Attack Level and Defense Level Demystified

Quilue - Sanctuary · April 2010

what i'm not sure is that, do we round to the nearest def level or take the actual number? like the 5.5 from tideform for example? i'm going to assume that the formula for negative A-D values is completely separate from that of positive A-D and 0. for now, i'm also going to assume that you round to the nearest whole number since this was the case for positive A-D values

the closest thing that i have come up with is a linear combination fitting the data Astypoo collected excluding
A-D >= 0:

0.7199307275798321` + 86.10617977450318` * 0.99`^-x - 85.82884302831084` * 1.01`^x

or

0.7199307275798321` + 0.99^(-443.32659606496776` - x) - 1.01^(447.45799728019944` + x)

where x is A - D.

the funny thing is, at x = -78, the reduction is about 54%, which is almost consistent with what fapfapfap experienced

it was kind of random that i just tried it out, but it fit the data decently.

kenlee · April 2010

Asterelle - Sanctuary wrote: »
ATT	DEF	DAM	DEC% 	ATT-DEF
0	0	1227	0	0
0	41.8	822	-33.00	-41.8
0	36.3	856	-30.23	-36.3
20	41.8	980	-20.13	-21.8
20	36.3	1029	-16.13	-16.3
0	5.5	1157	-5.70	-5.5
20	5	1411	14.99	15
20	0	1472	19.96	20
(1+(A-D)/100) matches exactly for positive values of (A-D) but not negative negative

may i know how you did your test?

you expected to be a diff of 41.8 when in fact higher lvl reduced your damage reduction
for me it looks like that real damage reduction have been modified by lvl difference. i mean, you are no longer lvl lvl 50 or 101 or w/e it was before lvl defences, your physical/magic defences are the same, lvl is modified so this also modify your damage reduction. could be a possibility but not enough data in that table, lvl diff. between players, defences...

this is just primary school math but if you dont provide some real test data its not enough solve this

Solandri - Heavens Tear · April 2010

I don't think (A-D) is right. A straight (1 - D/100) would mean that if you some how managed to hit D = 100, you would be invulnerable. Game devs don't like perma-invulnerability, and the GMs have frequently stated the code is set up to prevent that from happening. Based on damage to [?] bosses being 25%, everyone assumes the reduction is just capped at 75%. But what if there's more?

Look what happens if you assume it's:

(1 + A/100) * (0.99^D)
or
(1 + A/100) / (1.01^D)

ATT	DEF	DAM	DEC% 	ATT-DEF	A*.99^D	A/1.01^D
0	0	1227	0	0 	0 	0
0	41.8	822	-33.00	-41.8 	-34.30 	-34.03
0	36.3	856	-30.23	-36.3 	-30.57 	-30.32
20	41.8	980	-20.13	-21.8 	-21.16 	-20.83
20	36.3	1029	-16.13	-16.3 	-16.68 	-16.38
0	5.5	1157	-5.70	-5.5 	-5.4 	-5.3
20	5	1411	14.99	15 	14.12 	14.18
20	0	1472	19.96	20	20.00 	20.00

Not exact, and actually worse the smaller (A-D) gets, but it matches up pretty closely for the larger DEF values. It also fits well with the data point FapFapFap provided:

FapFapFap - Raging Tide wrote: »

Too lazy to compare but 68 def lvl reduced the dmg to 47%(+/- 1%) of the dmg with -10 def lvl (Fist BM dmg: ~850->~400).
So basically 78 def lvl reduced the dmg by 53%, maybe it's useful for u pwi-scientists

A = 0, D = 78
0.99^D -> -54.34%
1/1.01^D -> -53.98%

Quilue - Sanctuary · April 2010

kenlee wrote: »

may i know how you did your test?

you expected to be a diff of 41.8 when in fact higher lvl reduced your damage reduction
for me it looks like that real damage reduction have been modified by lvl difference. i mean, you are no longer lvl lvl 50 or 101 or w/e it was before lvl defences, your physical/magic defences are the same, lvl is modified so this also modify your damage reduction. could be a possibility but not enough data in that table, lvl diff. between players, defences...

