Enmity testing - Still Going!

[Kaeko]

Another thought based on our multipliers. Going with the idea that there is linear gain with anchors at 100 200 and 300 TP, we can see some trends as far as are estimated modifiers (I made a reasonable guess at the 200TP mod, which had some errors I think).

CE Mods:
@100TP = 0.090
@150TP = 0.100
@200TP = 0.110
@250TP = 0.155
@300TP = 0.200

Between 100 and 200 TP, the modifier increases by 0.0002 per 1TP above 100.

Between 200 and 300 TP, the modifier increases by 0.0009 per 1TP above 100.

[Therin]

Just got back home and here are the various ranges for the modifiers. Were these done using the Kaman+1 + Scorpion Arrow to ensure exact 100.0TP or using Joytoy?

The first half or so of the tests were done using the Kaman+1 and Scorpion Arrow combo which produced exactly 10.0 TP/hit. For the latter portion I picked up a friend's Opo-opo Necklace and used this method as it sped things up quite a bit.

[Spekkio]

The fact that it's generally linear sort of establishes our ranges then right?

For instance, caps from 100 to 200 tp go from 360 to 440, so it's safe to assume +1TP = +0.8 to the damage cap? For 200 to 300 tp, it goes from 440 to 620 to X (probably capped earlier), so it's +1TP = 3.6 to damage cap.

Would this be evidence for a fTP value of say 1.0 from 100-200TP and fTP = 4.0 from 200-300TP?

you're not actually increasing any caps. VE and CE damage are capped at 360 each, then that total is multiplied by the fTP modifier with that value capped at 750. if i read the data right, fTP at 100 is 1, fTP at 200 is about 1.2 and fTP at 300 is about 2.2. by extension, this means fTP at 150 would be about 1.1 and 250 would be about 1.7.

by comparing the data sets that don't cap out at 750 damage, we can see that by taking the damage at 100% TP and multiplying by the fTP modifier i listed above, we get the final damage for that step. this is very similar to the way that other ws work as i understand it. first it computes a base damage, then as the final step, it multiplies it by the fTP mod. the only difference in this case is that the final damage is capped at 750 in this.

[FailureMidgard]

Using the following #s:
3dispels, 100tp, no gorget: 86 dmg
3dispels, 200tp, no gorget: 105 dmg
3dispels, 300tp, no gorget: 192 dmg
3dispels, 100tp, yes gorget: 96 dmg

The first 3 numbers came from Therin originally, I reverified the first and second before testing the gorget.

FTP mod at 100 TP should be found by solving:
96/86 = (x+.1)/x
86(x+.1)=96x
86x+8.6=96x
8.6=10x
x=.86

For 200:
105/86 = y/.86
y=1.05 (this is just obvious)

For 300:
192/86 = z/.86
z=1.92 (same)

There is potential rounding error here, but it should be correct +/- .01 or .02, too lazy to figure out the exact margin of error due to the game rounding damage numbers.

[Kaeko]

Going to let the melee experts work on the fTP thing.

Here are some simple tests for VE:

Mainly I want to look for 2 things in these tests - (1) the caps generated by varying amounts of TP, and (2) if the modifiers are similar to CE. If the modifiers are similar, then it would be really nice since we could just focus on CE and then apply it similarly to VE. Also, VE is much more difficult in terms of precision since it's constantly decaying at a rate we cannot really measure precisely.

(1) Tests for VE Component Caps at various TP amounts:

Build X TP using a ranged / arrow combo that gives exactly 10.0 TP.
Have a 2nd player pull a mob with Silence/Slow/(1CE gainer).
Have PLD cure puller for 0 HP to get on hate list (+1CE).
Have PLD Sentinel > 2hr > Atonement in quick succession.
Note Damage.

We would expect these caps to be the same as the CE caps. Because this requires a 2hr, this one is annoying. We do already know that at 100TP the cap is 360 from Therin's old tests. Values at 150, 200, 250, and 300 would be great though.

