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A long one, but I'm tired of the unfounded bias towards Headless Horseman.

Many consider Headless Horseman to be overpower, having 560 avg. damage as a Death spell and always complain to KI to "nerf the spell" or "balance the spell". However in response KI never changed the spell and it still sits at 530-590 damage to this day. Of course this would enrage players, but very few know the actual reason why Headless Horseman stays at 560 damage and is still considered balanced.

If you just want to know what it is, read the next section the skip to "Headless Horseman's Hidden Utility".

The Hidden Effects
Believe it or not, Headless Horseman is not just a pure damage spell and I will get to why it is displayed as such later. Here are some facts you may not have known about Headless Horseman:

1. Headless Horseman is a DRAIN spell.
2. Headless uses normal Death DPP (85) instead or the lore Drain DPP (84).
3. Headless has a hidden utility that causes its final base damage to be 560.

The first one may be a real shocker as there is absolutely no indicator of this being a drain spell, but I want you to keep in mind that Headless is in fact a drain spell.

Base Damage Calculation
To calculate the damage of a spell, the following formula is used:

• Base = (DPP * [PipCost + 0.13*(PipCost - 1)] / PipCost) * (PipCost - CostReductions)

- The DPP is 85 instead of 84; in this end this only causes a 5 damage difference.

- The PipCost is 4 as expected.
- The CostReductions is 0 as Drains already have a reduced DPP, and once again I will explain why the hidden utility has a cost of 0.

• Base = (85 * [4 + 0.13*(4 - 1)] / 4) * (4 - 0)
• Base = 373.15

Thus if this was a regular Drain, Headless would have 375 base damage (or 370 with 84 DPP).

Rate Of Change in Damage for Drains
(I'm going to use since it looks like "delta"; symbol used for rate of change)

DPP is very different from damage. This is the damage dealt vs. the damage received; in terms of pips this would be your DPP vs. your opponent's DPP. In other words with respect to pips, damage = DPP.

However, as Drains heal back half the damage there is a 50% DPP bonus. For example, Storm vs. Drains:

• Difference in DPP = (125) - (76) = 50 DPP difference, but;
• DPP = (125 - 0.5*75) - (76) = 11 DPP difference. Let's isolate the DPPs;
• DPP = (125) - 0.5*(76) - 1*(76);
• DPP = (125) - 1.5*(76).

The equivalent Drain DPP is 1.5*76 = 114, so if we are talking about the flow of a battle the 76 DPP is actually 114 for Drains; specifically the DPP * (1 + healback%). Remember this!

Headless Horseman's Hidden Utility

Wouldn't you agree that it would be amazing if there was a Drain spell that simply "refuses to take the heal", thus pushing it onto your opponent as extra damage. This is exactly what Headless does.

As said above, if Headless was a Drain spell then it would have 375 (or 370) base damage. So if you were to push the 50% healback as damage, then the base damage would essentially be 1.5*375 which is 562.5 damage (559.725 with full calculation). Rounded we get the 560 base damage!!! Using 370, it would be 555 damage (553.14 with full calculation).

If you think this is unfair, Tier 1 Vampire would have 500 damage and Tier 5 Vampire would have 570 damage, which is higher than Headless.

Why The Confusion?
You may be wondering why they did not just write "375 drain damage; swap 50% to death damage". A couple of problems:

1. This would be a double hit, and a very broken one at that. So the 1.5x damage was added directly to the base damage.
2. Since you are not actually healing and the swap effect is already factored in, the spell type is Damage instead of a Drain.

And thus you get the "560 death damage" spell we all know.

Pros and Cons

Pros:

• With flat damage, the final amount of damage is slightly higher than a drain.
• Focus on damage instead of survival.

Cons:

• The damage gap from a utility would have a 1.5x effect. This is the reason why Headless' upgrade lost so much damage for the utility; 75 damage instead of 50.
• Damage enchants work like the old Drains, technically giving Headless 100% of the value to the final damage instead of 150%.
• The asset of bypassing absorbs is lost.

