Penetration (PV): Difference between revisions

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{{missing info| waiting for math extention to make this page look pretty. What is a critical hit's role in all of this?
{{tocright}}
TODO: add probability calculation table for quick reference}}
'''PV''' or '''Penetration Value''' or {{PV}} is a value assigned to all weapons and plays a key part in damage calculation during attacking.
'''PV''' or '''Penetration Value''' or {{Color| C |→}} is a value assigned to all weapons and plays a key part in damage calculation during attacking.
 
A '''penetration''' is a single application of a weapon's damage dice against the target. One attack might result in multiple penetrations, multiplying the weapon's damage dice accordingly. In game, penetrations are noted in the message log as a parenthetical multiplier after the damage, such as {{qud text|&W(x2)}} or {{qud text|&M(x5)}}.
 
While the full calculations behind penetration are complex, a key takeaway is that every two points of the attacker's PV will, on average, increase the attack's damage multiplier by one, while every two points of the defender's AV will reduce it by one.
 
== Background ==
There are two components to an attack.
* The first component is the '''hit'''. If an attacker's to-hit roll (heavily influenced by [[Agility]]) succeeds, the attack hits and applies on-hit effects.
* The second component is '''penetration'''. If an attacker's penetration roll (heavily influenced by [[Strength]]) succeeds, the attack penetrates and deals damage, and can also apply on-penetration effects (such as the stat-draining effect of a {{favilink|life sap}} or {{favilink|stat sap}}).
 
For more general information about attacking, refer to the relevant combat mechanics page:
* [[Melee combat]]
* [[Missile weapon combat]]
* [[Thrown weapon combat]]
 
==How PV Is Displayed==
A weapon's PV is displayed in game in one of the following ways.
 
{|class="wikitable"
!Weapon Type
!Display Format
!Example
!Notes
|-
! rowspan="3" | Melee
| style="text-align:center;" | <span style="font-size:120%><b>{{PV}}X</b></span>
|[[File:PV_example_basic.png]]
| rowspan="3" |
* '''X''' is the strength-modified PV of a melee weapon. This value changes if your strength changes.<br>(4 + [[modifier|strength modifier]] for one-handed weapons, or 5 + strength modifier for two-handed weapons).
* '''Y''' is the maximum achievable PV for this melee weapon. PV will be capped at this value regardless of your strength modifier. This maximum achievable PV shows up in game only if you've turned on the "Display detailed weapon penetration and damage in name" [[option]].
* '''≈''' represents [[vibro]] penetration, which automatically sets penetration equal to the target's [[AV]] value.
|-
| style="text-align:center;" | <span style="font-size:120%><b>{{PV}}X{{Color|K|/Y}}</b></span>
|[[File:PV_example_detailed.png]]
|-
| style="text-align:center;" | <span style="font-size:120%><b>{{PV}}≈</b></span>
|[[File:PV_example_vibro.png]]
|-
! rowspan="2" | Missile<br><span style="font-weight:normal;">(non-bow)</span>
| style="text-align:center;" | <span style="font-size:120%><b>{{PV}}X</b></span>
|[[File:Missile_PV_example.png]]
| rowspan="2" |
* '''X''' is the intrinsic PV of a non-bow missile weapon - non-bow missile weapon PV cannot be modified by ammo, strength, or other attributes.
* {{PV|pierce}} represents that after a successful penetration, the projectile will continue its path, attempting to attack anything it strikes until it reaches the end of the zone.
|-
|style="text-align:center;" | <span style="font-size:120%><b>{{PV|pierce}}X</b></span>
|[[File:Missile PV example pierce.jpg]]
|-
! Missile<br><span style="font-weight:normal;">(bow)</span>
| style="text-align:center;" | <span style="font-size:120%><b>{{PV}}X</b></span>
|[[File:Bow_PV_example.png]]
|
* '''X''' is the base PV of a bow. This can be modified by the ammo loaded in the bow. In the case of {{F|compound bow|plural}} and {{F|turbow|plural}}, it can also be modified by the wielder's strength. As of {{Patch|2.0.204.101}}, the display PV for these bows appears to not be accurate.
|-
! Thrown
| style="text-align:center;" | <span style="font-size:120%><b>{{PV}}X</b></span>
|[[File:Thrown_PV_example.png]]
|
* '''X''' is the maximum achievable PV for this thrown weapon. (similar to Y for melee weapons)
* The actual PV of a thrown weapon will be 5 + your strength modifier. This value is not displayed in game.
|}
 
Note that the descriptions above apply only to the value that is displayed in the game UI. For the purposes of actual PV calculations, as described in the sections below, the game subtracts 4 from the values that are shown in the UI. So, for example, the fullerite maul pictured above has a penetration value of 2 for the purposes of all in-game calculations. ([[:Category:Vibro_Weapons|vibro weapons]] are an exception to this rule.)


