Magic Damage Calculation (very accurate!)

[henry1007]

Edit: Formula had been updated after more testing, now much simpler and more complete.


Hi there! This is my first post on the forum (and it is going to be a long one!)
I've always been wondering how magic damage is calculated in IB2, and after update 1.3 is out I finally have time to crack it.
After a night's effort I'm able to determine a formula which so far calculates magic damage with pinpoint accuracy (in over 70 fine-tuned battles with suitable helmets, gems, and of course, rings).
I'm so happy with the result and decided to register on the forum and share with you all.
Let's get started!

Contents
1. Definitions
2. Formula
3. Examples
4. What if I'm healing myself instead of using offensive magic?
5. What if the enemy titan has resistance / opposite resistance to my magic?
6. What if I'm using Shield magic?
7. What if I get a different magic damage as opposed to the formula?
8. What's up with all the strange parameters in the formula?


1. Definitions
Before we come to the formula, let's make sure that we are on the same page.
Magic Level - The number shown on rings (e.g. The Holy Band is 10, Diruel is 8)
Magic Stat - This is your total magic stat, no matter coming from skill points or gems or equipments.

2. Formula
Basically, the formula is very simple:
Damage = "Effective Magic Stat" (minimum is 100) x Damage per Effective Magic Stat

The first item, "Effective Magic Stat" reflects the diminishing marginal return of Magic Stat.

Magic Stat From	To	"Effective Magic Stat"
0	10	10
10	110	1
110	210	1/2
210	310	1/4
310	410	1/8
410	above	1/16, etc (should follow same pattern afterwards)

It essentially means that when you have higher Magic Stat, the extra damage of adding 1 more magic is diminished.
e.g. if there's an extra damage of 20 when Magic Stat goes from 10 to 11, then...
extra damage = 10 when Magic Stat goes from 110 to 111
extra damage = 5 when Magic Stat goes from 210 to 211
etc.

The second item, Damage per Effective Magic Stat vary by Magic Level, and you may refer to the table below:

Magic Level	Damage per Effective Magic Stat
1	1
2	3
3	5
4	10
5	20
6	30
7	35
8	40
9	n/a
10	50

3. Examples
OK, you may ask, I've seen all the formula and tables and stuff, so how do I calculate magic damage?
Here goes some examples!

What is the magic damage using Dragoor Scale (Fire 7) with Magic Stat of 86?
Effective Magic Stat (from 0 to 10) = 10 x 10 = 100
Effective Magic Stat (from 10 to 86) = 76 x 1 = 76
Damage per Effective Magic Stat = 35 (Level 7)
Damage = (100 + 76) x 35 = 6160

What is the magic damage using The Holy Band (Holy 10) with Magic Stat of 437?
Effective Magic Stat (from 0 to 10) = 10 x 10 = 100
Effective Magic Stat (from 10 to 110) = 100 x 1 = 100
Effective Magic Stat (from 110 to 210) = 100 / 2 = 50
Effective Magic Stat (from 210 to 310) = 100 / 4 = 25
Effective Magic Stat (from 310 to 410) = 100 / 8 = 12.5
Effective Magic Stat (from 410 to 437) = 27 / 16 = 1.6875
Damage per Effective Magic Stat = 50 (Level 10)
Damage = (100 + 100 + 50 + 25 + 12.5 + 1.6875) x 50 = 14459.375 (That's 14459 taking away fraction part)

4. What if I'm healing myself instead of using offensive magic?
Simple, the healing amount is a fixed multiple of magic damage (but again, vary by Magic Level)
Below is yet another table showing the multiples:

Magic Level	Multiple
1	4
2	10/3 (yes, a fraction)
3	5
4	4
5	2.5
6	2
7	2
8	n/a
9	n/a
10	n/a

So if in the first example you're healing yourself with Dragoor Scale (Heal 7), the healing amount would be:
6160 x 2 = 12320 (times the multiple before taking away fraction part if there's any)

5. What if the enemy titan has resistance / opposite resistance to my magic?
Also simple, just times 1/10 (resistance) or 1.5 (opposite resistance) to the damage.
So if in the second example, you're using The Holy Band against one of the bosses in update 1.3, the damage would be:
14459 (after taking away fraction part) / 10 = 1445.9 (That's 1445)

6. What if I'm using Shield magic?
I haven't started testing on Shield magic yet... You may help by posting relevant data!

