All Physical Blood Pact FormulaeFollow

I said quite a while ago that I would be working on Physical Blood Pacts, here are the results of my work.

Summary
How are physical blood pacts calculated? Why does for example, Barracuda Dive do in the hundreds and Spinning Dive in the thousands on the same monster? After all, PDIF and fSTR are the same right? What other factors are at play? What makes (particularly Lv70 BPs) just so damn reliable? The answer to this question is as follows:

Physical BP Damage = (D+fSTR)xMxPDIF

where:-
*M is a multiplier which varies on each BP.
*fSTR is as normal for melee damage.
-Like Bare Fisted Hand-to-Hand Skill, the avatar has no Weapon Rank. This means fSTR caps are -1 to 8.
*PDIF is as normal for melee damage.
*D is the avatars "base damage", which thusfar has no formula figured out, estimates put it at D47~49 @ Lv75, though it is unclear how this is worked out, it may involve Avatar Level. See "Value of D and Avatar Attack" for more information.


Blood Pacts in italics may need further sample sets which may shift the multiplier +-0.5, so treat those as tentative results.

**Some of Titan's BPs (the ranged ones) appear to deal consistent damage on monsters, the formula for this is different to the one listed below.

Physical BP Damage = (D+fSTR)xMxPDIF

Leviathan
Barracuda Dive --- M=3.5
Tail Whip --- M=5
Spinning Dive --- M=12

Titan
Rock Throw --- Does not follow normal rules. Further testing needed.**
Rock Buster --- M=4
Megalith Throw --- Does not follow normal rules. Further testing needed.**
Mountain Buster --- M=12

Ifrit
Punch --- M=3.5
Burning Strike = Unknown (part magical)
Double Punch = Testing in progress.
Flaming Strike = Unknown (part magical)

Garuda
Claw --- M=3.5
Predator Claws = M=10?, subsequent hits M=2.

Ramuh
Shock Strike --- M=3.5
Chaotic Strike = M=9?, subsequent hits M=2.

Shiva
Axe Kick --- M=3.5
Double Slap = M=6, subsequent hit M=2.
Rush = M=5, subsequent hits M=2?

Fenrir - Seems to have higher D than the others (+7?)
Moonlit Charge --- M=1.5
Crescent Fang --- M=2
Eclipse Bite = Testing in progress.

Diabolos
Camisado = ?

Carbuncle
Poison Nails = ?

d+fSTR was calculated to be approximately 57 vs Lv0 Monsters. UPDATE: See the "value of d and avatar attack" section below.

Multi-hit Testing - Preliminary Results
By the looks of things, the multiplier M is set to a lower number for all subsequent hits on multi-hit blood pacts, which might explain why Rush damage is just so poor and why Predator Claws can do 1500 one time then 350 all too often (because the first crucial hit missed). Methodical testing is taking a long time on multi-hits because you need to account for any criticals on any one of the hits, which is very hard.

It would appear that Shiva's "Rush" does NOT allow for "overkill", so you will always score ~550 on Lv0 monsters whereas Garuda's "Predator Claws" and Ramuh's "Chaotic Strike" DO allow for overkill and do thousands (I've seen ranges of 1300-2300) of damage on Lv0 monsters. This was later confirmed on tougher monsters. Source: http://img.photobucket.com/albums/v156/kegsay/img_20091006_230810.png

Methodology
I suspected that Physical BPs would reflect other known physical formulas such as physical damage or weapon skill damage, but I didn't know which. On the one hand, the formula could be based on (DMG+fSTR)*PDIF like it is for Physical hits, or (DMG+fSTR+WSC)*PDIF, or even as it is for blue magic, (DMG+fSTR+WSC)*multiplier. It would be hard to test a lot of these, as we cannot alter an avatars attributes (STR DEX etc). Knowing that we cannot alter D (the base DMG weapon rating of our avatar) or WSC (the attribute +xx% bonuses), I could group the two together into another constant, in this case "d" (though I tend to use D and d interchangeably).