==Melee Weapon PV Calculation==
==Melee Weapon PV Calculation==


Melee weapons have a base PV of 4. The PV will increase by the creatures [[Strength]] [[modifier]] with an upper limit dictated by the weapon's bonus cap. Two handed weapons and the [[Sharp]] mod also increase base PV by 1.
The PV of melee weapons is calculated as the follows:
 
* Base penetration bonus,
A critical hit(natural 10) is guaranteed one penetration.
** For non-vibro weapons, the base penetration bonus is equal to the weapon penetration value shown on the equipment screen in-game, minus 4. For example, if the weapon shows {{PV}}7, your base penetration bonus is 3. ''Typically this bonus is the same as your strength modifier (or your strength modifier + 1 for two-handed weapons), but it can be capped to a lower value depending on the weapon.''
** For [[:Category:Vibro_Weapons|vibro weapons]], the base penetration bonus is always equal to the defender's [[AV]].
* +1 bonus penetration if the weapon has the [[Sharp]] modification,
* +4 bonus penetration if the enemy is [[asleep]],
* +1 bonus penetration to swarmer attackers for each additional swarmer enemy that surrounds their opponent,
* and additional bonus penetration from the [[Charge]], [[Lunge]], [[Long Blade Proficiency]], [[Improved Aggressive Stance]], [[Shank]], or [[Slam]] skills as applicable.


==Ranged Weapon PV Calculation==
A [[critical hit]] is guaranteed one penetration regardless of PV if the source of the critical hit is the player character.{{Code Reference|class=Combat|method=FireEvent|case="MeleeAttackWithWeapon"}}
{{missing info| is this the same for grenade launchers, thrown weapons, or bows?}}
Ranged weapon PV is determined by the PV of the gun itself. The PV of the bullet does not matter.


Critical hits on ranged weapons add a flat +4 PV to the shot.
==Ranged Weapon PV Calculation (Non-Bows)==
Ranged weapon PV is determined by the PV of the gun itself. The PV of the bullet does not matter and remains static no matter what ammo is loaded into the gun.


==Penetration Formula==
[[Critical hit]]s on ranged weapons add a flat +2 PV to the shot, increased to +4 if the weapon is a pistol and the user has [[Dead Shot]].
For a round of penetration, 1d10 is rolled three times.


penetration = (1d10 + PV-((penetration round)*2))
==Ranged Weapon PV Calculation (Bows)==
A bow's base PV is determined by the PV of the arrow loaded into the bow. The {{favilink|compound bow}} also has the effect of adding the wielder's [[strength]] modifier to the penetration value. The {{Favilink|turbow}} adds +4 PV to the shot and then adds the wielder's strength modifier to the penetration value.


If any of these + the attackers PV are greater than the opponents AV, the attack will penetrate once. If all three 1d10s + PV are greater than the AV, the attack penetrates once and another round of penetration is done, rerolling 3 more 1d10s + PV-2.
==Thrown Weapon PV Calculation==
Thrown weapon PV is calculated as follows:
# Start with a base penetration of 5.
# Add the thrower's [[modifier|Strength Modifier]], up to but not exceeding the PV ('''{{PV}}''') value shown on the thrown item in game.
#* A negative strength modifier cannot reduce this value below 5 for thrown weapons.
#* Objects that aren't explicitly thrown weapons have a maximum PV value of '''{{PV}}6'''.
# Minus 4 from the calculated total
#* Similar to melee weapons, the thrown weapon PV used for internal calculations is always 4 lower than what is displayed in game.


The chance of ''n'' penetrations goes by the formula:
==Penetration Formula==
{{Qud text|&amp;GStep 1}} - Roll the attacker's PV against the defender's AV value 3 times (let's call this a '''''triplet''''').
: {{Qud text|&amp;GStep 1a}} - Each individual roll within the triplet works as follows (let's call each roll a '''''singlet'''''):
::{{Qud text|&amp;GStep 1a.i}} - Roll <code>1d10-2</code>. Each time that the maximum result of <code>8</code> is rolled, perform the <code>1d10-2</code> roll again and continue adding the results together.
:: {{Qud text|&amp;GStep 1a.ii}} - Calculate the '''maximum possible PV''' (what the attacker's PV would be without a Strength bonus cap on their weapon) for the weapon. Then, reduce it to the internal PV of the weapon (what is displayed minus 4) if it is greater. Add this value to the roll calculated in {{Qud text|&amp;gStep 1a.i|unbolded}}.
:: {{Qud text|&amp;GStep 1a.iii}} - Note whether the total result from {{Qud text|&amp;gStep 1a.ii|unbolded}} is greater than the target's AV.
:{{Qud text|&amp;GStep 1b}} - If at least one '''''singlet''''' roll was greater than the target's AV, the attack penetrates one time (or one ''more'' time if this is a subsequent triplet). If all three '''''singlet''''' rolls were greater than the target's AV, reduce the '''maximum possible PV''' by 2, return to {{Qud text|&amp;gStep 1|unbolded}}, and perform another '''''triplet''''' of rolls to determine if the attack penetrates an additional time. ''(Continue this loop, reducing '''maximum possible PV''' by 2 each time, until at least one '''''singlet''''' fails to roll higher than the target's AV.)''


