FFXI damage equations and their implications explained
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Jul. 30th, 2007 | 07:30 am
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| FFXI damage equations and their implications explained in simple (!) but accurate terms | |
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This post is aimed at explaining some more advanced concepts on how damage works in FFXI, so that everyone (and monks especially) can more easily understand how to make the right choices to maximize their potential. ![]() |
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| [1]. Damage equations basics: fixed and variable range components | |||||||||||||
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| I have heard some people say things like "damage in this game is random, so I can believe what I want and from my experience math doesn't matter"... That's a big mistake. The damage in FFXI is accurately computed based on your stats, and then the game draws a very specific range around this and distributes random values within it, so you can tell what your max and min damage are and even estimate your average, all of which depend on your stats. Believing something like "ATK makes numbers less random"(?!) for example, as I heard people say before, shows some people just don't understanding how damage works in this game. Your normal melee damage is simply: meleeDamage = baseDamage x pDIF The baseDamage number is a simple fixed number mostly dependent on your STR and weapon. The pDIF number is a randomized number that falls within a max and min which are determined mostly by your ATK, plus a correction for level difference to the monster you are attacking. It's important to realize that the randomness added is very specific, so while looking at a few attacks might seem like the damage is arbitrary and unpredictable, the effect of specific stats is always the same and is in fact very predictable. To give you an idea of the relative magnitudes, the highest value that pDIF can take is 2.4, and usually the range between min and max is exactly 0.8, 0.5 or less. Critical hits damage is computed just by adding 1 to the normal pDIF value (and change the cap to 3), which proportionally is a very large increase and one of the reasons why critical hits are so good.
There is nothing hard about this, but what makes things complicated and tedious is that these two numbers are tiered (divided into regions or levels), capped in certain ranges, modified in others, and corrected for level differences, which also results in a lot of unintuitive effects where adding stats might have no effect until a certain threshold, and then create a sudden jump in damage at that point. Understanding this and how to always reach these thresholds optimally can increase your performance significantly and save you from making very wrong assumptions on the relative importance of stats and armor. I will start with a basic explanation and slowly add complexities, exceptions and their implications. ![]() | |||||||||||||
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| Intermission 1: Soloing Jelly NMs | ||
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If by now you are bored to death with all these numbers, here's a side story. | ||
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| [3]. Damage ranges and pDIF | ||||||||||||||||||||||||||||
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Here is where the randomness and your ATK vs monster's DEF come into play.
The fact that increases in ATK only show up in your damage as a ratio to the monster's DEF also makes it a lot less linear or intuitive. The same increase in ATK, say ATK+20, is a lot more significant at low levels than at higher levels (for example, take ATK=100 DEF=100 vs ATK=300 DEF=300, adding 20 to each case you have a cRatio change of 20% vs 6%). That's one reason why people who have recently leveled up monk through low levels tend to get an over-inflated expectation of ATK compared to what it actually does at 75. One other important consideration about pDIF is that critical hits raise pDIF by a whole point, which is a LOT, and one of the reasons why critical hits form merits and Destroyers, and stats like DEX are so important. But I will talk more about critical hits in the next post.
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| Intermission 2: The new expansion | |
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| By now I am sure most people watched it, but here are the two trailers for the new expansion: |
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| [4]. WeaponSkills damage and WS modifiers: | ||||||||||||||||||||||||||
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| If you ever hear anybody say something stupid like "modifiers are LOL", that's another person that doesn't understand how damage works in FFXI, and prefers to mindlessly repeat words he heard somewhere without any reason instead of trying to understand how thingsd work. That's especially true for monks, because we have very low modifiers for our best WS, the bulk of our damage comes from non-ws damage (usually 30% is from ws and the rest is from melee DoT). and we have some WS modifiers like VIT that are not otherwise offensive stats, so there is some reason to ask if and when modifiers are useful. That however doesn't mean that it's ok to be ignorant of how modifiers work or that they are less important than other stats on WS, especiially considering that you can use macros to swap gear on WS and that modifiers damage increase never caps while other stats can reach a point where adding more has no effect at all on damage. The damage from WS is easy to compute, it's basically the same as that for normal hits, plus a few extra terms: WSDamage = ((BaseDamage + WSC) x fTP) x pDIF For multiple-hit WS you just multiply this by the number of hits you will do. WSC is the famous WS modifier. fTP is always 1 for asuran fists, but it increases with TP for Dragon Kick, Howling fist, Raging Fists and Combo, although in most situations you are better off doing 2 WS instead of waiting for 200 or 300TP because for example fTP usually goes from 1 to only 1.5 from 100 to 200 TP. Notably Dragon Kick starts at fTP=2 for 100TP. Anyways, since everything else is the same, and I already covered fTP, the only term left is WSC , the WS modifier. As you know that's farily high for dragon kick, 50% STR and VIT, and only 10% STR and VIT for asuran which is our favorite WS because of its high consistent damage.
