Describing "magic hit rate" symbolically

It has been almost two years since Taruface 4B (my term of endearment because he didn't provide his character name, or you can call him "Lodeguy" from his blog address) began his extensive, brute-force investigation of "magic hit rate," and it seems pretty strange to me that his results haven't really gotten much traction in the FFXI "community" (at least the English-speaking contingent) in the intervening 24 months. Just a thought.

In fact, in the past few months I have heard several English-speaking players allude to the graphs that seem to have originated from this player's blog, but no one ever called these players out on their assertions (they are not trivial ones), and I myself wasn't able to find these graphs until recently. (I just waded through Google results until I found his blog.)

Anyway, I don't feel like rehashing my recent posts about magic hit rate, which are more or less summarized in the previous post. I did get it twisted in the last post about how the game calculates magic hit rate after bonuses, but after considering all the analysis of the data in its entirety, I propose a simple equation to model magic hit rate, which is comprised of the following factors and discards completely the idea of a check against "base" magic hit rate (which was poorly defined by me and is a pretty awkward concept in hindsight) to determine magic hit rate bonuses:

A - magic accuracy score with contributions from magic skill, magic accuracy, staff bonus (elemental magic accuracy), and INT (and other factors)

E - magic evasion score with contributions from INT and elemental resistance (and other factors)

L - a penalty (or bonus) due to a level difference between caster and target.

Then, magic hit rate, represented by the greek letter π (as a probability), could be modeled as



where X = 0.5 if the quantity in parentheses is negative, and X = 1 if the quantity in parentheses is positive. Yes, you could say this model describes a "check" against that quantity in parentheses.

Also, π seems to have an upper bound of .95 (95%) (I do not feel like showing this at the moment) and the lower bound could be anywhere between 0 and .20 (20%) if we are drawing an analogy to melee hit rate. If I had to hazard a guess, I would place the lower bound at 5% for the sake of symmetry.

Such a relation would account for the observation that the bonuses from elemental staves, magic skill, and magic accuracy all seem to be halved below 50% hit rate. It would also account for my observation regarding the staff bonus, from an initial magic hit rate below 50% to a final magic hit rate above 50%. (This is where I got it twisted to begin with.)

A distinct factor to account for the specific contribution of INT, conditional on ΔINT, is also warranted given the data, but I would like to see more regarding INT bonuses below 50% hit rate.

There is also the possibility that, akin to melee accuracy and combat skill, the accuracy (hit rate) contribution from magic skill is 0.9% (instead of 1%) above 200 magic skill, so that pure magic accuracy may be more effective than magic skill (within certain ranges of magic skill), but showing that such a difference is statistically significant (assuming it exists) is difficult.

Another thought: for things that are resistant to magic of a particular element (or to a particular spell, like Slow), the "magic evasion" score could completely dwarf the "magic accuracy" score so that it's futile to pile on magic accuracy.

Again, this is just a working model, but it is one based on data, and not idle speculation. That's pretty much all I have for now, and I don't want to be even more pedantic and talk about the everyday implications of all of this if this model indeed holds, so I'll just leave it at that.