7. What if I get a different magic damage as opposed to the formula?
There're two factors I can think of that may affect the result:
- The formula is only valid for update 1.3 (not likely)
- Very high Magic Stat (I've been able to test up to 4XX only, but my guess is that the pattern is the same)
If possible, if you observe any deviation please note your Magic Stat, Magic Level, any enemy resistance and magic damage and I'll double-check.

8. What's up with all the strange parameters in the formula?
The parameters are just end results of my calculations and I don't see any pattern in them.
Maybe a result of fine-tuning for game balance from developers.


Whoops... This is such a long post! I'm so happy to share my two cents. Comments welcomed

[Dzylon]

This is a very well thought-out and thorough post, well done! Though, with a magic stat of 7 and the High Storm equipped (level 1 lightning), only 100 damage is inflicted.

Edit: All of the higher-level tests I've done so far are accurate, though.

[henry1007]

This is a very well thought-out and thorough post, well done! Though, with a magic stat of 7 and the High Storm equipped (level 1 lightning), only 100 damage is inflicted.

Edit: All of the higher-level tests I've done so far are accurate, though.

Thanks! This is very encouraging. I haven't been able to test the low-end part of Magic Stat because I allocated over 100 skill points to Magic to play with The Holy Band :P
Probably there's a change in the increment for a lower Magic Stat than 210.... Just spent a sum of money to reallocate my skill points and start testing.

[henry1007]

This is a very well thought-out and thorough post, well done! Though, with a magic stat of 7 and the High Storm equipped (level 1 lightning), only 100 damage is inflicted.

Edit: All of the higher-level tests I've done so far are accurate, though.

I've restructured the formula after testing damage with Magic Stat < 110. The fact is that the first 10 Magic Stat is useless (Effective Magic Stat has a minimum of 100), so in your case with High Storm equipped, damage is 100 when Magic Stat is 1 to 10.

[agentblank]

Helpful post, thanks!

[ckd0214]

Welcome to the forums!

Magic Level	Damage per Effective Magic Stat
1	1
2	3
3	5
4	10
5	20
6	30
7	35
8	40
9	n/a
10	50

4. What if I'm healing myself instead of using offensive magic?
Simple, the healing amount is a fixed multiple of magic damage (but again, vary by Magic Level)
Below is yet another table showing the multiples:

Magic Level	Multiple
1	4
2	10/3 (yes, a fraction)
3	5
4	4
5	2.5
6	2
7	2
8	n/a
9	n/a
10	n/a

A simpler way for healing magic:

Magic Level	Heal per Effective Magic Stat
1	4
2	10
3	25
4	40
5	50
6	60
7	70
8	n/a
9	n/a
10	n/a

Also: up to 910 magic stat using Holy Band:

Effective Magic Stat (from 0 to 10) = 10 x 10 = 100 * 50 = 5,000 damage
Effective Magic Stat (from 10 to 110) = 100 x 1 = 100 * 50 = 5,000 damage = 10,000
Effective Magic Stat (from 110 to 210) = 100 / 2 = 50 * 50 = 2,500 damage = 12,500
Effective Magic Stat (from 210 to 310) = 100 / 4 = 25 * 50 = 1,250 damage = 13,750
Effective Magic Stat (from 310 to 410) = 100 / 8 = 12.5 * 50 = 625 damage = 14,375
Effective Magic Stat (from 410 to 510) = 100 / 16 = 6.25 * 50 = 312.5 damage = 14,687.5
Effective Magic Stat (from 510 to 610) = 100 / 32 = 3.125 * 50 = 156.25 damage = 14,843.75
Effective Magic Stat (from 610 to 710) = 100 / 64 = 1.5625 * 50 = 78.125 damage = 14,921.875
Effective Magic Stat (from 710 to 810) = 100 / 128 = 0.78125 * 50 = 39.0625 damage = 14,960.9375
Effective Magic Stat (from 810 to 910) = 100 / 256 = 0.390625 * 50 = 19.53125 damage = 14,980.46875

So the cap for the BEST ring in the game is 15,000 damage. The effective magic stat cap is 15,000/50 or 300.

By far the most effective increase comes from "10 to 110", with each magic stat adding 50 points of damage. The next most valuable increase comes from "110 to 210", with each stat point adding 25 damage. The reason these first two increases are special is because they also increse regen time, with the cap being around 18 seconds at 200 magic. Going up to 310 is optional, as it adds 12.5 damage per stat.