One of the most frequent misunderstandings that people have is that if you have a 10% modifier, each point of that stat you add will add 0.1 to the extra modifier damage. That's not how it works however because of truncation. Instead, adding a point of that stat will either add nothing at all or add a full point. That's the same as a 90% modifier by the way. The difference is that for a 90% modifier you are pretty much always justified in adding more, especially a lot more, but for a 10% modifier it only makes sense to add more if you are right at the next transition point, where adding one will make the truncated value jump up, while in other situations adding a lot more would still get truncated down to the same value so it wouldn't make sense to add it. In addition, since STR is used for the fSTR term too, something like STR+4 for example will always be better than ATK+5 (that was a question that was raised at some point on macro-swaps for WS) even if it didn't help break one of those modifier thresholds (unless it comes with added penalties like -DEX which would hurt your accuracy and criticals). Another important misconception is that since asuran fists is 8 hits, you need MORE accuracy than normal. I will discuss accuracy fully in the next post, but I really have to mention this because it's a very wrong assumption. Accuracy is the same and has the same caps regardless of how you group your hits. If your accuracy was only 50%, you should be equally worried whether you are using a 1hit WS or a 8hit WS. In fact if you care about skillchains you would be more worried about it in the single-hit WS since you might actually miss the whole WS instead of just some hits. For the same reason you also can't gain any advantage from adding more accuracy when your melee accuracy is already at its cap of 95%, there is no reason to swap in more accuracy for WS at that point, because it will have no effect. Each hit will still be 95% chance of landing, and you will likely get a perfect full-TP return asuran about two thirds of the time.
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| In the next post: | |
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| I already made this post too long, so I will leave the following topics for the next post(s): Additional Topic 1 (next post): Accuracy and evasion Additional Topic 2 (next post): Weapon Delay and damage ratio: faster weapons vs higher damage weapons Additional Topic 3 (next post): Critical damage and tiered DEX effects Additional Topic 4 (next post): Computing Kick attacks damage Additional Topic 5 (next post): Computing Chi Blast damage Additional Topic 6 (next post): Soloing Avatars (videos?) Additional Topic 7 (next post): Extra damage bonuses on monster weaknesses and weapons types. Additional Topic 8 (next post): Adding kick attacks parsing to your parser. ![]() |















(no subject)
from:
talifey
date: Jul. 29th, 2007 11:29 pm (UTC)
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I'm really looking forward to your next post on "Weapon Delay and damage ratio: faster weapons vs higher damage weapons" since I played thief I always felt there was something unfair about low dmg low delay weapons (though every drk also complains about high delay high damage which also makes sense because of lost swings at death) but against HNM seemed like low delay was hugely disadvantageous.
Also I hope when you do your critical analysis you comment on sneak/trick, while I know you're a monk I'm sure you went through the mnk/thf stage with dragon kick and I would find anything on that incredible interesting!
Good work :D!
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(no subject)
from:
genomeffxi
date: Jul. 29th, 2007 11:41 pm (UTC)
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A good translation is at http://www.freewebs.com/vzx-01
About SA/TA maybe I can add a little about it but usually as monk those are not very common concerns aside from very specific situations.
I know people complain about high delay weapons like gaxe or gkt, but then again it goes a little both ways because it's annoying to do a WS like asuran at the same time as someone else and only get 1 hit before the monster dies, while someone who does a big TachiGekko gets the full 1k damage parsed =P
SE says they are still planning on doing something to make single-wielders happier, like allowing you to wear something with stats on the other hand anyways, I hope they include h2h in that too.
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Funny
from: anonymous
date: Aug. 14th, 2007 04:00 pm (UTC)
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It's kind of funny that you predicted this. But it seems they're only including 2 handed weapons in this adjustment. Too bad eh. Do you have any thoughts as to whether they'll do something similar with h2h?
