavalry spell, especially neat against cavalry with a low amount of health. For example it usually kills about 13 entities or roughly 33% of an unit of Silver Helms or Empire Knights. The cavalry dies quickly, so healing them is not an option. Furthermore upgraded Traitorkin slows the movement speed of its target by 44%. It's self-explanatory that a 44% slow, even with a short duration, allows you to catch enemy units.


Usirian's Incantation of Vengeance:
The damage output is indeed a little bit worse than Melkoth's Mystifying Miasma. Well, the upgraded Usirian's Incantation comes with a 48% movement speed debuff. This spell could maybe use a really gentle buff, but isn't that far off from its competetion either.


Flensing Ruin:
I agree, that Flensing Ruin is probably one of the most significant outliers. It deals a lot of damage, but also reduces armour, without being more expensive than similar spells. That being said, it's possible to leave the AoE of Flensing Ruin, so it allows more counterplay than for example Final Transmutation. Nonetheless, Flensing Ruin could use some sort of nerf anyway. High damage AND -30 armour is nothing to sneeze at.



Long story short:
Yes, some of these spells deal slightly less damage than other spells. But in most cases you pay for additional benefits such as outright killing entities, leadership or movement speed debuffs.

doktarr

Cool stuff - really interesting to see this extension to other direct damage abilities.

One thing to note on Vengeance/Miasma/Flock/Devolve is that you need to hit a LOT of models in order to reach those theoretical maximum damage numbers. By my calculations, you need to hit 97 models in order to do 90% of maximum damage. If you toss one of those spells on a 45 model cavalry unit, you're going to do about 45% of maximum damage. (For anything less than about 60 models, you can expect to get a percentage of max damage roughly equal to the model count.)

With Flock and Devolve you can hit blobs to get bigger numbers, so this is more relevant to Miasma and Vengeance, where you really need to pick big units to get the advertised max damage.

(Also, as others have noted, these numbers appear to be for Ultra unit scale. But everything should scale at about the same rate so the comparisons are still valid)

Sarmatianns#6760

It is nice breakdown but ignores one crucial component, basically how long it takes to do damage.

For instance, even when Bjuna was at its strongest point, Miasma did more damage for WoM spent (not even taking speed reduction into account).

And, yet Bjuna was (almost) always taken, and Miasma sporadically. Simply put, doing a lot of damage at once, at a crucial point was way more important than damage done in small increments over a longer period of time, even at lower WoM cost.

Casting Bjuna on Chaos Knights while you charge them with Centigors meant basically an almost dead or neutered unit of Chaos Knights. If you try to do the same with Miasma, it would have meant a dead unit of Centigors.

Even if you take whether a unit is fighting another unit, and just compare damage over time, there is still the fact that you need several minutes to do damage with Miasma, for instance, and the unit being targetted sheds models very slowly, meaning it gets to be involved in battle more and with greater effect before it becomes neutered.

So, nice job, certainly an interesting read, but I'd be careful of using it as a basis for any balance changes.

AENARlON

I've made a substantial update to the OP. The main changes are as follows:

1) I've now counted the number of damage ticks for each spell and included this in the table. (I previously estimated ticks from duration and hp_change_frequency which resulted in systematic underestimation; something similar seems to be going on with the 'phases' data here: https://twwstats.com/abilities?q=direct)
2) I've also changed the damage stats so they refer to large unit size rather than ultra, as I agree large is more useful.
3) As Reym and Tlaxtlan Soothsayer noted, I was a bit hasty in my spell assessments. I've accordingly removed traitor-kin and devolve from the list of underperforming spells.
4) Presentation of the data has been tidied up in several respects.

AENARlON

doktarr said:

Cool stuff - really interesting to see this extension to other direct damage abilities.

One thing to note on Vengeance/Miasma/Flock/Devolve is that you need to hit a LOT of models in order to reach those theoretical maximum damage numbers. By my calculations, you need to hit 97 models in order to do 90% of maximum damage. If you toss one of those spells on a 45 model cavalry unit, you're going to do about 45% of maximum damage. (For anything less than about 60 models, you can expect to get a percentage of max damage roughly equal to the model count.)

With Flock and Devolve you can hit blobs to get bigger numbers, so this is more relevant to Miasma and Vengeance, where you really need to pick big units to get the advertised max damage.

(Also, as others have noted, these numbers appear to be for Ultra unit scale. But everything should scale at about the same rate so the comparisons are still valid)

Cheers!

You're right that you need large units to get value from Vengeance/Miasma/Flock/Devolve. The equation is actually really simple - for units below 100 models, the unit size is the percentage of max damage that you can expect to achieve. For instance, the expected outcome of hitting a 75 model elite infantry unit would be (0.18*75)/18=0.75=75% of maximum damage. Even a 60 model unit like chosen gives you 60% of max damage, which is still great given the superb max damage/WoM of a spell like Melkoth's.

And actually things don't scale at the same rate! At large scale unit HP is 75%. Vengeance/Miasma/Flock/Devolve do 83% of their damage (5 instead of 6 per tick). Bjuna does 89% (8 instead of 9). Traitor-kin and single entity spells do around 91.5% of their damage. Anyway, none of this is relevant to the data in the OP as it's all converted to large scale now, which makes things much simpler.

TlaxtlanSoothsayer

Sarmatians said:

It is nice breakdown but ignores one crucial component, basically how long it takes to do damage.

That's a good point, too.

Maybe one day someone is willing to spend a lot of time to include all the other variables such as cooldown, varying damage vs. units with different amounts of entities, or burst damage as well.

