Bonus Chapter: Power Levels – A (way to detailed) explanation.

So recently, a lot of technical sounding numbers and ranks have been thrown all over the place, and while they are meant as a system of measure to compare our cast to those around them, I realize given their relatively isolated location on Earth magic wise, that there was no particularly good way to explain that system without it seeming artificial. Originally, I was going to leave it to the Nanoha Canon proper to settle that, but upon looking deeply into it, there is actually very little given as to the explanation of Mage ranks, and between that and the changes I've made to that particular ranking system, I though it best to create this section to explain its methodology and context. Some of it is quite technical, so if that sort of bores you, please skip straight to the bottom to see the actual power rankings.

To start with, to give it the ability to be measured against, along with the rankings, I created a numeric measure of magic, the so called "Power Level", which is the measure of strength of a user's magic in terms of raw output, measured as units of mana, the name for individual particles of magic.

Specifically, power measurements use Magic per Mana Molecule, or MMM Units, sometimes referred to as M3 Units, though generally they will simply be referred to simply as "Magic Levels" or "Magic Units". It should be noted that levels are not additive, but dynamically logarithmic when comparing the power against another level. The standard to use that is an average of most mages in order to compare power is

(2.05) * sqrt((1.02X)/1000) + (x/1000)2 - X

where "X" is the users general mage output, which is the large numbers we've been seeing in the last two chapters, but this is not absolute and may vary based on the quality of the mage in question as well as their total mana capacity and recovery rate. A much more accurate equation would be

(((2*((1.1Z)/Y))(1.01+W) * sqrt(1.02X/1000)) + (X/1000)2) - X

where "X" is general mage output, "Y" is total mana capacity, "Z" is the recovery rate and "W" is a measure of the 'quality' of the mana, which is measured on a scale of -1 to 1 with an average of 0. That said, while reading mage levels is relatively simple, getting accurate readings for total mana capacity and recovery rate require special equipment and so cannot be done in the field, and a measure of the quality of mana requires even more specialized equipment that is not standard issue and requires a specialist to use properly, and so the first equation is used since it is roughly accurate for a mage of average mana capacity, recovery rate and mana quality.

That being said, these are NOT the equations that measure magic mage level, but simply equations to use as a baseline to compare two mages of different powers against each other, and that they are not an ultimate measure by any means since they don't include other factors such as skill and ability. That said, it can be used as a rough estimate of the actual strength of mages compared to each other purely in terms of magical might.

In any case, below is an actual chart of power rankings by level with their numerical power level ranges. For the most part, it is similar to the Nanoha Canon explained levels, with F equivalently being a non-mage and going up from there. That said, there are two important differences. The first is that unlike the canon, there are no "minus" levels, and in addition, only C rank and above have plus grades. Those grades felt somewhat arbitrary, and in truth when I started writing this story, my school had just gotten rid of "minus" grades in the grading system, and they never gave a plus grade for a D in any case, so that probably influenced my design here. The other, and probably most significant change though is the inclusion of a new level, one to represent the very peak of magic, an unreachable dream for all but the exceptionally small chosen few, to the point that many would be right to doubt their very existence, a level above SSS+, the Z level.

POWER RANKINGS

F CLASS:

F: 0 - 5000:

This is the official equivalent to being a non-mage. At this level, it is not possible to harness or enact magic or magical effects in any way.

E CLASS:

E: 5000 - 999,999

This is the absolute minimum level that a person can be and still be able to enact a magical phenomenon. They barely qualify as mages though, and are generally unable to enact any kind of refined magic or magic spell, instead simply being able to create small phenomenon that they are naturally inclined towards, and in this sense would probably be closer to what we know as espers than any kind of proper mage. In almost all cases, this is simply the level of an average mage with a non-awakened linker core, and thus is most commonly only seen in children.

D CLASS:

D: 1,000,000 – 9,999,999

Theoretically, this should be the minimum level any mage with an active linker core can achieve, and in truth many mages either when their linker core awakens or soon after naturally pass this level for the C class. It is rare that any mage remains a D class for very long, since just general use of magic should allow one to attain C class status, and thus this is generally a designation for a transitional phase for young mages while they learn to harness their power properly. That said, some mages with damage to their Linker Cores can also fall to this range.

D Class mages can cast refined spells, but their ability is limited by the fact that they have much smaller total capacities to work with on average, as well as a limit on the amount of magic they can use at any one time. D Class is not considered a fully matured Linker Core, and so it is unable to produce more than a few streams of power at once, limiting the number of magical actions that can be performed simultaneously. Because of this, it is next to impossible for a D Class mage to be able to augment themselves through the use of a device, as just the act of supporting an active device magically will generally prevent them from doing much else.

C CLASS:

C: 10,000,000 – 34,999,999
C+: 35,000,000 – 39,999,999

C class represents a standard mage in almost all regards, and is by far the most common mage class, with over 90% of all mages falling into this classification. This is the level a mage should attain simply through the regular use of magic given no other deficiencies, even without any kind of formal training or exercise. The vast majority of mages tend to fall in this class. This class has a subclass of C+ to denote those who despite being C class mages have a generally higher output then most others in their class. Generally, such mages tend to have natural predispositions to magic in general.

Unlike D Class mages, C Class mages have what is considered a fully matured linker core, and so they are not limited to the amount of magics they can cast based on their linker core. That said, the ability to use multiple magics is still up to the skill and talent of the individual mage. In any case because that limiting factor is gone, C class is considered the minimum requirement for a mage to use a device, and in doing so augment their magical capabilities.

