Edición de «Daño crítico»

'''NOTA: No confundir el daño crítico con el [[multiplicador crítico]], todos los mods que hacen referencia a "daño crítico" se deberían cambiar a [[multiplicador crítico]], que es concretamente a lo único que afecta.'''
{{Fecha}}
{{Infobox
|Box title = Daño crítico
|image     = Daño crítico.png
}}
<section begin=intro />
El '''daño crítico''' o ''golpe crítico'' se puede producir cuando se golpea a un enemigo con un arma. El daño normal se muestra de color blanco, pero si se produce un golpe crítico, el daño crítico se identificará de color amarillo, naranja o rojo (en el caso de golpear escudos seguirán siendo azul). El daño crítico esta influenciado por dos factores: la [[probabilidad crítica]] y su [[multiplicador crítico]], que están predeterminados por el arma y pueden ser aumentados mediante mods. Cada golpe o perdigón en el caso de escopetas tiene su propia probabilidad de provocar un golpe crítico.

Al contrario de lo que comúnmente se cree, los ataques cuerpo a cuerpo contra enemigos sin atacar no tienen garantía de hacer daño crítico. La [[Invisibilidad]] y [[Pantalla de humo]] solo otorga una bonificación por daño de sigilo ; Los crits reales cuando se cuelan o atacan a enemigos sin tiros simplemente aplicarán el multiplicador de daño crítico sobre el bonus de daño sigiloso.
<section end=intro />
{{clr}}{{tocright}}
'''Critical hits''' are otherwise normal [[Armas]] strikes that randomly deal increased [[daño]] on enemies. When a weapon deals a critical hit (or "crits"), the damage is displayed as a yellow, orange or red number on the [[HUD]] instead of the usual white coloring (bear in mind that critical hits on [[escudo]]s are still blue). The likelihood that an attack will be a critical hit is based on the weapon's ''critical hit chance'', and the additional damage dealt by a critical hit is determined by the weapon's ''critical damage multiplier''. Each attack, or each pellet in the case of shotguns (and similar weapons such as the [[Redeemer]]), rolls its own chance to critically hit.

Contrary to common belief, melee attacks against [[Sigilo|unalerted enemies]] are '''not '''guaranteed to crit. [[Invisibilidad]] and [[Pantalla de humo]] only grant a [[Sigilo#Stealth Attack|stealth damage bonus]]; actual crits when [[Sigilo]]ed or attacking unalerted enemies will simply apply the critical damage multiplier on top of the [[Sigilo]] damage bonus.

==Probabilidad crítica==
While each weapon has a base chance to critically hit, there exist [[mods]] to increase critical hit chance. These mods add together to make a single multiplier to the weapon's critical hit chance; they usually do not give percentage points nor stack multiplicatively. Some melee mods like [[Acometida de sangre]] and [[Golpe mutilador]] have different interactions with your final crit chance. [[Acometida de sangre]] will multiply your final crit chance, including mods. [[Golpe mutilador]] will add a flat 90% chance to crit, to your base crit chance when slide attacking. This would make a 10% crit chance weapon have 100% (0.1 + 0.9 = 1) crit chance, not 19% (0.1 x (0.9 + 1) = 0.19) like most crit mods would. Similarly to [[Golpe mutilador]], Melee [[Mod agrietado]] with the affix "''Critical Chance on Slide Attack''" will also give a flat crit chance.

{{MathText|Critical Chance {{eql}} Weapon Crit Chance {{mul}} (1 + Mod Crit Chance)}}
* '''Weapon Crit Chance:''' The innate probability of a weapon to land a critical hit.
* '''Mod Crit Chance:''' This is the total of all equipped mod bonuses added together. If you have a Rank 5 [[Punto de impacto]] giving +150% (1.50) and a Rank 5 [[Retraso crítico]] giving +48% (0.48) equipped, your Mod Crit Chance totals to 1.98.

This means that if a rifle with a weapon crit chance of 10% has a Rank 5 [[Punto de impacto]] equipped, its total crit chance will be 25%.