Nontheless, I think rymeintrinseca's summary (or doktarr's Spirit Leech & Fate of Bjuna analyzis in the other thread) are nice to put things into perspective a little bit.

doktarr

rymeintrinseca said:

The equation is actually really simple - for units below 100 models, the unit size is the percentage of max damage that you can expect to achieve. For instance, the expected outcome of hitting a 75 model elite infantry unit would be (0.18*75)/18=0.75=75% of maximum damage. Even a 60 model unit like chosen gives you 60% of max damage, which is still great given the superb max damage/WoM of a spell like Melkoth's.

This isn't quite right because of the cap at 18 models receiving damage. That cap means that it's not a straight binomial distribution, so the binomial mean isn't exactly right.

For lower model counts it's extremely unlikely that 19 or more models would be hit anyway (strictly zero for less than 19, of course), so approximating with a binomial distribution is very accurate. But as the model count creeps up, the percentage chance of a 19+ result getting capped at 18 starts to get larger.

It's still very close pretty far along - the difference doesn't get to a full percentage point until 75 models (i.e. 75 models take an average of 74% of max damage). The cap of 18 rapidly becomes more and more important after that - by 100 models the cap is cutting 8.5% of your efficiency (91.5% of max damage). You have to go to 131 models to get 99%, and 154 models to get 99.9%.

Sarmatianns#6760

TlaxtlanSoothsayer said:

Sarmatians said:

It is nice breakdown but ignores one crucial component, basically how long it takes to do damage.

That's a good point, too.

Maybe one day someone is willing to spend a lot of time to include all the other variables such as cooldown, varying damage vs. units with different amounts of entities, or burst damage as well.

Nontheless, I think rymeintrinseca's summary (or doktarr's Spirit Leech & Fate of Bjuna analyzis in the other thread) are nice to put things into perspective a little bit.

Sure, any indepth analysis like this one can only help.

But, those parts are simply harder to quantify. Difference in price, how likely are you encounter good targets (more important for expensive spells), whether the effect is persistent even if unit leaves AOE of the spell (soul stealer) or is cancelled (final transmutation), casting time, AP or non AP damage...

Those are all things that can basically either make a spell top tier or never taken or anywhere in between those two ends.

BovineKing#8781

Question any chance of doing the bound unique damage spells for lords durthu, wurzag and skrolk etc.

rambotop1playa

lol just spam skaven and win MP ez who even cares about lore of death anymore? I never see it get used lol.

AENARlON

doktarr said:

rymeintrinseca said:

The equation is actually really simple - for units below 100 models, the unit size is the percentage of max damage that you can expect to achieve. For instance, the expected outcome of hitting a 75 model elite infantry unit would be (0.18*75)/18=0.75=75% of maximum damage. Even a 60 model unit like chosen gives you 60% of max damage, which is still great given the superb max damage/WoM of a spell like Melkoth's.

This isn't quite right because of the cap at 18 models receiving damage. That cap means that it's not a straight binomial distribution, so the binomial mean isn't exactly right.

For lower model counts it's extremely unlikely that 19 or more models would be hit anyway (strictly zero for less than 19, of course), so approximating with a binomial distribution is very accurate. But as the model count creeps up, the percentage chance of a 19+ result getting capped at 18 starts to get larger.

It's still very close pretty far along - the difference doesn't get to a full percentage point until 75 models (i.e. 75 models take an average of 74% of max damage). The cap of 18 rapidly becomes more and more important after that - by 100 models the cap is cutting 8.5% of your efficiency (91.5% of max damage). You have to go to 131 models to get 99%, and 154 models to get 99.9%.

Thanks, I was oversimplifying and this is a very helpful clarification. "Unit size=percentage of max damage" still seems a decent rough rule to follow as it only stops being approximately true at levels where you're still getting a very high % of max damage.

AENARlON

BovineKing said:

Question any chance of doing the bound unique damage spells for lords durthu, wurzag and skrolk etc.

Sure! See highlighted items here:


The table has these limitations:

(1) duration*hp_change_frequency is used to roughly approximate the number of damage ticks; and
(2) all damage values are for ultra unit size (so roughly 10% more than you get at large)

I've included two new DPS stats, max damage/sec and SE damage/sec, primarily as tools for considering mortis engine-type effects.

I've left the regular spells in there (unhighlighted) in case this is helpful for comparison. For instance, in damage terms effagee of da git is essentially just spirit leech, blood statuette of spite is essentially Melkoth's mystifying miasma but with half the max_damaged_entities, and wail of malice is flock of doom with 50% more damage_amount. But if you're only interested in the spells you should use the updated table in the OP, which is in large unit scale and has accurate (manual) tick counts.

doktarr

The passive abilities are all pretty self-explanatory; just get near a crowd of enemies and you're set. (A similar idea applies to cursed blade or Reaper of Souls, which are hard to control.) And spirit-essence of chaos is its own category obviously.

After that, you can categorize the rest based on the damage_chance and max_damaged_entities columns.

• Effagee and Liber Bubonicus have basically the same usage profile as spirit leech, where they perform best against units with multiple models, but fairly high life per model (> 132).
  
  
• Daith's Sword splits the difference between Spirit Leech and Fate of Bjuna - it's bad against a single target but basically fine against anything with more than 12 models.
  
  
• Blood Statuette of Spite and Rod of Corruption are similar to Fate of Bjuna, where you want at least 45 models (or a high-value target with 30 models).
  
  
• Wail of Malice and The Curse are similar to Miasma/Flock of Doom, where the percentage of max damage tracks with the number of models you hit up through ~75 models, so the more you hit the better.
  

BovineKing#8781

Cool thanks!