Spell Power

Version 0.30: This article may not be up to date for the latest stable release of Crawl.

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

 Your Spells                      Power
a - Sting                         100%
c - Call Imp                      44%
d - Iron Shot                     11%

Each individual spell has a spell power cap placed on it. A cap of 100 means that if your spell power is higher than 100, it will be set to 100. This allows for low-level spells to scale quickly with skill, but prevents them from getting too strong.

Formula

Raw power

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

 ((Spellcasting / 2) + (2 * [average_spell_schools]))
 * enhancers
 * (Intelligence / 10)
 * mutations

• 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). Djinn instead use the generic Spellcasting skill for all of their spells.
• Spell Enhancers include magical staves, a potion of brilliance, 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.
• Mutations add a multiplier, depending on the mutation in question.
  • Wild Magic 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 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. This stacks multiplicatively with the other mutations.

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

Step down

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

Spellpower = 50 * log_2(1 + raw_power/50)

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

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	100 Power	150 Power	200 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

Maximum spell power can only be accomplished with three enhancers, assuming 40 Int and no mutations . If one has 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 a ring of wizardry. 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 spells like Passwall, the range increases based on spell power, after a step down.

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

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

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

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.

History

• In 0.28, the last two spells which didn't involve spell power (Blink and Passage of Golubria) now use it.
• Prior to 0.26, spell power display was fuzzed, displayed in terms of bars (##.) instead of percentages. Bars did not have equal value; lower bars represented less numerical power per bar.
• 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.