kegsay (kegsay) wrote,

Avatar PDIF and Attack calculations

A shameless rip from my thread on Allakhazam, which I've been using more of a blog which I really shouldn't do! The aim of all this testing is simple:
-What is the PDIF max absolute cap for avatars? [SOLVED]
-Is there an fSTR for avatars? If so, how does it work? [SOLVED]
-Do avatars have a 'base D' (e.g. DMG: weapon)? How is that calculated? [SOLVED]
-What is the attack penalty to Avatar's Favor?
-What is the Ratio cap? (AvatarAttack/MonsterDefence) [SOLVED]
-How much attack does Carbuncle have?
-How much attack does Fenrir have? [SOLVED]
-How much attack do the Celestial Avatars have? [SOLVED]
-Just what does 'Enhances Avatar Attack' do? Does it work for melee hits or just BPs? How much of an attack bonus? [PARTLY SOLVED]
-Redefine Blood Pact 'M' values and re-do all of the formulas with the knowledge obtained above.


A few simple tests were in order firstly. I went out to Sarutabaruta and whacked on Lv0 monsters (Bees/Mandys) and obtained a spread of damage from my avatar:

Garuda (No buffs except Karura) spread: 212-226
Garuda (Beast Roll (IV-Lucky) as /COR) spread: 212-226
Garuda (With favor on) spread: 212-226
Fenrir (With favor on) spread: 212-226
Fenrir (Favor + Ecliptic Growl (STR+7) spread: 220-235
Fenrir (Favor + Ecliptic Growl (STR+6) spread: 220-231
Fenrir (Favor + Ecliptic Growl (STR+5) spread: 216-231
Fenrir (Favor + Ecliptic Growl (STR+3) spread: 216-231
Fenrir (Favor + Ecliptic Growl (STR+2) spread: 216-226
Fenrir (Favor + Ecliptic Growl (STR+1) spread: 212-226
Carbuncle (Favor +mitts+EvkPig) spread: 192-201

There is a cap to PDIF for avatars, at which point adding more Attack does nothing (Beast Roll did nothing).

Avatar's Favor does not reduce the max amount of potential damage; no reduction in D or fSTR. It may reduce Attack since Atk/Def is capped in these tests.

Critical Hits were landed in these tests but did the same amount of damage as non-critical hits, indicating that, with enough attack, every single avatar's attack can be treated as a critical hit; there is no special "bonus damage" associated with criticals for avatars,  in the traditional sense.

The fSTR cap has not been reached on Lv0 monsters (STR+ improved results), pretty much showing there is no upper cap to fSTR for avatars.

(Caution: Haven't formatted this yet!)

Lesser Colibri Parses
[i]With: EvkPig+1 RoyRed(Dbl/Crit) SmnSpt+1 EvkRing SmnHorn NashGag FayCroz(BP/perp/Macc+1) SmnTrq SmnBlt SmnCape[/i]

Lesser Colibri Lv63 (DEF:231 EVA:243 VIT:52 AGI:52)
Melee Damage
Player Melee Dmg Melee % Hit/Miss M.Acc % M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 24345 92.73 % 349/21 94.32 % 43/88 63.98 38 91/144 117.00 10.89 %
Fenrir 50077 71.54 % 431/21 95.35 % 92/136 110.99 51 137/172 154.90 11.83 %

Melee Damage Taken
Player Melee Dmg Melee % Hit/Miss M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 573 100.00 % 9/3 52/76 63.67 0 0/0 0.00 0.00 %
Fenrir 7131 88.87 % 226/377 15/36 30.26 10 51/73 59.40 4.42 %
Lesser Colibri Lv64 (DEF:235 EVA:247 VIT:52 AGI:52)
Melee Damage
Player Melee Dmg Melee % Hit/Miss M.Acc % M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 21459 86.77 % 312/18 94.55 % 43/86 63.04 32 92/140 119.03 10.26 %
Fenrir 39917 59.21 % 358/20 94.71 % 88/126 107.06 36 138/165 151.19 10.06 %

Melee Damage Taken
Player Melee Dmg Melee % Hit/Miss M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 866 100.00 % 13/3 53/77 66.62 0 0/0 0.00 0.00 %
Fenrir 7179 89.52 % 220/326 21/37 30.77 13 48/76 62.31 5.91 %
Lesser Colibri Lv65 (DEF:241 EVA:253 VIT:55 AGI:55)
Melee Damage
Player Melee Dmg Melee % Hit/Miss M.Acc % M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 17635 89.27 % 267/8 97.09 % 42/83 61.71 22 96/134 114.36 8.24 %
Fenrir 34696 61.39 % 329/13 96.20 % 82/117 99.58 44 129/159 143.55 13.37 %

