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Spell Success

2015-07-25T11:27:26Z

Goaty666: clarified one part of the math

{{version016}}

{| style="float: right;"
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'''Spell success''' is the rate at which casting a [[spell]] can be expected to succeed.
As of 0.16.0 spell success rate is determined by a complex combination of:

* Spell-related skills
* [[Intelligence]]
* Spell level
* Armour and Shield penalty, mitigated by [[Armour (skill)|Armour skill]] and [[Shields (skill)|Shields skill]]
* Mutation Penalty ([[Good_mutations#Wild_Magic|Wild Magic]])
* Piety with [[Vehumet]] for [[Conjurations]] spells
* Any equipped wizardry items

== Spell success calculations ==

It is debatable whether the following formulae are of real use during a game. However, inflection points such when the extra armour EV penalty disappears are fairly easy to discern. Calculating this stuff on the fly is only for savants! However, one can refer example section of this page for Lv 9 magics, which requires tremendous amount of experience to be stabilized.

=== 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 Perfect success rate, your chance to fail has to be '''negative'''. More on that below.

To begin with, there's a 60% chance of failure. From this, two things are subtracted - twice the caster's Intelligence, and a value calculated from the user's relevant skills. This value is similar to (but simpler than) the [[spell power]]. Note that these two factors are the only ones that '''directly''' improve spell success, while other factors described below only serve to ''mitigate'' spellcasting penalties. Therefore, focus on these areas if you want to maximize your spellcasting chances, particularly spell skills.

Here's an overview of the basic formula, before stepdown and miscellaneous penalties and enhancers.

spellFailure = 60
- [6 * spell skills]
- [2 * Intelligence]
+ Spell difficulty
+ Armour/shield penalty

=== Spell skills ===

Now they use very familiar equation with spellcasting equation. The main difference is, spell skill boost effect of potion of brilliance is not counted here.

S_0 = [Spellcasting / 2] + [Average(SpellSkills) * 2]

spell skills = 50 * log_2 (1 + S_0 / 50)

This value (6 * spell skills) is naturally capped at 370, assuming level 27 on relevant spell skills and spellcasting.

=== Spell difficulty ===

A number is added, making spellcasting more difficult, dependent on the spell's level.

spellDifficulty = 3 (level 1)
15 (level 2) (+12)
35 (level 3) (+20)
70 (level 4) (+35)
100 (level 5) (+30)
150 (level 6) (+50)
200 (level 7) (+50)
260 (level 8) (+60)
330 (level 9) (+70)

=== Armour and shield penalties (Under Construction) ===

Armour/Shield Penalty = 19 * (armour penalty) + 19 * (shield penalty)

armour penalty = 0.4 * (Encumbrance Rating)^2
* (45 - Armour skill Lv) / 45
/ (Str + 3)

shield penalty = (EV Penalty) - (Shield Skill Lv) / (Player species factor)

Player species factor is 5 for normal species, 3 for large species, and 7 for small species, respectively. Spriggans have 9, though they only can use bucklers.

=== Step down ===

At this point, the spell failure is put through a step down curve. If it's over 45 (just into the 'Fair' range), it's unaffected, otherwise it needs to be progressively lower to improve the overall result. This is a stepwise curve, and complex to describe. In the table is the listed native chance to reach certain points (i.e., spell success bands), although note that there are a couple of further steps performed after this.

{| class="prettytable" border=1
|-
!Description!!Failure rate!!Needed fail chance
|-
|Fair||45%||45
|-
|Good||30%||10
|-
|Very Good||20%||−24
|-
|Great||10%||−80
|-
|Excellent||4%||−140
|-
|Perfect||0%||−180
|-
|}

From −60 to −180 it's linear, with each difference of 20 giving 2% in the final spell success chance. So penalties affect bad wizards more than good ones. Penalty mitigation (for armour) applies before this, so the stepping function doesn't change that.

=== Mutations ===

From now on, we work with STEPPED DOWN failure rates.

Placid magic: Failure Rate - 7 %
Wild magic: Failure Rate + 7 %
Anti-Wizadry: Failure Rate + 4 %

The unrandart [[Hat of the High Council]] offers +7 %, not +4 %. It is noted as separate line in source spl-cast.cc file.

