The *NEW* Magical Damage Improvement Review

[melanastere]

Several months ago I wrote an article about magical damage improvement. With the upcoming new Enhancement system this article had to be updated but eventually I decided to rewrite it entirely.

The post is up to date with Module 7.0

Foreword

For those who want to know more about damage improvement in DDO please proceed directly to Introduction section below. For those who only want to calculate their spell damage here is the formula:

Total damage = base damage * (1 + enhancement % + item %) * (1.5 + enhancement crit multiplier + item crit multiplier) * (1 + 0.5 if empower + 1 if maximize) * (any misc multiplier like 2 for purple damage)

The italic part only applies when a crit occurs.

example: the maximum damage one can do with a 14th level Cone of Cold (14d6) is:

Total damage = 84 * (1 + 0.4 + 0.5) * (1.5 + 0.75 + 0.5) * (1 + 0.5 + 1) * (2) = 84 * 1.9 * 2.75 * 2.5 * 2 = 2194



1) Introduction

In DDO each damage spell has a base damage number (BD). For example:

Magic Missile / 1d2+3 per missile / BD = 4-5
Scorching Ray / 4d3+12 per ray..../ BD = 16-24

In order to increase the damage done by these spells (let's call the resulting total damage TD) one does have several possibilities: Action Point Enhancements (APEnh), items, metamagic feats and misc multipliers. Some of those possibilities increase the base damage BD of the spell whereas some others act as multipliers to this increased base damage number (IBD).

It would be too long to list all the possibilities mentionned above so we will limit them to the fire domain and to wizard Enhancements. Out of this one would be able to generalize for any domain/class improvement in game.


2) Improvement of the normal damage BD:


Source / name............................../ initial / BD increase/ IBD
----------------------------------------------------------------------------
APEnh../ Wizard Elemental Manipulation I.../ WEM1..../ +10% of BD / 1.1 * BD
APEnh../ Wizard Elemental Manipulation II../ WEM2..../ +20% of BD / 1.2 * BD
APEnh../ Wizard Elemental Manipulation III / WEM3..../ +30% of BD / 1.3 * BD
APEnh../ Wizard Elemental Manipulation IV../ WEM4..../ +40% of BD / 1.4 * BD
item.../ Lesser Combustion................./ LC....../ +10% of BD / 1.1 * BD
item.../ Combustion......................../ C......./ +20% of BD / 1.2 * BD
item.../ Improved Combustion.............../ IC....../ +30% of BD / 1.3 * BD
item.../ Greater Combustion................/ GC....../ +40% of BD / 1.4 * BD
item.../ Superior Combustion.............../ SC....../ +50% of BD / 1.5 * BD



* Note that two APEnh don't stack, only the higher progression is applicable.

* Note also that two items don't stack with each other, only the best one is applicable.

* Note then that one APEnh and one item stack. If one benefits by the two best improvements above one would have +90% of BD i.e. IBD = 1.9 * BD.

* Note finally that if one doesn't have any of the improvements above, IBD = BD.



3) Multiplier to the improved damage above:


Be aware that without any crit Enhancement or item one has a base value of 0% critical chance for 1.5 times damage.



Source.../ name................................./ initial / effect
--------------------------------------------------------------------------------------
APEnh..../ Wizard Lineage of Elements I........./ WLE1..../ +3% chance to critical hit
APEnh..../ Wizard Lineage of Elements II......../ WLE2..../ +6% chance to critical hit
APEnh..../ Wizard Lineage of Elements III......./ WLE3..../ +9% chance to critical hit
APEnh..../ Wizard Lineage of Deadly Elements I../ WLDE1.../ +0.25 to the critical damage multiplier
APEnh..../ Wizard Lineage of Deadly Elements II / WLDE2.../ +0.5 to the critical damage multiplier
APEnh..../ Wizard Lineage of Deadly Elements III/ WLDE3.../ +0.75 to the critical damage multiplier
item...../ Minor Fire Lore....................../ MFL...../ +3% crit chance. +0.25 to crit multiplier
item...../ Lesser Fire Lore...................../ LFL...../ +6% crit chance
item...../ Fire Lore............................/ FL....../ +6% crit chance. +0.25 to crit multiplier
item...../ Greater Fire Lore..................../ GFL...../ +9% crit chance. +0.25 to crit multiplier
item...../ Superior Fire Lore.................../ SFL...../ +9% crit chance. +0.5 to crit multiplier
metafeat / Empower............................../ E......./ 1.5 times IBD
metafeat / Maximize............................./ M......./ 2 times IBD
metafeat / Empower+Maximize...................../ E+M...../ 2.5 times IBD
misc...../ purple damage......................../ P......./ 2 times IBD