(2) Test for estimating VE modifiers at various TP amounts.

Repeat the procedure above but do not use 2hr. Simply use Sentinel then Atonement. This will give you roughly 1800 assuming no enmity gear changes. If you Atonement in quick succession it'll be about ~1700 VE when you do it. We can hopefully determine if these modifiers mimic the CE modifiers we got. If they do I would feel safe calling them the same.

[Suiram]

fTP is always done in 256ths, on every other WS (and BLU spell), so a good starting point seems to be assuming that it works that way with atonement, too. It's also linear between 100% and 200%, and 200% and 300%, with an inflection point at 200%.

I expect the final formula to look something like this (what follows is not correct because it's off by 1~2 points of damage at certain values):
Final damage = the minimum of 750 and floor(fTP * fENM)
where fENM = min(CE*0.2,800) + min(VE*0.2,800)
and fTP(100~200%) = (115 + floor(((TP-100)/100)*26))/256
and fTP(200~300%) = (141 + floor(((TP-200)/100)*115))/256

Again, the above can't be the right formula, but it's probably something that's similar. The above, for the non-equation-inclined, takes up to 4000 enmity of each type, takes 1/5 of it, adds it together, then multiplies by a fraction of 256 which is ~45% at 100 TP, ~55% at 200 TP, and 100% at 300 TP, and then that is the final damage (or 750, whichever is lower). So while that's not exactly what happens, it could be something that would be mathematically equivalent if it weren't for how the calculations are actually performed. Like maybe it takes 10% of the enmity, and then multiplies it by (a fraction of 256 roughly equal to) 90%, 110%, and 200%, at 100, 200, and 300 TP, respectively, or it takes some other % of the enmity and does the fTP calculation based on that.

In any case, my intuition based on years of looking at ffxi formulas tells me that it most likely involves x/256 at the fTP portion, and that the individual enmity caps are likely 4000 CE and VE.

[Suiram]

Actually, something that would be helpful in working out the specifics, would be to see where the cap on the enmity component takes place. It might not be a cap on enmity at 4000, but rather a cap on the value of the function of enmity that takes place around where CE and VE are each at 4000.

So could someone do this test:
Get exactly 4000 CE and 0 VE and exactly 100% TP (not 100.x%, just to be safe). See if the damage is 360 or if it's something slightly below 360 like 359. If it's 359 or lower, and you have the time and inclination, retest a few times to find the exact CE value where you hit 360 (maybe try 4010, then 4005 if it's 360, 4020 if it's still less, etc). Likewise, if it's 360 at 4000 CE and 100% TP, maybe try 3999 CE and see what the damage is.

[Kaeko]

Suiram, should your estimated formula include WS secondary attribute modifier (0.83)?

[FailureMidgard]

fTP is always done in 256ths, on every other WS (and BLU spell), so a good starting point seems to be assuming that it works that way with atonement, too. It's also linear between 100% and 200%, and 200% and 300%, with an inflection point at 200%.

And what about tp values between 100/200?

You're saying that it's more like a step function approximating a linear function, and it always rounds down to the nearest 256th? Or the 100 and 200 values are 256ths and the rest is truly linear?

[Suiram]

And what about tp values between 100/200?

You're saying that it's more like a step function approximating a linear function, and it always rounds down to the nearest 256th? Or the 100 and 200 values are 256ths and the rest is truly linear?

Sorry, step function approximating a linear function, I just meant as opposed to a step function approximating some other kind of function.

And kaeko, I don't think it uses level correction. It seems to be more like Spirits Within, Starlight, and Moonlight in that portion of the equation, but with enmity rather than HP/club skill.

[FailureMidgard]

Sorry, step function approximating a linear function, I just meant as opposed to a step function approximating some other kind of function.

