Predicting your magic damage formula

[mammoth]

Here is a pretty good formula I got that predicts how much damage you could deal based on 1. the number shown on your ring 2. your total magic stats shown on the character page. TRY IT!!!! IT IS INCREDIBLY ACCURATE. You could use it to decide whether or not you should put more stats into magic

YOUR MAGIC DAMAGE = BASE(N) * (0.657 * LOG(MAGIC STATS) - 1.096);

-> Base(n) depends on the tier of your ring, ranging from 1 (High Storm, Worm Hole etc.) to 8 (Diruel). Here are its values
Base(1): 100
Base(2): 300
Base(3): 500
Base(4): 1000
Base(5): 2000
Base(6): unknown
Base(7): (only Devotion & Cog): 3500
Base(8): (only Diruel):4000

-> "log(magic stats)" refers to the natural logarithm of your magic stats. Here is a website that helps you calculate lagorithms. Choose Number Base = e and click "Enter"


HOW TO USE THIS FORUMLA

So for example, if you are currently using Diruel, and has a character with 188 total magic stats (gems+xp stats+stats on helmet etc.), you would deal approximately
BASE(8) * (0.657 * LOG(188) - 1.096)
= 4000*(0.657 * 5.2364 - 1.096)
=9377 damage (In reality, you would deal 9580)



The nerd inside me is very happy today.

[dknowle]

Nice analysis. How did you determine the formula? Best fit curve to data?

[asianlitarian]

I believe Magic 6 has a base of 3000. Not sure though. The Cog also has a base 7, and I'm trying to figure out the base for a Holy Band (Holy 10.)

[asianlitarian]

Alright, so the base of a 10 ring is approx.: 4400, or 4500 damage.
My magic stat is 454, and my damage is around 14500.
x*(.657*LOG(454)-1.096)= 14500ish
x*(.657*6.118097198-1.096), x*(3.299517859086)= 14500, x= 4394.581456824315

[mammoth]

Alright, so the base of a 10 ring is approx.: 4400, or 4500 damage.
My magic stat is 454, and my damage is around 14500.
x*(.657*LOG(454)-1.096)= 14500ish
x*(.657*6.118097198-1.096), x*(3.299517859086)= 14500, x= 4394.581456824315

Tested in OG... Totally forgot about the Cog. I have updated the list to include the Cog. Thanks! Yeah, I guess we could infer the base of Magic 6 from that Poison 6 ring. But for now I would wait for Illuminatus to become available to test it.

I haven't tested holy, because I am not sure whether we should add both the health and the damage to the stats. Thanks for the info!!

FYI, health regeneration has another formula, which, for the sake of not making this thread any more nerdier, I haven't not posted here.

[seleven]

for my case of 195magic with holy ring, the damage is 12125, i have no idea about the maximum amount of healing since i only have 10000 heath, everytime i cast magic, i must heal to max.
x*(0.657*LOGe(195)-1.096)=12125
x*(0.657*5.2729995586-1.096)=12125
x*(3.4643607100002-1.096)=12125
x*(2.3683607100002)=12125
x=5119.57

[=Silver=]

Fundamental approach

[Nafi Kacak]

Nice finding mammoth
Thanks for sharing it..
Give me calculator pls=)

[asianlitarian]

Hang on, I have an accurate measure of my magic now...
x*(.657*LOG(471)-1.096)=14565
x*(.657* 6.154858094-1.096)= x*(.657*5.058858095)=14565
x*3.323669767758=14565
x= 4382.204315630581

Strange... This seems to contradict Seleven's findings. Since base damage increases by 500 every stat after 6, 10 would seem to have a base of 5000..... I dunno what's wrong with my character.

[titanium]

You should not take the entire magic stats into a single function such as log(x). The "skill" part of the magic is worth 5 damage / skill point. The part that is added by items counts less. So if you have a holy band, 100 skill magic, and 200 item (gems/rings/etc) magic, then your damage is:

{450(base for the holy band) + 100*5 + SomeFunction(200) } * 10(holy band multiplier).