* Note first that two APEnh of the same type don't stack, only the higher is applicable.

* Note also that two Lore items don't stack but overlap. The best numbers from all the items are applicable.

* Note then that one APEnh from each type and one item stack. If one benefits by the three best critical improvements above (WLE3 + WLDE3 + SFL) one would get that 18% of the time the spell crits for 2.75 times damage.

* Note also that when no crit improvement is used TD = MD.

* Remark1: when one uses a crit improvement, instead of TD, one can calculate the mean damage (MD) done over time by doing the weighted average between the damage done with a crit and the one done without. For example if you have a Greater Fire Lore item the mean damage would be: MD = 0.91 * IBD + 0.09 * 1.75 * IBD = 1.0675 * IBD.

* Remark2: within this framework in order to calculate the effectiveness of a critical improvement, one can introduce the mean critical multiplier (MCM) given by:

MCM = (1-CC) + CC * CM

where CC is the critical chance and CM is the critical multiplier.

PLEASE SEE NEXT POST -->

[melanastere]

Let's calculate MCM in several situations.


(id) Combo............../ AP/ MCM................../ result
-----------------------------------------------------------
(1). no improvement...../ 0 / 1..................../ 1
(2). WLE1.............../ 1 / 0.97 + 0.03 * 1.5..../ 1.015
(3). WLE1 + WLDE1......./ 2 / 0.97 + 0.03 * 1.75.../ 1.0225
(4). WLE2.............../ 3 / 0.94 + 0.06 * 1.5..../ 1.03
(5). WLE1 + WLDE2......./ 4 / 0.97 + 0.03 * 2....../ 1.03
(6). WLE2 + WLDE1......./ 4 / 0.94 + 0.06 * 1.75.../ 1.045
(7). WLE3.............../ 6 / 0.91 + 0.09 * 1.5..../ 1.045
(8). WLE2 + WLDE2......./ 6 / 0.94 + 0.06 * 2....../ 1.06
(9). WLE3 + WLDE1......./ 7 / 0.91 + 0.09 * 1.75.../ 1.0675
(10) WLE3 + WLDE2......./ 9 / 0.91 + 0.09 * 2....../ 1.09
(11) SFL................/ 0 / 0.91 + 0.09 * 2....../ 1.09
(12) WLE1 + SFL........./ 1 / 0.88 + 0.12 * 2....../ 1.12
(13) WLE1 + WLDE1 + SFL / 2 / 0.88 + 0.12 * 2.25.../ 1.15
(14) WLE2 + SFL........./ 3 / 0.85 + 0.15 * 2....../ 1.15
(15) WLE1 + WLDE2 + SFL / 4 / 0.88 + 0.12 * 2.5..../ 1.18
(16) WLE3 + SFL........./ 6 / 0.82 + 0.18 * 2....../ 1.18
(17) WLE2 + WLDE1 + SFL / 4 / 0.85 + 0.15 * 2.25.../ 1.1875
(18) WLE2 + WLDE2 + SFL / 6 / 0.85 + 0.15 * 2.5..../ 1.225
(19) WLE3 + WLDE1 + SFL / 7 / 0.82 + 0.18 * 2.25.../ 1.225
(20) WLE3 + WLDE2 + SFL / 9 / 0.82 + 0.18 * 2.5..../ 1.27
(21) WLE3 + WLDE3 + SFL / 12/ 0.82 + 0.18 * 2.75.../ 1.315



* AP corresponds to the Action Point cost to get the corresponding Enhancements.

