# How do you all work out the relative costs of spells?

Magic system question here. Would much appreciate your help!

I've read a decent bit about writing magic and I think I have a decent grasp of Sanderson's laws.

My magic has a cost (you have to shed your blood to use it) and a limitation (the more magical energy you hold the harder it is to control - out of control magic may become unstable). All well and good, albeit derivative.

However, I was wondering how you're supposed to work out upper limits on spellcasting and the cost of spells relative to each other.

For example, it's relatively straightforward to say "The heavier something is, the harder it is to lift it with magic." You can also say more destructive spells cost more: i.e. a fireball is hard, a nuke-level explosion virtually impossible.

But what about when you get into more esoteric stuff? For example, if a villain wants to create a vacuum of air which prevents the hero from breathing, how do I gauge how long he can maintain such an unnatural thing for? What about levitation?

Is it maybe better to say "My magic is just one thing" - i.e. evocation (physically damaging energy spells) and avoid such problems altogether, or is there a better way to think about this?

Super grateful to anyone who has any thoughts or useful references to check out - thanks in advance!

• Magic is not quantitative but qualitative, that is depend on the spectators. Important point is to make sure when u create a set of rules for magic there must be consistency. – user6760 Nov 26 '19 at 8:40
• @user6760 You could make a quantitative magic system. But generally you wouldn't include it to much in the book, since it's boring to read long lists of numbers. Might be suitable for an appendix, though. And having it quantified helps you keep your world straight and preventing plotholes/deus ex machinae. – Gloweye Nov 26 '19 at 8:50

I've found it's best to have magic do simple things, and have wizards be smart and combine it for complex operations. For example:

### Pyromancy

AKA moving heat around or creating it

• Light a Campfire
• light your way in a cave (heat some metal to have it glow and give light that way)
• Fireballs (Though you mind need a delivery mechanism... heat up a ball of air and throw that. Should give an explosion after sufficient compression. But that requires Aeromancy - so we have to be creative! Bonus!)
• Freeze water (by pulling heat away)

### Aeromancy

AKA moving air around

• Wind
• "Kinetic punch" (invisible fist type attacks, which are really some compressed air you're moving around)
• Push air against their windpipe (Darth Vader choke)
• Personal flight (perhaps all dragons use this to get around that pesky cube-square law. Just have wind strong enough to move you upwards under you. Ofc, this would be far more efficient with wings...)

And so on. Then for the cost, you can make it dependent on the amount you need to move around. For example, rules like:

• Moving air gets harder the less air there is, so for example halving air pressure always takes the same amount of magic. Now your villain has to choose between killing that risky hero sooner, or expending more magic. After all, taking away 80% of the air will kill the hero, but taking away 90% will kill him slightly faster. But it's double the magic.
• Heat creation is more expensive than transport, so even fire mages can be in trouble in the arctic.

It will result in something else Sanderson is known for - making magic systems which are in essence quite limited, but which you can use creatively to great and awesome effect. It has the added bonus that perhaps the reader can also think up fun things to do, since they understand how your magic works. Which is highly supportive of Sanderson's first Law.

• Thanks for the response! I like this as I’m not a terribly scientific person and the idea of doing a huge amount of physics research is a bit intimidating. – DanB Nov 26 '19 at 9:32
• @DanB This allows you to go full physics nerd, or leave it somewhat up in the air. Generally, the second read better while the first helps stop plotholes. But even for just that purpose, you don't need a number everywhere. "How much magic does X cost" is probably no more accurate than different people trying to lift different things. This allows you to keep it a bit fuzzy. – Gloweye Nov 26 '19 at 10:52
• @DanB The solution is quite simple: Make your own physics! People who care about magic making sense don't actually want real conversions of energy/force into magic, they just want something that's consistent and sensible for the world it's in. So just create your own type of physics. Generate your own core "elements" (Energy, Mass, Force, Thought, Fate, Whatever), and just come up with your own rules. Just because it looks like our world doesn't mean it has to work the same way. This also allows some form of resistance (Opposing Thought and Fate can interfere with spell functions). – Man_Over_Game Nov 27 '19 at 0:20
• @DanB Otherwise, you risk making a mistake, which is going to happen eventually. It's best to just make a statement that your world works differently from ours, and now WE have to adapt to YOU. Coincidentally, this also means you're not restricting your writing based on artificial concerns. – Man_Over_Game Nov 27 '19 at 0:27
• It's best for a writer to make their own artificial concerns though. Even if it's just a ranking of X being harder to do than Y, so that you don't contradict yourself. There's two things you have to prevent: Deus Ex Machina and self-contradiction. Being consistent about what you magic can or cannot do will stop them both, as well as making your world feel more lived in. – Gloweye Nov 27 '19 at 7:49

