Math of Netherwitch Part 2: Magic

Last time, I dove heavily into Hp, Mp and damage calculations. This time, I’ll lead our deep spelunking venture into the spell casting elements of Netherwitch. For the purpose of this examination, we’ll take Sylvia from Chapter 34 again. Specifically, we’ll look at the ‘magical’ fraction of her attributes.

For your convenience, I gathered most of the relevant information below.

Magic: 81+21
Dominion: 559%
Mysticism: 202%

Spirit: 86+21
Integrity: 581%
Resolve: 207%

Wit: 81+21
Awareness: 236%
Capacity: 202%

Trait: Ether Affinity I
* +35% ether gathering rate
* A moderate reduction to the difficulty of filtering ether
* A moderate reduction to the difficulty of holding ether

Equipment: Ghost Lightning Staff
Ether: 180 / Lightning, Wind, Fire
Charge: 275%
Potency: 140%

Spells and Energy

Mages face numerous limits to their actions. The first of these is how much energy they can put into a spell. Just as humans can only throw objects with so much weight, demons are likewise limited when dealing with mana or ether. This restriction scales with Magic: Dominion. Generally speaking, the following is true:

Max Energy: 25 x Dominion x (Staff Modifier + Certain Traits) x Other Traits

Some spell types allow greater charging of energy. Usually, fire spells allow for double this number while also having better mana to ether ratios. Larger, slower cast spells used outside of combat might allow for 2x to 3x this value. Gate, for instance, allows 3x when casting. Hence, Sylvia can muster:

No Staff: 25 x 5.59 = 140
With Staff: 140 x 1.40 = 195
Fire Spells: 195 x 2 = 390
Long Slow Spells: 195 x 3 = 585

This is a hard limit. If a mage cannot muster the required energy, they cannot effectively cast a spell. This is similar to how, if a person cannot lift an object, they cannot throw it. If a caster is managing two, three, or four spells at the same time this limit is split between them.

This limitation can come into a play when casting advanced or high magics. Some spells require more energy than an unconsolidated or first consolidation mage can reasonably control. See mana minimums for selected spells below:

Wind Blade: 20
Lightning Bolt: 50
Meteor Blast: 90
Chain Lightning: 200
Black Hand: 750

Casting Speed (syllables)

Casting speed is another limitation to a mage's power. Outside of battle and other highly reactive environments, casting speed is mostly a matter of convenience. Faster casting certainly helps with some tasks, such as alchemically manufacturing cloth, but even in this case, different bottlenecks will eventually take hold.

Most often, casting speed is calculated as runes per a syllable. Note, however, that these same speed and action limits still apply even when casting with a gesture. As fast casting requires pulling runes from the mind as a ‘train’, the maximum rate is limited by the structural strength of the rune groups. This scales with Spirit: Integrity:

Max Casting Speed: 2.0 x Traits x Integrity x Special

Example Modifying Traits:
Warrior-class Demons: 0.5x to 1.0x
Magic-class Demons: 1.25x
Ultra-fine Mana: 1.5x
Silken Mana: 1.75x
*Swamp Hag (wood/earth/water): 1.5x
**Sylvia: 1.85x

Of these, only the swamp hag's 'wood mastery' trait is a special multiplier. Similarly, Sylvia is an oddity. Her System means her traits are usually slightly stronger than normal demons (Deep reservoir gives +12% mana instead of +10%).

Warrior-class bloodlines get the shaft here. Some of these bloodlines have poor affinity for magic, making spell casting hard. Mortals are likewise limited. By contrast, most magic-class demons have refined mana. This doesn’t usually show up as a System noted trait, however.

Considering this, we can estimate Sylvia’s theoretical casting speed. Then we can modify it by her personal fast casting skill level.

Sylvia (max): 2.0 x 1.85 x 5.81 = 21.5
Sylvia (familiar): Max x 0.8 = 17.2
Sylvia (unfamiliar): Max * 0.4 = 8.6
Esmeralda: 2.0 * 1.75 x 12.6 x 0.95 = 41.9

Thus, Sylvia can cast at 17.2 runes per a syllable for spells with which she is highly practiced. For spells for which she is less familiar, she typically casts at 8.6 runes per a syllable. Note, I always round the syllables required up. A 19 rune spell thus takes two syllables.

Casting Speed (time)

Syllables, however, are not time. How fast are spells in terms of sheer speed? This is determined by multiple factors. The biggest, however, is Wit: Awareness. This attribute determines both the speed of thought and mana. In battle, Agility: Celerity can also play a role, as this effects reaction speed. Spells react with thought, so both reaction speed and thinking speed matter.