Melee Damage Taken
Player Melee Dmg Melee % Hit/Miss M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 494 100.00 % 7/1 61/78 70.57 0 0/0 0.00 0.00 %
Fenrir 7771 90.32 % 231/266 21/39 31.60 15 51/75 63.00 6.49 %



Lesser Colibri Lv63 (DEF:231 EVA:243 VIT:52 AGI:52)
Melee Damage
Player Melee Dmg Melee % Hit/Miss M.Acc % M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 14251 87.47 % 201/8 96.17 % 43/88 64.13 23 87/140 123.30 11.44 %
Fenrir 32382 68.52 % 266/13 95.34 % 93/140 116.78 33 137/179 156.76 12.41 %

Melee Damage Taken
Player Melee Dmg Melee % Hit/Miss M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 450 100.00 % 7/2 48/72 64.29 0 0/0 0.00 0.00 %
Fenrir 5017 90.46 % 159/228 15/36 29.16 13 45/73 58.38 8.18 %
Lesser Colibri Lv64 (DEF:235 EVA:247 VIT:52 AGI:52)
Melee Damage
Player Melee Dmg Melee % Hit/Miss M.Acc % M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 22230 85.91 % 331/18 94.84 % 43/86 62.24 27 97/140 122.59 8.16 %
Fenrir 46608 60.41 % 404/29 93.30 % 88/137 110.57 43 138/177 155.65 10.64 %

Melee Damage Taken
Player Melee Dmg Melee % Hit/Miss M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 953 100.00 % 14/4 56/77 68.07 0 0/0 0.00 0.00 %
Fenrir 7965 91.67 % 260/351 16/37 29.15 12 48/76 61.33 4.62 %
Lesser Colibri Lv65 (DEF:241 EVA:253 VIT:55 AGI:55)
Melee Damage
Player Melee Dmg Melee % Hit/Miss M.Acc % M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 17971 88.44 % 275/15 94.83 % 42/83 61.22 22 82/141 112.82 8.00 %
Fenrir 38336 64.18 % 347/18 95.07 % 82/130 105.89 38 129/172 147.79 10.95 %

Melee Damage Taken
Player Melee Dmg Melee % Hit/Miss M.Low/Hi M.Avg #Crit C.Low/Hi C.Avg Crit%
Kegsay 823 100.00 % 12/2 53/80 68.58 0 0/0 0.00 0.00 %
Fenrir 7669 87.84 % 240/300 17/39 30.04 15 46/75 60.60 6.25 %

(I need to re-do this, but I'm leaving it in this format for now m(._.)m)

This comfortably proves that Avatar's Favor does inflict an attack penalty, even on normal melee hits. All results on the Non-Favor tests show higher overall spread and higher average damage. Critical hit rate seems unaffected. Defence seems unaffected.

Enhances Attack gear did nothing for improving the spread, showing it does truly just add attack. Clearly there is a PDIF cap as indicating by Beast Roll not improving the spread at all. The fact that there's no fSTR cap is surprising. Perhaps dSTR (Avatar STR - Monster VIT) is used completely differently than normal characters. Perhaps this completely replaces a base D (DMG: weapon) in order to scale effectively as the summoner levels (but no new "weapons" are given to the avatar). What this means is there is a hard-cap for melee/bp physical damage which cannot be exceeded, except by levelling up.

-Analysing fSTR

A very very important thing to note is that "step-up" improvement of damage for the STR+ spreads.

What this is getting at exactly is still unknown, but with more samples, a formula will hopefully be able to be made. Why is this strange you ask? The normal melee damage formula:
Damage = (D + fSTR)*PDIF
-PDIF is related to atk/def, capped in these cases, and the extremes (read: constants PDIF_min and PDIF_max) remain. These are constant throughout the STR tests.
-D. This doesn't change, except by levelling up (assumed). For PCs, this is done by getting a better weapon with higher DMG:
-fSTR. The only modifier for this equation being tested. But wait, this makes no sense:

Assume, for example, PDIF_min=1.5 PDIF_max=2 D=50 and fSTR=15. Look what happens with the SPREAD of damage:
fSTR Equation Min Max
15 (65)*PDIF 97.5 130
16 (66)*PDIF 99 132
17 (67)*PDIF 100.5 134

Key point --- Min and Max raise AT THE SAME TIME AS fSTR INCREASES!
This is NOT the case for avatars as illustrated above!