* One would note immediately that the Lore item is a great improvement. It's equivalent to having both WLE3 and WLDE2. So unless one has to wield something else in both hands a critical Lore item is definitely a must have.

* One would note also that in mean the critical feature doesn't give a striking multiplier. Doing 2.75 times damage from time to time is nice but the best mean multiplier is not much better than a simple Improved Combustion item. Don't forget thought that unlike the latter it applies to any spell level.

* Note from (13) and (14) that when one has already WLE1, choosing between WLE2 or WLDE1 leads to the same result but the latter costs less AP. Same remark from (15) and (16) and from (18) and (19). The rule is to invest in the two lines WLE and WLDE in parallel and don't maximize a line one after the other.



4) Calculations:

So now we can calculate the mean damage done. The formula is:

MD = BD * IBD * MCM * FM * MM

where BD, IBD and MCM are defined above, FM is the feat damage multiplier and MM the misc damage multiplier.


Let's put numbers and calculate the mean damage done in several situations. To illustrate it we will apply the results to one ray of a level 12 Scorching Ray spell.


(id) Combo......................../ AP / IBD......./ MCM..../ result../ MD....../ Crit damage
---------------------------------------------------------------------------------------------
(1)..no improvement.............../ 0../ 1........./ 1....../ 1......./ 16-24.../
(2)..SFL+WEM4...................../ 10 / 1+0.4...../ 1.09.../ 1.526.../ 24-36.../ 44-67
(3)..SFL+SC......................./ 0../ 1+0.5...../ 1.09.../ 1.635.../ 26-39.../ 48-72
(4)..WLE3+WLDE2+SFL+SC............/ 9../ 1+0.5...../ 1.27.../ 1.905.../ 30-45.../ 60-90
(5)..WEM4+SFL+SC................../ 10 / 1+0.4+0.5 / 1.09.../ 2.071.../ 33-49.../ 60-91
(6)..WLE1+SFL+WEM3+SC............./ 7../ 1+0.3+0.5 / 1.12.../ 2.016.../ 32-48.../ 57-86
(7)..WLE1+SFL+WEM4+SC............./ 11 / 1+0.4+0.5 / 1.12.../ 2.128.../ 34-51.../ 60-91
(8)..WLE1+WLDE1+SFL+WEM4+SC......./ 12 / 1+0.4+0.5 / 1.15.../ 2.185.../ 34-52.../ 68-102
(9)..WLE1+WLDE2+SFL+WEM4+SC......./ 14 / 1+0.4+0.5 / 1.18.../ 2.242.../ 35-53.../ 76-114
(10) WLE2+WLDE1+SFL+WEM4+SC......./ 14 / 1+0.4+0.5 / 1.1875 / 2.25625 / 36-54.../ 68-102
(11) WLE2+WLDE2+SFL+WEM4+SC......./ 16 / 1+0.4+0.5 / 1.225../ 2.3275../ 37-55.../ 76-114
(12) WLE3+WLDE2+SFL+WEM4+SC......./ 19 / 1+0.4+0.5 / 1.27.../ 2.413.../ 38-57.../ 76-114
(13) WLE3+WLDE3+SFL+WEM4+SC......./ 22 / 1+0.4+0.5 / 1.315../ 2.4985../ 39-59.../ 83-125
(14) WLE3+WLDE3+SFL+WEM4+SC+E+M+P / 22 / 1+0.4+0.5 / 1.315../ 12.4925./ 199-299 / 418-627




Conclusions:


1) Because now the number of APEnh slot is not fixed anymore, one can take both - damage improvement and crit mutlipliers - without restriction. Developing one of them only is still possible and each one of them leads to approximatively the same numbers.

2) Unlike before, the Superior Lore item is now always the best of the crit items.

