Difference between revisions of "Encumbrance rating"

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''Not to be confused with [[encumbered|encumbrance]] from inventory [[aum|weight]], an obsolete mechanic.''
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''For shield encumbrance, see [[Shields]]. Not to be confused with [[encumbered|encumbrance]] from inventory [[aum|weight]], an obsolete mechanic.''
  
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An '''encumbrance rating''' is a penalty applied by almost all body armour and [[barding]]s. This is a measure of how much your defensive equipment gets in the way of spellcasting, [[ranged weapon]]s, and attempts to [[ev]]ade enemy attacks. Multiple sources of encumbrance rating stack with each other. [[Shields]] also have a penalty, but it is handled differently and is never actually named in game (see [[Shields#Shield Penalties]]).
+
An '''encumbrance rating''' is a penalty applied to [[body armour]]. The heavier your armour, the higher the encumbrance rating. The higher the encumbrance, the higher the penalty is to [[ev]]asion, [[spell failure|spellcasting]], [[stealth]], and [[ranged weapon]]s. Encumbrance can be mitigated, but not removed, by [[strength]] and [[Armour skill]].  
  
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In general, the heavier your equipment, the greater the encumbrance rating will be. You can reduce the impact of your encumbrance rating by increasing your [[strength]] or [[Armour (skill)|Armour]], though the [[stealth]] penalty is always constant. For the purposes of evasion, there is a breakpoint at (ER-2) strength, where reaching this point provides the greatest gain per specific strength point, with strength having a slowly diminishing return from there.
+
This page exclusively covers body armour. Certain other armours may "encumber" you, but use different mechanics.
 +
*[[Barding]]s have a -2 [[EV]] penalty. This does not penalize casting, stealth, etc., and cannot be reduced by strength / armour skill.
 +
*[[Shields]] also have an encumbrance rating, but it's handled entirely differently. See [[Shields#Shield Penalties|Shields]] for more details.
  
 
See the [[Armour#Tables of Armours|Table of Armours]] for numerical details on all items with encumbrance ratings.
 
See the [[Armour#Tables of Armours|Table of Armours]] for numerical details on all items with encumbrance ratings.
  
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See this spreadsheet (and/or make a copy) for an armour penalty calculator: [https://docs.google.com/spreadsheets/d/1SgY-b12lecR1EHb7uopTqFP0E3FDr5_MsTHrwA0Z5MY/edit#gid=1843292358 Calculator]
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==Base Penalty==
 +
Body armour has a "base" penalty of:<ref>{{source ref|0.31.0|player.cc|5892}}</ref>
  
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==Penalties==
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[[File:Base AEVP.png|716px]]
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===Adjusted body armour penalty===
 
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[[Image:Baseencpenalty.gif]]
 
  
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Where ''e'' is the encumbrance rating of the armour, ''S'' is an arbitrary scale the base is used at for the particular penalty, ''a'' is the [[Armour (skill)|armour skill]] of the subject, and ''s'' is the [[strength]] of the subject.
+
Where:
 +
*"S" = scale. Scale essentially equals to 1 (100/100), meaning it has no impact the final result. It is used to increase the precision of encumbrance calculations.
 +
*"armour" = [[Armour skill]] and "str" = [[strength]].
  
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This penalty is not applied directly, rather it is used in evasion, to hit, and cast chance. For to hit the scale used is 20, while for evasion and cast the scale used is 100. This syntax is the same for the other formula.
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This equation can be simplified into the following form:
  
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===Adjusted evasion penalty===
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[[File:Simplified_AEVP_base.png|600px]]
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[[File:AdjustedEvasionPenalty.gif]]
 
  
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This amount is subtracted from your [[evasion]] along with other factors such as your [[size]] and [[dodge]] skill before being stepped down.
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While this equation is not used directly, it is used to determine most of the other penalties.
  
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===Dodging penalty===
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==Evasion==
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[[File:AdjustedDodgePenalty.gif]]
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Encumbrance rating has ''two'' effects on [[EV]]:
 +
# Encumbrance will directly lower your evasion. This is reduced by armour skill and strength.
 +
# Encumbrance will lower the effect of [[Dodging]] skill on evasion. This penalty is only reduced by strength.
  