My assumption now is that PDIF_min and PDIF_max do not use fSTR in them, after all, it would negate the whole point of it in the equation if it did. That means fSTR must itself have 2 variables, fSTR_min and fSTR_max which is used respectively in PDIF_min and PDIF_max. Knowing this, using our data table (and abusing the fact that it increases in increments of 4) and the fact that fSTR_max lags -behind- fSTR_min:

fSTR_min = dSTR/4 + 0.5
fSTR_max = dSTR/4 + 0.25

This matches the criteria of increasing fSTR by 1 every 4 dSTR (as suggested) as well as the "lag factor" of fSTR_max. In most cases, these two values will match:

fSTR_min = 51/4 + 0.5 = 13.25 (truncated to 13)
fSTR_max = 51/4 + 0.25 = 13

However, after increasing dSTR a certain amount, the observed effect is [b]fSTR_min jumps up a level whilst fSTR_max does not (it needs 1 more STR)[/b] which is observed now:

fSTR_min = 54/4 + 0.5 = 14
fSTR_max = 54/4 + 0.25 = 13.75 (truncated to 13)

This can clearly be seen in the table above, whereby the lower value always increases FIRST, then 1 STR later, the max value increases.

-Analysing D

Firstly, is there a D? What evidence is there that supports a hypothetical D? 'D' for Players is the DMG: rating on a weapon. Avatars have no weapons. If, however, there was no D, how is base damage calculated? Using just STR? If that was the case, you would expect damage to increase dramatically as STR is packed on, but this has never been observed. The only other variable for D therefore, is Level. So now my question is, how does Level relate to 'D'?

So I went out on a loljob combination of COR/SMN and hashed out some more numbers, the results weren't too surprising:
COR/SMN : No attack bonus; Fenrir
COR/SMN : Beast Roll Value:X (10)

So once again, attack has no effect on the spread, probably because it was capped already, even as Lv37 SMN. The spread is also not surprising, almost exactly half of the Lv75 value, showing linear scaling (fantastic!). This gives strong evidence for D scaling with level.

//more coming soon here!

The first major milestone has been reached. Utilising all of the spread information, specifically max spread information, I've been able to create a simple brute-force java program which went through all the possible generic BASE*PDIF values. Whilst BASE is split up into D and fSTR and PDIF involves some unknown calculations, we know the following:
(BASE+1)*PDIF = 231
(BASE+2)*PDIF = 235
Starting from BASE=30 up to 250 and PDIF=1.00 to PDIF=5.00 the program went through, listing any matches which meet ALL criteria. The following results were obtained:
Match D: 49 pdif:4.62
Match D: 50 pdif:4.53
Match D: 51 pdif:4.45
Match D: 52 pdif:4.36
Match D: 53 pdif:4.28
Match D: 54 pdif:4.2
First off, wow. The PDIF value is incredibly large, and the D value so incredibly small, could this really be the correct results? I then start plugging in D values for the other bits of data we have (Carby max (D:48), Lv37 avatar max, etc...) and only 1 value matched: PDIF:4.2

What does this imply? This means the MAX PDIF of an avatar is capped at 4.2, and D+fSTR=54 at level 75 vs Lv0 monsters.

Avatar Level D+fSTR
Fenrir 75 54
Carbuncle 75 48
Fenrir  37 27

Allow me to stress at this point that PDIF:4.2 might not be the one big number we're looking for. Avatar's get -50% physical damage taken as an innate trait. It's worth being open minded that they might get a 50% physical damage bonus as well. After plugging the numbers in again, accounting for this, the 'real' PDIF would be 2.8, with the 1.5x bonus added on afterwards. Please keep this in mind for higher level monsters (PDIF really borks at higher levels, which I have been unable to explain up to this point).

Min PDIF was slightly funny, since there is an fSTR_min and fSTR_max, so the D+fSTR values were off by about 1. The min value reached though was around 4.00 (if Carbuncle's fSTR_min didn't change) or 3.8 (if Lv37 Fenrir's fSTR_min didn't change).

For the sake of purpose, a few generalisations are going to be made in order to provide a rough estimation of how much base damage your avatar has:

Avatar base damage = (AVATAR LEVEL x 0.74) - (Monster VIT/4)

Example: Lesser Colibri = 75*0.72 - 52/4 = 41 BASE DAMAGE
Example: Greater Colibri = 75*0.72 - 67/4 = 37 BASE DAMAGE

This assumes fSTR has no lower cap. As for how PDIF is calculated, I still need to do more tests, but rest assured it is on the way. Max PDIF possible is 4.2. Min PDIF (when Ratio is capped) is either 3.8 or 4.0. There may or may not be a 50% bonus to damage being applied here, in which case divide all the PDIF's by 1.5 to get the 'actual' PDIF.