3(1-(AV-(PV-2n))/10) - 3(1-(AV-(PV-2n))/10)<sup>2</sup> + (1-((AV-(PV-2n))/10)<sup>3</sup>*(AV-(PV-2(n-1))/10)<sup>3</sup>
In summary, the attack penetrates and deals damage equal to its damage dice once for each '''''triplet''''' of rolls where at least one '''''singlet''''' was higher than the target's AV. <ref><code>XRL.Rules.Stat.RollDamagePenetrations()</code></ref>


which is derived from:
If all three rolls in the first '''''triplet''''' are equal to or lower than the target's AV, the attack fails to penetrate at all.


If A<sub>n</sub>, B<sub>n</sub>, C<sub>n</sub>, are each 1 successful roll at n rounds of penetration:
==Penetration vs. AV Chart==
The following chart shows the chances to penetrate against a creature depending on the relative value of attacker's PV versus the target's AV. Keep in mind that this chart corresponds to the internal PV value of a weapon. For example, the internal PV of a '''{{PV}}7''' weapon is '''3''', so a '''{{PV}}7''' weapon versus a creature with '''{{AV}}2''' would correspond to the '''+1 PV''' column of this chart. Similarly, the internal PV of a '''{{PV}}4''' weapon is '''0''', so a '''{{PV}}4''' weapon versus a creature with '''{{AV}}4''' would correspond to the '''-4 PV''' column of this chart.


(A<sub>n</sub> v B<sub>n</sub> v C<sub>n</sub>) - (A<sub>n</sub>^B<sub>n</sub>^<sub>Cn</sub>) (the probability that 1 or 2 out of 3 rolls hit)
In other words, when using this chart, assume the weapon has 4 less penetration than shown in the game UI.


OR
Once your PV equals or exceeds the target's AV, each +2 extra PV will ensure one additional penetration against the target.


(A<sub>n</sub> ^ B<sub>n</sub> ^ C<sub>n</sub>) ^ (~A<sub>n+1</sub> ^ ~B<sub>n+1</sub> ^ ~C<sub>n+1</sub>) (the probability that all 3 rolls hit, but the second round of penetration fails to penetrate at all)
{| class="wikitable"
|-
| style="border-top-color:transparent;border-left-color:transparent;" |
! -6 PV !! -5 PV !! -4 PV !! -3 PV !! -2 PV !! -1 PV !! PV == AV !! +1 PV !! +2 PV !! +3 PV !! +4 PV !! +5 PV !! +6 PV !! +7 PV !! +8 PV !! +9 PV !! +10 PV !! +11 PV !! +12 PV
|-
! At Least 1 Penetration
| 48.8% || 65.7% || 78.4% || 87.5% || 93.6% || 97.3%
| style="background:rgba(108,180,122,0.06);" | 99.2% || 99.9% || 100% || 100% || 100% || 100% || 100% || 100% || 100% || 100% || 100% || 100% || 100%
|-
! At Least 2 Penetrations
| 0.2% || 0.7% || 3.1% || 8.2% || 16.9% || 30.0%
| style="background:rgba(108,180,122,0.06);" | 47.9% || 70.9% || 99.2% || 99.9% || 100% || 100% || 100% || 100% || 100% || 100% || 100% || 100% || 100%
|-
! At Least 3 Penetrations
| {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || 0.01% || 0.09% || 0.7% || 2.8%
| style="background:rgba(108,180,122,0.06);" | 8.7% || 21.9% || 47.9% || 70.9% || 99.2% || 99.9% || 100% || 100% || 100% || 100% || 100% || 100% || 100%
|-
! At Least 4 Penetrations
| {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || 0.002% || 0.03%
| style="background:rgba(108,180,122,0.06);" | 0.3% || 2.1% || 8.7% || 21.9% || 47.9% || 70.9% || 99.2% || 99.9% || 100% || 100% || 100% || 100% || 100%
|-
! At Least 5 Penetrations
| {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}}
| style="background:rgba(108,180,122,0.06);" | {{Color|K|< 0.001%}} || 0.02% || 0.3% || 2.1% || 8.7% || 21.9% || 47.9% || 70.9% || 99.2% || 99.9% || 100% || 100% || 100%
|-
! At Least 6 Penetrations
| {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}}
| style="background:rgba(108,180,122,0.06);" | {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || {{Color|K|< 0.001%}} || 0.02% || 0.3% || 2.1% || 8.7% || 21.9% || 47.9% || 70.9% || 99.2% || 99.9% || 100%
|-
! Average # Of Penetrations
| 0.5 || 0.664 || 0.815 || 0.958 || 1.112 || 1.301
| style="background:rgba(108,180,122,0.06);" | 1.561 || 1.948 || 2.561 || 2.948 || 3.561 || 3.948 || 4.561 || 4.948 || 5.561 || 5.948 || 6.561 || 6.948 || 7.561
|}


[[Category:Mechanics]]
==References==
<references/>
[[Category:Battle Mechanics]]
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