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Where ''B'' is the base dodge bonus (formula shown), ''S'' is the relationship between strength and encumbrance, ''d'' is dodge skill, ''D'' is dexterity stepped down if it is above 24, and ''F'' is normalized size factor.
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===EV Penalty===
 +
Encumbrance will lower your EV by:<ref>{{source ref|0.31.0|player.cc|5887}}</ref>
  
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This penalty along with the evasion penalty impacts your ability to evade attacks. Due to the change of function when encumbrance nears strength, this penalty makes it a good idea to have a strength equal to or larger than two minus the encumbrance of the armour.
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[[File:Simplified_AEVP_EV.png|771px]]
  
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The size factor is normalized around medium size, and can be derived from the following table:
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This number is subtracted directly from your EV score.
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{|class="prettytable"
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−
! Size !! Size factor
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===Dodging Penalty===
 +
Encumbrance will also reduce the EV gained by Dodging skill and dexterity.
 +
 
 +
For '''Dodging Bonus''' = <code>(8 + 0.8 × Dodging × Dex) / (20 - size_factor)</code>. See [[Evasion]] for more detail.
 +
 
 +
This Dodging Bonus is then multiplied by a modifier:<ref>{{source ref|0.31.0|player.cc|2122}}</ref>
 +
 
 +
[[File:Dodging pen1.png|350px]]
 +
 
 +
For e = encumbrance. If (e-3) is 0 or lower, then there's no penalty to Dodging.
 +
 
 +
==Spellcasting Penalty==
 +
Encumbrance increases "spellFailure", which is not to be confused with your chance of actually failing a spell:<ref>{{source ref|0.31.0|player.cc|2166}}</ref><ref>{{source ref|0.31.0|spl-cast.cc|410}}</ref>
 +
 
 +
[[File:Simplified AEVP spell.png|660px]]
 +
 
 +
As a reference:
 +
 
 +
*1 [[intelligence]] = -2 spellFailure
 +
*1 [[Spellcasting]] skill = -3 spellFailure
 +
*1 (Spell School) skill = -12 spellFailure, divided by the number of schools of a spell
 +
 
 +
"SpellFailure" is then transformed multiple times to determine your actual chance of failure. See [[spell success]] for details.
 +
 
 +
==Stealth Penalty==
 +
Encumbrance reduces your [[stealth]] score:<ref>{{source ref|0.31.0|player.cc|3112}}</ref>
 +
 
 +
[[File:StealthPenalty.gif]]
 +
 
 +
Independent of armour skill or strength. This does not reduce the [[Stealth (skill)|Stealth skill]], so encumbrance doesn't impact the strength of [[stab]]s, nor does it impact the use of [[atropa]] and [[datura]] darts.
 +
 
 +
==Ranged Weapon Penalty==
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Encumbrance slows down [[Ranged Weapons]] (but not [[Throwing]] weapons). It increases the [[attack delay]] of these weapons, in units of [[decaAut]]:<ref>{{source ref|0.31.0|player-act.cc|360}}</ref>
 +
 
 +
[[File:AdjustedRangedPenalty.png|610px]]
 +
 
 +
This penalty is rounded to the tenths place in a weighted fashion, then added to your [[attack delay]]. Note that, because these are in units of decaAut, the equation is divided by 10. If you want regular [[aut]], multiply by 10.
 +
 
 +
==Analysis==
 +
In general:
 +
 
 +
*Armour skill has a linear impact on encumbrance. Every point in Armour reduces encumbrance by -2.2%.
 +
*Strength has a logarithmic impact - i.e. a diminishing return - on encumbrance. For everything except the Dodging penalty, going from 7 -> 17 strength will give the same % reduction as 2 -> 7 strength, which has the same reduction as 17 -> 37 strength.
 +
 
 +
===On Evasion===
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As mentioned above, strength has a diminishing return on encumbrance as a whole. But there exists a clear breakpoint, <code>e - 3 = str</code>, where the [[#Dodging Penalty|dodging penalty]] shifts from 1 equation to another. Beyond this point, strength starts to drop more rapidly. This breakpoint ''only'' applies to Dodging, not to casting or the general EV penalty.
 +
 
 +
This is the basis behind a rule of thumb, where strength should at least be the same number as encumbrance. However, this is not a hard rule. More strength is still likely to have a noticeable impact. And, if you don't have any Dodging skill, then str = (e-3) has next-to-no significance to your character.
 +
 