The "SomeFunction" part is what I haven't figured out yet. It is not a square root, linear, or 1/x function, and I'm not so sure it's a log function either. The damage in the above hypothetical case is somewhere around 14500.

[Xaranoth]

You should not take the entire magic stats into a single function such as log(x). The "skill" part of the magic is worth 5 damage / skill point. The part that is added by items counts less. So if you have a holy band, 100 skill magic, and 200 item (gems/rings/etc) magic, then your damage is:

{450(base for the holy band) + 100*5 + SomeFunction(200) } * 10(holy band multiplier).

The "SomeFunction" part is what I haven't figured out yet. It is not a square root, linear, or 1/x function, and I'm not so sure it's a log function either. The damage in the above hypothetical case is somewhere around 14500.

Interesting.... If this is true it would explain why the forum members above got such different results when trying to figure out the 10 base number for holy damage. Do you have the calculations somewhere for how you came up with that formula? Are there any other forum members out there who would be willing to run tests with titanium's formula to try and complete it?

Also, what are "(base for the holy band)" and "(holy band multiplier)"? Are those variables/unknown constants too, or just explanations of the numbers they're next to? If they are variables/unknown constants, are they the same?

Welcome to the forums!

[titanium]

Thanks. The base for the holy band was found by trial and error. I first remove all my magic gems and looked at the damage number. I had a character at magic skill = 86 and the damage was 8800. Now that seemed strange at first. I would have expected 8600 or something related to 86. So then I decreased my magic stat by 1 (by paying 100K to reallocate), and I saw the damage decrease by 50. I could then conclude that each magic skill point was worth 50 damage points when equipped with the holy band. My next task was to see if the holy band's "10" rating was a simple multiplier. So then what I did was to change rings to the black rose, which has a crystal "6" rating. I saw my damage reduce to exactly 60% of the damage that the holy band did. I could then conclude that the ring's numeric damage rating is just a simple multiplier of "something". This lent me to determine that the magic skill was worth 5 points each (before being multiplied by the ring's strength).

So now we have a siris at 86 magic that does 8800 damage. 86*5*10 of that must come from magic skill points (that's 4300). The rest must come from something else. I cannot actually confirm that the rest of the 4500 is ONLY attributed to the holy band and black rose rings, since I have only tried those 2. In fact, I do not even know if the 4500 points (450*10) is related to the ring at all. My character is level 105 so I cannot easily just level up by one, since i've cleaned out the store and most of the hidden items. I was giving mammoth the benefit of the doubt that it is somehow related to the ring, and that theory seems to be valid since a lowly shock 1 ring against this same titan certainly does not do anywhere near the damage from the forumula (it only does 17 versus the forumla value of 880).

Anyway, the shape of the damage curve does perhaps suggest a log function, but it sort of fits better to a square root or perhaps a cube root. more data is needed.

[Stelios]

Does the magic formula in the UTL not work anymore?

[Xaranoth]

Does the magic formula in the UTL not work anymore?

It's not that it doesn't work, it's that it sounds like it wasn't completely accurate to begin with.

@titanium, are you sure the titan in your example with the shock ring didn't have elemental resistance to shock? Cuz 17 sounds WAY too low, even for a level 1 ring. 880 sounds way too high too, I would expect somewhere around 100-200, depending on your magic stats. Unrelated, if you want to level up more in OG (tho the nature of it wouldn't be too conducive to testing magic) you could try negative rebirths (aka BG). I'm guessing it would get you up to about level 124.

[titanium]

@X: oops you are right. Switched to another low level ring and the damage is 181. My char is at 89 skill magic right now. I would have expected the damage to be 189, if the ring base is 100, and the 89 is only multiplied by 1 for a low level ring, and then (100 + 89*1 ) * 1 = 189. I'm beginning to think there are too many variables to try and reverse engineer this thing. We should just send an e-mail to ChAIR and see if they divulge.

I'm on this darn mission to see how high I can get in OG without going negative. I've spun that stupid rare wheel over 100 times now without getting anything new. That stupid wheel is definitely NOT very random. There is a much higher chance of getting certain items. Really ticks me off. I still have 3 black helmets, 2 black armors, 5 black rings, several black weapons etc. I can see some of them spin by on the wheel but no luck so far. But that's a different topic...

