Difference between revisions of "Shield (stat)"

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''This page is about the Shield [[stat]]. For the armour type, see [[Shield]]. For the player [[skill]], see [[Shields]].''
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{{version031}}
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''This page is about the Shield [[stat]]. For shields in general, see [[Shields]]. For the player [[skill]], see [[Shields (skill)]].''
  
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'''SH''' is one of your three physical defenses, along with [[AC]] and [[EV]]. It allows you to completely negate physical attacks (both melee and ranged) and some magical attacks. SH gained from wearing a physical shield is governed by the [[Shields skill]]; magical shields are unaffected.
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'''SH''' is one of your three physical defenses, along with [[AC]] and [[EV]]. It allows you to completely negate physical attacks (both melee and ranged) and some magical attacks. Unlike AC and EV, you have no innate SH score. SH gained from wearing a physical shield is governed by the [[Shields (skill)|Shields]] skill; magical shields are unaffected by that skill.
  
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SH can be improved by the following means:
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==Sources==
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*Wearing a [[Shields|shield]]
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The following items/abilities can increase your SH:
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*The [[Good mutations#Large Bone Plates|Large Bone Plates]] [[mutation]]
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*Wearing a [[shield]]; [[buckler]]s, [[kite shield]]s, and [[tower shield]]s, in ascending order of effectiveness and cumbrousness
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*[[The Shining One]]'s Divine Shield ability
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*Wearing an [[amulet of reflection]], [[Brooch of Shielding]], or [[ring of the Octopus King]]
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*The [[Condensation Shield]] spell
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*Having the [[Large Bone Plates]] [[mutation]]
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*The [[Deck of battle#Helm|Helm]] card
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*Using [[The Shining One]]'s Divine Shield
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*[[Qazlal]]'s Storm Shield passive
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==Blocking==
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<!-- This section is transcribed from the Shields page -->
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You can block melee attacks (inc. [[reaching]] attacks) and non-penetrating "projectiles" - these include [[ranged weapon]]s and certain spells like [[Iron Shot]] or [[Poison Arrow]].
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What can't be blocked by SH:
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*[[Penetration|Penetrating]] attacks: [[Javelin]]s, [[Bolt spell]]s, [[Starburst]]...
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*Almost everything with perfect [[accuracy]]: [[Magic Dart]], [[Smiting]], [[Chain Lightning]], Explosions ([[Fireball]], [[Damnation]]), [[Shatter]]...
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:([[Orb of Destruction]] is the only spell that ignores EV but can be blocked)
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*Enchantments: [[Agony]], [[Pain]], [[Confuse]], everything that checks [[willpower]]
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===Max Blocks===
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Each type of shield (or lack thereof) can only block a certain number of attacks per player turn:
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{| class="prettytable" cellpadding="10" border="9"
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|- align="center"
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! Shield type !! Max Blocks
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|-
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|None || 1
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|-
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|Buckler || 2
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|-
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|Kite shield || 3
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|-
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|Tower shield || 4
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|}
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===Calculation===
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If you are wielding a physical shield, its SH is determined as follows:<ref>{{source ref|0.31-b1|player.cc|2200}}<br>These values are divided by 200 by later functions.</ref>
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*Your '''Base SH''' is determined by type of shield. 3 for [[buckler]]s, 8 for [[kite shield]]s, 13 for [[tower shield]]s.
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*Add '''[[Shields (skill)|Skill Bonus]]''' of <code>(base_SH/40 + 0.19) * skill</code>.
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*Add '''[[Dexterity|Stat Bonus]]''' of <code>DEX * 38 * (base_SH + 13) / 5200</code>.
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*Add '''[[Enchant]]ment''' value. +1 enchantment = +1 SH.
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*Add 0.82 SH.<ref>{{source ref|0.31-b1|player.cc|2254}}<br>Divided by 2 by a later function.</ref>
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All other sources of SH ([[Qazlal]] shield, [[amulet of reflection]]...) are flat bonuses, and are added on top of the physical shield bonus. The final value is rounded to the nearest integer and displayed as the player's SH value.
