What formula could describe magic?

I am trying to build a systematic formula for how magic operates. This is based on magic as energy manipulation and transformation. It can be based on historical or modern esoteric magic principles.

I found the Q. Equation for magic system involving negative resistance and exposure time But its basic asumptions are different and the equations seems overly conplicated for a non-scientist.

Very tentatively, I came up with

$$E= \frac{PF}{R}$$

Energy/effect of the Spell = (Power used $\times$ Focus) $\div$ Resistance

$P$ = Amount of power being generated, Source of the energy and how well it is accumulated

$F$= Focus of the power, how well the energy is controlled/directed

$R$= Resistance to the desired effect based on the size of the effect, the laws of nature, easiness of the result, R could need a formula of its own.

So for instance, if one taps universal energy by connecting to an external source, $P$ is huge, but it is so unwieldy and uncontrolled that $F$ is tiny, whereas if one uses internal energy, like by meditating, $P$ is very small, but the focus is high.

If the "Belief" of the user is a factor as in esoteric magic, I could add a factor of $B$ (Belief that the magic will succeed). Also, since "Will" is an important part of ceremonial magic, it could be factored in, though it is already implied as part of the Focus.

Any ideas about other factors that should be taken into consideration?

• Magic is inversely proportional to the level of comprehension of the observer. Magic is quiet quantum. Without someone to go "Ooooh" it never bothers to exist. – candied_orange Aug 20 '16 at 15:23
• @CandiedOrange If a magician throws a lightning bolt in a dry forest and nobody is there to see it, then does doing so start a wildfire? – a CVn Aug 20 '16 at 22:00
• Yes, but everyone just thinks mother nature did it. – candied_orange Aug 20 '16 at 22:03

• Affinity? How attuned to magic or that particular branch of magic the magician is? Could be used to create a segmentation of magic, i.e. northern cultures have a water affinity of 0.9 but earth/air affinity of 0.3 and fire affinity of 0.1 so they mostly use water-based spells while southern cultures are the opposite etc. or to rank magicians based on their power, those with a higher affinity are plainly more powerful than those without.

• Wisdom? A measure of how much the magician knows about that particular type of magic and therefore how well they can use it (like, a novice magician might only throw around fireballs in combat while an experienced wizard can use them to cauterize a wound as well).

• Purity? Impure mana might be harder to control/have less predictable effects or simple result in weaker spells.

• Number? The more magicians there are the easier it is to control the spell, altough this might be factored into "focus" already.

• Will? If the magic is based on spirits or otherwise something that has a will in its own the outcome of the spell might depend on how aligned the goals of the spell and the spirits are. This could actually be made of the subformula Will = (alignment of goals*(strength of will of the spirit/strength of will of the caster)).

• Mana type? This is basically the same thing as "will" but doesn't involve sentience. Trying to cast a fire-based spell using water-based mana (or a water spirit/water crystal or whatever) should be more difficult while using fire-based mana should be easier.

• Environment? This might already be factored in outside of this formula but casting a fireball while inside a snowstorm should be harder than casting it in the desert.

• Interference? This could weaken spells when a lot have been cast in the vicinity in a short period of time (making large-scale battles less efficient) or when there are a lot of magicians around (also making large scale battles less efficient but not affecting duels between two high-ranking wizards).

• Quality? A magic circle neatly drawn with chalk on stone could work better than one hastily scribbled into the dirt with a stick. Same goes with the pronounciation of a magic formula or the precision in the doses of an alchemistic recipe.

• Devotion? A mutable version of "affinity". The more time/energy somebody spends on praying to the relevant god/strengthening their bond with the spirits/studying etc. the stronger their spells.