[Stelios]

This is all too complicated for me, if I put about 350 points into magic it'll start to level out and I shouldn't add any more, correct?

[titanium]

S, my best guess right now based on a small set of data is to say that you don't want more than about a 3-4x ratio between your added magic from gems/rings and your base magic skill. So if your siris has 100 magic skill points, don't add more than about 300-400 in gems/ring points. (That's a long winded way to say "Yes" to your question). That statement is true for damage done. As far as the time it takes to recharge the magic, I'm not sure but I think SAB's IB2 guide has some info on that part.

With limited gem slots, it seems better to use them for attack or health than for magic, beyond that point. Is it me or is shield useless in IB2? I haven't increased it in 50 rebirths and never needed it. But then again I'm not a level 1000 or anything.

[Stelios]

I have 0 SP in magic and one +275 ring I was going to upgrade to about 350. So that would be a 300:1 ratio, which is well outside of the ratio you recommended

[titanium]

you really have 0? I thought the game started with 1 and even when you redistribute the minimums are 1. Your case is certainly outside the usual, so I have no idea what adding another 75 points of magic from gems will do. just try it. it's only (fake) money. you can earn it back in a few battles.

[Xaranoth]

@X: oops you are right. Switched to another low level ring and the damage is 181. My char is at 89 skill magic right now. I would have expected the damage to be 189, if the ring base is 100, and the 89 is only multiplied by 1 for a low level ring, and then (100 + 89*1 ) * 1 = 189. I'm beginning to think there are too many variables to try and reverse engineer this thing. We should just send an e-mail to ChAIR and see if they divulge.

I'm on this darn mission to see how high I can get in OG without going negative. I've spun that stupid rare wheel over 100 times now without getting anything new. That stupid wheel is definitely NOT very random. There is a much higher chance of getting certain items. Really ticks me off. I still have 3 black helmets, 2 black armors, 5 black rings, several black weapons etc. I can see some of them spin by on the wheel but no luck so far. But that's a different topic...

No those wheels aren't random at all lol, except within a very small range of items. Have you gotten all of the items from the maps? There's quite a few from those. You could also try equipping drop weapon and item gems, and drop rare item gems. And two of the black items in each category (light, heavy, dual, shield, helmet, armor, and ring) are unobtainable in OG without going to BG or NG. There's also two other rings and a helmet (cryo loop, illuminatus, and the vim) that can only be gotten through CM. so you probably have most of the stuff you can get, of not all of it.

Shield is useless if you use dual exclusively. But if you use light or heavy you'll want shield. The higher end shields have quite a bit of shield points (like kerrack with 100), so if that's good for you then you won't need to add more shield SPs, especially if you have some shield gems. The other thing to consider is that titans will take off up to five shield points per hit in higher RBs, but not higher than that unless you go into NG.

And as far as magic goes, most players in high RBs or NGs prefer the rings that have hex gem slots instead of magic. You can use these for Titan break+ gems or gold+ gems, among others. For example I could use a holy band that deals ~13,000 damage, and generally takes a little longer than one break cycle to charge, or I could use a iridix with a TB+2 that allows me to do an extra ~27,000 damage per break.

[titanium]

So a bit more data I've discovered on ring damage. Some of this contradicts mammoths findings so I'm not real sure since I suspect that mammoth has played a lot more than me. However I do have dozens of data points from 2 different characters (of mine).

Rings seem to come in strengths from 1-5. For example, worm hole and high storm are strength=1, manak ring is strength=1.5, and holy band/black rose are strength=5. Of course, those strengths are then further multiplied by the numeric magic factor of the ring spells (holy-10, crystal-6, etc). The ring damage (not including healing or shield) seems to follow this formula:

Definitions:
RingStrength = attribute of the ring, 1 to 5
MagicSkill = the portion of magic from your character
MagicItem = the portion of your magic stat from gems/rings
SpellMultiplier = the strength of an individual spell, like Holy-10, Crystal-6, or Ice-2.

