Spell Power

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Version 0.18: This article may not be up to date for the latest stable release of Crawl.


Most spells use a spell power value to determine their damage, range, duration, etc. You can display your spell power for known spells by bringing up your spell list with z, then ?, then !, which will display a screen looking like this:

 Your Spells                      Power
a - Call Imp                      ###.......
b - Blink                         N/A
c - Conjure Flame                 #####...
d - Iron Shot                     ######....

Most spells have a capped spell power. A cap of 100 means that if your spell power is higher than 100, it will be set to 100. This is done to prevent players from casting super-powered low-level spells. The dots stop at the cap while the bars indicate how much effective spell power you have.

Contents

Equivalence

The amount of bars of spell power shown in spell description does not increase at the same rate as the actual spell power. Here is a table of what values can be hidden behind the various possible description shown by the game :

Value          Description
0-9          #.........
10-14        ##........
15-24        ###.......
25-34        ####......
35-49        #####.....
50-74        ######....
75-99        #######...
100-149      ########.. 
150-199      #########.
200          ##########

Here is a graph of the bars versus power:

Bars versus numeric power

Formula

First, the game calculates raw spell power using the following formula.

 ((Spellcasting / 2) + (2 * [average_spell_schools]) + brilliance)
 * enhancers
 * (INT / 10)
 * wild magic
 * augmentation
  • Average spell schools is the average of all the skills necessary for the spell - up to three schools for some spells (e.g. Mephitic Cloud, which requires Conjurations, Poison Magic, and Air Magic).
  • Brilliance is the effect of a potion of brilliance. The boost is equal to three average skill levels, but is still applied even if your average skill level has reached the max of 27. This boost is wholly separate from the wizardry effect and from the temporary Intelligence gain (which also affects spell power).
  • Enhancers is a factor calculated from rings of fire, staves of cold, a robe of the Archmagi, etc. You get +1 for every enhancer and -1 for every dampener. If the factor is positive, your spell power is multiplied by 1.5(factor). If it is negative, it is multiplied by 0.5(factor), effectively halving your power every dampener. The factor is capped at ±3.
  • Wild Magic is a mutation that increases your spell power, but decreases your success rate. The bonus is ×1.3, ×1.6 or ×1.9 depending on how many levels of this mutation you have.
  • Subdued Magic is a mutation that decreases your spell power, but increases your success rate. The penalty is /1.3, /1.6, or /1.9 depending on how many levels of this mutation you have. This is equivalent to x0.77, x0.63, or x0.53.
  • Augmentation is a demonspawn mutation which increases your spell power and gives a slaying bonus at high HP. The spellpower bonus is ×1.4, ×1.8 or ×2.2 depending on how much augmentation bonus you have.
Mutation Level HP <50% HP > 50% HP >66% HP >75% HP >83%
1 0 1 1 1 1
2 0 1 1 2 2
3 0 1 2 2 3

Once the raw spell power value is determined, a stepdown function is applied to obtain the real spell power:

Final Power = 50 * log_2(1 + spellpower/50)

This is capped at 200, and for values under 50 the exact spellpower is used instead.

Spell power stepdown function.png

Approximately, every 50 real spell power is twice as difficult to obtain; and there is an absolute maximum of 200 real spell power. For example, 50 raw spell power is equivalent to 50 real spell power; 100 raw spell power is equivalent to 50 + 50/2 = 75 real spell power; and 500 raw spell power is equivalent to 50 + 100/2 + 200/4 + 150/8 = 168 real spell power. The maximum of 200 real spell power is reached at 750 raw spell power.

Example: Spell Power Milestone

 Base Value = (Spellcasting / 2) + (2 * [average_spell_schools])

Since the base value of spell power is capped at 67.5, without any enhancers spell power of 150 (raw spell power of 350) is achievable with INT 52. In most cases, however, spellcasters wear enhancers that making their spell more powerful. One can calculate required base value for hitting specific spell powers. As an example, requirements of 100(########..), 150 (#########.), and 200(##########) are calculated with INT=40 (quite high!)

# of Enhancers Power ########.. Power #########. Power ##########
0 37.5 87.5 187.5
1 25 58.3 125
2 16.7 38.9 83.3
3 11.1 25.9 55.6
1 +
Wild magic 2
12.5 29.2 62.5

Maxed out spell power without potion of brilliance can only be accomplished with three enhancers, or two enhancers with a wild magic mutation. If one have Wild Magic Lv 2, then only one enhancer can max out your spell power. However, in this situation spellcasting success rate falls off dramatically, forcing the player to use wizardry ring. Demonspawn with augmentation 1 can enjoy max spell power with two enhancers, while one with augmentation 3 can enjoy maximum spell power with only one enhancer.

Spell Range

For most spells the range starts out at maximum, but for some spells like Flame Tongue the range increases based on spell power, after step down. Given that Flame Tongue is the most common spell with variable range, it serves as a useful example. Flame Tongue has a spell power cap of 40 for range and 25 for damage.

If the spell power (pow in the following) is above the power cap, the spell has maximum range. Otherwise:

 range = [pow*(maxrange - minrange) + (powercap/2)] / (powercap + minrange)

That's a bit involved. It helps to notice that the addition of powercap/2 is to do rounding up (otherwise it will round down). So we have:

 range = [pow*(maxrange - minrange)] / (powercap  +  minrange)

This is the ratio of pow to powercap, over the possible ranges. In effect, it is linear in range with spell power - once you get to about halfway between the maximum and minimum ranges, you are at about half of the power cap. 'About', because of the round up vs round down function.

In the table below, values of numerical power where either the range or displayed power change are shown. Note that the maximum power for Flame Tongue is 40.

Numerical power Power Range
0 #..... @>...
5 ##.... @>...
7 ##.... @->..
10 ###... @->..
15 ####.. @->..
20 ####.. @-->.
25 #####. @-->.
34 #####. @--->
35 ###### @--->

History

Prior to 0.18, the Wild and Subdued Magic mutations had larger effects on spellpower. Prior to 0.10, a different stepdown function for spellpower was used.