this is just primary school math but if you dont provide some real test data its not enough solve this

it was all done in one sitting, Ast and a lvl 12 psychic. Ast had no weapon on, the psy had no armour on.

defense levels were gotten through voodoo and tideform, attack levels on Ast's side were gotten through frenzy

@Solandri
i don't know how ? bosses reduce damage by 75% honestly...if it's simply out of level difference, then the reduction should decrease as i level, assuming all ? bosses are lvl 150. bosses and mobs might just get a hidden boost for being in different shades of orange.

this begs the question of how def level is different from a simple turtle buff. i know turtle flat out takes a percentage of incoming damage.

what i was assuming was that, at 100 def levels difference, incoming damage is cut in half. in other words, it boosts your existing reduction by 100%. thus, 100 def level would not make you invulnerable

Telarith - Sanctuary · April 2010

Solandri - Heavens Tear wrote: »

I don't think (A-D) is right. A straight (1 - D/100) would mean that if you some how managed to hit D = 100, you would be invulnerable. Game devs don't like perma-invulnerability, and the GMs have frequently stated the code is set up to prevent that from happening. Based on damage to [?] bosses being 25%, everyone assumes the reduction is just capped at 75%. But what if there's more?

In this particular case, it would be just like fist attack speed: determining the ceiling the devs put on this particular feature. Fists could do 10 APS pretty easily, but ceiling limits to 5. So it's determining what the ceiling imposed is as opposed to stating the obvious that they wouldn't let us be immune to all damage that is being worked on. But that won't be done for a while, unless someone gets a psychic in the water with DEF lvl sharding. Though getting even intervals might be a better idea, or even getting someone sharded with DEF stones for a straight amount. Level difference and partial DEF lvl on a newly implemented skill may not be the best method for verifying things.

kenlee · April 2010

i think i read the gap is 99% not 75%

about this
0 41.8 822 -33.00% -41.8
0 36.3 856 -30.23 -36.3

and after a few calc. i get -33.26% for first line (pretty close) and -28.68% for second line (not that far either) and i havent considered any of the above formulas so this tells me again that you have to provides all datas or.. the test subjecs are not the same for all negatives values

edit: didnt se all those posts above so quick

Solandri - Heavens Tear · April 2010

Quilue - Sanctuary wrote: »

@Solandri
i don't know how ? bosses reduce damage by 75% honestly...if it's simply out of level difference, then the reduction should decrease as i level, assuming all ? bosses are lvl 150. bosses and mobs might just get a hidden boost for being in different shades of orange.

I'm afraid I muddied the waters a bit with that comment. I thought the damage reduction from [?] bosses was well understood?

http://www.pwdatabase.com/pwi/drop

If a mob is >=40 levels above you, you only do 25% of your normal damage to it. Since [?] mobs are level 150 and the highest player level is 105, they are always >40 levels higher, so everyone has their damage against them reduced by 75%.

I thought that this reduction was independent from the +/- 1% from ATK and DEF level mods though? I didn't mean to confuse the issue by adding another variable. I just mentioned it to illustrate a case where they have put in a hard cap.

kenlee · April 2010

Solandri - Heavens Tear wrote: »

If a mob is >=40 levels above you, you only do 25% of your normal damage to it. Since [?] mobs are level 150 and the highest player level is 105, they are always >40 levels higher, so everyone has their damage against them reduced by 75%.

wasnt talking about pve since this test was about pvp and for pve there are weapons like warsoul (pw-my) that remove that difference or atk lvl shards or now atk lvl skills on tideborn classes

FitHitDShan - Sanctuary · April 2010

The closest fit I can find is a pretty good fit(within 1% on each of the observations), but still not perfect:

[Damage] = [Damage Dealt] * (1 + [Attack Level]/100) * (.99^[Defense Level]) with Defense Level truncated.