=== Sap status ===

Failure Rate + Sap duration(in terms of turns) / 10 (%)

=== Wizardry, Vehumet, and other factors ===

Finally (phew!) spellcasting success boosts from items and other sources are applied. Note that these are actually calculated as a reduction in the fail chance, so in the table below, a low number is better.

* Vehumet knocks 1/3 off the fail chance for Conjurations for disciples in good standing (piety over 70).

* Rings of wizardry and staves of wizardry give some assistance, given by their "Wizardry" bonus in that column, but they suffer from decreasing cumulative effects. Other spell enhancers, such as rings of fire/ice or staves of various kinds, do not affect spell success chances, only their power. Wizardry effect is determined using this formula:

Reduced Failure rate = Failure rate * 6 / (7 + # of Wizardry Items)

* Potion of brilliance: Failure rate / 2 (Directly to max level of reduction)

Note that there is an hard cap of 50% for the effect of all enhancers. For Vehumet worshippers, one wizardry bonus brings a character to the 50% limit, eliminating the need for multiple Wizardry effects..

===The final step===

The number we have obtained isn't the final chance of failure. The game doesn't compare that number with a random number between 0 and 99, but with the sum of three numbers divided by three.
(1d101 + 1d101 + 1d100 - 3)/3 < fail chance

This is equivalent to applying this transformation to the chance of failure:

[[Image:Spell_success_transformation.png]]

This sigmoid function makes it more difficult to decrease your failure rate when it is high or low, but it will go down very quickly when it is in the middle. Up to raw failure rate of 33%, one can use this formula:

N = (raw_failure_rate) * 3
Real Failure Rate = N * (N+1) * (N+2) / 6 / 101 / 101 (in unit of %)

This can be tabulated for usefulness.

{| class="prettytable" border=1
|-
!Raw Fail chance!!Actual fail chance
|-
|32%||14.9%
|-
|30%||12.3%
|-
|28%||10.0%
|-
|26%||8.1%
|-
|24%||6.4%
|-
|22%||4.9%
|-
|20%||3.7%
|-
|18%||2.7%
|-
|16%||1.9%
|-
|14%||1.3%
|-
|12%||0.8%
|-
|}

==Example: Stabilizing [[Fire Storm]] within 90% success rate==

For pure-magic build, stabilizing Fire Storm before the Vault is strictly required. In this example, required skill level for reaching is calculated. For the failure rate of 10%, raw failure rate of 28% is required. Let's set Int=32, a decent value for spellcasters but not sufficient for end-game annihilator. Assuming no armour/shield penalty. This argument can be applied with any of Lv 9 spells, if one exclude Vehumet effect.

* Without any aid: Raw rate of 2% is stepped down to 28%, so 2% is the point that should be achieved. This is equivalent to 54.0 point of spell skills, requiring '''(school skill*2 + spellcasting*0.5) = 55.7'''. Even if the spellcasting is maxed out to 27, the average school skill value of 21.1 is required to cast Fire storm within 10% failure.

* With an aid of a wizardry ring: A wizardry option knocks 1/4 of failure rate before sigmoid function, so the required raw fail rate is 38%. Raw rate of 32% is stepped down to 38%, and '''(school skill*2 + spellcasting*0.5) = 48.6'''. This value is quite easy to be achieved now, and average of 19.4 Lv including spellcasting is sufficient for 10% failure rate.

* Vehumet worshipper, or two wizardry rings: These enhancements knock off 1/3 of failure rate before sigmoid. Now the raw fail rate required before stepdown is 38%, and '''(school skill*2 + spellcasting*0.5) = 47.3'''. Required average skill Lvs, including spellcasting, is 18.9. Worshipping Vehumet really offers tremendous benefits for high-level spells.

* Vehumet with a wizardry ring: Maxed out enhancer effect. Raw fail rate of 56% can be used without stepdown, and '''(school skill*2 + spellcasting*0.5) = 43.3'''. Required average skill Lvs, including spellcasting, is 17.3. If one regulates spellcasting up to 15, then 17.9 Lv of each school level is sufficient!

* [[Potion of brilliance]]: Maxed out enhancer effect with increased intelligence. Raw fail rate of 66% can be used without stepdown. '''(school skill*2 + spellcasting*0.5) = 41.1''' is required, and this reduction is huge if the caster is not aided by any of enhancers!