This accounted for one thing, but it does nothing to explain why Barracuda Dive for example does ~300 damage and Spinning Dive does 1000+. Why? With all the research done in other aspects of FFXI, WSC never goes above 100% for a stat, and I had no reason to think it would for BPs. This would indicate a multiplier is in effect, like it is for blue magic. This formed my equation (d+fSTR)xMxPDIF.

To test what each value was, I needed to eliminate more variables. I chose to fight Lv0 monsters in order to cap fSTR so it was constant. Since D was also constant, this would just leave M and PDIF. I could calculate PDIF by finding the min and max values for the blood pacts, and using 1.6 and 2.4 as the PDIF as is known for physical weapon skills (yes this has changed for PCs, but the change is minor (x1~1.05) and there is no reason to think that SE would have changed pet damage calculations when they changed PC ones). I ignored BPs which dealt critical damage (though used them as verification for my equations knowing they have 3.0 PDIF) and obtained the following data:

Spinning Dive (SPREAD:1195-1577)
1296
1336
1519
1379
1577
1195
1964c
1404
1500
1337
1955c
1805c
1935c
1360
1326
1367


Barracuda Dive (SPREAD:334-488, CRIT:596)
352
446
444
388
368
375
596c
437
356
430
425
379
334
433
386
488
370
364
472
596c
343
381
421
EDIT: Apologies, critical hits were marked incorrectly.

Physical Hits (SPREAD:212-226)
220,224,216c,220c,218c,218,216,216,221,218,215,226
217,221,222,218,217,218,218,213,215,220,220,221,222
212,217,216,220,225c,226,215,216,217,217c,212,221,218c
220,221,212,216,219,224,223,217,222,219,223,213,220
222,217c,218,225,220,213
Note: Pets have a damage cap at PDIF = 4.0, Source: BG

Using this data I obtained an average for Spinning Dive/Barracuda Dive for BASE where BASExPDIF=Total DMG and BASE = (d+fSTR)xM. In order to obtain d+fSTR (which is the constant for all 3 tests), I used physical hits (since max damage dealt would be the 4.0 multiplier, the damage cap). I then applied this d+fSTR to the Blood Pacts in order to find M. This obtained the formulas listed above.

Verification
This is all good and well, but how could I be sure "yup this is it"? I looked back on my parse data on Lesser Colibri which I was testing normal melee damage dealt by Leviathan over several hours for the purpose of obtaining the min/max damage dealt. I chose Lesser Colibri because they are plentiful, easy to get to, and their "vital" stats (VIT DEF and Lvl) are known, so there are no unknown variables to do with the monster, only the avatar. But alas, without knowledge of Avatar STR or Base Damage, how would I work out if the formula was correct? Thankfully, the formula for BP damage is remarkably similar to that of normal melee hits, in fact, only the multiplier is different. Knowing this, I simply took my min/max melee values, x12 and obtained theoretical min/max BP damage for Spinning Dive. This was as follows:

 
Lesser Colibri L63 
Leviathan             19033  100.00 %      176/9   95.14 %    87/120   104.64     14   135/163  148.64    7.95 % 
 
Lesser Colibri L64 
Leviathan             18874  100.00 %      181/9   95.26 %    82/117   100.40     16   127/160  144.25    8.84 % 
 
Lesser Colibri L65 
Leviathan             36257  100.00 %     372/18   95.38 %    75/112    93.55     35   119/153  135.20    9.41 % 

---x12---
Note: Min/Max Crit may be unreliable as there weren't many critical hits, non-crits are more accurate.

Lesser Colibri L63
Spinning Dive MIN/MAX = 1044-1440
Spinning Dive MIN/MAX crit = 1620-1956

Lesser Colibri L64
Spinning Dive MIN/MAX = 984-1404
Spinning Dive MIN/MAX crit = 1524-1920

Lesser Colibri L65
Spinning Dive MIN/MAX = 900-1344
Spinning Dive MIN/MAX crit = 1428-1836

Which was then tested.....

Lesser Colibri L63 (SPREAD:1139-1215)
1215,1126,1195,1139
Lesser Colibri L64 (SPREAD:1096-1303)
1131,1277,1127,1114,1277,1095,1735c,1202,1096,1303,1712c,1166
Lesser Colibri L65 (SPREAD:1003-1237)
1021,1052,1237,1161,1226,1209,1551c,1003,1048,1224,1101,1051

which confirms the x12 Multiplier for Spinning Dive.