If the code truncates Defense, it probably also truncates Attack, but we only have round number observations. Note that even Qui's psychic could be used to get more information on extreme values and whether it is the net effect of Attack and defense (modified by a positive/negative logic switch - which was the next closest fit) or the above. Between white and black voodoo and switching which of you is attacking so you can use the more extreme penalty part of these skills, you should have been able to get a lot more test values.

Asterelle - Sanctuary_1381265973 · April 2010

FitHitDShan - Sanctuary wrote: »

The closest fit I can find is a pretty good fit(within 1% on each of the observations), but still not perfect:

[Damage] = [Damage Dealt] * (1 + [Attack Level]/100) * (.99^[Defense Level]) with Defense Level truncated.

If the code truncates Defense, it probably also truncates Attack, but we only have round number observations. Note that even Qui's psychic could be used to get more information on extreme values and whether it is the net effect of Attack and defense (modified by a positive/negative logic switch - which was the next closest fit) or the above. Between white and black voodoo and switching which of you is attacking so you can use the more extreme penalty part of these skills, you should have been able to get a lot more test values.

I'm worried that a 1% error at a defense level of 41 would translate to a much greater error at the extreme high defense levels some people are shooting for in their end-game gear. I basically made the same mistake at defense level 10 and it would be nice to have a formula that works at all defense levels. I'll try to find a high level psychic later today when I go home.

kenlee · April 2010

FitHitDShan - Sanctuary wrote: »

If the code truncates Defense, it probably also truncates Attack, but we only have round number observations.

i was wondering the same if game likes to truncate/round atk/def lvl numbers like they do with atk speed
hope Asterelle will give the answer with that psy. i also want to know lvl of the psy after test, the other test person will be you i suppose

Asterelle - Sanctuary_1381265973 · April 2010

Really anyone can test it -_-"

How hard is it to actually physically write down damage before and after voodoo? Just do weaponless damage like wingspan or gush or something.

Asterelle - Sanctuary_1381265973 · May 2010

I just did a test to get some more data with a high level psychic.. here's the data from before

Asterelle - Sanctuary wrote: »

ATT	DEF	DAM	
0	0	1227	
0	41.8	822	
0	36.3	856	
20	41.8	980	
20	36.3	1029	
0	5.5	1157	
20	5	1411	
20	0	1472

And here is the new data with even higher defense level along with predictions from proposed formulas.

ATT	DEF	DAM	(A-D)/100	1.01^(A-D)	.99^(D-A)	
0	0	836	836		836		836
0	66	466	284		433		430	
0	76	437	200		392		389
20	76	500	367		478		476

Defense level is less effective at high defense levels than any proposed formula. At high defense levels every defense level seems to further reduce damage by only about 0.6% more. I don't yet see a grand unified formula that works over the full range of values. Fiting a formula to high defense levels doesnt work well with lower levels and vice versa.

Any guesses? I'd really like to fix the first post.

EDIT: FIXED copy paste error

Mosz - Heavens Tear · May 2010

sorry if this was taken into account or im wrong, just proposing
this is hard to test with 2 people that are not the same level, why? is there not a built in atk/def lvl(or it might be a seperate variable??) difference based on each lvl difference between players ?
what i mean in math terms or so
LVL 100 arch vs lvl 70 psy= 30 atk/def lvl from lvl factor
or maybe its 30% off the top
or similar to boss lvl difference?(doubt it)
or maybe ???

I could be wrong, haven't tested personally, sorry

Asterelle - Sanctuary_1381265973 · May 2010

Mosz - Heavens Tear wrote: »

sorry if this was taken into account or im wrong, just proposing
this is hard to test with 2 people that are not the same level, why? is there not a built in atk/def lvl(or it might be a seperate variable??) difference based on each lvl difference between players ?
what i mean in math terms or so
LVL 100 arch vs lvl 70 psy= 30 atk/def lvl from lvl factor
or maybe its 30% off the top
or similar to boss lvl difference?(doubt it)
or maybe ???