However, past 310 magic, the damage will diminish greatly. This is the cutoff point. Beyond here, you will recieve less than 1k damage per 100 magic, while before you'd get more than 1k. In fact, going beyond 310 magic is pointless, seeing as how it will take 300 more stat points to get to the next 1,000. It also only adds 6.25 damage per stat, and doesn't do as much damage as adding attack.

Compared to adding to attack, 100 magic points from 310 to 410 adds 625 damage per 18 seconds (magic regen cap). 100 attack points in one dual break = 1x, 1x, 2x, 2x, 2x, 3x, with each x equalling 100 points of damage and the number in front is how much to multiply the x by. That's a total of 900 damage. This is assuming a full combo can be completed. Going from 210 to 310 outpaces attack by a little, but 310 to 410 is wasted skill points.

Side note: eventually, the enemies health gets high enough that even a full 15k damage from the holy band will be but a scratch. At this point, magic is useless except for interrupting stepbacks. And by then, you've probably played enough to know how to avoid those attacks by now. If not, you probably die a lot.

[asianlitarian]

I agree with your last paragraph. On a level 1000 titan over RB 200, a Holy Band does 1/7 of total damage.

[Vile Majesty]

Thanks a lot for your findings, been wondering how to calculate magic damage for some time.

Welcome to the Forums

[=Silver=]

Nice research
Welcome, Henry!

One more interesting topic to research is magic regen cycle timing.

[ckd0214]

Check this out silver: http://forums.epicgames.com/threads/...0-magic-points
Regen caps at 100 points. 18 seconds.

[Laygh]

Check this out silver: http://forums.epicgames.com/threads/...0-magic-points
Regen caps at 100 points. 18 seconds.

So 100 for regen, 200 for damage? Ok.

[Vile Majesty]

One question which slipped past my head earlier, henry: for a ring without any offensive spell, like the Circle of Life, how do you calculate it's magic damage? You used the Dragoor Scale and it has on offensive spell to help you derive its magical damage.

Also your table on Heal spell's power seems to imply, from how I understand it, that a Heal 2 is better than a Heal 7 for instance given the same magic damage. Perhaps I misunderstood something? Mind clarify?

[ckd0214]

One question which slipped past my head earlier, henry: for a ring without any offensive spell, like the Circle of Life, how do you calculate it's magic damage? You used the Dragoor Scale and it has on offensive spell to help you derive its magical damage.

Also your table on Heal spell's power seems to imply, from how I understand it, that a Heal 2 is better than a Heal 7 for instance given the same magic damage. Perhaps I misunderstood something? Mind clarify?

A simpler way for healing magic:

Magic Level	Heal per Effective Magic Stat
1	4
2	10
3	25
4	40
5	50
6	60
7	70
8	n/a
9	n/a
10	n/a

I see the confusion. Heal magic works by multiplying the final answer for damage by the chart he has. This ^ is a simpler way of writing it, as this replaces damage per effective magic stat with heal per effective magic stat.

A ring w/o offensive magic spell would calculate the same, except with the effective heal chart I put up replacing the effective damage chart henry has.

@Laygh I prefer one Rare Magic Gem, out of simply wanting to have a rare magic gem. Not to mention that it is actually a very good cutoff point for the magic, although one capped magic gem is slightly better, it lacks the coolness of "rare".

[Vile Majesty]

I see the confusion. Heal magic works by multiplying the final answer for damage by the chart he has. This ^ is a simpler way of writing it, as this replaces damage per effective magic stat with heal per effective magic stat.

A ring w/o offensive magic spell would calculate the same, except with the effective heal chart I put up replacing the effective damage chart henry has.

@Laygh I prefer a cutoff of 310 magic, because that's when damage from spells no longer does more than attack. At 410 you still get a return of about 600 more damage on Holy Band, and heal about 2,000 more (I belive) with Dragoor Scale Heal 7. But the difference is 18,000 and 20,000 on Dragoor Scale, and 13,700 versus 14,300 on Holy Band.

Thanks ckd for clarifying. So a Heal 7 is still better than a Heal 2.

[Laygh]

@Laygh I prefer a cutoff of 310 magic, because that's when damage from spells no longer does more than attack. At 410 you still get a return of about 600 more damage on Holy Band, and heal about 2,000 more (I belive) with Dragoor Scale Heal 7. But the difference is 18,000 and 20,000 on Dragoor Scale, and 13,700 versus 14,300 on Holy Band.