Generally the following is true:

Casting Time: Syllables x 200ms / Awareness
Min Time (power): Fraction of Max Mana Used x 500ms / Awareness
Min Time (base): 300 ms / Awareness

For Sylvia this can be reduced to:

Casting Time: Syllables x 85ms
Min Time (power): Cost / 195 x 221ms
Min Time (base): 127 ms

The minimum time frame here are important. The base limit means, ‘■’ is half again longer than most would expect. The power limitation is also a strong restriction. If a mage casts spells which use the maximum amount of mana they can muster, the timing is actually halfway between ‘■■’ and ‘■■■’.

All this said, usually two peer level mages will have near identical Wit: Awareness stats. Consequently, ‘■’ is about as fast as an ordinary person can throw a real punch (not a jab). Whereas ‘■■■’ is about the speed of a full on kick. If you’re thinking in game terms, these are your fast attacks and slow attacks respectively.

Anything beyond ‘■■■■■’ thus becomes a 'charged attack' in gamer speak. Which, we all know, demands a large opening lest there be an interrupt.

Of course, this only matters if someone is there to cause the interrupt. A slow caster can throw big spells happily if there is no one there to stop them, as shown neatly in Chapter 18 by the dark elf.

Ether and Mana Considerations

Mana can be blended with ether to reduce cost. The exact ratio is determined by the individual spell but can be augmented, to an extent, by traits. Typically, spells require that 12.5% (1/8) to 33% (1/3) of the energy comes from mana. The purpose of mana is to supply the cohesive intent while herding the ether. It is possible to cast without mana. Tools like lightning cannons use raw ether. However, such spells require 4x to 20x as many runes.

And they'll still use some mana, because the runes evoked by a mage contain mana in and of themselves.

However, all this presupposes sufficient ether is available for casting. And ether availability is another major restriction on a mage’s casting speed. Without ether, a mage must burn pure mana. As a results, spells will cost 3x to 8x as much. Therefore, ether recovery rates are important.

Staff Recover Rate: 5 x Mysticism x Charge Rate x Traits x Arts
Palace Recover Rate: Base x Mysticism x Traits x Arts
Ether Filter: (2 + Traits) x Mysticism x Traits x Arts

In Sylvia’s case, she has the art ether breath to improve her charge rate. This art consumes a small amount of mana but, in exchange, boosts her ether recovery rates by 1.65x. Hence, we can calculate her ether rates as:

Staff (no art): 5 x 2.02 x 2.75 x 1.35 = 37.5 eth/s
Palace (no art): 5 x 2.02 x 1.35 = 13.6 eth/s
Filtration (no art): (2+1) x 2.02 x 1.35 = 8.2 eth/s

Staff (art): 37.5 x 1.65 = 61.9 eth/s
Palace (art): 13.6 x 1.65 = 22.4 eth/s
Filtration (art): 8.2 x 1.65 = 13.5 eth/s

Notice how ether recover rates are much slower than casting speed. Thus, mages are forced to pause and catch their breath during long engagements. If they don't, their mana pool will run dry quickly.

Another interesting tidbit is that palace regeneration is purely passive and requires no mental effort. Staff regeneration demands mild mental effort. By contrast, raw filtration of ether is a high mental effort task which can lead to distraction.

Finally, all our calculations thus far presuppose the primordial elements under normal planar energy levels. We can adjust these numbers by environment by multiplying by the following:

Chaos (planar): 0.2% to 0.3%
Life (planar): 2% to 3%
Primordial (planar): 100%

Chaos (starry void): 2% to 3%
Primordial (starry void): 8% to 9%

Primordial (Earth): 0.1%

Gathering chaos domain ether is ten times faster in the starry void. But, as can be brutally seen, it's still 40 times slower than gathering primordial energy on an ordinary plane.

Climbing the Quality Chain

As a mage’s casting speed increases, most mages will strive to climb the quality chain. Why? Because high-level spells are better. Not just in their effects, but in their impact.

Maxed Lightning Bolt: 31 runes, 500 attack, 50 pierce, 150mp
Maxed Lightning Lance: 89 runes, 1850 attack, 100 pierce, 500mp
150mp Lightning Lance: 89 runes, 625 attack, 100 pierce

Calculating from pure rune totals, three lightning bolts can be cast in same time frame as a lighting lance. However, three maximized lightning bolts are clearly inferior to a single maximized lightning lance (1500 versus 1850).

But this is a dynamic situation. If the mage doesn’t have the raw power to maximize a lance, casting multiple bolts quickly can result in more raw damage than a single lance.

However, there is also the damage calculation math to consider. These same bolts when put against Leonid's shield, for instance, produces results much more favorable for the lance. This leads mages to tactical decision making. What's more important, speed or efficiency? Is the opponent guarding, or are they fragile and soft?

Thus, you'll often see Sylvia cast basic spells even as she grows in her casting speed. And when the high magics begin to appear, the advanced spells will likewise linger for quite a while.