Wyvern Breath Testing

[Ophannus]

So back in 2005 I attempted to find the formula for calculating Elemental Breaths because loldrg and there was no previous testing done at that time. The value I derived back then was Floor(Current HP * 0.182) which equated to a 180 breath at 991 HP. With Wyrm Armet, I'd have a 210 damage breath so the modified formula for breath became floor(Current HP * 0.212) which added up again nicely to the expected damage.

Fast forward to a few weeks ago with the addition of AF2+2 augments. Messing around on the test server, the formula above did not coincide with the actual damage observed, the observed value was far lower than the expected damage. Noting Yugl's tests finding that BLU Breaths are not decimals but Fractions I feel like Wyvern Breaths are fraction based as well but the fraction for 0.182 is something like 91/500 which seems too far out there. My second hypothesis is that the original formula is lacking and is probably a bit more complex than I thought. Back then I thought it was simply a percentage of the Current HP but it may in fact be a more complicated formula something along the lines of:

floor(Current Wyvern HP * [Insert Decimal] + level or some kind of integer)/x
Or something along those lines.

Any mathologists have any insight?

[Byrthnoth]

1) Is elemental breath affected by Wyvern TP?
2) What data values do you have?
3) Can you just modify your level and keep Wyvern HP constant? For instance, drop 5 levels and put Wyvern HP+50 on.

[Yugl]

1) Yes (You can clear this by using healing breath)
3) Doubt it

I gave him the fraction 181/990 to try out, so we'll see how that works.

The testing for BLU Thunder Breath was just to find the correct value since the existing value was incorrect. You can get a fractional value of 0.625 using 27/40.

[Motenten]

For 180 damage on 991 HP, it would be 186/1024 or 187/1024. For 210 damage on 991 HP it would be 217/1024 or 218/1024. The addition of the armet could be +30 (from 187 to 217) or +32 (from 186 to 218), but probably not +31 (either of the other two options).

Find any three items that will modify the wyvern's HP and provide the damage values generated with them equipped. That should be able to validate the numbers as either being solely from HP (and thus exactly what the ratio is), or not being solely from HP. If it's not solely from HP, it should be possible to estimate the offset to see if it's related to level.

[Ophannus]

Luckily Wyvern TP only affects m.acc for Elemental Breath and not potency/damage.

[Yugl]

Unorganized post since I'm testing as I write this post.

Did a few tests on Buffalos at Abyssea Uleg (No Cruor or Atmas used)
- Wyvern HP is exactly 1351 HP at level 99 (Tested using Tarsel Slam)
- Frost Breath yielded 1 and 15 DMG when used at 1HP
- Frost Breath yielded 60 and 240 DMG when used at 1351HP (Later confirmed max damage using a Goblin at Battalia; Flame breath for 240DMG)

The 15 DMG has to be full damage at 1HP. The reason for this is because a minimum 1/2 resist would require 30DMG to yield 15DMG. However, even a 1/8 resist would not be enough to yield 1DMG if 30DMG were the max. It is unlikely that SDT is present to reduce the damage to 1/16 since Wyvern picks the least resistance element (Default is Flame Breath). This also proves that Wiki's (HP*Multiplier) formula is incorrect provided step functions are irrelevant.


The given HP is PRIOR to wyvern leveling up. Thus, you any tests moving forward need to account for XP gained doing this test.

If level is part of the equation, either the wyvern's level is different from the DRG's or the formula is not a straight division as with BLU breaths (99/6 = 16.5 and 99/7=14.143). Since Wyvern breath damage increases with Wyvern HP gear, Wyvern's Current HP, NOT Wyvern HP% is used.

I then tested using Drachen+1 legs:
- Flame Breath for 273 DMG at 1553 HP

Using the 15 as a static added damage (Since only HP changed), I tried the following:
(240-15)/1351 and (273-15)/1553

Using the 1024 system, I found 171/1024 works for the former, but not for the latter. Using a fraction between the two works, so it seems this is not functioning on the 1024 system. I randomly tried multiplying the fraction by 30 and got 4.993, so I tried (5/30 => 1/6). This worked for both values, so I tried using Wyvern Mail (HP+65) with the Drachen Brais. I used Spirit Link and the Wyvern returned 277HP. This means that the AF+1 legs calculated after additive Wyvern HP gear.