==See also==

* [[Spell power]]
* [[Miscast effect]]

[[Category:Magic]]

Portal Projectile

2015-07-22T18:07:27Z

Goaty666: Removed reference to picking up corpses

{{version016}}
{{Spell
|name=Portal Projectile
|level=3
|school1={{Translocations}}
|school2=
|school3=
|castingnoise=3
|spellnoise=see [[Noise#Ranged_combat|ranged combat noise]]
|sources=<div>
*[[Book of Spatial Translocations]]
</div>
}}

{{Flavour|This spell allows the caster to teleport fired or thrown missile directly to their targets for a short duration, spending an additional small amount of magic for each shot. Teleported projectiles have their accuracy (but not damage) greatly improved.}}

'''Portal Projectile''' is a level 3 [[Translocations]] spell which grants your ranged weapons [[smite]]-targeting, allowing you to attack any target in your [[line of sight]] regardless of units in between, and with substantially increased accuracy. Alternatively, it allows you to teleport any item in your possession with similar targeting. Each ranged attack while Portal Projectile is active costs 1 additional MP; if you run out of MP, your projectiles travel normally until you regain MP.

All [[wall]]s block Portal Projectile, even if you can see through them.

==Strategy==
*Its low spell level makes it easy for most characters to master. Any player focused on ranged attacks can benefit from it.
*Portal Projectile makes taking out summoners hiding behind a pack of summoned fodder easy. Even better is when you have your own pack of summons and you can still fire without risk of hitting them.
*Alternatively, if you can pin a weak monster between yourself and something dangerous, you can pelt the threat while it waits patiently for the weak foe to get out of the way.
*The item teleporation ability offers some interesting, if convoluted, attack options, such as sending a potion of poison out and then casting [[Ignite Poison]].
*While most ammo brands will still function as normal with this spell, the [[returning]] and [[penetration]] brands are disabled.

==Monster Version==
The following monsters can cast Portal Projectile:
*{{monsterlink|Naga sharpshooter}}
*{{monsterlink|Vashnia}}

Deep Dwarf

2015-07-22T03:03:34Z

Goaty666: Updated for v016, section on Elyvilon was outdated.

{{version016}}
''This article is about the player [[species]]. For the monster, see [[Deep Dwarf (monster)]]. For a list of all monstrous deep dwarves, see [[List of deep dwarves]].''
{{flavour|Deep Dwarves are short, hardy people who, unlike their extinct surface relatives, never left the underground homelands. Living there for countless generations made them turn pale and lose all ability to regenerate on their own (nor are they receptive to any effects which merely hasten regeneration), as well as all ability to recover from losses to their primary attributes over time. On the other hand, Deep Dwarves have developed the ability to instantly counteract small doses of damage. Their empathy with the earth makes them sense their surroundings; this ability increases in power as they gain experience levels.

Given their lack of innate healing, few Deep Dwarves venture out for adventures or even combat. Those who do bring a wand of heal wounds, or rely on divine assistance.

Naturally, Deep Dwarves are quite adept with all arts of avoiding blows and damage. Offensively, they are skilled users of axes, crossbows, and slings. Deep Dwarves are highly spiritual beings, often portrayed as actual spirits by outsiders; because of this, their skill with invocations is great. They are most at home with the magic of earth and death.

Deep Dwarves are gifted forgers. Their armour and weapons are very well-crafted and much more durable than the products of lesser artisans, and particularly dangerous when in the hands of a true Dwarf. In addition, Deep Dwarves can tinker with gadgets so as to recharge them. However, each time they do so, they lose a bit of their magical essence.}}

==Innate Abilities==
*[[Bad mutations#Slow Healing|Slow Healing 3]]: Deep Dwarves cannot [[heal]] lost HP or stat [[attributes]] naturally, nor benefit from any non-divine form of regeneration (including the [[Regeneration]] spell).
**Deep Dwarves will not passively regain MP if wearing an [[amulet of guardian spirit]].
*[[Good_mutations#Passive Mapping|Passive Mapping 1]]: Deep Dwarves can sense parts of the layout of the dungeon around them.
*Damage Reduction (also known as "damage shaving"): Deep Dwarves suffer less damage from every source. This applies separately to every source of damage, every time it is dealt; thus, for instance, damage shaving generally negates the effects of all but the worst cases of being [[poison]]ed.
*[[File:Device recharge.png]] Device Recharging: Deep Dwarves can recharge wands and rods at the cost of 1 permanent MP.
{{flavour|At the permanent loss of one magic point recharge a wand or rod.}}

Deep Dwarves have a base [[Strength]] of 11, [[Intelligence]] of 8 and [[Dexterity]] of 8 (before Background modifiers).