 +
The % of [[#Dodging Penalty|Dodging Bonus]] is tabulated below, as an example:
 +
{| class="wikitable"
 +
!colspan=3| [[Fire dragon scales]] (e=11) !! !! colspan=3 | [[Plate armour]] (e=18)
 +
|-
 +
! Strength !! % of Dodging !! Delta
 +
!
 +
! Strength !! % of Dodging !! Delta
 +
|-
 +
|5 || 31.25% ||
 +
!
 +
|12 || 40.0% ||
 +
|-
 +
|6 || 37.5% || +6.25%
 +
!
 +
|13 || 43.3% || +3.3%
 
|-
 
|-
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| Little: [[Spriggan]] || 2
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|7 || 43.75% || +6.25%
 +
!
 +
|14 || 46.6% || +3.3%
 
|-
 
|-
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| Small: [[Kobold]], [[Halfling]] || 1
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|'''8''' || 50% || +6.25%
 +
!
 +
|'''15''' || 50% || +3.3%
 
|-
 
|-
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| Medium: Most Races || 0
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|9 || 55.5% || +5.5%
 +
!
 +
|16 || 53.1% || +3.1%
 
|-
 
|-
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| Large: [[Troll]], [[Ogre]], [[Centaur]], [[Naga]] || -1
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|10 || 60% || +4.5%
 +
!
 +
|17 || 55.9% || +2.8%
 +
|-
 +
|11 || 63.6% || +3.6%
 +
!
 +
|18 || 58.3% || +2.4%
 
|}
 
|}
 +
Note, again, that this is '''only the impact on Dodging bonus'''. Remember that there is ''another'' EV penalty on top of this. Overall, every point of strength will give less EV than the previous point of strength. (Of course, you should still have high strength if you plan to wear heavy armour).
  
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===Stealth penalty===
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===On Spellcasting===
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[[File:StealthPenalty.gif]]
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====Armour skill vs Spell skill====
 +
*Encumbrance increases SpellFailure by <code>19/225 * encumbrance^2 * (90 - 2armour) / (str+3)</code>. This can be rearranged to <code>-armour * 38/225 * encumbrance^2 / (str+3)</code>.
 +
*Having 1 of every spell school (except Spellcasting) reduces SpellFailure by 12.
 +
*Therefore, each level in Armour is worth <code>19/1350 * encumbrance^2 / (str+3)</code>, or roughly <code>1/71 * encumbrance^2 / (str+3)</code>, levels in each spell school.  
  
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This penalty is subtracted from your [[stealth]] score.
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For example, if you have 11 strength and [[fire dragon scales]], 1 Armour skill = <code>1/71 * 11^2 / 14</code> = 0.122 levels in each spell school. This is a ratio of 8.21 Armour skill : 1 in each spell school. If you have a dual-school spell, like [[Iron Shot]], 4.1 Armour skill = 1 Earth Magic OR 1 Conjurations, while 8.21 Armour = 1 Earth AND Conjurations.  
  
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===Spellcasting penalty===
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Of course, this analysis does '''NOT''' include the fact that Armour increases your [[AC]] and [[EV]]. You may want to train Armour for those reasons, or train spell schools to increase power.
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[[File:CastPenalty.gif]]
 
  
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If this added to your shield penalty is positive, then this is added to your failure chance. See [[spell success]] for more information.
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====Strength vs Intelligence====
 +
*For a given change in strength 'x', strength reduces SpellFailure by <code>(1/<str+3> - 1/<str+x+3>) * 19/225 * encumbrance^2 * (90 - 2armour)</code>.
 +
*Intelligence reduces SpellFailure by 2 per point.
  
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===Ranged Weapon Penalty===
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For example, you have 11 strength, fire dragon scales, and 0 Armour skill. On level up, you have a choice of 2 str or 2 int. The impact of +2 str is equal to <code>(1/14 - 1/16) * 19/225 * 11^2 * 90</code> = 8.21 SpellFailure, greater than 2*2 = 4 SpellFailure from intelligence.
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{{crawlquote|[ (e)^2 / 2250 ] * [ (90-2a) / (S + 3) ]}}
 
  
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This penalty, in [[decaAut]], is added onto [[attack speed|weapon delay]] to [[Ranged Weapons]], but not [[Throwing]].
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Of course, intelligence also increases [[spell power]], while strength also reduces [[shield]] encumbrance.
  
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==Encumbrance Penalty Analysis==
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==Spreadsheet==
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By calculating the second derivative of the dodge penalty plus the evasion penalty (formula shown above), we can measure the gains from additional strength for any given character. Using this information we can determine what value you would want to raise your strength to for the greatest benefit. The graph on the right shows a spike in gains from strength at two lower than the encumbrance rating of the armour, however a few points after that spike tend to be fairly beneficial as well. This relationship leads to the rule of thumb for strength that you should at least raise it to the same number as your encumbrance, however more strength is still likely to have a noticeable impact.
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See this spreadsheet (and/or make a copy) for an armour penalty calculator: [https://docs.google.com/spreadsheets/d/1SgY-b12lecR1EHb7uopTqFP0E3FDr5_MsTHrwA0Z5MY/edit#gid=1843292358 Calculator] (outdated as of 0.27)
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[[File:Diff2StrengthVsEncumbrance.png|thumb|The gains in dodge from strength for common body armour.]]
 
