Spell Success - Revision history

Hordes: 0.34

2026-02-14T20:37:18Z

0.34

Hordes at 09:09, 24 October 2025

2025-10-24T09:09:56Z

Hordes: /* Final Step */

2025-07-30T11:11:01Z

‎Final Step

Patrick2011b: commit 20a70ad added the spellFailure cap in 0.26

2025-04-08T22:04:49Z

commit 20a70ad added the spellFailure cap in 0.26

Patrick2011b: spellFailure is capped at 210 before going through the stepdown; also update to 0.32

2025-04-08T21:54:31Z

spellFailure is capped at 210 before going through the stepdown; also update to 0.32

Hordes: /* Analysis */

2025-03-16T12:25:31Z

‎Analysis

Hordes: /* Final Step */

2024-10-25T10:14:45Z

‎Final Step

ForkInBrain: 0% success rate -> 0% failure rate

2024-03-27T04:01:23Z

0% success rate -> 0% failure rate

Ge0ff: mention forms affecting spell success in pre-0.31

2024-02-16T20:51:12Z

mention forms affecting spell success in pre-0.31

Hordes: /* Modifiers */ update forms

2024-02-15T18:30:20Z

‎Modifiers: update forms

@@ Line 1: / Line 1: @@
-{{version032}}
+{{version034}}
 {| style="float: right;"
 | __TOC__
@@ Line 93: / Line 93: @@
 The following modifiers are added after the STEPPED DOWN failure rates above. However, it is still considered the ''raw spell failure chance'', which is adjusted by a sigmoid function later.<ref>{{source ref|0.32.1|spl-cast.cc|461}}</ref>
-'''Positive (+spell failure):'''
+Additive and subtractive modifiers are applied first, then multiplicative modifiers (like Vehumet and Wizardry) are applied afterwards.<ref>{{source ref|0.34.0|spl-cast.cc|534}}</ref>
 *[[Wild Magic (mutation)|Wild Magic]]: +4% per level
 *Disrupted Magic (-Wiz) [[Ru|sacrifice]]: +4% per level
 *[[Orb]] of [[energy]]: +10%
 *[[Vertigo]]: +7%
 '''Negative (-spell failure):'''
 *[[Subdued Magic]]: -2% per level
-The wizardry and Vehumet multipliers are applied after all others.<ref>{{source ref|0.32.1|spl-cast.cc|469}}</ref>
+'''Multiplicative:''''
 After all modifiers have applied, you will get a cumulative ''raw spell failure chance''. This is converted into the final success via the function below.
@@ Line 151: / Line 162: @@
 |-
 |}
-<nowiki>*</nowiki>SpellFailure required to reach a given raw fail chance, ''assuming you don't have any modifiers like [[wizardry]]''. E.g. if you have wizardry x1, having 1 SpellFailure = (28% * 0.75) raw failure = 21% raw failure.
+<nowiki>*</nowiki>SpellFailure required to reach a given raw fail chance, ''assuming you don't have any multiplicative modifiers like [[wizardry]]''. E.g. if you have wizardry x1, having 1 SpellFailure = (28% * 0.75) raw failure = 21% raw failure.
 ==Strategy==

@@ Line 154: / Line 154: @@
 ==Strategy==
-It is debatable whether these formulae are of any practical use during a game.
+It is debatable whether these formulae are of any practical use during a game. Simply training a skill, checking the spell failure every so often, and stopping once a satisfactory failure% is achieved is generally enough.
 It may be nice to know a few things from a strategic point of view.
-*High level spells take a massive amount of XP to train, and it can be useful to know how many levels you'd need.
+*High level spells take a massive amount of XP to train, and it can be useful to know how many levels you'd need up front.
 *You can quantize your level of armour [[encumbrance]]. A caster could say "a set of [[fire dragon scales]] gives a spell penalty equal to 6 levels of each spell school". Then, you could determine if wearing FDS is worth it, both short-term ("can I cast a spell in this ''right now''?") and long-term ("can I cast a spell in this ''when I reach Zot''?").
 *You can calculate the relative value of a skill. For example, you can see when a level of <Spell School> would be more valuable than a level of Armour skill, or when a point of [[strength]] is worth more than a point of [[intelligence]].

@@ Line 126: / Line 126: @@
 {| class="prettytable" style="text-align: center" border=1
 |-
-!SpellFailure*!!Raw fail chance!!Actual fail chance
+!SpellFailure (unmodded)*!!Raw fail chance!!Actual fail chance
 |-
 |13||32%||14.9%

@@ Line 239: / Line 239: @@
 ==History==
 *Prior to [[0.31]], the raw failure rate multiplier from wizardry/Vehumet was capped at 50%. Therefore, you could only have a maximum of 5 stacks of wizardry, or 1 stack of wizardry with Vehumet's bonus. Also, some [[transmutations]] increased your spell failure: [[Spider Form]] (+10%) and [[Blade Hands (spell)|Blade Hands]] (+20%).
 *Prior to [[0.22]], spell_schools went through a stepdown, <code>50 * log2(1 + spell_schools/50)</code>, which penalized the caster if <code>(Spellcasting/2) + (2* AvgSpellSchool) > 50</code>. However, spellFailure for level 9 spells was 330 instead of 340.
 *Prior to [[0.20]], the [[#Step down|Step down]] function was different, relying on breakpoints rather than a polynomial. Also, more breakpoints existed elsewhere in the spell failure calculation.

