Beyond -50 Enmity

[eva00r]

Hey,

I was reading @ SCH's topic in WoG area and realized that I should purpose a theory of -Enmity. Currently there are a lot of -Enmity gears that you can access with mage jobs, some leets can even go beyond -50. I realized that benefits from -Enmity stats is just like a benefit from Haste stats. Unlike linear growth benefit from +Enmity, -Enmity's benefits is growing up at exponential rate.

According to Kaeko's research, -1 Enmity = -1% Enmity generated from you. So that explains, -Enmity stats is retardly good beyond -50. Your hate from whatever is reduce to half at -50, one-third at -66, one-fourth at -75 ... and 1/100 at -99.

With the fact above, I'm going to propose a theory of maximum curing before capping CE, the number of how much hp you can cure before reaching that will go beyond your imagination.

Suppose a WHM with -0 enmity can cure (1-4) to anyone for 5,000 HP before getting his CE capped at 10,000 CE.
with -50 enmity, you can cure for 10k HP before reaching cap
with -66 enmity, ~15k
with -75 enmity, 20k
with -90 enmity, 50k
and with -99 enmity = 495k !

This is sick.

However, I need a prove for the cap of -Enmity stat. If there is a cap of -Enmity stat, my whole post will be partially wrong. Obviously my gears are limited, so I am seeking for a tester to help.

[Ichthyos]

I don't have the link handy, but someone said tests suggested that enmity +/- is calculated like this:

observed enmity of an action = action's base enmity * (1 + 0.01 * enmity increase) / (1 + 0.01 * enmity reduction)

If this is the case then you observe decreasing, not increasing, returns when piling on enmity reduction.

[Maxxthepenguin]

I think we need to just make a big list of FFXI functions and their mathematical basis, I'm not sure on the words but there is a relation between how enmity and haste work; haste affects delay the same way as enmity- affects enmity gain. Accuracy's effect on damage over time is inverse to how haste effects DoT. It would really help clarify a lot of functions in this game and help understand how much of each is effective or how much is needed to be effective.

[Kirschy]

I haven't had the time to double check so don't take the following for absolute. But slow/haste on recast appears to work like:

New Recast = Recast * (1-FASTCAST) * (1+HASSO/SEIGAN) * (1-HASTE) * (1+SLOW)

Enmity doesn't work this way as I got a perfect 80 CE value for Monomi: Ichi /w +4 Enmity merits and a -4 Enmity belt. Either Ichthyos's equation is correct, or total enmity is calculated first.

[Yutuyu]

I really doubt that equation is correct. It adds in needless complexity to the calculation that has to occur every hit. Just from a programming viewpoint, why do divisions every time, when you can just do a very simple multiplication after adding some numbers together. Most likely the equation is something like:

Actual Enmity = Base Enmity * (1 + .01*(PlusEnmity - MinusEnmity))

[eva00r]

I second this equation, for both simplicity in programming and performance in calculation.

Actual Enmity = Base Enmity * (1 + .01*(PlusEnmity - MinusEnmity))

You will get 80 perfect CE with +4 and -4 Enmity with this equation also. ( 1 + .01*(0)) = 1

Provable by wearing +20 Enmity and -10 Enmity gears together.
Case 1 = (1 + .01(20-10)) = 1.1 Enmity [Yutuyu's equation]
Case 2 = (1 + .2)/(1 + .1) =~ 1.09 Enmity [Ichthyos's equation]

[Suiram]

Kaeko demonstrated it works in the way described as "Yutuyu's equation" above, in the 4th installment on his blog: http://kanican.livejournal.com/14209.html

Results

Enmity Change     CE Change
  -10              -32
  -5               -16
  -2               -7
  -1               -4
  0                 0
  +1               +3
  +2               +6
  +5               +16
  +10              +32

Were it calculated as Ichthyos suggested, it would have been a CE change of 29 in the enmity-10 case.

