Shinomi's Grimoire: Classifications - Casting Ranking

Aside from Practitioner Ranking in terms of how many Themas they have mastered, there is also something to be considered to how many times and how fast they can execute their spell starting from initialization of the Lor to overwriting Zaak. As it would be expected, a Septette can generally cast their spells faster and more frequently than a Trinity and same goes for Trinity in comparison to Practitioners. However, even so, there are differences between in the same Practitioner Ranking, and as such, a more precise measurement method was needed to gauge oneself and their opponent.

Important variables to determine the Casting Rank of an individuals are:

1. Spell Cooldown;

2. Lethality;

3. AOE;

4. Duration;

5. Maximum Cast Count;

6. Casting time;

7. Calculation Precision;

From those variables we can construct a simple equation to account for exponential growth and their compounding effect once each of the variables increases:

Let: c be spell cooldown in seconds, L be lethality rank (A = 5, B = 4… F = 0), A be AOE rank (Strategic = 5, Tactical = 4 … None = 0), d be duration in seconds, m be maximum casting count, t be casting time, s be an infinitely small value, approaching 0.

Using these predefined variables, let R_s be Casting Ranking value for a single spell:

Which can be further simplified down to:

An alternative form could be expressed using the sum function such that one could avoid using large values that appear from multiplication.

Let set S be {m, d, e^eL, e^eA}:

From there, we can create a sum of logarithms that expresses the whole of a practitioner's spell arsenal.

Let there be a set I such that it contains every spell a practitioner has, where In contains elements of the Spell { S={m, d, e^eL, e^eA}, c, t}.

Let function f = R_s.

Let set R be a set such that R_n = f(I_n).

Let function g be such that g(R_n) = S_m.

Let R_c be a value calculated from set R such that each iterated value is weighted against its own maximum cast count.

Which can be further simplified down to:

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