## Costs are Inherently Fuzzy

Even in Sanderson's own work exact costs for doing things are rarely specified. To see why I will create powers for a new superhero: Average-man. Average-man has a superpower that allows him to move quicker than normal. I'll name it running.

So running needs a few things. First are some limitations, I don't want him running as faster than light, it would cause all sorts of problems with relativity. So Average-man at top speed can run a little bit slower than someone on a bike.

I also need a cost for this running, so he can't run all the way for New York to San Francisco. I go for the stereotypical cost of using the power makes him tired. Specifically, it creates excess heat and increases his required oxygen intake beyond what his body can get from the surrounding air, but other than specific cases like running on top of a mountain or in a desert, it is functionally the same as being tired.

Realistic Cost Breakdown

So at what rate does he become tired? Well it depends on how much he uses his running power. I will define three teirs of power-use calling them Sprint, Jog, and Walk.

• Sprint: Average-man is running as fast as he can. He can do this for a few minutes, before he becomes too tired to run.
• Jog: Average-man is using about half his max running capacity. He can do this for several minutes before he begins to feel tired, but can keep the pace for maybe a half hour.
• Walk: This doesn't tired Average-man much at all. He can do this for long periods of time without much stress.

So for any use of his running power, I need to put is somewhere on that continuum. The exact cost will depend on how fast he is going, and the circumstances surrounding him. (e.g. If he's carrying something heavy, it's going to increase the cost.) This basic continuum will allow me to write the character's powers in a realistic manner, because few of us can quantify how long we can run for, or exactly how much energy we have left.

Unrealistic Cost Breakdowns

• Average-man has 200 stamina points....
• Average-man can extract X joules of energy from his meals, and moving at the rate of Y costs Z joules of energy, so I can calculate that by eating a massive meal before he runs...

What this means for your Magic

You can assign fuzzy costs based on the needs of your story and general limitations you want your characters to have.

Is levitating more like jogging, walking, or sprinting? That depends on how much you want your villain to fly. Possibly a light-jog, so he can do it for quite a long time, but it requires enough effort where he isn't floating everywhere all the time. Creating a vaccuum? Maybe that's more like a sprint, he can do it for a few minutes before he gets tired, just enough time to kill the hero. Or if you want your villian powerful, it's easy and he can suffocate a whole village with ease. As long as you are internally consistent, it is fine.

• Or, if I can pull a line from the Gargoyles episode, The Gathering (part 1): "energy is energy, whether generated by science or sorcery." (relevant scene) – Draco18s no longer trusts SE Nov 27 '19 at 1:44

You can rate spells for intensity, size, duration, number, and range, and let the cost be the sum or product of these numbers.

Intensity:

1. Minor (create dim light, change temperature +/- 10 C, create a breeze, lift an object, cosmetically change something, dispel a minor effect, etc.)
2. Moderate (lightly damage something, create fire, cold or intense light, hurl an object, moderately change something, dispel a moderate effect, etc.,)
3. Major (severely damage something, create intense fire or cold, create dead object, majorly change something, teleport an object, dispel a major effect, etc.)
4. Huge (e.g. destroy or disintegrate something, create living being, totally transform something, dispel a huge effect, etc.)

+1: Cannot be dispelled.