And kaeko, I don't think it uses level correction. It seems to be more like Spirits Within, Starlight, and Moonlight in that portion of the equation, but with enmity rather than HP/club skill.

And by this logic, a gorget adds 2/256? 3/256? or .1? to the ftp...

[Suiram]

And by this logic, a gorget adds 2/256? 3/256? or .1? to the ftp...

Would be 25 or 26, not 2 or 3, but yes, that would be the idea. I could confirm which over the weekend with Vidohunir probably, if I didn't throw away my thunder gorget (I can't remember if I did).

Edit: A quick google search shows that the accepted value is 25/256.

[FailureMidgard]

Would be 25 or 26, not 2 or 3, but yes, that would be the idea. I could confirm which over the weekend with Vidohunir probably, if I didn't throw away my thunder gorget (I can't remember if I did).

Yea, pretend I'm not being retarded. ;p

I was thinking .01 for whatever dumb reason. Really need to know gorget exact value before trying to find any exact formula on atonement though....

[Kirschy]

And by this logic, a gorget adds 2/256? 3/256? or .1? to the ftp...

Yea this was easier to prove back when crits were capped at 3.0. Gorget was shown to be 25/256.

[Suiram]

I was thinking .01 for whatever dumb reason. Really need to know gorget exact value before trying to find any exact formula on atonement though....

Oh that's a brilliant idea. I can't believe I didn't think of that last night. You're suggesting do a WS with gorget and identify the damage difference, use that to figure out what the actual fTP values are, and then use that to figure out what the enmity function is (and thereby determine the entire formula)? That should make this easy.

Edit:
For other people, what I mean here is that depending on what % of enmity is then multiplied by fTP, gorget will improve damage to greater or lesser degrees. So for instance, if it takes 1/4 of enmity and fTP is something like 92/256 at 100% TP, then adding gorget will increase damage by 27%. On the other hand, if it takes 1/20th of enmity and fTP is something like 460/256, then adding gorget would only be a 5% increase in damage.

Rather than playing around with different combinations of "divide enmity, multiply by some x/256 so that damage works out to roughly 9% of TE," until we find one that works for all values, we could just use gorget to nail down fTP right at the outset.

[FailureMidgard]

Yea this was easier to prove back when crits were capped at 3.0. Gorget was shown to be 25/256.

Thanks.

Oh that's a brilliant idea. I can't believe I didn't think of that last night. You're suggesting do a WS with gorget and identify the damage difference, use that to figure out what the actual fTP values are, and then use that to figure out what the enmity function is (and thereby determine the entire formula)? That should make this easy.

Yes, if you scroll up, I already posted my test with gorget last night, approximating the ftp values at .86, 1.05, and 1.92 at 100/200/300 tp, but this isn't exact. I also argued with Kaeko for a bit about this last night!

Anyway, I'm 100% confident that those numbers are in the correct neighborhood. I'm trying to figure out exact numbers in your 256 model, but needed the true value of the gorget. I really need a test at 160/170 TP with exactly 3dispels worth of CE atm.

[Suiram]

Thanks.



Yes, if you scroll up, I already posted my test with gorget last night, approximating the ftp values at .86, 1.05, and 1.92 at 100/200/300 tp, but this isn't exact. I also argued with Kaeko for a bit about this last night!

Anyway, I'm 100% confident that those numbers are in the correct neighborhood. I'm trying to figure out exact numbers in your 256 model, but needed the true value of the gorget. I really need a test at 160/170 TP with exactly 3dispels worth of CE atm.

Sorry, I can't believe I overlooked that lol Looks like ~216/256? I have to run out the door or I'd like to look at this more. If that doesn't lead to something, maybe repeat your gorget test at slightly higher enmity (1920 maybe) so that the numbers are bigger and easier to manage.