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If you are [[paralysed]], [[petrified]], or if [[dexterity]] is 0, then SH is set to 0 regardless of any other factors.
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===To-hit vs SH===
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The game compares the attacker's "pierce value" to the defender's "block value".
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The attacker's pierce value is dependent on their [[to-hit]] (accuracy) and the type of attack:
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* '''Melee attack:''' <code>1d(15 + to_hit/2)</code>
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* '''Ranged attack:'''  <code>1d(1.3×to_hit)</code>
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The defender's blocking value is equal to:
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* '''All attacks:''' <code>2d(4×SH)/6 - 1</code>
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* Divide by 3 against melee attacks from [[invisible]] opponents.
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If the blocking value is greater or equal than the attacker's pierce value, and you haven't exceeded the max block count, the attack is blocked.
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==Strategy==
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Generally, SH is less effective per point than EV.
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*In almost all cases, +1 EV is a better defense than +1 SH. [[#1 EV vs 1 SH|See below]] for the formulas.
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*There is no limit to the amount of attacks you can dodge. There ''is'' a limit to the attacks you can block in 1 turn.
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*EV defends against penetrating attacks, while SH doesn't.
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However, shields give high amounts of SH. Wearing a [[kite shield]] instantly brings you from 0 to >8 SH, while gaining 8 EV takes a lot of effort. A shield will almost certainly give more SH than the EV you lose by wearing it. Also, blocking is unaffected by [[armour encumbrance]].
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The main costs of wearing a shield are the inability to wield [[hand|two-handed]] weapons, and the shield [[shields#Penalty|penalties]] (which can be reduced and eventually removed with [[Shields skill]]).
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==References==
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<references/>
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===1 EV vs 1 SH===
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In melee, enemies have a [[to-hit]] of <code>1.5 * HD + 18</code> unless they have the [[fighter flag]]. For melee attacks:
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*EV dodges if <code>2d(2EV - 1) / 2 > 1d(to_hit + 1) - 1 </code>.
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*SH blocks if <code>2d(4SH - 1) / 6 >= 1d(15 + to_hit/2)</code>.
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SH becomes relatively better when the enemy's to-hit value rises. The highest HD of any enemy in the game is 30, so for sake of example, set to-hit = (1.5 * 30 + 18) = 63. Now, let's say you had 30 EV and 30 SH.
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*30 EV: <code>2d(59) / 2 > 1d(64) - 1</code>; the chance of dodging is 46.48%.
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*30 SH: <code>2d(119) / 6 >= 1d(46.5)</code>; the chance of blocking is 42.12%.
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In extreme cases, if you have much more EV than you do SH, gaining +1 SH could be stronger than 1 EV. This only applies for melee attacks. If an enemy has a to-hit of 36:
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*60 EV, 20 SH:
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**Dodge if <code>2d(119) / 2 > 1d(37) - 1</code>; the chance of dodging is 93.36%.
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**Block if <code>2d(79) / 6 >= 1d(33)</code>; the chance of blocking is 39.14%.
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**Chance to either block or dodge is 95.96%.
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*50 EV, 30 SH:
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**Dodge if <code>2d(99) / 2 > 1d(37) - 1</code>; the chance of dodging is 90.88%.
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**Block if <code>2d(119) / 6 >= 1d(33)</code>; the chance of blocking is 59.01%.
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**Chance to either block or dodge is 96.26%.
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In this case, +10 SH ''technically'' offers more defense than +10 EV. But, since you can only block so many attacks per turn, you should still prefer having EV over the same amount of SH.
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For ranged attacks, 1 EV is objectively better than 1 SH in all cases.
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Overall, if you have the choice between +1 EV and +1 SH, pick the EV. However, you'll rarely have this choice in practice. With even decent Shields skill, the shield EV penalty will be small, so you can often have both high EV and high SH at the same time.
  
 
[[Category:Stats]]
 
[[Category:Stats]]

Latest revision as of 09:33, 11 March 2024

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

This page is about the Shield stat. For shields in general, see Shields. For the player skill, see Shields (skill).

SH is one of your three physical defenses, along with AC and EV. It allows you to completely negate physical attacks (both melee and ranged) and some magical attacks. Unlike AC and EV, you have no innate SH score. SH gained from wearing a physical shield is governed by the Shields skill; magical shields are unaffected by that skill.