@@ Line 1: / Line 1: @@
-{{version031}}
+{{version032}}
 {| style="float: right;"
 | __TOC__
@@ Line 15: / Line 15: @@
 The source code talks in terms of chance of ''failure'', not success. Therefore, we want the spellFailure chance to be as low as possible - in fact, to reach a 0% failure rate, your chance to fail has to be '''negative'''. More on that below.
-The base failure before ''any'' modifiers is as follows:<ref>{{source ref|0.30.0|spl-cast.cc|406}}</ref>
+The base failure before ''any'' modifiers is as follows:<ref>{{source ref|0.32.1|spl-cast.cc|401}}</ref>
    spellFailure = 60
@@ Line 23: / Line 23: @@
                 + Encumbrance penalties
-* 60 is an arbitrary base chance of failure.
+*60 is an arbitrary base chance of failure.
-* Increasing intelligence and spell skills (skills respective to the spell ''and'' [[Spellcasting]]) will decrease failure.
+*Increasing intelligence and spell skills (skills respective to the spell ''and'' [[Spellcasting]]) will decrease failure.
-* Higher level spells are more difficult, wearing armour/shields make it more difficult.
+*Higher level spells are more difficult, wearing armour/shields make it more difficult.
-=== Spell skills ===
+spellFailure is capped at 210 at this point.<ref>{{source ref|0.32.1|spl-cast.cc|441}}</ref>
-"Spell_skills" takes into account Spellcasting and an average of a spell's schools (e.g. a Conjurations / Fire spell will take the average of the [[Conjurations]] skill and [[Fire Magic]] skill). This is calculated with the following equation:<ref>{{source ref|0.30.0|spl-cast.cc|413}}</ref>
-<ref>{{source ref|0.30.0|spl-cast.cc|377}}</ref>
+===Spell skills===
    spell_skills = [Spellcasting / 2] + [Average(Skill_level) * 2]
-=== Spell difficulty ===
+===Spell difficulty===
-Higher level spells are more difficult. Each level of spell adds a number to your spell failure rate:<ref>{{source ref|0.30.0|spl-cast.cc|422}}</ref>
+Higher level spells are more difficult. Each level of spell adds a number to your spell failure rate:<ref>{{source ref|0.32.1|spl-cast.cc|417}}</ref>
    spellDifficulty =   3 (level 1)
@@ Line 45: / Line 47: @@
 (level 9)   (+80)
-=== Encumbrance penalties ===
+===Encumbrance penalties===
-Both Armour and Shield penalties for spells are derived from their [[EV]] penalties. First, calculate the ev penalty, then calculate the spell penalty. Armour and Shields do not influence each other.
+Both Armour and Shield penalties for spells are derived from their [[EV]] penalties. First, calculate the ev penalty, then calculate the spell penalty. Armour and Shields do not influence each other. [[Mountain Dwarf|Mountain Dwarves]] treat the armour encumbrance as half of its normal value.
-'''Armour'''<ref>{{source ref|0.30.0|player.cc|5723}}</ref><ref>{{source ref|0.30.0|player.cc|2131}}</ref>
+'''Armour'''<ref>{{source ref|0.32.1|player.cc|6147}}</ref><ref>{{source ref|0.32.1|player.cc|2265}}</ref>
    ev penalty = 1/225 * [[encumbrance]]^2 * (90 - 2 * [[Armour (skill)|armour_skill]]) / ([[str]] + 3)
    spell penalty = 19 * ev penalty
-'''Shield'''<ref>{{source ref|0.30.0|player.cc|5739}}</ref><ref>{{source ref|0.30.0|player.cc|2134}}</ref>
+'''Shield'''<ref>{{source ref|0.32.1|player.cc|6163}}</ref><ref>{{source ref|0.32.1|player.cc|2273}}</ref>
    ev penalty = 2/5 * [[Shields#EV_Penalty|encumbrance]]^2 / (5 + str) * (27 - [[Shields_(skill)|shield_skill]]) / 27
    spell penalty = 19 * ev penalty
-== Step down ==
+==Step down==
-At this point, the spell failure is put through a complicated post-processing curve:<ref>{{source ref|0.30.0|spl-cast.cc|463}}</ref>
+At this point, the spell failure is put through a complicated post-processing curve:<ref>{{source ref|0.32.1|spl-cast.cc|458}}</ref>
   (x^3 + 426x^2 + 82670x + 6983254) / 262144 IF spellFailure < 43
@@ Line 89: / Line 91: @@
 ==Modifiers==
-The following modifiers are added after the STEPPED DOWN failure rates above. However, it is still considered the ''raw spell failure chance'', which is adjusted by a sigmoid function later.<ref>{{source ref|0.30.0|spl-cast.cc|466}}</ref>
+The following modifiers are added after the STEPPED DOWN failure rates above. However, it is still considered the ''raw spell failure chance'', which is adjusted by a sigmoid function later.<ref>{{source ref|0.32.1|spl-cast.cc|461}}</ref>
 '''Positive (+spell failure):'''
@@ Line 101: / Line 103: @@
 *[[Subdued Magic]]: -2% per level
 *[[Wizardry]]: multiplied by ×<code>6 / (7 + sources)</code>%, assuming you have at least one source. (×75% for Wiz x1, ×66.6% for Wiz x2, and so on.)
-*[[Vehumet]]: multiplied by ×66.6%.<ref>{{source ref|0.30.0|spl-cast.cc|335}}</ref> (Note: this is not considered a source of wizardry, but it multiplicatively stacks with wizardry.)
+*[[Vehumet]]: multiplied by ×66.6%.<ref>{{source ref|0.32.1|spl-cast.cc|339}}</ref> (Note: this is not considered a source of wizardry, but it multiplicatively stacks with wizardry.)
-The wizardry and Vehumet multipliers are applied after all others.<ref>{{source ref|0.30.0|spl-cast.cc|475}}</ref>
+The wizardry and Vehumet multipliers are applied after all others.<ref>{{source ref|0.32.1|spl-cast.cc|469}}</ref>
 After all modifiers have applied, you will get a cumulative ''raw spell failure chance''. This is converted into the final success via the function below.
 ==Final Step==
-In short, the game doesn't compare your raw failure chance with a number from 0 to 99. Instead, it compares the raw failure to the sum of three numbers divided by three.<ref>{{source ref|0.30.0|spl-cast.cc|2533}}</ref>
+In short, the game doesn't compare your raw failure chance with a number from 0 to 99. Instead, it compares the raw failure to the sum of three numbers divided by three.<ref>{{source ref|0.32.1|spl-cast.cc|2636}}</ref>
   (1d101 + 1d101 + 1d100 - 3)/3 < fail chance
@@ Line 151: / Line 153: @@
 <nowiki>*</nowiki>SpellFailure required to reach a given raw fail chance, ''assuming you don't have any modifiers like [[wizardry]]''. E.g. if you have wizardry x1, having 1 SpellFailure = (28% * 0.75) raw failure = 21% raw failure.
-== Strategy ==
+==Strategy==
 It is debatable whether these formulae are of any practical use during a game.