==Preferred Backgrounds==
*'''Warriors:''' [[Fighter]], [[Hunter]]
*'''Zealots:''' [[Berserker]]
*'''Mages:''' [[Necromancer]], [[Earth Elementalist]]

==Level Bonuses==
*+1 [[strength]] or [[intelligence]] (equal chance) every 4th level.
*20% more [[HP]] than average.
*Average [[MP]].
*+6 [[magic resistance]] per level.
*At level 14, gain [[Life Protection|Life Protection 1]].
*At levels 9 and 18, your [[Good mutations#Passive Mapping|Passive Mapping]] is upgraded to ranks 2 and 3, respectively.

===Damage Reduction===
The formula for Deep Dwarves' damage reduction is 1d(2 + (1d(1 + experience level / 3) - 1)). This is applied against all damage they receive, even against attacks that are normally irresistible like [[smiting]] or [[hellfire]]. The table below only lists selected levels; unlisted levels also see small increments in damage reduction. It is not applied to damage from spell activation sources, such as [[Makhleb]]'s abilities.

{| class="prettytable"
!Level !! Damage reduced
|-
|1 & 2 || 1-2 (avg. 1.5)
|-
|5 || 1-3 (avg. 1.75)
|-
|8 || 1-4 (avg. 2)
|-
|11 || 1-5 (avg. 2.25)
|-
|14 || 1-6 (avg. 2.5)
|-
|17 ||1-7 (avg. 2.75)
|-
|20 || 1-8 (avg. 3)
|-
|23 || 1-9 (avg. 3.25)
|-
|26 || 1-10 (avg. 3.5)
|}

==Starting Skills and Equipment==
Deep Dwarves start with the skills and equipment listed for their background, with these exceptions:
*A [[wand of heal wounds]] with 5 charges.

==Difficulty of Play==

{{Beginner}}

Deep Dwarves are an easy species to play, so long as you work around their lack of natural recovery from HP loss and stat drain. They start the game with a wand of heal wounds, one of the most powerful items in the game, and also have the ability to recharge it or any other wand or rod at the cost of 1 permanent point of their maximum magic. Deep Dwarves also have powerful damage shaving that scales up with their character level. However, one should take into account Deep Dwarves' lack of natural regeneration when choosing his or her [[god]] and background. Some strategies for how to offset this disadvantage can be found below.

{{species_aptitudes|Deep Dwarf}}

==Strategy==
Initially, you start with a wand of healing, and the ability to recharge at the cost of one max MP. Use it. You're not going to regain that lost health naturally, so whenever your HP is at least 20 points or so below maximum, heal. Don't be afraid to use the recharging ability - it is better to end with 45 max MP instead of 50 than it is to die. Save [[potions of curing]] for situations where you have a negative status effect, such as [[rot]] or [[confusion]] - using them to simply heal HP is wasteful. Use the wand instead, charging it if necessary.

Later on, you will need a source of renewable healing, in addition to the usual means of non-renewable (consumable) healing. Consumable healing will quickly be exhausted if you don't find another way to heal. There are only a few ways to go about this:

===Healing Through [[Necromancy]]===
Deep Dwarves cannot use the [[Regeneration]] spell, but they can use [[Vampiric Draining]]. This spell requires a living target in melee range to be effective; luckily, the game provides plenty of these. It is only found in the [[Book of Necromancy]] or in randart spellbooks. Vampiric Draining can be obtained in three ways:
*By starting as a [[Necromancer]]
*By finding it randomly
*While [[Kikubaaqudgha]] worshipers normally only have a 50% shot at getting Vampiric Draining, the fact that they can't cast Regeneration means that Deep Dwarves will always receive it at * piety.

Gifted necromancers can also use [[Borgnjor's Revivification]] to heal, but this is as much of an emergency spell for Deep Dwarves as it is for any other character, given its cost in max HP.