PDIF testing

Methodology is pretty complicated since we can't alter attack easily, nor know the attack value. The general idea is to fight progressively harder monsters until the formula MAX DMG = 4.2 * BASE DAMAGE no longer applies, it will be less, e.g. 4.1 or 3.8. When this occurs, we can deduce that Ratio is now uncapped. For PCs, this occurs when Attack/Defence is greater than 2. For avatars though, this could be anything. Back of the envelope calculations suggest Lesser Colibri PDIF_max is around ~3.3. Using Studio Gobli's DEF calculations, along with the Melee Damage Spreadsheet Calculator (primarily used for melees), I can slowly increase the DEF rating by fighting different monsters until Ratio becomes uncapped (doesn't abide by 4.2*BaseDamage). At this point, I still will not know if the cap is 2.0, 3.0 or what, I'll just know it is uncapped. I can then use minor Pet:Attack+ modifiers to hopefully prove this. After that, I can put on Avatar's Favor and quantify the actual attack penalty. That is my goal at this time.

Death Jackets
I went out to Mis.Coast and targeted Death Jackets. I went SMN/WAR for Defender and used a loldagger in order to get my Attack low. I swapped gear in and out until they checked Low Defence in order to work out their DEF Level and VIT, which were as follows:

All tests done with Fenrir.

@177, check low def -ETHEREAL+SWIFT
@176, does not check low def
=>141.6DEF = Lv34, VIT37

@181 low def -ETHEREAL
@180 not low def -ETHEREAL ERRANT RAJAS
=>144.8DEF = Lv35, VIT37

@187, low def - orochi/ethereal/rajas
@186, not low def - orochi/ethereal
=>149.6DEF = Lv36, VIT40
(Ignore the gear notation, that's to remind me which gear I need to equip to get that Attack value)

Most of the bees were of levels 34 and 35, there were a few 37s but I didn't need to include them since my aim is only to compare 2 different bee types. I chose to compare the Lv34 bee and the Lv35 bee. The difference in DEF is 3. My results:

Lv 34 Death Jacket - 141 DEF 37 VIT
Spread: 184-193
Criticals did same damage as regular hits, just like Lv0s.

Lv 35 Death Jacket - 144 DEF 37 VIT
Spread: 184-193
Criticals did same damage as regular hits, just like Lv0s.

Identical spreads, but is this spread still capped (with PDIF_max=4.2 and PDIF_min=3.8 or 4)? I plugged in some numbers:

193(.2) = 4.2 * 46
184 = 4 * 46
174(.8) = 3.8 * 46

This comfortably pushes 3.8 off the spot for PDIF_min, as only PDIF_min=4.0 works for the data set we have. This also indicates Ratio is still capped on these monsters. This also allows me to further refine my "avatar base damage" estimation, I changed it from 0.72* to 0.74*. Tried out a few more combinations:

AvatarLvl of BeeMin DamageMax DamageFavor?Ratio Capped?DEF of BeeVIT Offset (37)

* = Min value may not have been reached.

Fenrir behaves in a capped (Ratio) manner throughout the tests, except the final one. With a D+fSTR value of 46, the values match perfectly with the model. When the VIT offset increases by 3, note how fSTR_min is penalised but fSTR_max isn't, much like the ecliptic growl tests but in reverse. This gives a D+fSTR_min value of 45, but it still behaves in a capped manner (45*4=180). Even with Favor, Fenrir holds strong, except in the last test, where an anomaly of 179 cannot be explained without Ratio being uncapped.

Carbuncle on the other hand does not. Initially on Lv34/35 monsters without Favor, he behaves in a capped manner (D+fSTR value of 41, 41*4=164, 41*4.2=172(.2)), however when Favor is activated, the lower bound is violated; the numbers drop down to 150s. Also note on Lv36 monsters, without favor, this violation starts to occur, indicating that Carbuncle's Ratio is sadly, no longer capped. Do note that the upper bound still applies, the VIT offset is correctly applied, but even if you apply the offset to the lower bound, the numbers are just too low to be accounted for by just fSTR changing. This proves Carbuncle has a lower attack value compared to Fenrir, in addition to a lower D+fSTR value shown from earlier tests. I did a final test with Lv36 Bees, coupled with Pet:Attack+5. This did not recap Ratio. Therefore, presuming Ratio caps at 2, Carbuncle has between 288 and 292 inclusive attack. Tossing in Summoner's Pigaches did nothing, so assuming that the pigaches add more than 4 attack, it can be safely assumed they do not work on melee hits.