Thanks for the parser link. I forgot you'd probably not want to disclose your email either, duh.
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(no subject)
from:
zerozephr
date: Jul. 30th, 2007 04:58 am (UTC)
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Completely unrelated to the post, but how's life on Diabolos? I'm thinking of migrating since Ragnarok's end game scene really stinks.
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(no subject)
from:
genomeffxi
date: Jul. 30th, 2007 05:20 am (UTC)
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Eh I wouldn't recommend it here =P
I might be wrong of course because I've been pretty detached from LSs for such a long time and just playing on my own schedule but from the little I can tell, there is not much to pick from.
There are a lot of young LSs and inexperienced LSs which might be good for entry-level people, but I don't even know of many people doing new activities like salvage or einherjar consistently and successfully. Even older LSs have been plagued by a lot of drama and a lot of revolving new players or weird or biased distribution schemes.
Plus it costs real $$$ to move. If you really want to move you might want to make a mule a few times in a couple of worlds first or see if you can't make the changes you want in your current world.
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awsome
from: anonymous
date: Jul. 30th, 2007 09:53 am (UTC)
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Re: awsome
from:
genomeffxi
date: Jul. 31st, 2007 08:32 am (UTC)
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it might take a couple week for the next post though =P
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(no subject)
from:
lurkakitty
date: Jul. 30th, 2007 07:11 pm (UTC)
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(no subject)
from:
genomeffxi
date: Jul. 30th, 2007 08:55 pm (UTC)
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Although you probably won't find my posts very interesting now that you play a different game :p
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(no subject)
from:
lurkakitty
date: Jul. 31st, 2007 12:49 pm (UTC)
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(no subject)
from: anonymous
date: Aug. 3rd, 2007 02:58 am (UTC)
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cant wait for next one.
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Accuracy
from: anonymous
date: Aug. 3rd, 2007 04:15 pm (UTC)
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As it stands right now, the only acc+ I have on is a Chiv. Chain, and the additional accuracy from having capped hand-to-hand merits. Most things, aside from mamool, either show up as low evasion, or no message. The problem I'm having comes from the exceptions, mostly merit party things. Before I spend a lot of time and money on gear that I may end up not actually needing, I was wondering what you would suggest.
I'm aware that getting Byakko's Haidate would give me a decent accuracy boost (from the DEX+15), but I'm not certain if that's enough. I was considering changing my Chiv. Chain out for a PCC, and getting 2x Snipers. Most of my gear, aside from Limbus gear, falls in line with your gear topic. Osode, Destroyers, Okote, etc.
Anyway, sorry for the long-winded question, I would just like to know if I NEED to replace my gear, or if I'm doing fine.
Thanatosmazus, Asura Server
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Re: Accuracy
from:
genomeffxi
date: Aug. 3rd, 2007 06:23 pm (UTC)
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The same is true for a sniper's ring (unless you are switching out a rajas which I wouldn't recommend and would only give you 1% more).
If you want to know also how that will feel you can try to get similar effects from focus (focus with af1 and then switching back your ohat can give you 10% more hit rate).
Check what your meleeHit% is in general and on the high-eva monsters in merit PTs specifically (keep in mind some THF monsters etc just need more acc than others even in the same camp). After that you can better decide what you feel comfortable with in terms of hit% and decide if you want to change gear, use more accuracy food, etc.
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(no subject)
from:
genomeffxi
date: Aug. 6th, 2007 09:43 pm (UTC)
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Your question was:
The answer is yes 2 STR= 1 atk, which is why when comparing small amounts of the two usually the base stats like STR win over.
For example with 5STR vs 5ATK you are really comparing 5STR vs 2.5ATK
About ATK capping, that definitely can happen, but mostly when you are fighting easy monsters (farming materials on too weak or low EP) or have a lot of buffs from bards (most likely not in your case as RDM). Increasing STR however will NOT change this capped situation, that cap on ATK is only based on your ATK vs the monster's DEF. I think as a RDM you probably won't be in a capped ATK situation unless you are fighting too-weak for farming.
Aside from that, that's fine to go around and have fun soloing with strange combos like your RDM/RNG. I think you can experiment with interesting things like holy bolts which I think do higher damage when your MND is high (so should be good for RDM/RNG maybe?)
But as far as meleeing RDM has low offensive melee stats, low attack and accuracy also from low skill rating on weapons so you might need ATK the most and you are not likely to risk capping it much, although if you are really just deciding between 5STR and 5ATK you would want to go with 5STR.