===Passive Divine Healing===
Two gods passively give HP for kills:
*[[Makhleb]] gives HP for killing most enemies. He is by far the more common choice, since his healing is useful everywhere, and his other abilities are useful to just about any character build.
*[[The Shining One]] gives HP on killing "evil" enemies (namely demons, undead, and many spellcasters). This alone is not sufficient in most areas of the game, however; only in certain optional areas of the game is this likely to be a reliable, consistent source of healing. Also note that worshiping The Shining One will preclude necromantic means of healing.

===Active Divine Healing===
Three gods have [[Invocations]] which can heal Deep Dwarves. All of these abilities cost piety, although to varying degrees.
*[[Elyvilon]] gives two healing abilities, Lesser and Greater Healing. Both cost piety, but they are gained reasonably early on (at * and **** piety, respectively), so most players will be unlikely to lose them. However, piety is only gained through exploration. Training [[Invocations]] skill will increase the effectiveness of Lesser and Greater Healing.
*[[Trog]] gives a regeneration ability at ** piety, Trog's Hand. Unlike all other forms of regeneration, this works on Deep Dwarves. The ability does not require Invocations to be effective - rather, it becomes more effective with increasing piety. Moreover, because worshipers of Trog are punished for training or casting spells anyway, one can lean on the Deep Dwarves' recharge ability more liberally, as the loss of max magic points is of no concern. Training [[Evocations]] under Trog for (among other things) greater max MP, and using a combination of the wand of heal wounds as well as Trog's Hand, can be an effective means of negating Deep Dwarves' liabilities. Note that Trog will also not allow any forms of healing that involve spellcasting, and that too much use of Trog's Hand may diminish how often one can use the powerful Brothers in Arms ability.
*[[Yredelemnul]] gives worshipers the ability to drain ambient lifeforce at **** piety. This ability is quite expensive, requires considerable Invocations investment (the max it can heal you is Invocation*2), and only works on living monsters. Taking Yred for the sole purpose of this ability is inadvisable.
*[[Ru]] lets you use Draw Our Power at *** piety. This ability also has a cost attached to it, giving you slight drain upon using it. In a similar vein to Yredelemnul, taking Ru solely for this ability may not be wise.

===Vampiric Weapons===
Vampiric weapons will heal Deep Dwarves when they hit a living target. Unfortunately, they are quite rare, and there is no way to guarantee that they will be on a useful weapon. An early vampiric weapon may give a Deep Dwarf more flexibility in god choice, however.

===Non-Renewable Healing===
Deep Dwarves can also heal themselves through the following consumable means:
*Quaffing a [[potion of curing]] or [[potion of heal wounds]]. You can use [[potion of ambrosia|potions of ambrosia]] to heal yourself a reasonable amount between fights, but remember that this won't work if you have [[Clarity]].
*Zapping a [[wand of heal wounds]].
*The [[Elixir]] card, found in the Decks of War, Defense, and Changes. Unfortunately, none of these are gifted by [[Nemelex Xobeh]]. At low power, this card may only induce the Regeneration spell, which is a waste on Deep Dwarves.
*The Potion card, found in Decks of Wonders. At low power, this has a 54% chance of some form of HP healing (27% each of duplicating Potion of Heal Wounds or Potion of Curing). At higher power this chance drops off, as other non-healing effects also show up and dilute your odds. It hits a 21.6% chance of healing (10.8% of each potion type) at maximum power.
*The Alchemist card (Deck of Wonders) is the only card guaranteed at all power levels to give a healing effect that works on Deep Dwarves. In this case, the healing costs you [[gold]], however.
*Xom will occasionally heal worshipers.

===So What Does All This Mean?===
All of this essentially means that Deep Dwarves who wish to maximize their chances for success are fairly limited in their choice of god. Necromancers have the most flexibility; since they start with Vampiric Draining, they can do reasonably well with any "non-good" god they desire, although it may still be advisable to pick one who gives renewable healing. All others, with the exception of those who get lucky and find a Book of Necromancy early on, are strongly incentivized to choose between Makhleb, Elyvilon, Trog, and Kikubaaqudgha. Yredelemnul is a very iffy option, while The Shining One is only effective for the purposes of Deep Dwarf healing in specific, optional areas of the game.

[[category: Dwarf]]

{{species}}