Sources

The following items/abilities can increase your SH:

Blocking

You can block melee attacks (inc. reaching attacks) and non-penetrating "projectiles" - these include ranged weapons and certain spells like Iron Shot or Poison Arrow.

What can't be blocked by SH:

(Orb of Destruction is the only spell that ignores EV but can be blocked)

Max Blocks

Each type of shield (or lack thereof) can only block a certain number of attacks per player turn:

Shield type Max Blocks
None 1
Buckler 2
Kite shield 3
Tower shield 4

Calculation

If you are wielding a physical shield, its SH is determined as follows:[1]

All other sources of SH (Qazlal shield, amulet of reflection...) are flat bonuses, and are added on top of the physical shield bonus. The final value is rounded to the nearest integer and displayed as the player's SH value.

If you are paralysed, petrified, or if dexterity is 0, then SH is set to 0 regardless of any other factors.

To-hit vs SH

The game compares the attacker's "pierce value" to the defender's "block value".

The attacker's pierce value is dependent on their to-hit (accuracy) and the type of attack:

  • Melee attack: 1d(15 + to_hit/2)
  • Ranged attack: 1d(1.3×to_hit)

The defender's blocking value is equal to:

  • All attacks: 2d(4×SH)/6 - 1
  • Divide by 3 against melee attacks from invisible opponents.

If the blocking value is greater or equal than the attacker's pierce value, and you haven't exceeded the max block count, the attack is blocked.

Strategy

Generally, SH is less effective per point than EV.

  • In almost all cases, +1 EV is a better defense than +1 SH. See below for the formulas.
  • There is no limit to the amount of attacks you can dodge. There is a limit to the attacks you can block in 1 turn.
  • EV defends against penetrating attacks, while SH doesn't.

However, shields give high amounts of SH. Wearing a kite shield instantly brings you from 0 to >8 SH, while gaining 8 EV takes a lot of effort. A shield will almost certainly give more SH than the EV you lose by wearing it. Also, blocking is unaffected by armour encumbrance.

The main costs of wearing a shield are the inability to wield two-handed weapons, and the shield penalties (which can be reduced and eventually removed with Shields skill).

References

  1. ↑ player.cc:2200 (0.31-b1)
    These values are divided by 200 by later functions.
  2. ↑ player.cc:2254 (0.31-b1)
    Divided by 2 by a later function.

1 EV vs 1 SH

In melee, enemies have a to-hit of 1.5 * HD + 18 unless they have the fighter flag. For melee attacks:

  • EV dodges if 2d(2EV - 1) / 2 > 1d(to_hit + 1) - 1 .
  • SH blocks if 2d(4SH - 1) / 6 >= 1d(15 + to_hit/2).

SH becomes relatively better when the enemy's to-hit value rises. The highest HD of any enemy in the game is 30, so for sake of example, set to-hit = (1.5 * 30 + 18) = 63. Now, let's say you had 30 EV and 30 SH.

  • 30 EV: 2d(59) / 2 > 1d(64) - 1; the chance of dodging is 46.48%.
  • 30 SH: 2d(119) / 6 >= 1d(46.5); the chance of blocking is 42.12%.

In extreme cases, if you have much more EV than you do SH, gaining +1 SH could be stronger than 1 EV. This only applies for melee attacks. If an enemy has a to-hit of 36:

  • 60 EV, 20 SH:
    • Dodge if 2d(119) / 2 > 1d(37) - 1; the chance of dodging is 93.36%.
    • Block if 2d(79) / 6 >= 1d(33); the chance of blocking is 39.14%.
    • Chance to either block or dodge is 95.96%.
  • 50 EV, 30 SH:
    • Dodge if 2d(99) / 2 > 1d(37) - 1; the chance of dodging is 90.88%.
    • Block if 2d(119) / 6 >= 1d(33); the chance of blocking is 59.01%.
    • Chance to either block or dodge is 96.26%.

In this case, +10 SH technically offers more defense than +10 EV. But, since you can only block so many attacks per turn, you should still prefer having EV over the same amount of SH.

For ranged attacks, 1 EV is objectively better than 1 SH in all cases.

Overall, if you have the choice between +1 EV and +1 SH, pick the EV. However, you'll rarely have this choice in practice. With even decent Shields skill, the shield EV penalty will be small, so you can often have both high EV and high SH at the same time.

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