I could be wrong, haven't tested personally, sorry

If you fight something lower than you then there is no level based damage reduction. Attacking something higher will lower your damage up to a maximum of 75% reduction fighting enemies more than 40 levels higher (like ?-bosses). The table for level reduction is here:
http://www.pwdatabase.com/pwi/drop

Attacking something lower level than you will let you do full 100% damage (which is then mitigated by target defense). Attack level / Defense level has nothing to do with this type of reduction. You can easily see in FB19 with the dominance blessing that a higher attack level will let you do more than your maximum base damage.

At low defense levels (1+(A-D)/100) seems to hard to find a match for higher defense levels.

A_Noob - Dreamweaver · May 2010

Numbers are off ^
for example 0.99^76 = 0.466
I think you based hypothetical damage taken off already reduced damage lol instead of 836

Asterelle - Sanctuary_1381265973 · May 2010

A_Noob - Dreamweaver wrote: »

Numbers are off ^
for example 0.99^76 = 0.466
I think you based hypothetical damage taken off already reduced damage lol instead of 836

Yah error in the spread sheet lol <_< fixed.

Motoko - Raging Tide · May 2010

Asterelle - Sanctuary wrote: »

If you fight something lower than you then there is no level based damage reduction. Attacking something higher will lower your damage up to a maximum of 75% reduction fighting enemies more than 40 levels higher (like ?-bosses). The table for level reduction is here:
http://www.pwdatabase.com/pwi/drop

Attacking something lower level than you will let you do full 100% damage (which is then mitigated by target defense). Attack level / Defense level has nothing to do with this type of reduction. You can easily see in FB19 with the dominance blessing that a higher attack level will let you do more than your maximum base damage.

At low defense levels (1+(A-D)/100) seems to hard to find a match for higher defense levels.

Just because it works this way for mobs, doesn't mean it works that way for players. A simple way to test would be, have a 100+ level player attack a low level with his gear on. Then have them attack a 100+ that is wearing no gear. If you are right, the low level player will take less damage. If you are wrong, the 100+ player will.

Telarith - Sanctuary · May 2010

One extra thing: In Nirvana, the bosses that deal straight damage (i.e. the 5K damage dealt by the first boss) receives no damage reduction from DEF lvl. So mobs dealing straight damage seem to blast straight through, whether it is an error or not is uncertain.

Solandri - Heavens Tear · May 2010

nm, I see what you did. Revising.

Ok, first I normalized all your damage figures to the 0 ATK, 0 DEF case. Then I sorted your two data sets (0 ATK and 20 ATK).

ATT	DEF	DAM	
0	0	1.000	
0	5.5	0.943	
0	36.3	0.697
0	41.8	0.670	
0	66	0.557	
0	76	0.523
20	0	1.200
20	5	1.150	
20	36.3	0.839	
20	41.8	0.799	
20	76	0.598

Next, for the DEF values which were tested at both 0 and 20 ATK, I divided the two to find the ratio of normalized damage.

DEF	Ratio
0	1.20	
5.5	1.22 (actually 5.5 and 5, which probably accounts for this being high)
36.3	1.20
41.8	1.19
76	1.14

That's not quite what I was hoping for. The slight drop at 41.8 and sharp drop at 76 DEF suggests a discontinuous function or some modifier for the ATK bonus which doesn't become significant until DEF > ~40, and really kicks in at DEF > 60.

For the 0-36.3 ATK range however, this does suggest the ATK factor is just DAM * (1 + ATK/100) * (whatever DEF does).

Was there anything else particularly different about the psychic you tested on? How are you accounting for level reduction in damage, or was the target always same or lower level than the attacker? And I would kill for a 20 ATK, 66 DEF data point so I can make another ratio and compare to the 76 DEF ratio.

Asterelle - Sanctuary_1381265973 · May 2010

Ooo that seems promising! I'll try to get 0 / 66, 20 / 66 combo.