Size

1. Small (< 5 kg or affecting area a few centimeters across)
2. Medium (5-50 kg or affecting area a few meters across)
3. Large (50-500 kg or affecting area a few hundred meters across)
4. Huge (500-5,000 kg or affecting area some tens of kilometers across)
5. Vast (more than 5,000 kg or affecting a large country)

Duration

1. Brief (less than a minute)
2. Short (less than an hour)
3. Moderate (a few days)
4. Long (less than a year)
5. Indefinite (until dispelled or naturally eroded)

Note: Wounds (damage) last until naturally healed; destruction/disintegration is forever.

Number

1. A single target/object within range
2. Up to 4 separate targets/objects within range
3. Up to 15 separate targets/objects within range
4. Up to 60 separate targets/objects within range
5. Up to 250 separate targets/objects within range

Range

1. Self/touch
2. 10 meters
3. 100 meters
4. Line of sight
5. Anywhere the caster has been
• This seems very close to the approach used in rulesets for the pen&paper roleplaying game Ars Magica, which attempt to quantify arbitrary spell effects. – Peteris Nov 26 '19 at 19:45
• @Peteris: I have never played Ars Magica, but there is a similar (though simpler) system in TSR's role-playing game Dragonlance: The 5th Age". I also helped develop a similar, but more complex system for the original *Sovereign Stone game. – Klaus Æ. Mogensen Nov 28 '19 at 9:06

# Work

As in the physical unit.

The amount of energy that has to be expended divided by the time over which it is released.

A Nuclear explosion is hard because they are in the 10s of thousands of tnt of energy released in milliseconds. So the work is much higher.

Conversely a tnt stick is much easier. 1 tnt worth of energy released in the high millisecond/second time duration. Much less work.

A room devoid of atmosphere?

How much energy would be needed to clear it, and keep it clear? The energy required is simply that of evacuating 1 atmosphere (or even just a fair bit of it, humans are fragile), while preventing that atmosphere to rush back in.

• A pump would make it much easier.
• A small hole that can be plugged would help.
• An otherwise air tight room would really help.

Divide that by how long it took. A strong user can do it quickly, a weaker user could do it slower.

Levitation? Inverse gravity, the effort to accelerate at 9.6m/s^2 in the vertical direction opposite to gravity. Perhaps also the dexterity to finely control this otherwise it would be a wild ride.

# Avoid it, use Soft Magic

Sometimes its better to not explain the ability directly, allow the magic to be soft. If the villain is known to be an accomplished magic user, how they do the magic is less important then how their use of the magic is villainous, or what challenge it offers to the hero.

Similarly if the hero is powerful and untrained, you can allow the magic to be soft. They are capable of the unimaginable, but that it happens without reason or intention and this can quickly change a situation from bad to worse. The story drives from the fact that the hero has to contend with themselves and wrestle some form of control, or adapting to their own unreliability.

If you do go for soft, focus on the non-magic issues. As the magic is inherently in-explicable.

Soft magic can co-exist beside hard magic. You will need to be clear that those having the soft-magic are odd and do not cleanly fit within the hard magic (as they don't). Otherwise you will get a uh that's not right reaction from the reader.

• Keep in mind the OP references Brandon Sanderson's first law of magic: "The amount of plot fixing you can do with magic is directly dependent on how well the reader understands the magic". That basically means that any beneficial magic by the Hero has to be understood, which you contradict here. (and I'm on Sanderson's side with how bad an idea that is.) – Gloweye Nov 26 '19 at 8:10
• I think energy can be a good approximation but you also have to consider force. Levitating a boulder or keeping a volume under vacuum requires zero energy but would be hard to do for extended duration with your muscles. – Michael Nov 26 '19 at 16:10
• @Michael Holding a boulder against the force of gravity requires that you impart an equal and opposing force to gravity continuously over time. Keeping a volume as a vacuum will take energy proportional to the pressure being exerted by the surrounding atmosphere/liquid (1 atmosphere at earth sea level) delivered continuously over time. So there will be individuals who simply cannot achieve those energy outputs sustained over time. That is why circumstance is important. A Vacuum tube with a pump operable by magic could allow a lesser magician to produce the same effect. – Kain0_0 Nov 27 '19 at 22:08
• @Kain0_0: The thing is, it doesn’t take energy to sustain a vacuum or levitate a boulder (otherwise a vacuum bottle or mountain would continuously require energy). Nothing in those examples moves and work is force times distance. – Michael Nov 28 '19 at 5:39
• @Michael ... Please tell me that you are not serious. A Vacuum bottle and a mountain resist the force through their macro and atomic structures. If there is insufficient energy to deform/move the structure or break the atomic bonds, the structure resists the force, otherwise it deforms/breaks/shatters. The atoms are bonded together through chemical bonds. These bonds are mediated by electrons and protons. When they are formed energy is radiated out. To break the bonds sufficient energy must be imparted back into the system for the bond to break. What part of that does not require work? – Kain0_0 Nov 28 '19 at 22:42

