Introduction

It has been long known to Black Mages that resists aside, Magic Attack Bonus, or MAB for short, is the stat that you want to focus on when it comes to raising your nuke damage. However, it is also known that for lower tier nukes, INT adds more damage than MAB.

Out of this comes the question of when the transition period is, and thus there is a need to relate the two together.

Today, a fairly common rule of thumb is that “2INT ≈ 1MAB,” which has been largely shown to be true from general observation.However, I have not yet come across any mathematical support for this statement.As advanced warning, there is a decent amount of math involved, which brings about two issues—first, not everyone likes math, so I’ll have to step away from the mathematics from time to time to explain what is going on. In addition, I have no idea what kind of math background my reader, you, would have.

To be safe, I am going to write for someone who has a high school background in Calculus, or someone in their freshman year in college.

By providing mathematical support for the claim, not only do we get absolute, logical proof that the relation holds true (under certain circumstances), but we can verify its accuracy, and if need be, further refine the rule.

But in all honesty, I was bored. Very, very bored. ^^

Edited to clarify some things pointed out by Robonosto.
## 6 comments:

A+++++

Awesome post.

This is really good support for such rules of thumb and a good way to illustrate how changes to the magic damage function work.

However, later claims hamper your fine work, particularly your assertion that your work illustrates that MAB "has diminishing returns" is ludicrous (to be blunt) after having invoked differential calculus

andeconomics concepts. It is easy to fashion some sophistry that "INT has diminishing returns," too. So what?First, the concept of rate of return can be described as a rate of change of output (damage in this case) with respect to some input, be it INT or MAB. The partial derivatives presented here describe the rate of return (with respect to some input) and diminishing return refers to a decreasing rate of return. Percent changes have nothing to do with this.

If you disagree with all this, there is no point in reading further.

Second, as you have already shown, the rate of change of damage with respect to MAB does not depend on MAB. In contrast, the rate of change of damage with respect to INT does depend on (current) MAB.

Consequently, changes in INT become

moreefficient (with respect to increasing damage) as MAB increases, whereas the efficiency of MAB is the same regardless of MAB level.Your final derived expression demonstrates that changes in INT become more efficient with increasing MAB, not that "MAB has diminishing returns."

@Robonosto:

Good point- thanks for picking that up. I'll admit that the end part was rather rushed, so not as clearly thought out as the rest of the post. I'll probably have to rewrite and edit that last bit now, heh.

The images created for the equations are inserted as img elements with class="mathimg". So you should be able to make the borders disappear by just defining how img.mathimg is supposed to look in your .css files.

I'm actually in Calc 3 studying partial derivatives at the moment. The question you answer here is one of the questions that inspired me to study mathematics in the first place.

It's amazing to see what I'm learning and how it can be used come together in such a fun way~! Thanks.

/bow

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