View source for Empower Vs Maximize

This page is to record opinions and some supporting facts around the discussion of which of these two feats is more worthwhile to take. Please keep discussion to the discussion page, or to the many threads on this subject.

==Reasons for Empower.==
* Only requires a spell slot 2 levels higher than normal or 1 with Arcane Scholar.
* On average an empowered spell does slightly more than 75% of the damage of the same maximized spell
* Required feat for Arcane Scholars

==Reasons for Maximize==
* More damage than empowered on average
* Damage is not random

==Reasons for both==
* Allows the spell to be used in more spell slots, covering up to three slot levels.
==Mathematics==

Empower effectively increases the damage potential of a spell by up to 50%, by increasing the damage output directly. This means that there are still variables.

The following table shows the lowest, average and the highest possible damage per die with a spell

{| border="1" cellpadding="1" cellspacing="1" style="width: 200px;"
|+Lowest/Average/Highest damage
|
| style="text-align: center;"|'''Normal'''
| style="text-align: center;"|'''Empowered'''
| style="text-align: center;"|'''Maximized'''
|-
| style="text-align: right;"|'''d2'''
| style="text-align: center;"|1/1.5/2
| style="text-align: center;"|1.5/2.25/3
| style="text-align: center;"|2/2/2
|-
| style="text-align: right;"|'''d3'''
| style="text-align: center;"|1/2/3
| style="text-align: center;"|1.5/3/4.5*
| style="text-align: center;"|3/3/3
|-
| style="text-align: right;"|'''d4'''
| style="text-align: center;"|1/2.5/4
| style="text-align: center;"|1.5/3.75/6
| style="text-align: center;"|4/4/4
|-
| style="text-align: right;"|'''d6'''
| style="text-align: center;"|1/3.5/6
| style="text-align: center;"|1.5/5.25/9
| style="text-align: center;"|6/6/6
|-
| style="text-align: right;"|'''d8'''
| style="text-align: center;"|1/4.5/8
| style="text-align: center;"|1.5/6.75/12
| style="text-align: center;"|8/8/8
|-
| style="text-align: right;"|'''d10'''
| style="text-align: center;"|1/5.5/10
| style="text-align: center;"|1.5/8.25/15
| style="text-align: center;"|10/10/10
|-
| style="text-align: right;"|'''d12'''
| style="text-align: center;"|1/6.5/12
| style="text-align: center;"|1.5/9.75/18
| style="text-align: center;"|12/12/12
|-
| style="text-align: right;"|'''d20'''
| style="text-align: center;"|1/10.5/20
| style="text-align: center;"|1.5/15.75/30
| style="text-align: center;"|20/20/20
|-
| style="text-align: right;"|'''d100'''
| style="text-align: center;"|1/50.5/100
| style="text-align: center;"|1.5/75.75/150
| style="text-align: center;"|100/100/100
|}



Scaling the results by dividing through by the normal results:

{| border="1" cellpadding="1" cellspacing="1" style="width: 200px;"
|
| style="text-align: center;"|'''Normal'''
| style="text-align: center;"|'''Empowered'''
| style="text-align: center;"|'''Maximized'''
|-
| style="text-align: right;"|'''d2'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|2/1.33/1
|-
| style="text-align: right;"|'''d3'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5*
| style="text-align: center;"|3/1.5/1
|-
| style="text-align: right;"|'''d4'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|4/1.6/1
|-
| style="text-align: right;"|'''d6'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|6/1.71/1
|-
| style="text-align: right;"|'''d8'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|8/1.78/1
|-
| style="text-align: right;"|'''d10'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|10/1.82/1
|-
| style="text-align: right;"|'''d12'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|12/1.85/1
|-
| style="text-align: right;"|'''d20'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|20/1.90/1
|-
| style="text-align: right;"|'''d100'''
| style="text-align: center;"|1/1/1
| style="text-align: center;"|1.5/1.5/1.5
| style="text-align: center;"|100/1.98/1
|}
It is clear that the advantage of maximized increases with the die size (from 1.33 to 1.98) but the advantage of empowered is constant (1.5). Note that Empower has a greater maximum damage potential than Maximize, but that on average it performs worse (75.75% of maximize for d100 to 93.75% for d4) for most die sizes, breaking even on average with d3 and only with d2 (112.78%) is the average of Empower better than Maximize. Note that due to law of large numbers the chance of this occuring decreases with the number of dice rolled. For example, with 1d6 empower will do more damage than maximize with a roll of 5 or 6, which has a 33% (2/6) chance of occuring. With 2d6, empower will inflict more damage than maximize with a roll of 9 or higher, which has a 28% (10/36) chance of occuring. With 3d6, empower will do more damage than maximize with a roll of 13 or higher, which has a 26% (56/216) chance of occuring.