(1351*0.15) + 65 = 267HP (Incorrect value)
(1351 + 65)*(0.15) + 65 = 277HP (Correct value)

This means a total of 1628HP with Drachen Legs+1 and Wyvern mail.
- Flame Breath for 286DMG at 1628HP

(1628)*(1/6) = 271.33333 => 271
271 + 15 = 286DMG

Thus, (1/6 HP) appears additively within the formula

What needs to be figured out is how items and deep breathing affects the damage. Also, I need to figure out whether that 15 DMG is static or a miniature formula.

I'll post this now, but I'll see if I can keep testing (Or go back to writing spellcast). So far, we have:

[15 + {(Wyvern HP + Wyvern HP Items)*Wyvern HP Multiplier Items}*{1/6}]

[Yugl]

Wyrm Armet+1
- Flame Breath 240 DMG (Before Armet) at 1351HP
- Flame Breath 268 DMG (With Armet) at 1351HP
- Flame Breath 280 DMG (With Armet) at 1416HP

Test for a HP Multiplier using 1024 system:
(268-15) = 253
(253/225)*(1024) = 1151.XXX => 1152/1024

Check:
(1152/1024)*(225) = 253
253 + 15 = 268

At this point, 1152/1024 works. Further checks:

(15 + ((1416/6)*(1152/1024))) = 280 DMG (The multiplier holds, order not determined though)

Further check using Drachen Legs+1 and Wyvern Mail:
- Frost Breath 319 DMG at 1628HP (With Armet)

[15 + {{(1351 + 65)*1.15}*(1152/1024)}*{1/6}] = 320HP

[15 + {{(1351 + 65)*(1152/1024)}*1.15}*{1/6}] = 320HP

Hmmm. Going to step back and do Legs+1 and Armet:
- Flame Breath 304 at 1553HP (With Legs+1)

Back to spellcast and maybe work on this later...

Lancer Torque
- Flame Breath 240 DMG at 1351HP (Without Torque)
- Flame Breath 244DMG at 1351HP (With Torque)
- Flame Breath 272DMG at 1351HP (With Torque and Armet)

First test implies Torque before (1/6) division.

1351*(1042/1024) = 1374
1374*(1/6) = 229
229 + 15 = 244 (Correct damage)

Compared with

1351*(1/6) = 225
225*(1042/1024) = 228
228 + 15 = 243 (Nope!)

I found (1042/1024) by taking 244-15 and then diving the difference by 225 (The value before any multipliers using 1351HP).

[Yugl]

Ok, found the correct order. The +15 is actually tied with the HP/6 part (Much like BLU spells/Elemental WS, which gives reason to believe the 15 is actually a function of sorts).

[{FLOOR(Total Wyvern HP/6) + 15} * Wyvern Breath Bonus Items] produces the correct numbers for each (I won't write them up again since I listed the total HP and DMG values). The Armet term was incorrect though. The new value is (67/60 or [7/60 + 1]) for Armet. Using the data for Torque, the value is (61/60 or [1/60 + 1]). This term stacks additively with Armet, seemingly.

[(FLOOR{HP Total/6} + 15) * (1 + Armet Bonus + Torque Bonus)]

[(FLOOR{1351/6} + 15) * (1 + 7/60 + 1/60)]

[(225 + 15) * (1 + 7/60 + 1/60)]

[(240)*(68/60)] = 272 DMG (Correct value found when using Armet and Torque)

Thus, only level-up bonus and Deep Breathing require testing.

[Rena]

BLU breaths (and as far as I can tell from what limited information I have, at least some mob TP moves as well) traditionally had two divisors, one for HP, and one for level. The latter, at least, was represented in fractions of 256 (technically no greater accuracy than fractions of 16 was required, but that is of little relevance), they did not have any abnormal fractions as the OP cites. Thunder breath is the only one to differ from this with a floor(HP/2)*1.35 formula. Given that it is a very recent addition, I would not use this as a base for determining formulae for older breaths.

From looking at what data is available, it would seem that wyvern breath damage is a function of both HP and level, but I do not see any immediately obvious formula. More data, preferably without relic head, would probably be useful, with level and HP noted. (And with regards to HP, how accurate are the HP values used?)

[Yugl]

1. I wouldn't try to say Wyvern breaths are like BLU breaths; just drawing the correlation you brought up about having a 2 part system (LV + HP) and implying that the 15DMG bonus is probably a function of level rather than a static modifier. Not sure if that was to me or the OP, but I know I referenced BLU within my post, so just making sure I'm not ignoring you on that issue.