Of course if the graph is piecewise function with high defense levels it could be the same for high attack levels...

Again anyone can help add data <_< just use a weapon less skill before and after frenzy / blessing.

Illyana - Dreamweaver · May 2010

I seem to vaguely recall a post by eatwithspoons where he mentioned that def levels had been "fixed" so that you cannot be impervious to damage, but for the life of me I cannot find it now.

Solandri - Heavens Tear · May 2010

Solandri - Heavens Tear wrote: »
Next, for the DEF values which were tested at both 0 and 20 ATK, I divided the two to find the ratio of normalized damage.
DEF	Ratio
0	1.20	
5.5	1.22 (actually 5.5 and 5, which probably accounts for this being high)
36.3	1.20
41.8	1.19
76	1.14
That's not quite what I was hoping for.

I posted that late last night and wasn't thinking on all gears. What I'm trying to do is figure out how ATK and DEF are related in the formula. Damage is just a function of ATK and DEF:

dam = f(ATK, DEF)

But f(ATK, DEF) can have many forms. Say it's:

dam = g(ATK)^n * h(DEF)^m

Then if you keep h(DEF) the same, but vary g(ATK) and divide to get a ratio, it should eliminate h(DEF)^m from the equation. That's what I was trying to do.

dam1 = g(0)^n * h(DEF)^m
dam2 = g(20)^n * h(DEF)^m

dam2 / dam1 = g(20)^n / g(0)^n
h(DEF) is canceled out.

Unfortunately that's not what I got. It worked for low DEF, but at high DEF, DEF still appears to influence the damage even though all you varied was the ATK. So the formula can't be a straight product.

You can do similar tests for dam = g(ATK) + h(DEF) to see if it's a simple sum (I think we've already disproved that one though). And if we get more ATK values you can do the same thing to see if g(ATK) can be canceled out of a ratio.

With more data, further analysis of the ratios can yield a simpler pattern, which can help you unlock the relationship. e.g. while

dam = f(ATK, DEF)

doesn't yield an easy to model formula

dam = g(ATK, DEF) / h(DEF)

may yield a simpler formula for g(ATK, DEF). You eliminate the pesky h(DEF) by taking ratios as above.

dam2 / dam1 = g(ATK2, DEF) / g(ATK1, DEF)

There's probably something about commutative and associative properties of functions which describes what I'm doing, but it's been over 12 years since I took formal math courses.

Illyana - Dreamweaver · May 2010

@Solandri

Hey, is there an archer hiding underneath all that tiger fur? You could have fooled me.

kenlee · May 2010

why do you think only archers know basic math??
he is a veno and we do calc. too

A_Noob - Dreamweaver · May 2010

I'm a sin and I do math too!!!
2+2=5 see?

Illyana - Dreamweaver · May 2010

A_Noob - Dreamweaver wrote: »

I'm a sin and I do math too!!!
2+2=5 see?

Nuu, you're a cheze in disguise!

SneakyStalk - Harshlands · May 2010

errr, I DONT GET IT -.-

could someone de-elenacostel-it for me plz?

lol

Quilue - Sanctuary · May 2010

SneakyStalk - Harshlands wrote: »

errr, I DONT GET IT -.-

could someone de-elenacostel-it for me plz?

lol

OK i de-elenacostel it npnp:

I'm a little teapot
Short and stout
Here is my handle
Here is my snout
When I get all steamed up
Hear me shout
Tip me over and
Pour me out!

Olba - Sanctuary · May 2010

Quilue - Sanctuary wrote: »

OK i de-elenacostel it npnp:

I'm a little teapot
Short and stout
Here is my handle
Here is my snout
When I get all steamed up
Hear me shout
Tip me over and
Pour me out!

So we have a teapot that can pour itself out of itself? How does that work? I think that breaks quite a few laws of physics and general logic. And no, Banach-Tarski isn't going to help you there.

Attack Level and Defense Level Demystified

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