This was repeated for all of the M values without italics.

Note on anomalies
There have been a number of minor anomalies whereby the range has been overshot (usually by about 1-2% damage). The reason for this still remains unclear, though I suspect it is because the values for PDIF aren't quite fully known (wikipage on PDIF is out of date), especially for avatars (which can go to a 4.0 PDIF hardcap).

Enhances avatar Attack gear
What does "enhances avatar attack" do exactly for physical blood pacts? It has already been determined that it does nothing for melee hits, so what about BP? It will do one of two things:
A- Enhance M
B- Add Attack to the PDIF Calculation
If A, by how much does it increase M? Proportional or Static?
If B, how much extra Attk is added? Will it allow PDIF to exceed the soft caps of 2.4 for non-crit and 3.0 for crit? Tests below:

Punch (No Boots)
3.5x Multiplier
RANGE:313-470 (Calculated)
CRIT:509-588 (Calculated)

Test Min/Max:344-465

|344
|351,353,364,389,396,397
|402,402,404,405,414,427,435,445,445
|452,453,465
|525c,532c,537c,538c,547c,567c,576c

591c <- see anomaly section

Punch (With Boots)
3.5x Multiplier
RANGE:313-470 (Calculated)
CRIT:509-588 (Calculated)

Test Min/Max:330-469

|330,338,339,339,348,350
|352,353,355,364,380,388,389,391,392,393
|409,417,425
|451,452,469
|517c,525c,539c,543c,547c,

597c

Clearly there is little if any difference here. Certainly not very noticeable. There may very well be a difference between the two results, but with the modest 30 trials each, it's unclear. Furthermore, with AF2 Boots did result in a highest maximum (597 vs 591), but as there already are known outliers without including the AF2 boots, no conclusions can be drawn here. In order to see differences clearly, I needed to get bigger numbers. This brings in Test#2...

Mountain Buster (No Boots)
12x Multiplier
RANGE:1075-1612
CRIT:1747-2016

Test Min/Max:1174-1569
|1174,1186
|1203,1221,1227,1251,1298,1299
|1307,1315,1336,1386,1389
|1481
|1526,1532,1569

1841c,1966c,2008c

Mountain Buster (With Boots)
12x Multiplier
RANGE:1075-1612
CRIT:1747-2016

Test Min/Max:1265-1566
|
|1265
|1325,1328,1358,1366,1383,1390,1393
|1426,1450,1467,1473
|1530,1530,1536,1540,1566

1877c,1881c
2041c <- anomaly


Looking at these results, it still looks around the same, though one can't help but notice the shift in numbers towards the upper end for the test with boots. I can say with some certainty that "Enhances Avatar Attack" does not alter the M value (else there would be a new maximum value), and merely adds attack to the PDIF calculation. How much attack does it add to the PDIF calculation? Looking at the results, it would appear that there is something going on behind the scenes, but what exactly? More research will be needed to find out. There is ~100 damage between the min damage test without boots and test with boots.

Damage Graphs in relation to PDIF

Best Case Scenario (All hits land for every BP, PDIF is the same for every hit)
http://img.photobucket.com/albums/v156/kegsay/ComparingBPs-1.jpg
Blue=Predator Claws
Yellow=Rush/Chaotic Strike
Orange=Spinning Dive
EDIT:Corrected an error with the graph. This shows one interesting thing: Rush isn't actually useless. Well it is, but if all hits landed with the same PDIF, it would surpass that of Spinning Dive. I suspect because Rush has five hits, it lets it down significantly, so it never really puts out the damage this graph suggests. Do bear in mind this says that PDIF is the same for ALL hits, which is not what would happen ingame. This also excludes misses.

