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
*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
Barracuda Dive --- M=3.5
Tail Whip --- M=5
Spinning Dive --- M=12
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
Punch --- M=3.5
Burning Strike = Unknown (part magical)
Double Punch = Testing in progress.
Flaming Strike = Unknown (part magical)
Claw --- M=3.5
Predator Claws = M=10?, subsequent hits M=2.
Shock Strike --- M=3.5
Chaotic Strike = M=9?, subsequent hits M=2.
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.
Camisado = ?
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
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)
Barracuda Dive (SPREAD:334-488, CRIT:596)
EDIT: Apologies, critical hits were marked incorrectly.
Physical Hits (SPREAD:212-226)
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.
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 %
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)
Lesser Colibri L64 (SPREAD:1096-1303)
Lesser Colibri L65 (SPREAD:1003-1237)
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)
591c <- see anomaly section
Punch (With Boots)
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)
Mountain Buster (With Boots)
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)
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:
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
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:
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.
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.
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.
fSTR caps are -1 and 8 for avatars. This means that mob VIT doesn't affect Blood Pact damage very much.
"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.
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