@@ Line 164: / Line 164: @@
 ===Skill Req'd to Cast L9 Spells===
-Say you wanted to [[Fire Storm]] reliably. For sake of example, we're trying to reach a 10% failure rate. You can look at the table above: to get a 10% actual failure rate, you'd need 28% raw failure. If you have no wizardry, 28% raw failure = 1 SpellFailure.
+Say you wanted to [[Fire Storm]] reliably. For sake of example, assume you want to reach a 10% failure rate. To do this, you can look at the table above.
 Using the [[#Base Chance|SpellFailure]] calculations at the top of the page, you can calculate what's needed to get to 1 SpellFailure. For this example, assume you have 30 intelligence, no wizardry, and 0 encumbrance from armour/shields.
@@ Line 184: / Line 186: @@
 *'''Vehumet + Wizardry x1''': {14 Spellcasting, 20.2 avg_skill}, {18.9 Spellcasting, 18.9 avg_skill}
-These numbers apply to any level 9 spell in the game, not just Fire Storm... again, ''assuming you have 30 int / 0 encumbrance''. If you're wearing [[swamp dragon scales]] and a [[kite shield]], for instance, it'll take more skill to cast. Change the values of spell level, intelligence, encumbrance as you see fit.
+These numbers apply to any level 9 spell in the game, not just Fire Storm... ''assuming that you have 30 int / 0 encumbrance''. If you're wearing [[swamp dragon scales]] and a [[kite shield]], for instance, it'll take more skill to cast. Change the values of spell level, intelligence, encumbrance as you see fit.
 ===Measuring Encumbrance===

@@ Line 111: / Line 111: @@
   (1d101 + 1d101 + 1d100 - 3)/3 < fail chance
-This is equivalent to applying this transformation to the chance of failure:
+This is equivalent to applying this transformation to the chance of failure (x-axis: raw failure rate; y-axis: actual fail %):
 [[Image:Spell_success_transformation.png]]
@@ Line 124: / Line 124: @@
 {| class="prettytable" style="text-align: center" border=1
 |-
-!SpellFailure Req'd*!!Raw fail chance!!Actual fail chance
+!SpellFailure*!!Raw fail chance!!Actual fail chance
 |-
 |13||32%||14.9%

@@ Line 13: / Line 13: @@
 ==Base Chance==
-The source code talks in terms of chance of ''failure'', not success. Therefore, we want the spellFailure chance to be as low as possible - in fact, to reach a 0% success rate, your chance to fail has to be '''negative'''. More on that below.
+The source code talks in terms of chance of ''failure'', not success. Therefore, we want the spellFailure chance to be as low as possible - in fact, to reach a 0% failure rate, your chance to fail has to be '''negative'''. More on that below.
 The base failure before ''any'' modifiers is as follows:<ref>{{source ref|0.30.0|spl-cast.cc|406}}</ref>