2. Have you read the Random Facts Magic post I made on thunder breath? I came to the same conclusion as you in terms of value (0.5 * 1.35 = 0.675 = [27/40]), but I am curious about you representing the value as HP/2*1.35. Are you saying that the (HP/2) gets floored before applying the 1.35 multiplier rather than a straight 0.675 multiplication?

3. I'll try to get more data on wyvern level, but that typically requires Reseph's Tarsal slam for each level (Since the HP value remains anonymous each level that isn't 99). The HP values I provide are precise since Tarsel Slam places you at exactly 1HP and I did not filter the damage (SS available if needed). My concern is how to do a good level test when HP will vary in accordance with level. The only method I can think of would require doing a bloody reseph each time I wanted to do a level check. I also speculate that there is either an additive component or the wyvern's level is less than 99 since there is no division to allow 99 to equal 15 when floored.

[Yugl]

Deep Breathing:
- Straight 2x multiplier
- Appears to be AFTER Armet

Tested using Drachen Legs+1 to place my Wyvern at 1553 HP (FLOOR[1351*1.15])

If Armet before DB: FLOOR [FLOOR {FLOOR (1553/6)+15} * {67/60}]*[2] = 608 DMG
If DB before Armet: FLOOR [FLOOR {FLOOR (1553/6)+15} * {2}]*[67/60] = 609 DMG

Observed value: 608 DMG

Therefore, Armet before DB

Resist:
- I observed a 134 DMG breath against a TW Rabbit while wearing Armet and Drachen Brais+1
** However, I had unequip > Reequiped the Brais without spirit linking, so the Wyvern only had 1351HP
- I just cranked out the numbers and it seems that this value cannot give me an indication of where resist falls in accordance with other multipliers

[Rena]

2. Have you read the Random Facts Magic post I made on thunder breath? I came to the same conclusion as you in terms of value (0.5 * 1.35 = 0.675 = [27/40]), but I am curious about you representing the value as HP/2*1.35. Are you saying that the (HP/2) gets floored before applying the 1.35 multiplier rather than a straight 0.675 multiplication?

Correct. This would not be apparent in your tests since you used even HP values, for which the flooring would make no difference.

3. I'll try to get more data on wyvern level, but that typically requires Reseph's Tarsal slam for each level (Since the HP value remains anonymous each level that isn't 99). The HP values I provide are precise since Tarsel Slam places you at exactly 1HP and I did not filter the damage (SS available if needed). My concern is how to do a good level test when HP will vary in accordance with level. The only method I can think of would require doing a bloody reseph each time I wanted to do a level check. I also speculate that there is either an additive component or the wyvern's level is less than 99 since there is no division to allow 99 to equal 15 when floored.

99 could be divided by 6.5, which is simple enough, if still using a decimal. This would not work with the values in the OP however, and ends up being a few points off. Since there was no Tarsal Slam back at 75, I'm still curious about how the OP arrived at the conclusion of wyvern HP at 75.

[Yugl]

Interesting...

If you have data that you can post (Or link to), that would help BG-Wiki since we want to cite the correct people and have links to data supporting the information we post.

I think the OP's conclusion was from Wiki-Wiki's Elemental Breath Page. However, that page has zero support.
OP says he found the formula himself by setting Wyvern HP to 991 HP.

Edit: Post within another thread obviously. I wouldn't want to link to this page since we want our data to be somewhat correctly located!

[Ophannus]

I got the Wyvern HP at 75 by using Call Wyvern and then equipping Drachen Brais(HP+10%) and using Spirit Link and then deriving from that how much HP was healed vs how much HP it was boosted by. I think my original value was somewhere between 990-994 using other methods such as fully healing my wyvern using Shepard's Tonic and Drachenessences from various Wyvern HP% (50%, 1%, 75% etc) and nailed it down to 991 exactly. Was back in like 2006 so it's a bit fuzzy but I thought the wyvern breath formula matched the blu breath paradigm at the time which was simply a % value of your HP such as Heat Breath being HP*0.5 or hip press being HP* 1/3. I didn't think it was so complex because it seemed as if all breath spells/attacks were akin to Spirits Within which were just a fraction of your current HP or so. #badmath

[Yugl]

Slight departure from Smiting Breath. Restoring breath's formula is slightly inaccurate on the other Wiki. Tested 0.1757 versus (45/256) and found the latter to predict correct values. Not much else test though. HP value used was 1411 (Base HP + 60 HP in gear). I assume most inaccuracies were due to the inability to pin down precise HP values prior to the introduction of Reseph.