Garuda's results are some of the most surprising. It appears firstly that Garuda has less attack than Carbuncle (Carby passed his Lv35/No Favor test, Garuda did not), Secondly, outlined in red are when caps are in effect, but then immediately, the next value up for BOTH Favor/No Favor are uncapped. I have tried desperately to show Lv34 Favor test is not capped, but it's not happening, it seems to really be. This will be very helpful for determining the Ratio cap and actual attack value of an avatar (in this case Garuda), as this is such a strange occurrence that can only happen in certain circumstances.

Several more tests will now be done on weaker monsters, specifically with Carbuncle, in order to get a quantifiable value for Avatar's Favor attack penalty. As a sidenote, I tried using a Beak Necklace with Pet:Atk+5 and Summoner's Pigaches, but the results were just as grim:

Lv35 Bee without Favor = 164-172
Lv35 Bee with Favor only = 151-172
Lv35 Bee with Favor AND Pet:Attack+5 = 151-172
Lv35 Bee with Favor AND Summoner's Pigaches = 152-172 (note this may go to 151, I didn't test this much.)

The point here is that, individually, the items were not enough to counter-act the Attack Penalty by Avatar's Favor.

Massive problems with calculating PDIF. For PCs, If you do not meet the cap of 2.0 Ratio, you can't get the max damage (ignoring criticals for now). For avatars, as outlined in the graphs above, you can still hit max potential even without capping Ratio. This is most clearly seen on Carbuncle VS Lv37 Bees, the upper bound still clearly meets the model for capped Ratio. What this indicates possibly is that there is a STATIC amount added to Ratio prior to capping. E.g. CapAtTwo[Ratio+0.2]. This is extremely important, mainly because, I ask a simple question:

Have you ever seen your avatar hit for 0? (when there isn't Stoneskin/Immunities) This static amount would give a strong case to explain this.

I have attempted to plug in the results into another brute force Java program (with a cap of 4.2 on ratio cap), but with less success:
Cap:1.8 Attack:254
 Cap:1.9 Attack:268
 Cap:2.0 Attack:282
 Cap:2.1 Attack:297
 Cap:2.2 Attack:311
 Cap:2.3 Attack:325
 Cap:2.3 Attack:326
 Cap:3.9 Attack:555
 Cap:3.9 Attack:556
Cap:4.0 Attack:566
 Cap:4.0 Attack:567
 Cap:4.0 Attack:568
 Cap:4.1 Attack:581
 Cap:4.1 Attack:582
 Cap:4.1 Attack:583
 Cap:4.2 Attack:595
 Cap:4.2 Attack:596
 Cap:4.2 Attack:597
Total: 87

It's worth noting Crimson Howl has had little impact (actually none) on the spread of damage, as I've outlined below:
Level of BeeEnhancementMinDMGMaxDMG
Ifrit35Crimson Howl (23/256)182193
Ifrit36Crimson Howl (23/256)184*193
Ifrit37Crimson Howl (23/256) + Pet:Attack+5176193
* = Presumed failure, stopped testing before I could show this to be uncapped.
All purple results are uncapped.

Plugging all these values into the program yields no results, so either Crimson Howl calculations are wrong, I'm missing a value of attack decreasing (e.g. dSTR playing a role in attack), or Lv34 Bee with nothing on is uncapped. Good thing to note is that Ifrit follows Garuda's lead, suggesting they have the same attack value.

So I went and tossed another merit into Avatar Physical Attack (+2) and redid the Lv35 test with Pet:Atk+5:
Ifrit vs Lv35 Bee with +7Atk Spread: 183-193.

I then took away both merits (-2 offset) and repeated on Lv34 Bee which was previously capped:
Spread: 184-193

This indicates that Attack for avatars must be pretty high. Accounting for this quartered my program output:

 Cap:3.3 Attack:468
 Cap:3.4 Attack:482
 Cap:3.5 Attack:496
 Cap:3.6 Attack:510
 Cap:3.6 Attack:511
 Cap:3.7 Attack:524
 Cap:3.7 Attack:525
 Cap:3.8 Attack:538
 Cap:3.8 Attack:539
 Cap:3.8 Attack:540
 Cap:3.9 Attack:552
 Cap:3.9 Attack:553
 Cap:3.9 Attack:554
 Cap:4.0 Attack:566
 Cap:4.0 Attack:567
 Cap:4.0 Attack:568
 Cap:4.1 Attack:581
 Cap:4.1 Attack:582
 Cap:4.1 Attack:583
 Cap:4.2 Attack:595
 Cap:4.2 Attack:596
 Cap:4.2 Attack:597
Total: 22

Getting pretty high then. However, you then expect Crimson Howl to have had a notable effect, but this was not the case. Perhaps Crimson Howl doesn't work for melee hits, or is calculated differently for Ifrit? Perhaps there's a cap on the amount of bonus attack?