Value of D and Avatar Attack
Using the melee ranges for Lesser Colibri above, I created a program to run through my estimated ranges (D=40~60, Attack=400~500) and obtained the following data:

Lesser Colibri Leviathan Melee Hit Range (Colibri referred to by their DEF rating)

Mob#241 = 75/112
Mob#235 = 82/117
Mob#231 = 87/121

Calculation for Damage:

Minimum
((ATK/DEF)*1.2-0.8)*DMG
Maximum
((ATK/DEF)*1.2)*DMG

Note: There was a +-2DMG allowance to account for PDIF variations with my formula and if I have potentially missed the hardcap by 1
Matches for Mob#241:

 
Attack    D+fSTR Value 
 472          48 
 477          47 
454~457       50 
460~467       49

Matches for Mob#231:
None. (Suspected I have not hit the hard caps!)

Matches for Mob#235:

 
Attack    D+fSTR Value 
 484          48 
491~495       47 
 498          46

Observations
Avatars have 460~485 attack.
Avatars D+fSTR Value for Colibri appears to be 47-49.





Damage Chart against five fictional Monsters
This is the fruition of my research into Physical Blood Pacts, the Blood Pact chart VS different fictional monsters of varying strengths:

http://img.photobucket.com/albums/v156/kegsay/BPDMG.jpg

Notice how Rush and Chaotic Strike are actually the same in terms of damage. Just a shame in order for Rush to perform, it needs to land -all 5 hits-, versus 3 for Chaotic.

















tl;dr version

#1
Physical Blood Pact damage = (normal melee hit) x M
M is a multiplier, which is listed for each BP in the list at the top of the page.

#2
The base value of "D" which is base damage still remains murky for avatars, but it has been calculated at 47~49DMG for celestial avatars at Lv75. Fenrir seems to have higher than this, which also explains why Fenrir tends to deal harder hits than the celestials.

#3
fSTR caps are -1 and 8 for avatars. This means that mob VIT doesn't affect Blood Pact damage very much.

#4
"Enhances Avatar Attack" gear does not alter M in any way, it merely adds attacks to the PDIF calculation. It does not allow avatars to break the 2.4 and 3.0 soft-cap for PDIF. How much Attack is added is still under investigation.

#5
Avatars have 460~485 attack at level 75 and they have no level correction factor when calculating PDIF (which is why they rock on Wyrms).

Edited, Oct 8th 2009 7:21pm by kegsay

Updated OP with information on Multi-Hit BPs (updated subsequent hits value M) and the peculiarities with Rush.

Whoever thought allowing one multi-hit BP (but not the rest) to not overkill was silly. You would think SE would stick to all or nothing, but I guess not.

Ah yes! I do recall this as well Pergatory. I have been so used to playing with the sound off that I almost forgot. I'll definitely look into that more, firstly by finding out how many different sounds are in the .dats to see just how much information I can glean from that. Many thanks for mentioning it.

Sorry I'm not a SMN but if both Titan and Leviathan's lvl 70 BPs have an M12 why do SMN stick to Spinning Dive on mobs that don't have any specific damage type affinity i.e piercing/blunt?

Leviathan has Spring Water as well, which has a few more uses than Earthen Ward, and Leviathan looks damn cool when he's fighting.

Haven't had time to read it yet, but I find my ranged attacks to be pretty consistent on COR so most likely ranged attacks on Titan is simply treated as ranged attacks in the formula. I.e. terrible crit effects, but decent consistency.

It also brings up the question if 2004 Titan wouldn't actually have had no level correction on ranged attacks (though who would want a SMN using 1 ranged attack a minute on Kirin and such when you could have a RNG doing 10 per minute)

Added graphs, tested values for D and Attack, obtained tentative values.

It should be noted that it will be nearly impossible to ever obtain a precise value for D and Attack, and even Accuracy as there is just no way to A:Test it and B:Increase/Decrease core attributes related to it. Estimates only I'm afraid, but hey, they're accurate.