[Yugl]

DB:

Ok, so further testing at different HP values (Brais+1, 1.8x HP via Atma, and so forth) shows Wiki's 42 base to be correct. I believe this value is the same across ALL level ranges given the date of the formula (Appears to be during the 75 cap era). Testing with Deep Breathing (DB), I find that DB adds (50/256) to the HP multiplier. However, this is pending further testing that Radec suggests doing.

Edit: Ok, values used for DB tests were

1351 HP (Base):
- NQ HB: 279 HP healed
- DB HB: 543HP healed

2431 HP (Base + 1.8x in Atmas)
- NQ HB: 469 HP healed
- DB HB: 944 HP healed

Armet:

Looking like a (30/256 bonus) to the HP multiplier.

1351HP (With Armet): 437 HB

Armet+2 (Observed value from Ophannus):

Looks like a (43/256 bonus) to the HP multiplier (13/256 increase from NQ armet)

1351 HP (With Armet): 506 HB observed

(1351*(45+43/256)) = 464 floored
464 + 42 = 506 HB (Same as observed)

Armet + DB:

Seems they stacks additively (45+30+50/256) => 125/256

Predicted:
(1351* (125/256)) = 659
659 + 42 = 701 HP

Observed HB: 701 HP

Glassbelt and Lancer's torque (Ophannus provided the observed value):

Looks like a (5/256) bonus to HP modifier.

Observed: 305HB

Check:
(1351*(45+5/256)) = 263
263+42 = 305 HB (Same as observed)

Armet+2 with DB augment:

Looks like (5/256) added, per merit, to the DB's original HP modifier.

IF THIS IS ACCURATE, then . . .

Observed value: 902

902-42 = 860
(860/1351)*(256) = 162.XXX (162 or 163)

[(162/256)*(1351)] + 42 = 896 X
[(163/256)*(1351)] + 42 = 902 (Observed value)

We now have to account for 5 merits, original DB value, and Armet+2

Armet+2 = 43
Original DB value = 50
Base value = 45
Total = 138

(163-138) = 25

Divide by 5 (Since the bonus is per merit and the observed value was with 5 merits)

(25/5) = 5

(5/256) Bonus

Base value is

[Yugl]

If people want to add values to corroborate or refute this, do so since I'm getting sick of this (Tedious stuff). I'll reformulate formulas for Elemental and Healing breath here that I believe work (Healing breath could use more data points for comparison).

Elemental is missing: Resist, Glassbelt + Lancer Torque values, Armet+2, and Armet+2 with augmented DB value
Healing is missing: TP bonus
Both are missing: XP bonuses (Level?)

Elemental: FLOOR [FLOOR {FLOOR (HPw/6)+15} * {Breath Multiplier}]*[Deep Breathing]

Healing:[(HPw)*(Breath Multiplier)] + 42

HPw = Wyvern's Total HP
Wyvern's Total HP = FLOOR[(Wyvern's base HP + Additive Wyvern HP gear)*(Multiplicative Wyvern HP gear)]

Breath Multiplier Total (Elemental) = Unknown at the moment
Breath Multiplier Total (Healing) = ({45/256}+{Breath Multiplier Armor})

[Ophannus]

We'd need to determine the amount of HP gained per parameter increase. Wiki lists it at a +6% bonus per increment at 200exp per increment for a cap at 1000 which would indicate a +30% Wyvern HP bonus(if that's the case I wish there was another way to obtain this bonus without EXP, for boss Steady Wings of like 3k when factoring in Wyvern HP and Max-Current HP bonuses)

I'd have to retest Elemental breaths for 99 but I know at 90, breaths did 210 naked with just the armet and 214 with Glassblower or Lancers so they have the same bonus. Should be easy to test augmented DB for elemental breath since DB simply doubles the potency of the breath(360ish base breaths become ~720 or so with deep breathing with full HP gear and other enhanced breath gear)

[Byrthnoth]

I think this link may prove itself useful:
http://www.bluegartr.com/threads/555...t-Observations

[Yugl]

Two benefits of that thread:
- No HP gained upon leveling up (I'll check this myself later)
- If Wyvern HP as truly 991HP at 75 and the damage was 180 DMG, then my formula remains accurate and 15 appears to be a static base damage rather than level dependent; I'll confirm on the test server later today using ballista

Assuming my Ballista test is correct, this will be useful for providing an average HP range at all levels (Even those where Brais+1 does not apply). Interestingly, 991-1351 offers a clean 15HP per level. However, this obviously is not the entire formula (If even part of the formula) because 15*99 exceeds the Wyvern's current HP value.