# Use physics

Kain0_0 has the right idea, but (as Michael notes) makes the same mistake I (initially) made when designing my own magic system; forgetting that Work != Force.

### Work

Start with Kain0_0's answer. For anything that does Work, you can calculate the cost in Watts or Watt-Hours. (The former is more useful if you minimize Magic's

This works for magical effects that can be reduced to energy changes; moving things, increasing or decreasing heat, chemical changes (breaking or creating chemical bonds), or many electrical or electromagnetic effects.

### Force

If magic allows you to exert force, and it sounds like you want that, you probably want that to also cost something. Otherwise, things like keeping all the atmosphere out of a room, or hovering, become effortless, which leads to all sorts of world-breaking abilities. (Pushed out of an airplane? Need to lift an ocean liner? No problem; just cancel gravity, it's free!)

I asked about this (How can I meaningfully define the energy cost of magical levitation?) but haven't received any satisfactory answers. I ended up just making up a number for this cost, but I don't have any explanation for it. That being the case, I suppose you could use whatever number achieves the level of "oomph" you want your magic to have.

### Distance

One way in which I limited my magic was by adding a distance based "falloff cost". In my case, I went with an arbitrary and excessive curve. (I haven't pegged it to an exact formula, but it probably has an exponent of 3-5 or more.) You can easily specify that the efficiency of magic is somehow a function of the distance between the magic user and where the effect is happening. Both linear and inverse square falloff have strong foundations in real physics, but you can use whatever you like (it is magic after all), or omit this entirely.

### Cost

Now that you have a means to calculate the cost of any particular bit of magic, how do you "pay" for it? Does the energy come from the user's metabolism? (This is how my system works, also many others including the magic in Eragon.) If you go this route, How much can a magician lift if constrained by her own body's energy?, Magic and physics with human power output and How can wizards do such powerful things running on pure human metabolism? may be useful. Can the user "store up" energy somehow, or is their power limited to real-time metabolism?

You mentioned using blood... does magic extract energy from that according to $$e = mc^2$$, or does it just allow you to channel energy from somewhere else? You don't give enough information to answer this, so you can probably make up whatever conversion rate you want.

The differentiation you mention reminds me of the difference between Li and Jin in martial arts. I'll gloss them here, but I highly recommend the work of others to really understand the terms.

Li is brute force, like creating gigantic fireballs or moving heavy objects. It's character is 力, which fittingly looks quite a lot like a plow being drug through the earth. As you have noticed, this is easy to quantify and assign limits to.

Jin, 勁, is a bit more tricky. It captures the concept of skillful power. The character shows the idea of passes through, or under, like a river underneath a city. Me lifting a rock may be Li, but an Olympic grade deadlifter can only achieve those great lifts by power that goes through all limits of the human body that we thought possible, and empowers the lift with an energy that makes us all stand in awe.

And key to understanding how to balance these powers is the little I shaped symbol in the corner, Gong, 工. The Chinese meaning of this word is somewhat along the lines of "work." The first word of "kung fu" is this symbol (for phonetic reasons, sometimes it's written gong, other times it's written kung. But it's the same word). It's the concept of work and gains which comes from doing work.

