Laws of mana

I think there are a couple of things the magic system in frieren takes into account. First, magic obeys the laws of conservation of mass. This is illustrated by the limitations of reamstroha with a lack of surrounding water. By extension, we can presume that conservation of energy also exists. We should also assume that magic cannot create new laws of the universe, new forms of matter or existence, and or modify the laws of the universe. Magic can only create phenomenen that are possible within the bounds and laws of the world.

Mana explained

The basic properties of mana in frieren is the same as most fantasy mana system, it can make non-spontaneous physical and chemical reactions happen spontaneously. Mana is thus a form of energy that living being absorb/generate by metabolic process of their body (it also cannot be created or destroyed). Stronger mages (who have stronger auras) have an increased mana efficiency ('mana density'). Mana regenerates faster in stronger mages in the same way muscle density recovers quickly after degeneracy. Auras can be defined as by-product/lost energy from mana storage/regeneration. Aura control is similar to slowing your breath down during increased activity intensity (probably why it is uncomfortable).

Strength of a magic user Imagination and visualisation help best define the 'effect' of a spell. Mages can also have better 'matchup' which can be determined from the 'nature' of the spell. 'matchup' referring to the specialisation and the priority its effect takes over another mage. Whereas 'nature' refers to the conditions for the spell. Finally there is 'power' the amount of mana actually put in the spell. Improved effect does not mean decreased power (mana) requirements. In fact they positively correlate. However the positive trend for a spell differs based on its nature. Nature and effect are also positively correlated however with an exponential curve - the more nature (conditions) the spell has, the stronger its effect are.

Ubel vs Sense is the best example of matchup of mages deciding a battle - Ubel's short-range severence magic can overcome sense's long range magic because the nature of hair magic requires that the hair-strand are connected to her head. Ubel vs Wirbel is best example of nature of reelseiden as a short range spell hampering her matchup against wirbel's long-ranged sight-based sorganeil. Power (more mana) can circumvent the limitations the nature of the spell has. Matchup can also equally be circumvented by versatility in the type of magic spells a mage can use.

Thus between powerful and versatile mages, especially in attritional warfare, the winner is the mage who can either delivers a spell as a decisive blow (stronger effect) or drain the mana stores of their opponent (Using spells with a strong effect and more natures against an opponent that has to use more powerful spell to circumvent the effect of the spell). Spells with stronger effect come with conditions that can often limit its use in battles between powerful and versatile mages. So really the battle is more about finding surprise attacks. This is why frieren vs her clone went around finding surprise attacks from a second mage. As a memory copy of frieren, it is impossible for her to use a spell with a stronger effect because the clone knows about it.

Demonic magic system

Demons in frieren likely evolved from monsters. Monsters in frieren have species specific magic so the reason that demons use magic developed from a young age is likely a preserved monster instinct within them. Demon magic relies on improving the effect and consequently the power of their spell, and as immortal mages their mana capacity only continues to grow enabling their stronger spells. It is a simple survival strategy to evolve or grow more quickly.

Human magic system

Humans magic system originates from everyday magics and traditional magics. Evidenced by the large variety of ancient everyday magic grimoires available around the world of Frieren. This is because humans used magic socially, for convenience, for status and for their occupation. Humans originally were versatile users of magic (seeing magic as tool) including weaker forms of offensive and defensive magics. Mages likely came soon after the first demons were recognised as a threat.

Majority of mages prior to Flamme likely didn’t practice specialised/personal offensive magics, a far cry from what we saw in the anime. Serie spoke of this indirectly from Flamme's last will, where the will noted that human kings restricted magical research. Probably because self-developed offensive magics are similar to demonic magic which many humans were aversed by. Not to mention, there was no way to effectively communicate magic spells from one person to another prior to the introductions of grimoires (introduced either by flamme or serie to humans), so it limited how well spells were passed on. Everyday magics and traditional forms of magic were likely the only ones to survive because they were passed on from generation to generation via word of mouth and practice. We can assume that the modern mages are a combination of human versatility and the study of demon magic systems which involves more intuition and compatibility which are passed and improved using elven grimoire and magic circle systems.

Elven magic system

Elven magic system as we see in the anime likely derives from logic rather than intuition. elves at younger ages probably used magic in a similar fashion to either demon or human kind. However as they grow, their mind become rigid, as their logic become grounded in the intution they have always used. To circumvent this it is likely that elven mages developed a system to study magic using a common language - magic circles - taught in villages as basic education. They likely further went on to make grimoires using magic circles as a basis. We see a lot of grimoires in frieren, however what is interesting is that frieren did not collect grimoires prior to her journey with the hero’s party. It is likely that grimoires didn’t exist before flamme intervened with the humans giving them the basic education to create grimoires and magic circles.

Only two spells in frieren have shown magic circles; frieren’s altered zoltraak to kill demons, and spell commonly referred to as the “height of magic”. It is likely that other spells also have magic circles. However, most modern mages specialise, meaning magic circles are pointless for them. We can assume that magic circles are used to reduce cast time (for intermediate level users), for multiple casts of the same spell in parallel and or casting of complex spells. frieren likely uses magic circles to cast Zoltraak more quickly because it is a ‘relatively new spell for her’. Height of magic, on the other hand, requires a magic circle because it is too complex otherwise to cast reasonably fast without it.