Unfortunately no, because Fenrir does not appear to have the same stats as the other celestial avatars. Yes, you could obtain some attributes for Fenrir using Ecliptic Growl, but you couldn't then generalise it to the Celestials. Ifrit has an attack bonus, and if you wanted to be even more precise, there are Augments with Pet:Attack+X on them, but you would need small increments (e.g. having Attk+1,2,3,4,5,6,7,8,9,10), test all of those with an incredibly large sample size (Attack+ such a small number would only raise by PDIF by the smallest amount, you're looking at +0.005% on anything EM+, possibly +0.05% on Lesser Colibri, but still it's too small. Accuracy would be near impossible as well without some rigorous testing, again with a range of Accuracy (preferably enough to match EVA of the mob, which would have 75.0% hit rate). I believe SMN does not have enough augmentable equipment which can meet these strict requirements to obtain to-the-digit attack/accuracy or D.

That's assuming that there are different audio files for each combination of hits and misses. It could be that there are only two simple sound effects for a hit and a miss - and the reason we're hearing variations of the hit sound effect is because the same .dat file is being played over itself multiple times.
Also, the sounds aren't especially reliable - I've noticed that sometimes when I use Predator Claws, the attack will make one long "woosh" sound as though the attack completely missed - and yet the attack deals max damage. Go figure.

Found the files. There are only 2, hit and miss noises. Found them using POLUtils and trial and error.

Located in:

FINAL FANTASY XI/sound/win/se/se032/

Files:
se032071 = Rush Miss
se032072 = Rush Hit
se032124 = Predator Claws Miss
se032125 = Predator Claws Hit

Link to sounds in .wav format (1.65MB):
http://www.filefront.com/14689057/Avatar_se.rar

Best of luck to further testing fellow Summoners!

EDIT: To offer further input, I believe you will hear the "hit" noise if the first hit lands and you will hear the "miss" noise if it doesn't land. If you could make an attempt to keep an eye out for that, it would be appreciated. It can easily be distinguished because Predator Claws will do 300 ish instead of 1000+. Rush will still do a good chunk of damage on its "miss" noise though, I suspect to see values around 600, instead of 1000+

Edited, Oct 9th 2009 4:04pm by kegsay

Yea, no joke. Incredibly informative. 4 years ago, I had merited my avatar attack, and tested it after each upgrade with Carbuncle's melée attacks on TW-- sheep in Konschtat Highlands at 75. Your post explains why there was no damage increase. I never used Blood Pacts.

I am not enough of a professional to sit and figure out hard facts and formulas and such, and I commend you for such extensive work.

I based my own judgement of +attack mechanics when I was leveling BRD. I played both minuets and occasionally some random hit with the dagger may have gone up a maximum of 8-10 points or so. And even then, damage was incredibly random with the low minimum hit having been nearly the same. Since then I had just assumed +attack to be the same minimal increase with everything.

Incredibly presumptuous, I would understand a BRD's effect of minuet on an entire group of melée fighters, but +attack merits on an avatar with such potential random damage was not something I did. I deleted them and allocated them onto elemental perpetuation instead. For the last few months, I have been thinking of going back to avatar magic attack merits, or avatar magic accuracy.

This is another reason I was never a firm believer of +attack, whether character or pet. Once again, incredibly presumptuous to think that way, but until I can physically see the difference, it is something I will never buff. That is also why I chose pet: double attack/crit over pet: +15attack/ranged attack for my BST and PUP.

*Edit: I forget to add Sacrifice Torque. I use it for the hell of it. I suppose Sacrifice Torque, boots, merits, and augments put together may make a significant damage boost.

This post simply helps confirm my presumtuous beliefs even more. Really awesome work on all that research and information.

Edited, Oct 10th 2009 1:58pm by FinalPlay

Which is bringing me on neatly onto my new thread which I will post once I obtain 10 more bits of test data. Basically, "Enhances Avatar Attack" gear is =crap=. Too small to notice.

Was just browsing the COR forum and saw a link to roll info.

Kind of interesting to see that BST roll without a BST is like crimson howl unless lucky or 7 up. Considering that crimson howl never has made visible damage increase for me (though your new testing might show it SHOULD) it seems like COR shouldn't boost BPs by much either.

That would btw be kind of interesting info to your post.

No attack boost values
8% boost (crimson/no BST bonus roll)
16% boost (BST bonus roll)
24% boost (crimson + BST bonus roll)

Drachen roll might not be needed to include since it is magic.