[FailureMidgard]

Ok, so, correcting earlier formulas:

96/86 = (x + 25/256) / x
96x = 86x + (86*25)/256
10x=(86+25)/256
x=(86*25)/(256*10)
x=(43*5)/256 = 215/256 (~.8398 ) @ 100tp

At 200 TP, we're getting 105 damage, 105/86*215=262.5, so either 262 or 263?
At 300 TP, we're getting 192 damage, 192/86*215=480/256.

[Spekkio]

i think i made the same mistake as you, suriam, in assuming that all we could do was determine a ratio for 100 tp to the other two anchors forgetting that the gorget gave us a known quantum that we could use as a yardstick. we do need to be careful that there's not some dirty rounding errors in here. there are 3 places as best i can tell in the formula that set a cap on the figures and it might floor the numbers at this step too introducing some extra fuzzyness to our math.

[FailureMidgard]

Ok, bear with me, lookover my math, and tell me if you see a problem with any of my assumptions or math. If they are ok, then I think this is a more accurate guess at the FTP values than my last post, which I've acknowledged was a rough estimate.
All numbers are done with exactly 3 dispels of CE, and 0 VE, and I'm kinda working backwards.

Given: 100tp>86 dmg.
Assumed: Final (FTP) step of damage calculation is of the form (D*x)/256, where x/256 is the actual FTP mod, and D is floored damage value before the FTP calculation. x=215.
Math:
86 = floor(D*x/256)
86 = floor(D * 215/256)
If 86=D*215/256, then D=102.4
If D=102, then 102*215/256=85.66, floors to 85. Wrong.
If D=103, then 103*215/256=86.50, floors to 86. Possible.
If D=104, then 104*215/256=87.34, floors to 87. Wrong.
Conclusion: Thus, based on the assumption that we have an integer before the FTP step, and x=215, the base damage value must be 103.

Given: 100tp+gorget>96 dmg.
Assumed: Gorget makes new x value (call it x') equal to old x + 25. x' = x + 25, or x' = 240.
Math:
96 = floor(D*240/256) = floor(103*240/256) = floor(96.56) = 96
Calculation works...

Given: 200tp>105 dmg.
Assumed: y/256 is the FTP mod at 200. y is ~262.
Math:
105 = floor(D*y/256)
If y=261, floor(103*261/256) = floor(105.0 ) = 105. Possible.
If y=262, floor(103*262/256) = floor(105.4 ) = 105. Possible.
If y=263, floor(103*263/256) = floor(105.8 ) = 105. Possible.

Given: Nothing.
Assumed: Gorget makes y' = y + 25, or y' = 286, 287, or 288.
If y'=286, floor(103*286/256) = floor(115.0 ) = 115.
If y'=287, floor(103*287/256) = floor(115.4 ) = 115.
If y'=288, floor(103*288/256) = floor(115.8 ) = 115.
Conclusion: Gorget test at 200 TP will not narrow this at all.

Given: 300tp>192 dmg.
Assumed: z/256 is the FTP mod at 300. z is ~480.
Math:
192 = floor(D*z/256)
If z=480, floor(103*480/256) = floor(193.1) = 193. Wrong.
If z=479, floor(103*479/256) = floor(192.7) = 192. Possible.
If z=478, floor(103*478/256) = floor(192.3) = 192. Possible.
If z=477, floor(103*477/256) = floor(191.9) = 191. Wrong.

Given: Nothing.
Assumed: Gorget makes z' = z + 25, or z' = 503 or 504.
If z'=503, floor(103*503/256) = floor(202.4) = 202.
If z'=504, floor(103*504/256) = floor(202.7) = 202.
Conclusion: Gorget test at 300TP will not narrow this at all.

So, the FTP @ 100TP is 215/256, the FTP @ 200TP is 261/256, 262/256, or 263/256, and the FTP @ 300TP is 478/256 or 479/256. A gorget test at 200 or 300 TP will not narrow this down at all. If anyone has a suggestion to narrow it further, I'm open, but I can't think of a good way off the top of my head, besides going and testing values at every 1.0 TP value.