When damage resistance is involved, if the DR is high enough to block a maximized spell, then an empowered spell can do more damage if it is a spell that makes multiple attacks with a low number of dice. For example the spells [[Flame Arrow]], [[Scorching Ray]], [[Isaac's Lesser Missile Storm]] and [[Isaac's Greater Missile Storm]]. For example, against an opponent with 10 points of magic DR a maximized IGMS will do 20 points of damage and on average a empowered IGMS will do 16 points of damage. Against an opponenent with 11 points of DR a maximized IGMS will do 10 points of damage and on average a empowered IGMS will do 12 points of damage on average. This is not something you would want to try with [[Disintegrate]], A maximized disintegrate does 240 points of damage, for an empowered disintegrate beat that damage it would have to roll higher than a 160 on 40d6 (which has a roughly 3% chance of occuring based on 1000000 rolls).

* Because of rounding, Empowered d3s may give less than 50% more. For example, an [[Acid Splash]] will give a maximum of 4, only a third more than its normal maximum. This also lowers the average damage increase to a third. However, values are usually rounded after all the dice are calculated, so a spell which gave multiple d3s would suffer no more than any other spell for which you rolled an odd number. Note that because of this rounding, ''all'' spells have a slightly lower average than 1.5 times the base.
Another important variable is static modifiers to the roll. For instance, Cleric Healing spells are in the form '''xd8+level''' (usually to a cap). The greater the ratio of this bonus to the die number, the more advantageous Empower becomes over Maximize. For one spell (Cure Light Wounds, Mass), an Empowered version will ''always'' heal more than the maximized version, and for many others the odds are >50%.

'''20th-Level Cleric. Low/Average/High'''
{| border="1" cellpadding="1" cellspacing="1" style="width: 90%;"
! scope="col"|Spell
! scope="col"|Dice
! scope="col"|Normal
! scope="col"|Empowered
! scope="col"|Maximized
! scope="col"|Emp>=Max
|-
|'''Cure Light Wounds'''
| style="text-align: center;"|1d8+5
| style="text-align: center;"|6/9.5/13
| style="text-align: center;"|9/14.25/19.5
| style="text-align: center;"|13
| style="text-align: center;"|62.5%
|-
|'''Cure Moderate Wounds'''
| style="text-align: center;"|2d8+10
| style="text-align: center;"|12/19/26
| style="text-align: center;"|18/28.5/39
| style="text-align: center;"|26
| style="text-align: center;"|67.19%
|-
|'''Cure Serious Wounds'''
| style="text-align: center;"|3d8+15
| style="text-align: center;"|18/28.5/39
| style="text-align: center;"|27/42.75/58.5
| style="text-align: center;"|39
| style="text-align: center;"|76.56%
|-
|'''Cure Critical Wounds'''
| style="text-align: center;"|4d8+20
| style="text-align: center;"|24/38/52
| style="text-align: center;"|36/57/78
| style="text-align: center;"|52
| style="text-align: center;"|77.03%
|-
|'''Cure Light Wounds, Mass'''
| style="text-align: center;"|1d8+20
| style="text-align: center;"|21/24.5/28
| style="text-align: center;"|31.5/36.75/42
| style="text-align: center;"|28
| style="text-align: center;"|100%
|-
|'''Cure Moderate Wounds, Mass'''
| style="text-align: center;"|2d8+20
| style="text-align: center;"|22/29/36
| style="text-align: center;"|33/43.5/54
| style="text-align: center;"|36
| style="text-align: center;"|95.31%
|}
This is also true for at least one Wizard/Sorcerer Spell: Magic Missile, which has a 65.14% chance to do better damage Empowered over Maximized at caster level 9 (5d4+5).
[[Category:Metamagics]]
[[Category:Feats]]
[[Category:Class feats]]