For monk we often have to choose between more unbalanced choices, like 6STR vs 22 ATK, where it makes more sense to pick the larger ATK boost often and it is more important to know where your ATK might be capped to switch gear appropriately.
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A good word
from: anonymous
date: Aug. 7th, 2007 03:25 am (UTC)
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Hades
I've been reading your work for a few months now and i just wanted to say, great work man, truly amazing stuff
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(no subject)
from:
genomeffxi
date: Aug. 13th, 2007 07:13 pm (UTC)
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[2]. The fixed part of your damage: Base damage and fSTR
from: anonymous
date: Aug. 13th, 2007 08:42 pm (UTC)
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This makes sense to me, the equation works out to 50.2, and rounded down it would be 50.
Then you mention that the equation is different for H2H, H2H*0.11+D.
This does not make sense to me. I assume that D stands for the Damage+ on the weapon, so 18, but 292*0.11+18 = (aprox.) 50 not 53. 292*0.11+18+3 = 53, the value you give. Is this a typo in your writing, or am I misinterpreting "D"?
This is my first time trying to tackle any conception of Damage Equations and I'm still having trouble trying to figure out the base equation without truncation etc. so I'm just hoping for some clarification.
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Re: [2]. The fixed part of your damage: Base damage and fSTR
from:
genomeffxi
date: Aug. 13th, 2007 09:43 pm (UTC)
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The right equation is the one that adds up to 53, with the +3, because even without skill (think of when you first start the game and have 0 H2H and bare fists and still do damage), you have a natural base +3 damage even without weapons.
The confusing part is that the damage of destroyers is in fact 53, but if you used that in a damage calculator or tried to compare to other weapons you would only get the right number for 50 and not 53, that's why for a long time people thought it was 50 and not 53. Basically destroyers is 53 but it caps at the same damage as a weapon with 50 damage (think swords etc). That's because the rank of destroyers is just 2, not 5, because the rank is computed off of just the 18+3, as a static value (18+3)/9=2 rank, instead of using the weapon damage rating of 53 to compute rank as other normal swords etc do (53/9=5 rank). The numbers for max damage of 189 per punch happen to be the same because that 3 difference between 53 and 50 happens to balance out to the 3 difference between rank2 and rank5. In general you can use 50 in damage calculators as a decent approximation, but the correct value is really 53 with a lower cap (equivalent to a 50 weapon) due to the rank from the static value on the weapon that doesn't consider H2H in the rank (maybe it was easier to code).
It was sort of an afterthought in the post, and didn't really change all the examples much so I left it as a side discussion to not complicate things too much. For most comparisons or understanding the effect of adding X STR or Y atk it doesn't really matter much anyways.
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Re: [2]. The fixed part of your damage: Base damage and fSTR
from: anonymous
date: Aug. 14th, 2007 05:09 pm (UTC)
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Awesome
from:
ajinin
date: Aug. 15th, 2007 06:09 am (UTC)
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I am a big fan of + attack gear but now I see that isn't always the best route to go. I always wondered why the hell I see so many monks with + STR gear for AF, which is not a bad thing but I always thought to myself, well if the mods are 10% for both STR and VIT then there's only so much STR you can put into the WS for mods before it reaches the highest point. I believed that and your posts showed me my assumption was correct :D! I don't have the best gear, but my mods for AF are I believe + 15 STR + 17 VIT.
I was in a pt with a friend and he was decked out in STR gear while I invested in both STR and VIT gear (sticking to my belief / assumption having an equal amount of both will help more) and sure enough when we did our AF I out dmg'ed him. Needless to say he was like, "Wtf!" It just goes to show ya that not everything is about the best gear, but it's more about how much knowledge you have of your job and its abilities.
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(no subject)
from:
genomeffxi
date: Aug. 18th, 2007 11:23 pm (UTC)
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ATK does factor in WS except in very specific conditions where it is already capped and in your case you are probably not in that scenario.
STR is very good, but if you are comparing 5 of one vs 20 of another, you have to consider the quantity too, I would still recommend wearing okotes over temple for normal meleeing and even WS after boosting with temple except in again very specific situations.