Also, to what maxx was asking before. The general rule for equations used in FFXI is that you get accelerating returns when the formula to determine the bonus is "total = 1 - change" (haste, -enmity, damage taken/shell, etc.), and diminishing returns when the formula is of the form "total = 1 + change" (MAB, MDB, +enmity, DA, etc.)

The interesting part is that calculations of the first sort usually have some kind of cap on the individual terms, so if the game actually lets you get to -100 or -99 enmity, that would be interesting indeed. I know the cap on +enmity is +100, but has it been confirmed that the cap on -enmity isn't -50 or thereabouts?

[Maxxthepenguin]

I know that suiram, I'm saying we should make a list to help clarify for the people who don't.

[Suiram]

Then the Random Question thread would die lol

[Maxxthepenguin]

A world where a random question thread is not needed would be a wonderful world indeed.

[Charismatic]

Yep, put it in an easy to digest format with lots of graphs and pictures and maybe some people will actually give it the time of day.

(Without pretty pictures, you can't hold my attention for long!)

[Yutuyu]

Well the first step would be to collect a list of the mathematical equations that apply to FFXI. You'd probably want to include information that's even as simple as a constant bonus given by JAs (like what percent attack increase berserk is), then split things by job-class which are relevent to specific JAs, and everything else put in general.

Just make a big math sheet, then put some pretty colors behind it like the old Skillchain charts had.

EDIT: The first step is just compiling a list of what would need to be put down.

[Yutuyu]

If you started to include things like how much enmity a specific ability generated (provoke), the formulas for spells, et cetera, it'd probably become such a large listing that it's unlikely a single page would do.

[Ichthyos]

Ah, I went to look for it and realized the post I was thinking of was for Haste and Slow percentages. My bad.

[Max™]

Man, that is actually a cool idea.

Would be neat to have the formulas for the various mods/calculations, and graphs you could look at like those swings per second/haste value and rukes chances of landing multi-hit WS one.

Wonder how you'd represent stuff like fStr, pDif, fTp and WS Mods though.

[Yutuyu]

Man, that is actually a cool idea.

Would be neat to have the formulas for the various mods/calculations, and graphs you could look at like those swings per second/haste value and rukes chances of landing multi-hit WS one.

Wonder how you'd represent stuff like fStr, pDif, fTp and WS Mods though.

Instead of delving into pdif it'd be a lot more productive to talk about "average damage." That takes the randomness out of it and pdif ends up being exactly equal to your cratio. So instead of giving an equation like this:

Damage = pDif*(fSTR+Base Damage)
It'd be
Average Damage = cRatio*(fSTR+Base Damage)

You'd just have to add in a warning that if your cRatio is situated at a spot where the boundary of pDif around it is not circular, you'll get bad information. But that's okay, but in every conceivable application of the formula you'll likely be centered within an ideal boundary region. The only time you won't is if your pDif is getting capped or cut off from being negative, which is rare in serious applications.

cRatio to pDif is probably the most confusing term. And if you don't use pdif you can boil down cRatio even further into:

Your ATK/Target's DEF - .05*(Target's Level - Your Level) (Where Target's Level - Your Level is bounded such that if it is negative, a 0 value should be used.)

The more nonsense-looking factors you can extract out of the equation, I think the more accessible it is to the average user. Get rid of fSTR too and replace it by the approximation and you end up with...

If Target's Level > Your level
Approximized Average Damage = (Your Attack/Target's Defense - .05*(Target's Level - Your Level))*((1 + your STR - monster VIT)/4 + Base Weapon Damage Rating)

If Target's level =< Your Level
Approximized Average Damage = (Your Attack/Target's Defense)*((1 + your STR - monster VIT)/4 + Base Weapon Damage Rating)

Which, while still somewhat confusing, is much more clear because it's all written in terms of values everyone should be able to understand.