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Mordisco.png|link=Mordisco
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==Multiplicador crítico==
When a weapon deals a critical hit, the amount of damage it would do is simply multiplied by the crit multiplier, which is calculated by a formula similar to the crit chance formula.

{{MathText|Crit Multiplier {{eql}} Weapon Crit Multiplier {{mul}} (1 + Mod Crit Multiplier)}}
* '''Weapon Crit Multiplier:''' The innate crit multiplier of a weapon.
* '''Mod Crit Multiplier:''' This is the total bonuses of all equipped mods added together. Equipping both [[Sentido vital]] and [[Disparo martillo]] at maximum rank (1.20 and 0.60, respectively) will yield 1.80 as the Mod Crit Multiplier.

Crit Multipliers are applied directly to modded weapon damage in the damage calculation and all calculations, including elemental mod damage, occurs after this multiplier has been applied. Simply put, a weapon's damage on crit is as follows:

{{MathText|Critical Damage {{eql}} Damage {{mul}} Crit Multiplier}}


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Sentido vital.png|link=Sentido vital
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Municiones de hoja.png|link=Municiones de hoja
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Disparo de metralla.png|link=Disparo de metralla
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Rompeobjetivos Prime.png|link=Rompeobjetivos Prime
Punta hueca.png|link=Punta hueca
Balas afiladas.png|link=Balas afiladas
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Filo sangrante.png|link=Filo sangrante
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==Críticos naranjas y rojos==
If the critical hit chance for a weapon exceeds 100%, not only will every shot be a critical hit, but there is a chance for an orange crit to occur. '''Orange''' crits are critical hits that deal even more damage than normal '''yellow''' crits, and are called such because their damage is displayed with orange numbering. Once a weapon's critical chance exceeds 200% every attack has a chance to '''red''' crit, which deals even more damage. When the chance to crit exceeds 300% all damage numbers will be displayed in red, but the crit multiplier varies based on the ''level'' of critical chance. The crit level starts at 1 for yellow crits, level 2 crits are hits from any critical chance greater than 100%, and level 3 crits are hits from any critical chance greater than 200%. This pattern continues indefinitely with critical level increasing by 1 each time the critical chance exceeds another 100%.

{{CustomCollapsible|Crit Levels Table|||}}

{| class="wikitable" style="text-align: center; margin: 0.5em auto"
|-
! Modded Crit Chance
! Crit Level
|-
| 0.01% to 100%
| style="color: black; background: #ffff7f;" | 1
|-
| 100.01% to 200%
| style="color: black; background: #ffd27f;" | 2
|-
| 200.01% to 300%
| style="color: black; background: #ff7f7f;" | 3
|-
| 300.01% to 400%
| style="color: black; background: #ff7f7f;" | 4
|-
| 400.01% to 500%
| style="text-align: center; color: black; background: #ff7f7f;" | 5
|-
| •<br />•<br />•
| style="text-align: center; color: black; background: #ff7f7f;" | •<br />•<br />•
|-
| 100% {{mul}} (''n'' - 1) to 100% {{mul}} ''n''
| style="color: black; background: #ff7f7f;" | ''n''
|}
{{CustomCollapsible/End}}

For orange crits (level 2 crits) the critical damage multiplier can be determined from the formula:

{{MathText|Orange Crit Multiplier {{eql}} 2 {{mul}} (Crit Multiplier {{sub}} 1) + 1}}

More generally, the critical damage multiplier of any hit can be determined from the following formula:

{{MathText|Total Crit Multiplier {{eql}} Crit Level {{mul}} (Crit Multiplier {{sub}} 1) + 1}}

This is because the displayed crit multiplier isn't displaying the damage increase on a crit, it is showing your total damage on a crit. A yellow crit with a 3.0x multiplier is only adding 2.0x of the damage, because the weapon does 1.0x damage at base already. For this we subtract 1.0x in order to get the bonus damage, which is more important for crit calculation.