Your experience might have been bad with raging and better with howling for a couple of reasons, one might have been low accuracy giving you low dmg on raging, the other might have been you were fighting something like crabs/steelshells a lot where fewer-hit wss can have some advantage over raging. If those conditions remain true, then I think you can keep using howling fist. However you should switch to raging fists as you improve your gear, and use something like a parser to better compare the two, sometimes the impressions you get can be a bit biased, like you will tend to remember only the highest damage and forget the times howling completely missed (something that is less likely with raging) etc.
Scorpion harness is ok but it's only 5acc over your AF1 body, so you might want to see if you can get even more accuracy somewhere else (rings, neck etc) for the same cost.
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Cruven
from: anonymous
date: Aug. 19th, 2007 04:39 am (UTC)
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Stat wise....
with my melee gear on...
Str+15 (+21 with sole sushi)
Dex 57+9
Vit: 67+7
Attk: 281
Def: 240
Okote stats i lose 4STR, Def lowers to 234 and attk raise to 299.
H2h skill is capped at 202.
Most Damage ive done so far in ym monk career is 1174 on a TW Floating eye in Ranguemont Pass. With no food. a Boost before Raging fists and temple gloves on (AF is the only monk gear i have at the moment im using. everythin else is a bit pricy for me.)
of course i am still "noobish" (self term)on the monk job since i was told my LS has had a history of good monks. I jsut however cant get them to give me any tips >_
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(no subject)
from:
valyana
date: Aug. 21st, 2007 05:01 am (UTC)
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At high and low cRatio, pDIF has a range of 0.8. For cRatio near 1.0, it only has a range of 0.5. I believe that the game still rolls a random number from 0-0.8, but that 0.3 of that range (37.5%) gives a pDIF of 1.0.
In the tiers just above and below the middle range, I believe something similar happens. At cRatio = 0.5, pDIF 1.0 is no more likely than any other value. But as cRatio increases, it becomes more and more likely until it hits 37.5% at cRatio = 5/6.
If my theory is valid, this makes attack more effective in those tiers (and less effective in the middle area) than you would expect by just averaging the min and max values. You still see a bump up in effectiveness going from high def to neutral def, but it's much smaller.
I derived formulas for average pDIF from this theory; you can find them in
http://wiki.ffxiclopedia.org/Maximizing
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(no subject)
from:
genomeffxi
date: Aug. 21st, 2007 05:35 am (UTC)
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I guess one way would be to look at the distribution of hits over a long series of battles using the same stats. You can basically plot all those values as a histogram and see what is the most likely value and how it tapers off on both sides.
One possibility is that the peak of the distribution curve is at the average between min and max, and the other possibility that you are suggesting is that the peak is further, basically the distribution gets one of the slopes chopped off.
In ascii art that would be something like:
|...*...|''''''|...*..|
|.*****.|''->''|.***.|
|*******|''''''|*****|
VS
|...*...|''''''|...*.|
|.*****.|''->''|.****|
|*******|''''''|*****|
If you run some tests to get this type of data I'll be interested in seeing it. Either way attack is less effective in these areas but it would not be as bad as half the normal effect if this was the case.
In areas where atk is capped however I have not seen any increase at all in the average either, you can see back to my post on critical hits and kick attacks when I did meat vs no food on farming mobs. If your suggestion was true I would expect to see an increase in average even in a capped situation as the distribution would still shift up and just get truncated differently, so I suspect that the distribution might still be set based on the endpoints in that situation and probably also in the half-capped ares.
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(no subject)
from:
valyana
date: Aug. 21st, 2007 05:42 am (UTC)
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(no subject)
from: anonymous
date: Jun. 9th, 2008 02:01 pm (UTC)
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(no subject)
from: anonymous
date: Jun. 15th, 2008 09:53 pm (UTC)
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Hmm...that seems unbelievable. Will it give you more consistence max pDIF damage instead of min pDIF though? or is it totally useless?
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(no subject)
from:
genomeffxi
date: Jun. 15th, 2008 11:40 pm (UTC)
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There are specific caps on your damage range and they are used before adding the randomness in the range of damage. The game doesn't care about how much more ATK you have outside of those caps.
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(no subject)
from: anonymous
date: Aug. 30th, 2008 12:04 am (UTC)
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(no subject)
from:
genomeffxi
date: Aug. 30th, 2008 02:08 am (UTC)
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The longer answer is those values are fully known for a few common xp monsters, and for all the others there are well-known formulas take use family type, job, level to determine defense and even evasion, and you can use that to determine VIT too. See for example the more complete http://www.geocities.co.jp/Playtown-Par
(if you can read japanese)
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