[Yutuyu]

You can make even more useful equations from these also. Take them to start with:

If Target's Level > Your level
Approximized Average Damage = (Your Attack/Target's Defense - .05*(Target's Level - Your Level))*((1 + your STR - monster VIT)/4 + Base Weapon Damage Rating)

If Target's level =< Your Level
Approximized Average Damage = (Your Attack/Target's Defense)*((1 + your STR - monster VIT)/4 + Base Weapon Damage Rating)

Say you want to know which of two pieces of gear is better. Then you're looking for the difference in damage between setup 1 and setup 2. That's easily accomplished by subtracting the damage formulas for each setup from each other, and you'll end up with a much simplier equation if you do it symbolically rather than calculate the value both times. For example, lets go with the first equation.

If Target's Level > Your level
Approximized Average Damage = (Your Attack/Target's Defense - .05*(Target's Level - Your Level))*((1 + your STR - monster VIT)/4 + Base Weapon Damage Rating)

Going to use the AAD acronym instead of writing approximated average damage, and a couple other known acronyms to simplify the process. You'll see many terms will actually cancel out.

For simplicity's sake, c = - .05*(Target's Level - Your Level)*DEF

AAD = (ATK/DEF + c/DEF)*((1+STR-VIT)/4 + BaseD)
AAD = (ATK + C)*(1/DEF)*((1+STR-VIT)/4 + BaseD)

Then let AAD1 denote the first setup's and AAD2 denote the second's. Assume both setups are being applied on the same mob.

AAD1 - AAD2 = (1/DEF)*(ATK1-ATK2)*(BaseD1-BaseD2 + (STR1-STR2)/4)

Or

AAD1-AAD2 = (ATK1-ATK2)/DEF * (BaseD1-BaseD2+(STR1-STR2)/4)

Which is an extremely easy way test 2 different pieces of gear and see which performs better in terms of raw damage (NOTE: This equation can only test STR & ATK, you can see that ACC & haste, etc. play no role in it, and thus their roles cannot be ascertained, but at least it can explain competing amounts of STR & ATK).

EDIT: Interestingly enough, you can work crit bonuses into the equation easy enough too, because a crit bonus is essentially just a pDif increase of 1 which will occur a certain % of the time. Over time you can boil the damage a crit adds into the equation down into a factor of .01*Crit Percent added to your (ATK1-ATK2)/DEF. Similarly other factors can be included.

[Ferien]

Instead of delving into pdif it'd be a lot more productive to talk about "average damage." That takes the randomness out of it and pdif ends up being exactly equal to your cratio. So instead of giving an equation like this:

Damage = pDif*(fSTR+Base Damage)
It'd be
Average Damage = cRatio*(fSTR+Base Damage)

You'd just have to add in a warning that if your cRatio is situated at a spot where the boundary of pDif around it is not circular, you'll get bad information. But that's okay, but in every conceivable application of the formula you'll likely be centered within an ideal boundary region. The only time you won't is if your pDif is getting capped or cut off from being negative, which is rare in serious applications.

I wouldn't be so quick to assume that. First off, the information on otherwiki has been incorrect for months, as they've changed the cap and the formulas for pdif since then. Also, even before the changes, it wasn't tremendously difficult to be close to or at the cap on xp mobs, and now, 2Hers have an even easier time.

Even ignoring that, if I remember correctly, tests done on pdif (I think Aurik did them?) showed that it wasn't normally distributed, and you couldn't just assume a mean/median by plugging numbers into the formula and getting the regional boundaries.

Also, there's the fact that any change of Attack is going to change the boundaries of pdif, and the larger the difference, the less weight your approximation holds.

[Max™]

Said better than I was trying to put it in my head, thanks.

The approximations would be nice, but it doesn't work that simply, why I went with the straight formulas and what that would take.

[Yutuyu]

It's true it doesn't serve as a proper approximation for average damage because the distribution isn't normal, but it does serve as a proper approximation for the "midpoint" of damage. Because the extremes and the distribution are centered around the midpoint, shifting the midpoint will have the effect of shifting every data point the same, because the "length" of the distribution is constant. As such "comparing midpoints" is an effective way of ascertaining gear's effect on overall damage.