The implications of these 13 results are startling. Avatars have a ton of attack. But that's not all. This puts into perspective several augments. Pet:Attack+5 only adds ~1% to your attack, a hardly worthy amount. Furthermore, Attack+15 is just 3%. Do not this excludes 'Enhances Avatar Attack' gear, since this only works on Blood Pacts and needs more testing to quantify. Also, this means that you needn't worry about capping attack on harder level monsters, with caps of 3+, you'd need 999+ attack (most likely not possible due to caps on attack value?) to cap on any monster with over 333 DEF. This also means the merits in Avatar Physical Attack are completely and utterly worthless. With 5 merits you'd have Attack+10, equivalent to 2% increase in attack. This also means that DEF is very important for ratio. Consider:

Ratio = 2.5
Decrease DEF by just 10:
Ratio = 2.631
An increase of about 0.13, which would alter PDIF by at least that much, probably more.

Increase ATK by 10:
Ratio = 2.55
An increase of about 0.05.

What I'm trying to say is:

If you wish to increase your damage with avatars, it's far better to lower the monster's defence than it is to raise your avatar's attack.

Dia ftw?

How does Ratio feed PDIF?

I'm starting to think that perhaps Ratio is used more directly in PDIF than it is for PCs, as in, perhaps Ratio is used by itself followed with a static addition/subtraction to form PDIF_min and PDIF_max? The cap on Ratio is getting so high, it can actually meet 4.0 and 4.2 after all. My theory is as follows:

PDIF_max = Cap@4.2[Ratio + SOME_CONSTANT]

This would account for why you can still hit max numbers even if Ratio is uncapped. This would also account for why critical hits do the same damage as normal hits (for PCs, 1.0 is added to Ratio to form a critical hit. For avatars, this would be negated by the cap!) An alternative form would be:

PDIF_max = 4.2Cap[ SomeCap[Ratio] + CONSTANT]

This seems needlessly complicated though, so I suggest the former. After all, PC PDIF max is calculated (in laymens terms, prior to the 5% static randomiser):

PDIF_max = 1.2 * Cap@2.0[Ratio]

Since the Ratio cap is getting so high now, it's made me doubt there is a multiplier being applied to Ratio. Instead I think there is a static addition, which would explain why Avatars do well on high level monsters, since the poor Ratio value isn't being enhanced further by multiplying. As for 'Is there a cRatio'? I don't know. I haven't seen any evidence to prove there is, so I will have to tackle that at some point. To work out what this constant might be, I will have to fight tougher monsters, until the Max PDIF cap is no longer applied. Once I know this, I can look at the difference between when the min PDIF cap was violated and when the max pdif cap was violated, and hopefully obtain some difference which can be equated using Ratio. PDIF_min clearly does not get an addition when Ratio drops below cap, but it might get a subtraction in order to get the 4.0 cap:

PDIF_min = Cap@4.0[ Ratio - CONSTANT]

If this were true, Ratio would have to cap higher than 4.0, perhaps 4.2? The PDIF min for PCs is:

PDIF_min = 1.2 x cRatio - 0.8

In other words, identical to max but with a constant taken away. We know there must be some addition for PDIF_max (not multiplication, else max potential would still drop in relation to Ratio, see PC Max PDIF) due to avatars still hitting the upper cap when Ratio isn't capped, which is then capped at 4.2, but what could it be? The generic model to fill is:


Multiplier may be 1, Constant may be 0. PDIF_max *must* have a constant added to it.

But before we do that, it's reasonable to ask 'But Kegs, what's to say attack affects melee hits at all? In all of your tests, you've failed to shift ratio back up to the cap! Will adding attack really boost melee hits?' So I did a test on COR/SMN on Lv34 Death Jackets. The results? Yes, it works:

Ifrit [COR/SMN] - No Attack Bonuses.
Lv34 - frac/alky/ethereal

Ifrit [COR/SMN] - Lucky IV Beast Roll.
Lv34 - frac/alky/ethereal

A modest improvement. However, does this mean Pet:Attack+ gear have an effect? Let's see:

Ifrit [COR/SMN] - Pet:Attack+5.
Lv34 - frac/alky/ethereal
(more critical hits due to larger sample, as I wanted to be sure on this.)

By the looks of it, yes, Pet:Attack+ gear does indeed work on normal melee hits. As expected, the amount it works is laughable, but hey, least it confirms that gear can increase PDIF.