3) Before the change the typical damage improvement combo was [ Greater Combustion APEnh + SC + GFL ] which gave a mean damage multiplier of 2.09. The new typical damage improvement combo is given by (6) and has a mean damage multiplier of 2.016. Those who want to max the damage improvement will spend 15 more AP and get a mean damage multiplier of 2.4985 and hence pay 15 AP for an extra 1.2 multiplier.

4) Of course one can always multiply his damage by 1.5, 2 or 2.5 with metamagic feats and the max achievable damage improvement is given by (14). To the max with three crits in a raw (one for each ray) a level 14 Scorching Ray would score 1881. Though it’s more reasonable to consider one crit only and the spell would score 1083. With one crit only and in the same situation a fail saved fireball would score 1567 and a Cone of Cold 2194.

5) Before the change the max mean damage multiplier was 13.965 and the max crit damage was 456-684. With the new Enhancement system the max mean damage multiplier is 12.4925 and the max crit damage is roughly the same. Actually the damage done within this new system is quite the same as before (it becomes slightly better with Module 4). Even if one can improve fire or cold with the same Enhancement, one spell deals only one type of damage.



As a final note, I would add that apart from the metamagic feats all of this is applicable to wands and scrolls if one replace the Wizard Elemental Manipulation with the Wizard Wand and Scroll Mastery line.

Don't hesitate to make some comments/corrections

^mel

[Dazalarian]

Great analysis!

Keep up the good work

Cheers,
-Daz

[dyvim]

It's a great topic that should be sticked...

Pehaps it will be even better with less abbreviations though (if you got the time Mela^^)
only for the text as I undestand that it is neccesary in your tables...

ex:

Originally Posted by Melanastere

MD = BD * IBD * MCM * FM * MM
where FM is the feat damage multiplier and MM the misc damage multiplier

but... what means BD, IBD, MCM ?

Oh!! a last thing, do you think you can use the table feature of vBcode?

[melanastere]

Originally Posted by dyvim

ex:
but... what means BD, IBD, MCM ?

Everything is written in the text

BD = Base Damage
IBD = Improved Base Damage
MCM = Mean Critical Multiplier

Originally Posted by dyvim

Oh!! a last thing, do you think you can use the table feature of vBcode?

I tried but it was messy. Will try it again next time.

[ArKhaN]

Quote :
*Even if one can improve fire or cold with the same Enhancement, one spell deals only one type of damage.*

Hey Mel :P
this could be wrong if at some point mages could get the feats Energy Substitution and Energy Admixture ^^
I used to have an Archmage / Avatar of Magic in PnP, who was casting Dual elements fireballs :P i mean 2 FB instead of one, and i was able to change the element at will ^^

But of course we won't see that in ddo i guess :P i'm just speaking like an old fool ^^

Cheers,

ArK

[dyvim]

Originally Posted by melanastere

Everything is written in the text

Of course it is... but it's pehaps 50 lines above...
A short remind could be usefull, or if it is possible the formula with the entire words (if it doesn't needs two lines)
I think it could be easier to read...

[melanastere]

Originally Posted by ArKhaN

this could be wrong if at some point mages could get the feats Energy Substitution and Energy Admixture ^^
I used to have an Archmage / Avatar of Magic in PnP, who was casting Dual elements fireballs :P i mean 2 FB instead of one, and i was able to change the element at will ^^

Yup, good point. Sweet dreams

Originally Posted by dyvim

Of course it is... but it's pehaps 50 lines above...
A short remind could be usefull, or if it is possible the formula with the entire words (if it doesn't needs two lines)
I think it could be easier to read...

I have to confess that it's not easy to read... I'll try to write something simpler and more easy to read when I have time

[Odysseus]

Is purple damage always x2?

I always thought that mummies were more vulnerable to fire than other enemies with this vulnerability.
Also in PnP fire vulnerability is x1.5 damage... Do cold creatures always get x2 in DDO? What about undeads in general?

Would be nice to have sure info about this.

[Elonderil]

In DDO I think vulnerability to a specific element is x2, but I'm not entirely certain. I lack the numerical where-with-all to stomach paying attention to it hehe.