In my opinion, having a 0 pip cost for the altered swap utility and 5 extra damage is more of a balance comparing pros to cons.

Comments
I plan to use the upgraded Vampire for survival and Headless for damage, especially since Drains are "nerfed" when you are at full health (working on a spell for that).

I really wanted to spread awareness of this fact, especially with the changes to the spellement upgrade path. The previous 595 avg. damage at tier 5 was fine if you compare it to Vampire, a non-lore spell, with 570 at tier 5. However, because players were unaware of how Headless Horseman's damage is calculated, they complained and the branch got changed.

twinabc on Jul 18, 2022 wrote:

Hey John,

Interesting post. However, Headless does not have a "hidden" utility that you speak of. This is not how spell design works for death non-drain hits. Yes, the spell has a cool animation and it is a highly sought spell by death wizards due to its current base damage. However, for a death lore spell, it is overpowered. You may not be willing to accept that, but a quick math calculation would tell you that this spell is overpowered.

The current formula that is used to calculate base damage is the following: DPP(Pips + 0.13(Pips - 1)). This is not entirely clear from the designers, since they have not shared lore dpp for each school like they have with standard and shadow-enhanced dpp for each school, but my understanding is that shadow-enhanced and lore dpp are intended to be equivalent.

Death's lore dpp would be 105 dpp if it is the same as death's shadow-enhanced dpp. If Headless were to be audited, the base damage would be the following: 105(4 + 0.13(3)) = 460.95, which rounds to 460. With a damage range of 60, the base damage would be 430-490. It would still be a powerful spell for death wizards if it were audited to the appropriate base damage values.

To compensate for the Headless nerf, if they were to audit it to the appropriate base damage, Ship of Fools is actually underpowered for a death lore spell. A buff for Ship of Fools would be welcome by death wizards if it is audited to the appropriate base damage value while Headless receives a nerf if it is audited to the appropriate base damage value.

Feel free to provide any questions if you need anything clarified.

True, but as I mention we are talking about Drains and not pure Death damage; they have different DPP. Death's lore DPP is 105 while Drain's lore DPP is 84. Not to mention Ship Of Fools is balanced as AoE's receive a 25% reduction in damage. Here's some calculations for you.

Ship Of Fools [no utility; AoE]
Base Damage = 84*[(4 + 3*0.13)/4]*(4 - 0)*(1 - 0.25) = 276.57 -> 275 Drain damage
Damage = ~275*1.5 = 412.5 total damage

Headless Horseman [healback swapped to damage (0 pip reduction; Drain DPP nerf); single hit]
Base Damage = 84*[(4 + 3*0.13)/4]*(4 - 0) = 368.76 -> 370 Drain Damage
Damage = ~370*1.5 = 555 total damage

Lord Of Night [halved valued single target trap Infection utility (0.25 pip reduction); single hit]
Base Damage = 84*[(5 + 4*0.13)/5]*(5 - 0.25) = 440.496 -> 440 Drain damage
Damage = ~440*1.5 = 660 total damage

What you're suggesting:

Lord Of Night [halved valued single target trap Infection utility (1.20 pip reduction); single hit]
Base Damage = 105*[(5 + 4*0.13)/5]*(5 - 1.2) = 440.496 -> 440 Drain damage
Damage = ~440*1.5 = 660 total damage

So unless you're trying to say Lord Of Night's utility is a 1.2 pip reduction, higher reduction than a regular Infection utility, and lore Drains should use Death's lore DPP, that would imply that regular Drains should also use Death's regular DPP instead of 76.

Yes, the spell has a cool animation and it is a highly sought spell by death wizards due to its seemingly high base damage. However, for a death lore spell, it is balanced. You may not be willing to accept this, but as quick math calculations have shown us, these spells are balanced.

twinabc on Jul 20, 2022 wrote:

Headless Horseman

For Headless, I'm not following your logic. You just use the base dpp of 105 and the base damage function to determine the base damage. I have done this in my previous post. It is as simple as that. It's the same way with spells like Banshee, Skeletal Pirate, etc., but they just have a different base dpp (85).