Went and tested Ifrit on higher level monsters in Gustav Tunnel. Finally, the upper PDIF cap has been violated:

Hawkers in Gustav Tunnel
@210 - lowdef
@209 - notlowdef
157-189 (c189)
Max PDIF capped on this monster.

@214 = low def
@213 = not low def
156-189 (180-189c)
Max PDIF capped on this monster.

@217 = lowdef
@216 = notlowdef
Ifrit: CAP @ 184.8
149-184 (177-181c)
Max PDIF capped on this monster.

@221 = lowdef
@220 = notlowdef
Ifrit: CAP @ 184.8
146-184 (177-184c)
Max PDIF capped on this monster.

Labyrinth Lizard in Gustav Tunnel
@224 - lowdef
@223 - notlowdef
Ifrit: CAP @ 189
146-186 (180-189c)
This one was tested to death with samples to ensure accuracy.

So the magic number before the cap no longer applies for PDIF_max is 179DEF and for PDIF_min is 144DEF. I'll write more on this in the morning! Do note that there may be +-2DEF in accuracy here, since I can't exactly tweak the monster's defence and re-test. This is pretty accurate though, with no more than 2DEF out.

Hilltroll Paladins:

Lv83=450DEF, 109VIT (Incr.Tough), Ifrit D=~28

It's also worth a note that PDIF max still remains above 1 for the massive 450 DEF value of Hilltroll Paladins. I highly doubt PDIF max will be allowed to drop below 1. However, this does seem to confirm the massive attack value of avatars. Another note are the critical hits, which actually are overlapping (or may not be, e.g. 32.1 and 32.9). Either way, this will be important in determining the value a critical hit adds to PDIF, so all in all, good testing. How did I kill the troll you ask? SMN/NIN! Ohoho.

I've come a long way since first starting this mammoth testing of PDIF, but the end is nearly in sight. An attack value for celestial avatars will soon be ready. In the mean time, here's the  graph with all known values plotted:

Various monsters tested: (continually updated)
All in respect to the blue line (PDIF_min):
-Hawkers (4 points at PDIF=3.5)
-Lesser Colibri (The 3 points at PDIF=2)
-Colibri (The 3 points at PDIF=~1.2)
-Flamingo (The 3 points at PDIF=1)
-Greater Colibri (needs re-testing; PDIF=~0.75)
-Hilltroll Paladin (PDIF=~0.4)

PDIF values were calculated using my Avatar Damage calculation to find D+fSTR, then simply doing MinDMG/(D+fSTR) and MaxDMG/(D+fSTR). Note that when a critical hit occurs, PDIF is increased by 1.0 just like for players. Also note that at very high DEF levels (read: last row), this rule is broken by more than what can be associated to by lack of sample size. This most likely is due to the constant which is added/subtracted from PDIF min. Do note that 1.14-0.43 = 0.71, very close to that common recurring constant, 0.75.

This graph looks very similar to how PDIF scales for Players. Allow me to quickly show you the Player calculations roughly, specifically the minimum values:

0 <= cRatio <= 1.25
fMin(cRatio) = 1.2 * cRatio - 0.5. If Result is less than 0, cap at 0.

1.25 <= cRatio <= 1.5
fMin(cRatio) = 1

1.5 <= cRatio <= 2
fMin(cRatio) = 1.2 * cRatio -0.8

This appears to be highly related since very clearly you can see that PDIF min hits 1.0 and stays there for a certain amount of DEF before swapping to another equation. Therefore I can conclude that just like Players, Avatars have 3 equations for PDIF which vary based on Ratio. As for just where the boundaries are for these equations, I have to still work out. However, if it's anything like Players, it should only be a few DEF higher.

A major problem which I can see with the graph is the painfully straight line from when PDIF_min is uncapped to when it reaches PDIF min=1, if the formula really involves Ratio (Attack / Defence) then it should be a curve (500/1=500, 500/2=250, 500/3=166 etc...) but this is not the case. The only other way I can think of therefore is that instead of there being a 'Ratio', there's actually a dAttack (Attack - Defence) instead. At least, at lower levels (sub ~280DEF). Tested this on Lesser Colibri (Adding 5 attack should be the same as subtracting 5 DEF) and the results were the same as the baseline test. Myth busted.

Estimations for PDIF

Did a test with extremely low levels of Ratio (Lv37 Ifrit VS Lesser Colibri), my model predicts D=13, though I highly suspect D=15:

L65 - DEF241, D=~13

If D=15:

As you can see, D=13 doesn't quite match up with Crit=1.0 bonus, but put in D=15 and it matches perfectly, so I suspect the discrepancy is model error. This appears to hold true on higher level monsters as well, indicating there's a hardcap of 0.333 and 1 when Ratio is extremely low.