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[[File:AdjustedDodgePenaltySecondDerivative.gif]]
 
  
 
==History==
 
==History==
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*Ranged weapon penalities were added in [[0.19]].
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*Ranged weapon penalties were added in [[0.29]].
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*Armour to-hit penalities were removed in [[0.28]]. Specifically, they were:
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*Armour to-hit penalties were removed in [[0.28]]. Specifically, they were:
 
[[File:ToHitPenalty.gif]]
 
[[File:ToHitPenalty.gif]]
 
*Armour no longer slows down unarmed melee attacks, and some of the mathematics have changed between 0.13 and 0.17.
 
*Armour no longer slows down unarmed melee attacks, and some of the mathematics have changed between 0.13 and 0.17.
 
*Encumbrance ratings were introduced in [[0.13]], replacing the EV penalty system.
 
*Encumbrance ratings were introduced in [[0.13]], replacing the EV penalty system.
 +
 +
==References==
 +
<references/>
  
 
[[Category:Game mechanics]]
 
[[Category:Game mechanics]]

Latest revision as of 21:55, 2 June 2024

Version 0.31: This article may not be up to date for the latest stable release of Crawl.

For shield encumbrance, see Shields. Not to be confused with encumbrance from inventory weight, an obsolete mechanic.

An encumbrance rating is a penalty applied to body armour. The heavier your armour, the higher the encumbrance rating. The higher the encumbrance, the higher the penalty is to evasion, spellcasting, stealth, and ranged weapons. Encumbrance can be mitigated, but not removed, by strength and Armour skill.

This page exclusively covers body armour. Certain other armours may "encumber" you, but use different mechanics.

  • Bardings have a -2 EV penalty. This does not penalize casting, stealth, etc., and cannot be reduced by strength / armour skill.
  • Shields also have an encumbrance rating, but it's handled entirely differently. See Shields for more details.

See the Table of Armours for numerical details on all items with encumbrance ratings.

Base Penalty

Body armour has a "base" penalty of:[1]

Base AEVP.png

Where:

  • "S" = scale. Scale essentially equals to 1 (100/100), meaning it has no impact the final result. It is used to increase the precision of encumbrance calculations.
  • "armour" = Armour skill and "str" = strength.

This equation can be simplified into the following form:

Simplified AEVP base.png

While this equation is not used directly, it is used to determine most of the other penalties.

Evasion

Encumbrance rating has two effects on EV:

  1. Encumbrance will directly lower your evasion. This is reduced by armour skill and strength.
  2. Encumbrance will lower the effect of Dodging skill on evasion. This penalty is only reduced by strength.

EV Penalty

Encumbrance will lower your EV by:[2]

Simplified AEVP EV.png

This number is subtracted directly from your EV score.

Dodging Penalty

Encumbrance will also reduce the EV gained by Dodging skill and dexterity.

For Dodging Bonus = (8 + 0.8 × Dodging × Dex) / (20 - size_factor). See Evasion for more detail.

This Dodging Bonus is then multiplied by a modifier:[3]

Dodging pen1.png

For e = encumbrance. If (e-3) is 0 or lower, then there's no penalty to Dodging.

Spellcasting Penalty

Encumbrance increases "spellFailure", which is not to be confused with your chance of actually failing a spell:[4][5]

Simplified AEVP spell.png

As a reference:

  • 1 intelligence = -2 spellFailure
  • 1 Spellcasting skill = -3 spellFailure
  • 1 (Spell School) skill = -12 spellFailure, divided by the number of schools of a spell

"SpellFailure" is then transformed multiple times to determine your actual chance of failure. See spell success for details.

Stealth Penalty

Encumbrance reduces your stealth score:[6]

StealthPenalty.gif

Independent of armour skill or strength. This does not reduce the Stealth skill, so encumbrance doesn't impact the strength of stabs, nor does it impact the use of atropa and datura darts.

Ranged Weapon Penalty

Encumbrance slows down Ranged Weapons (but not Throwing weapons). It increases the attack delay of these weapons, in units of decaAut:[7]

AdjustedRangedPenalty.png

This penalty is rounded to the tenths place in a weighted fashion, then added to your attack delay. Note that, because these are in units of decaAut, the equation is divided by 10. If you want regular aut, multiply by 10.