{ 90*RingStrength + RingStrength*MagicSkill + SomeFunction(MagicItem) } * SpellMultiplier = Damage

So in our original example from my very first post

{ 90*5 + 5*86 + 0 } * 10 = 8800 (holy band damage for a character with 86 magic, but no additional magic from items)
{ 90*5 + 5*86 + 0 } * 6 = 5280 (same character with a Black Rose crystal-6ring)

Turquoise Band (light-2) on a character with 13+0 or 14+0 magic. Ring strength is 1.5
{ 90*1.5 + 13*1.5 + 0 } * 2 = 309
{ 90*1.5 + 14*1.5 + 0 } * 2 = 312

Fire Circle (fire-3) on that same character with 14+0 magic. Ring strength is 1 2/3 (1.66666...)

{ 90*1.66 + 14*1.66 + 0 } * 3 = 520

The big question is what is the "SomeFunction" of the added on magic. This is the additional damage that is done by magic points from items or gems. I'm not sure what it is, but additional damage tails of quickly after you add more than about 3x the magic points relative to your base magic.

Note that the "heal" spells seem to use a different formula than the damages created by attack spells. Haven't figured that out yet. The ring strength seems to be different for heal spells -- the fire circle seems to have a strength of 5 for the "heal-2" spell.

OK this is my last post on this topic. The horse is dead. On to something else...

[Stelios]

you really have 0? I thought the game started with 1 and even when you redistribute the minimums are 1. Your case is certainly outside the usual, so I have no idea what adding another 75 points of magic from gems will do. just try it. it's only (fake) money. you can earn it back in a few battles.

Oops, I have 1. The ratio remains the same. Thanks for the info, will play around

[Victor Ruidera]

edit: I think I got it. But does this also applies dor IB1?

[titanium]

OK so I lied about not posting here again. This was really bugging me since I hate math problems that remain unsolved. I think I have the REAL answer on the ring damange and "how much magic should I add" and the reason you can't make a mage in this game.

After you go past a total of 110 magic points, whether by skill points or by items does not matter, then the damages starts to tail off dramatically. It goes down by half again every 100 points past 110. So from 110 to 210, you get 1/2 the damage per magic point, and from 210 to 310 you get 1/4 the damage, and so on. To accurately calculate damage, you need to know the inherent strength property of the ring, which as far as I can tell must be obtained by observation.

Here's the forumla:
ring damage = (90 + MagicUpTo110 + Magig(210-110)*.5 + Magic(310-210)*.25 + Magic(410-310)*.125 + .... ) * RingStrength * SpellMultipler

So, for example, if you character has 289 magic points, the formula for the holy band (which has a ring strength of 5) and the holy spell-10 :
(90 + 110 + 110*.5 + 79*.25) * 5 * 10 = 13487

This means that it probably doesn't make sense to keep increasing your magic past about 310 since you get far fewer damage points per magic point.

Those familiar with the infinite series 1/2+1/4+1/8+1/16... will recoginze that the theoretical maximum damage predicted by my formula is 15500, since the holy band has the largest known damage. I think I have seen on person report damages over 20,000, which means that the rules may change when your character's skill points are very high. I have a character with magic 216 and this is not high enough to change the equation.

Here are some ring strengths for the above equation:
barbok, cuauag : 1
soulless circle : 1.5
compass: 1.66666 (1 2/3)
thorne, tome band, dark crystal : 2.5 (damage at magic=110 is spell strength*500, or 2000 for spell4. at magic=220 it is 2500 damage)
the sacrifice, jade band : 4 (damage at magic=110 is spell strength*800, or 4000 for spell5. at magic=220 damage is 5000)
holy band, black rose, dragoor scale, venom kiss : 5 (damage at magic=110 is spell strength * 1000, so 10K for holy10, 7K for fire7, etc)

The "heal" spells have different multipliers. They seem to be more than double the points of the spell damage. For example, the heal2 spell of the fire cirlce ring give you 2x more heal points than the fire3 spell does damage, in the same ring.