For example, a melee weapon with a base 3.0x crit multiplier and [[Destructor de órganos]] installed would have a multiplier of 5.7x for level 1 (yellow) crits. If that weapon were to have a Critical Chance of over 100% it would be capable of achieving level 2 (orange) crits and they would have a multiplier of 10.4x, and if that weapon reached a Critical Chance over 200% it would be capable of level 3 crits dealing 15.1x damage.

==Disparos a la cabeza críticos==
[[File:AklexCritDifferences.png|thumb|This picture displays a headcrit dealing 4x regular headshot damage using an unmodded [[Lex]].]]
[[Partes del cuerpo del enemigo|Ciertas partes del cuerpo]] on enemies, most notably heads, will receive additional damage when struck. This location-based damage increase is usually a 2.0x multiplier, but if the strike is a critical hit, then the strike receives an additional 2.0x multiplier on top of the location multiplier and the crit multiplier. This means that while a normal bodyshot results in your weapon's listed damage (before mitigation), a critical headshot from a weapon with a 2.0x crit multiplier would deal 8.0x the listed damage.

{{MathText|Critical Headshot Damage {{eql}} Damage {{mul}} Critical Multiplier {{mul}} Headshot Multiplier {{mul}} Headcrit Multiplier}}
* '''Critical Multiplier:''' This is what has been calculated in the previous section entitled "Critical Damage Multiplier". It is the combination of a weapon's crit multiplier and the bonus multipliers from installed mods. It will be listed when hovering over your weapon selection while in the [[Arsenal]].
* '''Headshot Multiplier:''' This is 2.0x in almost all cases, as damage dealt to enemy heads typically receive double damage.
* '''Headcrit Multiplier:''' This is exactly 2.0x and is not subject to other changing factors.
The ''headcrit'' multiplier seems to be specific to heads and not generalized to all special body parts. The MOA, for example, has a "[[wikipedia:Fanny Pack|fanny pack]]" which normally receives 3.0x damage, but does not seem to receive any additional multipliers during a critical hit. The [[Golem Jordas]], however, has a 1.0x multiplier on his engines, but still receives quadruple damage if critically hit.

'''Redheads''' are the culmination of all these possible multipliers. There is no additional increase in the headcrit multiplier; you can simply replace the Crit Multiplier in the previous formula with the Red Crit Multiplier result from the preceding section.

{{MathText|Redhead Damage {{eql}} Damage {{mul}} Red Crit Multiplier {{mul}} Headshot Multiplier {{mul}} Headcrit Multiplier}}
* '''Red Crit Multiplier: '''This is double your critical multiplier, minus 1.00 exactly.
* '''Headshot Multiplier: '''typically 2.0x.
* '''Headcrit Multiplier: '''Still 2.0x.
This means that a player wielding [[Dread]] with all related mods could deal up to '''60.0x''' their normal damage.

==Critzone==
The critical hit mechanic increases the average damage output or damage potential of all weapons capable of inflicting critical hits. The magnitude of this increase is dependent on your aim as a player, as headcrits provide a greater damage bonus than a separate headshot and a critical hit combined. Therefore, the higher your headshot accuracy, the higher the value of the crit stats of your weapon. This effect on your [[Daño|sustained DPS]] can be assimilated into the general damage gain by using an estimation of your headshot accuracy.

Recall the formulas above for critical hit chance and critical damage multipliers. Your damage per shot without considering headshots is equal to:

{{MathText|Avg Damage Per Shot {{eql}} Damage {{mul}} (1 + Crit Chance {{mul}} (Crit Multiplier {{sub}} 1))}}

A good eye will notice that the above equation partitions the total average damage into two factors: damage that crits, and damage that doesn't. When crit chance is increased, a greater portion of shots deal crit damage instead of normal damage. When headcrits are included, the equation gets complicated because there are four different cases: headshots that crit, headshots that don't, bodyshots that crit, and bodyshots that don't.