Analysis

In general:

  • Armour skill has a linear impact on encumbrance. Every point in Armour reduces encumbrance by -2.2%.
  • Strength has a logarithmic impact - i.e. a diminishing return - on encumbrance. For everything except the Dodging penalty, going from 7 -> 17 strength will give the same % reduction as 2 -> 7 strength, which has the same reduction as 17 -> 37 strength.

On Evasion

As mentioned above, strength has a diminishing return on encumbrance as a whole. But there exists a clear breakpoint, e - 3 = str, where the dodging penalty shifts from 1 equation to another. Beyond this point, strength starts to drop more rapidly. This breakpoint only applies to Dodging, not to casting or the general EV penalty.

This is the basis behind a rule of thumb, where strength should at least be the same number as encumbrance. However, this is not a hard rule. More strength is still likely to have a noticeable impact. And, if you don't have any Dodging skill, then str = (e-3) has next-to-no significance to your character.

The % of Dodging Bonus is tabulated below, as an example:

Fire dragon scales (e=11) Plate armour (e=18)
Strength  % of Dodging Delta Strength  % of Dodging Delta
5 31.25% 12 40.0%
6 37.5% +6.25% 13 43.3% +3.3%
7 43.75% +6.25% 14 46.6% +3.3%
8 50% +6.25% 15 50% +3.3%
9 55.5% +5.5% 16 53.1% +3.1%
10 60% +4.5% 17 55.9% +2.8%
11 63.6% +3.6% 18 58.3% +2.4%

Note, again, that this is only the impact on Dodging bonus. Remember that there is another EV penalty on top of this. Overall, every point of strength will give less EV than the previous point of strength. (Of course, you should still have high strength if you plan to wear heavy armour).

On Spellcasting

Armour skill vs Spell skill

  • Encumbrance increases SpellFailure by 19/225 * encumbrance^2 * (90 - 2armour) / (str+3). This can be rearranged to -armour * 38/225 * encumbrance^2 / (str+3).
  • Having 1 of every spell school (except Spellcasting) reduces SpellFailure by 12.
  • Therefore, each level in Armour is worth 19/1350 * encumbrance^2 / (str+3), or roughly 1/71 * encumbrance^2 / (str+3), levels in each spell school.

For example, if you have 11 strength and fire dragon scales, 1 Armour skill = 1/71 * 11^2 / 14 = 0.122 levels in each spell school. This is a ratio of 8.21 Armour skill : 1 in each spell school. If you have a dual-school spell, like Iron Shot, 4.1 Armour skill = 1 Earth Magic OR 1 Conjurations, while 8.21 Armour = 1 Earth AND Conjurations.

Of course, this analysis does NOT include the fact that Armour increases your AC and EV. You may want to train Armour for those reasons, or train spell schools to increase power.

Strength vs Intelligence

  • For a given change in strength 'x', strength reduces SpellFailure by (1/<str+3> - 1/<str+x+3>) * 19/225 * encumbrance^2 * (90 - 2armour).
  • Intelligence reduces SpellFailure by 2 per point.

For example, you have 11 strength, fire dragon scales, and 0 Armour skill. On level up, you have a choice of 2 str or 2 int. The impact of +2 str is equal to (1/14 - 1/16) * 19/225 * 11^2 * 90 = 8.21 SpellFailure, greater than 2*2 = 4 SpellFailure from intelligence.

Of course, intelligence also increases spell power, while strength also reduces shield encumbrance.

Spreadsheet

See this spreadsheet (and/or make a copy) for an armour penalty calculator: Calculator (outdated as of 0.27)

History

  • Ranged weapon penalties were added in 0.29.
  • Armour to-hit penalties were removed in 0.28. Specifically, they were:

ToHitPenalty.gif

  • Armour no longer slows down unarmed melee attacks, and some of the mathematics have changed between 0.13 and 0.17.
  • Encumbrance ratings were introduced in 0.13, replacing the EV penalty system.

References

  1. ↑ player.cc:5892 (0.31.0)
  2. ↑ player.cc:5887 (0.31.0)
  3. ↑ player.cc:2122 (0.31.0)
  4. ↑ player.cc:2166 (0.31.0)
  5. ↑ spl-cast.cc:410 (0.31.0)
  6. ↑ player.cc:3112 (0.31.0)
  7. ↑ player-act.cc:360 (0.31.0)
Retrieved from "http://crawl.chaosforge.org/index.php?title=Encumbrance_rating&oldid=80462"