Final Graph:

If for whatever reason this graph picture goes down, the formulas on it are:
DEF = 0~140 ---> pdif_min=4 ||| pdif_max=4.2
DEF = 141~280 ---> pdif_min=-0.022*DEF+7.116 ||| pdif_max=-0.0184*DEF+7.115
DEF = 280~315 ---> pdif_min=1 ||| pdif_max=~1.8
DEF = 316~500 ---> pdif_min=-0.0027*DEF+1.645 ||| pdif_max=-0.0018*DEF+1.95
DEF = 500+ ---> pdif_min=0.333 ||| pdif_max=1

Avatar PDIF Formula

Created a working model based on these results+graph. Celestial avatars have 504 attack.

0 <= Ratio <= 1 then:
PDIF max = 1
PDIF min = 0.333

1 < Ratio < 1.6 then:
PDIF max = Ratio*4/6 + 2/6
PDIF min = Ratio*7/9 - 4/9

1.6 <= Ratio <= 1.8 then:
PDIF max =
PDIF min = 1

1.8 < Ratio < 3.6 then:
PDIF max = 2.4 * Ratio - 2.52
PDIF min = 5/3 * Ratio - 2

Ratio > 3.6 then:
PDIF max = 4.2
PDIF min = 4

- There is a hard cap of 4.2 for PDIF. This cannot ever be exceeded.
- Critical hits add 1.0 to PDIF, but they cannot break the hard cap.

Summary on PDIF - What you should know

Fenrir has the most attack.
Carbuncle (!) is next.
Celestial avatars have the least attack.
You wouldn't think this though, since Carbuncle has a much lower D value.

Celestial Avatars have more than 468 attack. Working model suggest 504 attack. No ratio cap on Avatars has been discovered.

From the graph outlined above, several things should become obvious:
1. Attack+ gear has a varying effect on the damage potential of your avatar, sometimes it'll shift PDIF up more, other times not.
2. The weaker the monster, the more attack boosts PDIF, and the more damage you'll do per unit Attack.
3. The stronger the monster, the less attack boosts PDIF, and the less damage you'll do per unit Attack.
4. There are 2 sets of caps:
PDIF max must be between 1 and 4.2.
PDIF min must be between 0.333 and 4.
5. Because of #3, Attack (precisely Pet:Attack+) on anything of HNM-level is useless. Enhances Avatar Attack has yet to be re-examined since it only applies to blood pacts.

Side note: Previous tests on Enhances Avatar Attack came to the same conclusion (Attack improves PDIF at varying amount for different DEF values) hinting that Blood Pacts do indeed follow these calculations.

Final Few Questions

- How does Attack scale with level?
- How do Blood Pacts fit in with this?
- How much Attack do Carbuncle and Fenrir have?
- How much of an Attack penalty does Avatar's Favor give? Is this straight Attack- or a penalty directly to PDIF?

Fenrir Attack
Simply reverse engineered my own formula, using data from Lesser Colibri parses right at the start:
DEF231 Colibri says: 566~584 attack
DEF235 Colibri says: 566~577 attack
Therefore, I estimate that Fenrir has around 570 attack.


Fenrir + Celestial Avatar base damage = (AVATAR LEVEL x 0.74) - (Monster VIT/4)

Carbuncle base damage = (AVATAR LEVEL x 2/3) - (Monster VIT/4)

Celestial Avatars have 504 attack at Level 75. Carbuncle has more. Fenrir even more.

0 <= Ratio <= 1 then:
PDIF max = 1
PDIF min = 0.333

1 < Ratio < 1.6 then:
PDIF max = Ratio*4/6 + 2/6
PDIF min = Ratio*7/9 - 4/9

1.6 <= Ratio <= 1.8 then:
PDIF max =
PDIF min = 1

1.8 < Ratio < 3.6 then:
PDIF max = 2.4 * Ratio - 2.52
PDIF min = 5/3 * Ratio - 2

Ratio > 3.6 then:
PDIF max = 4.2
PDIF min = 4

- There is a hard cap of 4.2 for PDIF. This cannot ever be exceeded.
- Critical hits add 1.0 to PDIF, but they cannot break the hard cap.

Blood Pacts follow these PDIF calculations as well, but the M values may change from section to section, more testing is needed to define how it changes.
All M values should work for 1.8<Ratio<3.6 section.

Enhances Avatar Attack gear does NOT work on melee hits!
Tags: maths!, smn!, testing!
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