B CLASS:

B: 40,000,000 – 89,999,999
B+: 90,000,000 – 99,999,999

At most only around 8% of mages will make it to this classification. B class denotes a mage that is much stronger than average, either through training or in rarer cases natural predisposition to magic. It is considered a great achievement to reach this rank of power, and it is around this level that special traits within one's magic may begin to appear. B+ is a designation for those who reach the top of this class. B class mages also have the reserves of start casting much more complicated spells and enacting complex phenomena that may not be possible with lower levels of magic such as basic Summoning or Sealing Magic, and as such is considered the minimum level for such magics. In any case, it generally requires a large amount of training or inborne talent for a normal mage to attain this level, but with a steady application of the former is possible for most mages.

If a mage's magic has a strong enough inherent trait, it becomes much easier to see at this level. Incredibly strong Elemental Affinities and other Attributes become easier to see and use at this level. Thus, while not an ironclad rule, it is generally knowledge that this is the level at which unique abilities and specialties for a mage can appear.

A CLASS:

A: 100,000,000 – 119,999,999

A+: 120,000,000 – 124,999,999

AA: 125,000,000 – 149,999,999

AA+: 150,000,000 – 159,999,999

AAA: 160,000,000 – 184,999,999

AAA+: 185,000,000 – 199,999,999

A Class is the highest level of power a normal mage can hope to achieve, and is considered an immense achievement that less than 0.5% of mages will ever achieve. These mages are immensely powerful, and are considered the elite in terms of mages in general. Their power is great enough to overwhelm dozens of lower class mages in combat without much trouble. Not only that, but being more powerful, their linker cores naturally saturate their bodies with a large amount of magic, which naturally augments physical characteristics and makes them more resistant to foreign magic when necessary. To go along with that increased power is significantly larger magic capacities and recovery rates that allow them to cast advanced magics that would not be possible with the reserves of lower mages. In addition to this, those at the A range also have an easier time enacting phenomena with their magic directly, even if using the same quantity of magic as a lower leveled mage due to their actual mana being of a higher level. Also, because of this, there are many more subdivisions of this class than of normal classes for the sake of easy comparison and organization, especially because it covers a wider range of power levels.

As with all magic, the more powerful it is, the more its unique properties start to reveal themselves, and so A Class mages magic generally starts to show more unique traits than lower class mages. While particularly strong characteristics can be seen in the magic of B Class mages, at the A class level even weaker traits make themselves known through magic, and thus it is at this level that mages start to differentiate themselves from their peers in terms of their unique brands of magic.

S CLASS

S: 200,000,000 – 284,999,999

S+: 285,000,000 – 319,999,999

SS: 320,000,000 – 449,999,999

SS+: 450,000,000 – 499,999,999

SSS: 500,000,000 – 799,999,999

SSS+: 800,000,000 – 999,999,999

S Class is the class of the strongest, those born with innate power and talent that dwarfs that of other mages. So rare is their power that it is likely that on an ordinary planet, there is only a very few of such mages. In terms of probability, it is so small that it isn't even worth measurement, but TSAB officially lists the chance of a mage becoming S class as 0.000028%, with the chance of a mage reaching SSS+ as 0.000000000002%, effectively one in five hundred billion, an infinitesimally small chance of one appearing on every hundred or so worlds. Within general understanding, it is believed that this is not a level of power that can be attained merely through training and practice, but that one must be born with an especially strong potential in order to achieve it, though in truth there is anecdotal evidence to show that it is possible to train to this level under unknown circumstances, even if it would exceed their own measured potential, though this is exceedingly rare. Its sheer strength of magic dwarfs that of all the classes below it, and at the higher levels, the sheer radiance of power when in use can overwhelm ordinary mages on its own.

No two S class mages's magic is the same, for at this level of power there are infinite intricacies that differentiate any one person's magic from another that are much more obvious than with weaker magic. It is also at this level that you will find mages that specialize in a specific trait or ability, even among their piers in the lower classes, the most famous example being Elementalists, though they can appear at lower levels, they are much more prevalent in this class.

It should be noted that unlike the lower ranks, the TSAB will actively try to recruit mages of S rank or higher with incredibly lucrative offers in order to add their immense abilities to its ranks.

Z CLASS:

Z: 1,000,000,000+

The absolute pinnacle of magical existence. Only measured by a level exceeding all other measurements and having no upper limit. It is considered the impossible dream or all those who practice magic, as well an absolute that cannot be fought against. Z Class is the domain of only the very strongest in existence. Their powers are vast and defy common sense, to such a degree that whole fields of science have been known to revolve around their existence. It is said that all mages who attain this mythical rank go down in history as legends and myths with no exception. Their powers are so great that they have been known to affect the planet that the mage is on just by the exercise of their power, changing the weather and causing damage merely by the power that emanates off them, leading some civilizations to believe that such people are actually the incarnations of gods or other deities. So few mages ever attain this level that while such mages are generally publicly known, there are some that doubt their legitimacy, believing that it is beyond the purview of mortals to be able to have and use so much power at once. Throughout history, they have been acknowledged as both Gods and Devils for their strength, or in the case of a military they are on their own considered super weapons of the highest order, and are demonstrated as such more as weapons of deterrent than actual combat forces.

There is no logic to use to define the chance of their existence in a normal population, for a population would no longer be able to be called normal simply by the nature of including a mage of such power. So strong are these mages that even passively without any effort on their part, they generally find themselves at the center of all major struggles and events on their world or in their vicinity in some form, for their power is considered too great for even the passiveness of destiny and fate itself to ignore.

It should be noted that given the nature of their existence, the TSAB actively attempts to recruit mages of this level, generally with incredibly lucrative offers beyond that which they would offer to any lower rank, with some stories stating they've even purchased entire planets as part of such offers to retain such legends in their ranks.