Which brings to the test I recommend. Develop a sense not of how much power a particular spell has, but a sense of how much work has to be spent to develop a control over it. How many years did the villian spend practicing his skills at vacuum manipulation before the hero appeared. (Likewise, how many years did your dread pirate spend developing an immunity to iocane powder)

Finally, consider that anyone who develops this sort of skill through work is not going to waste it. If they have a particular power like this, they will want to use it for more than just a one-shot at the hero's head. They'll want to work it into their life. What does that look like? That tells you the shape of this gong fu. Don't focus on the brute force skill of pumping a vacuum. Concentrate on what flows through their life. Perhaps this means they focused on controlling winds around them. The vacuum is just an ultimate manifestation of winds pushing away from a point. How would they use that wind control in every day life? How would they not waste all that effort they spent learning it.

Then, use the rule of cool in the inverse. Is a character who acts this way "too cool" for the story? You'll get a sense of believability rather quickly.

And then you can also map this to how convenient circumstances are, and how little has to be done. Gandalf from Lord of the Rings is an excellent example of this. We get a sense of just how extraordinarily powerful he is, but he chooses to exhibit his skills only in the way which takes advantage of circumstances to decrease how much Jin, how much skilled power he must demonstrate.

### A Spell Toolset

Sanderson's First Law: "The amount of plot fixing you can do with magic is directly dependent on how well the reader understands the magic". This does not mean that magic has to have intrinsic rules in-story. It just means that you have to define the cost and effect of each spell that is used by the characters.

While Sanderson loves "hard magic" systems, where the reader is granted an understanding of the core underpinnings of the principles that allow the characters to create the desired effects, other authors use softer systems that are nonetheless following the First Law. Basically, the characters acquire a "toolset" of spells, each with their own specific cost and effect, and the reader is made aware of them. These become the tools by which the characters can solve problems, even if the reader does not understand the deep, fundamental principles upon which these spells are ultimately built.

A good example of this is Harry Potter. The author never explains where magic comes from, how new spells are developed, and why moving a wand in a particular way with a particular incantation has a particular effect - but these things don't need to be explained, since the main characters never create new spells. We know the main spells in Harry's arsenal, and have a general grasp of what the main characters are capable of accomplishing with magic - all advanced spellcrafting is used to create the setting, but not to solve problems within the story.

Remember, the purpose of magic within a setting is to make the plot happen. While you can create an elaborate "magical physics" system and build off of that, it is not necessary to do so - as long as the reader has a general understanding of what the main characters are capable of, it doesn't matter why their abilities work the way they do.

Reality is NOT balanced, ignore balance for balance sake, but think about intended story consequences

Reality has serious bias towards ranged weapons (from crossbows and muskets on). It ruined big part of beauty of battles, as distance increased and uniforms become less and less flashy. Nukes are totally OP, as they undermine any logic of open war between great powers.

Magic should have similar impact. Don't think about balance for balance sake. A spell can be ultra expensive and practically useless. Supernatural does not care about our feelings and balance. Create your spells as you see fit. Then think, how the most annoying metagamer would exploit it for efficiency sake. That would be a good approximation how world would work. Accept that under natural conditions you have no uniformity, but rather something like Pareto distribution - 20% of spells would be cast 80% of time.

If you really desire balance:

Mages use mana for different schools of magic, that are in sort of balance. If people start to use much more of one school they are using it up and it makes harder to get it. It keeps relative balance, but costs would change.

I think that you need a better grasp of the physics you are looking at.

You have an idea about how much power you want. You dont want a nuclear explosion but you do want a certain size explosion to be possible. This gives you an idea of the power output of your people. You dont need an exact number but just a ballpark.

Now lets say the villain makes a vacuum. To make it and maintain it you need to constantly put enough force into your spell to keep pushing the air (or gas) away and pull a vacuum. This can then be compared to the average explosive power you want spells to have. Dial this down as a ln explosion is likely going to be a single momentary energy input while a vacuum takes longer.

If you want the costs can vary per speciality. You dont want a certain ability to be so useful that it trumps everything else so you could say such spells require more energy and have further limitations. Such limitations are necessary because creating a vacuum can allow you to rip lung tissue apart with ease and kill anyone.

At that point you have to ask yourself: what do you want? Do you want a heavy focus on power fantasy where the characters cut armies to ribbons or do you want your magic to be a more thoughtful process that enhances the users? Or anything in between? Its your choice.