What's the point of having 600 extra damage? IMO that is an insignificant amount of damage.Especially when that could go into something much more worthy, such as shield, or attack. Put the 200 extra SP into attack and you could get 1000-2000 damage per brake. Much better than getting 600 extra damage for something you can only use every once and awhile. Sorry if I sound ignorant but I am really not a magic person.

[ckd0214]

What's the point of having 600 extra damage? IMO that is an insignificant amount of damage.Especially when that could go into something much more worthy, such as shield, or attack. Put the 200 extra SP into attack and you could get 1000-2000 damage per brake. Much better than getting 600 extra damage for something you can only use every once and awhile. Sorry if I sound ignorant but I am really not a magic person.

edited my post so I said I'd only use on rare magic gem, my brain is asleep now. Dunno what I was thinking.

What I did, though, was find that 410 magic adds 600 attack from 310. 310 adds 1,250 from 210. Each costs 100 stat points. If I added 100 to attack, I'd get 900 damage from a dual combo, (x+x+2x+2x+2x+3x), the shortest possible ultra with dual. Going to 410 makes it so that the 600 attack will always be less useful than if I added to attack, so I thought the cutoff was 310. Then I remembered a usual dual break lasts far longer than that. D'oh.

[Bimasakti]

Thanks for information in this thread..
I think for the low level titans, magic is useful..Holy band and ring of man were my favorite in OG
I used to use them to get heal..
But if you fight the titan above level 2000, it will be useless...
I would rather allocate my skill point to attack stat..
And if my HP get low, I would swith to Kudgel equipped with 2 heavy health gem (on slash get 1000 hp/ gem)..
By using heavy weapon, you will have the opportunity to get at least 6 slashes, meaning you will gel 12,000
Since I allocate HP only 15.100, this will be sufficient during the long fight..

just my two cents

Cheers

[asianlitarian]

Technically, as long as you have one magic gem that you buff, you shouldn't have a problem balancing magic with SP.
The number of gems you have really don't matter because you're still leveling your total count either way.

[Laygh]

edited my post so I said I'd only use on rare magic gem, my brain is asleep now. Dunno what I was thinking.

What I did, though, was find that 410 magic adds 600 attack from 310. 310 adds 1,250 from 210. Each costs 100 stat points. If I added 100 to attack, I'd get 900 damage from a dual combo, (x+x+2x+2x+2x+3x), the shortest possible ultra with dual. Going to 410 makes it so that the 600 attack will always be less useful than if I added to attack, so I thought the cutoff was 310. Then I remembered a usual dual break lasts far longer than that. D'oh.

Lol you really should've said something about the magic gem. That would've completely changed what I may have said.

[ckd0214]

Also, gems are more versatile compared to stats; resetting stats costs 1M gold at time, while unsocketing gems costs 50k at worst. Or 5k in BG.

[Soki]

Great work Henry! this should be added into UTL too, same as SpencerTT's hit bound break windows and weapon class comparison guide. Here is the link http://forums.epicgames.com/threads/...8#post30685288

[=Silver=]

Check this out silver: http://forums.epicgames.com/threads/...0-magic-points
Regen caps at 100 points. 18 seconds.

I saw it, like some other threads on this topic, but my question is still not answered: I'm interested not much in how first regen speeds up with more magic pts, but how regen slows with casting in the same fight. The fact is that it takes longer and longer with each cast to regen, but there are caps for "quickest first" and "slowest last" regen. The fact also is that the more magic pts you have the lower this "regen plateau" stays.

The first who showed this in figures was Curi, but it was long ago, and for IB1. No one did this quantification since that time

[ckd0214]

I vaguely recall this... however I don't believe anyone has any tests done on IB 2 yet. Not really in a position to test it myself.

The way I see it, though, adding magic past the 200s/one rare gem is pointless in terms of first regen and attacking/healing power due to diminishing returns. So I'll just keep it there, unless we find that the regen plateau caps near ___, then I'll stop my gem there.

[Vile Majesty]

The fact also is that the more magic pts you have the lower this "regen plateau" stays.

Explain what you mean by "regeneration plateau"?

[=Silver=]

Explain what you mean by "regeneration plateau"?

The distance between the fastest and slowest caps. The more magic pts you have the lower and "more horizontal" regen speed curve is.

Imagine you have enough magic pts for ten casts in a row to increase only from 15 to 20 sec (where the slowest is about a 60 sec)

Btw, NG number has a severe influence here.

[ckd0214]

Yeah, NG magic is pointless as regen caps sooner and damage can be dealt in easier ways.