Ship of Fools

Death drain spells take a 1/9th damage reduction in comparison to Death damage spells. AoEs also take a 25% damage reduction (only exception to this is the 7 pip AoEs). Two ways to determine the appropriate base damage for Ship of Fools:

Method 1: Use Death damage lore dpp (105 dpp) and then multiply the base damage amount by 8/9ths.

105(4 + 0.13(3)) = 460.95 * 0.75 (due to AoE) = 345.71 * 8/9 (due to drain) = 307.3, which rounds up to 310 (rounding to nearest 5).

Method 2: Determine Death drain dpp first by multiplying Death's damage lore dpp by 8/9ths and use that dpp to determine base damage

105 * 8/9 = 93.3 (approximately)

93.3(4 + 0.13(3)) = 409.58 * 0.75 = 307.19, which, again, rounds up to 310 (rounding up to nearest 5)

Lord of Night

Lord of Night not only is a single target drain, but it also has a utility of applying an infection trap on the target. One pip of damage is lost due to tempo (the spell doing two things at once). The cost of the infection trap is zero pips. This leaves four pips for the drain.

Using Method 1 from before: 105(4 + 0.13(3)) = 460.95 * 8/9 = 409.73, which rounds to 410 (rounding up to the nearest 5).

The Final Bastion has a great article in regards to modeling the spell audit for lore spells. I think you should check it out. It is a great resource and I'm sure you would gain a lot from it.

So first I'll summarize what we are disagreeing on.

1. Expression to calculation damage.
2. Pip cost of a utility.
3. DPP of a lore Drain.

Since 105*(8/9) = 93.33333... DPP, I'll state 93.3 for simplicity but all calculations use the exact value, and for argument's sake I'll be working with this value.

Expression Difference
Both expressions are essentially the DPP multiplied by a pip factor (ie. f(p)*DPP). For now, let's say we agreed on a DPP, the utility values, and are just debating the pip factor. If you expand both expressions you will see that the only difference is that the function I used has an additional factor of 0.13*(CostReductions / PipCost). In other words with no cost reductions, this monomial is nulled and the expressions are the same. At the very most the monomial yields 0.13, so the maximum difference in damage is 0.13*DPP between the pip factors.

Since the DPP you are arguing has a higher value, let's use that in the calculation.

• Max Difference in Damage (Single) = 93.3*0.13 = 12.13333... damage
• Max Difference in Damage (AoE) = 0.75*93.3*0.13 = 9.1 damage

In other words, via the pip factors the damage value we get from calculations will at most be 15 damage for single hits and 10 damage for AoE hits due to rounding; and that's for when the CostReductions are equivalent to the PipCost so you can expect about 0-10 damage difference for both single hits and AoEs. Long story short, both pip factors can be considered correct and only KI knows the exact calculation (it even could be different). Thus, what remains is the DPP and utility costs.

Again for arguements sake, I'll use your calculation since for a 5 pip hit like Lord Of Night and "1" cost reduction, the damage would be a 5 difference at most with rounding.

Utility Costs
Fundamentally you are correct; an Infection has a pip value of 0, and due to adding a utility an additional cost reduction of 1 would be applied. However, you are disregarding the fact that Infection needed an effect value of 50 in order to become a 0 pip spell. With a lower value, it would theoretically have a negative pip cost and that's the value inputted.

Consider this: what if only Virulent Plague was in the game? This would mean Winged Sorrow has a lowered version of V.Plague, but would you still value the utility's cost as 2 pips? Of course not! It's a lowered value so of course it will have a lowered pip cost; in this case it would be a 1 pip cost.

Now let's look at Lord Of Night's utility. Ignoring the fact it's a trap, it has a lowered version of Infection, but would you still value the utility's cost as 0 pips? Of course not! It's a lowered value so of course you will have a lowered pip cost. So it's not that Lord Of Night should be at 410 damage, but rather it's the fact that the utility is not valued at 1.

Using 93.3 DPP, this would mean the utility is valued at -0.287 pips. Using 84 DPP, this would mean the utility is valued at -0.750 pips. To say which is correct depends on how little is this utility valued which is debatable, however KI do love their 5s so -0.75 sounds more accurate than -0.29 but that would just be biased. Though, the only other card to compare is Diablo Qarin, a TC. Death TCs seem to have 85-105 DPP (irony) making Diablo Qarin's utility cost -0.110 at most, and if a -90% is -0.11 at most then I doubt a -25% would be -0.29 considering comparing Bad Juju to Weakness.

Thus with 84 DPP, Lord Of Night's utility is mostly likely balance compared to using 93.3 DPP.

DPP Of A Lore Drain
Yes, lore DPP is equivalent to the shadow DPP, but once again Drains are being underestimated. Let's rank the hit types (excluding heals) by their DPP, with Drains including the 50% healback.

1. Storm (125)
2. Drains (113-114)
3. Fire (100)
4. Myth (90)
5. Balance/Death (85)
6. Ice/Life (83)

Now let's rank the shadow DPP.

1. Drains (140)
2. Storm (130)
3. Fire (120)
4. Myth (115)
5. Balance/Death (105)
6. Ice/Life (100)

Do you see how Drains now surpass Storm's DPP? By the fact that shadow pips are limiting, this is not much of an issue right now, but KI is likely going to give Death wizards a hard time obtaining another pure shadow Drain spell, especially an AoE. But what would this be fair if a spell was spammable? Of course not, and thus is the reason why lore Drains are further nerfed. With 84 DPP for lore Drains, this is the ranking:

1. Storm (130)
2. Drains (126)
3. Fire (125)
4. Myth (115)
5. Balance/Death (105)
6. Ice/Life (100)

The exact same order as the regular DPP. That is why it makes sense for lore Drains to have a 20% (1/5; 2/10) reduction in damage while regular and shadow drains have a 11.1% (1/9) reduction in damage. Essentially it would have to be above 83.34 DPP and below 86.66 DPP but -20% make a solid 84 DPP.

Conclusion
All of these facts point to lore Drains having 84 DPP and never referred Headless Horseman.

Ship Of Fools = 84*[4 + 0.13*3]*0.75 = 276.57 -> 275 damage
Lord Of Night = 84*[(5 - [1 - 0.75]) + 0.13*(4 - [1 - 0.75])] = 439.95 -> 440 damage

Now here, after I realised the Drain DPP was 84, was the main reason why I figured Headless Horseman was a Drain. First off yes, the spell seemed really overpowered, so there was either a pip bonus or a multiplier bonus. The most easiest to find was if there was a multiplier bonus:

• damage = DPP*4.39*multiplier
• multiplier = damage / (DPP*4.39)

Before I had isolated the multiplier and used 105 DPP, but that left a 21.488% bonus which seemed too random, and I tried 85 DPP which left a solid +50% bonus and thought Headless just used a trap before hitting and thought, "Yep, that's pretty OP."

After Ship Of Fools was released is when I figured out the 84 lore Drain DPP and realised that the 50% belonged to a Drain's healback. That is when I discovered the hidden utility. Though they really make it confusing using 85 DPP instead of 84.

For more proof, Headless just got a new utility for its spellement; a school-specific mantle. A regular mantle would cost 0 pips, but due to this being school-specific the value is decreased. Using -0.5 as the value is still somewhat useful, this becomes the damage:

Headless Horseman = 85*[(4 - [1 - 0.5]) + 0.13*(3 - [1 - 0.5])]*(1+0.5) = 487.69 -> 485 damage

Really, you just had the incorrect lore Drain DPP.