{{MathText|Avg Damage {{eql}} Headcrits + Headshots + Crits + Hits}}
* {{MathText|Headcrits {{eql}} Crit Chance {{mul}} Headshot Rate {{mul}} Crit Headshot Damage}}
** '''Crit Headshot Damage''' is defined in an earlier section.
** '''Headshot Rate''' is your personal estimate of how many of your total hits are headshots.
* {{MathText|Headshots {{eql}} (1 {{sub}} Crit Chance) {{mul}} (Headshot Rate) {{mul}} 2 {{mul}} Damage}}
* {{MathText|Crits {{eql}} Crit Chance {{mul}} (1 {{sub}} Headshot Rate) {{mul}} Crit Damage}}
* {{MathText|Hits {{eql}} (1 {{sub}} Crit Chance) {{mul}} (1 {{sub}} Headshot Rate) {{mul}} Damage}}

As an example, with a weapon of '''100''' damage per shot, '''10%''' crit chance, and '''2.0x''' crit multiplier, if you can land a headshot 80% of the time, your calculation is as follows:
* {{MathText|Headcrits {{eql}} 0.1 {{mul}} 0.8 {{mul}} 8.0 {{mul}} 100 {{eql}} 64}}
* {{MathText|Headshots {{eql}} 0.9 {{mul}} 0.8 {{mul}} 2.0 {{mul}} 100 {{eql}} 144}}
* {{MathText|Crits {{eql}} 0.1 {{mul}} 0.2 {{mul}} 2.0 {{mul}} 100 {{eql}} 4}}
* {{MathText|Hits {{eql}} 0.9 {{mul}} 0.2 {{mul}} 100 {{eql}} 18}}

So, your average damage per shot is actually:

{{MathText|Avg Damage {{eql}} 64 + 144 + 4 + 18 {{eql}} 230}}

Hence, the critical hit mechanic increased your average damage by '''130%''' in this example. For contrast, if you landed headshots only 20% of the time but kept all other variables the same, critical hits increased your average damage by a mere '''40%'''. This is why it is so important for crit-based weaponry to be used accurately &mdash; critical hit statistics and headshots synergize very well.

For advanced usage, this entire calculation and its difference from the original average damage per shot can be described as the '''critzone''' modifier. In the first scenario above, the critzone modifier was '''2.3''', and in the case where you only had 20% headshot accuracy, the critzone modifier was '''1.4''' instead. Mathematically, all of the equations above can be condensed into the following:

{{MathText|Critzone Modifier {{eql}} (1 + Headshot Rate) {{mul}} (1 + Crit Chance {{mul}} (Crit Multiplier {{mul}} (3 {{sub}} 2 {{div}} (1 + Headshot Rate)) {{sub}} 1))}}

===Calculating Red Critzone Modifiers===
Perhaps unintuitively, calculating the redzone modifier is simpler than when the critical chance lies below 100%. This is because the headcrit modifier applies to all headshots. This by no means relaxes the dependence of average damage output on headshot rate, though.

{{MathText|Critzone Modifier {{eql}} (1 + 3 {{mul}} Headshot Rate) {{mul}} (1 + Critical Chance {{mul}} (Crit Multiplier {{sub}} 1))}}

In this case, headshot accuracy and average crit modifier are indeed two independent factors and can be examined and treated separately:

{{MathText|Crit Modifier {{eql}} 1 + Crit Chance {{mul}} (Crit Damage Multiplier {{sub}} 1)}} <br />
{{MathText|Zone Modifier {{eql}} 1 + 3 {{mul}} Headshot Rate}}

For example, a weapon with a 125% crit chance and 2x crit damage multiplier has an average crit modifier of:

{{MathText|Average Crit Modifier {{eql}} 1 + 1.25 {{mul}} (2 {{sub}} 1)}}<br />
{{MathText|Average Crit Modifier {{eql}} 1 + 1.25}}<br />
{{MathText|Average Crit Modifier {{eql}} 2.25}}

With a player's headshot accuracy of 80%, the zone modifier is:

{{MathText|Average Zone Modifier {{eql}} 1 + 3 {{mul}} 0.8}}<br />
{{MathText|Average Zone Modifier {{eql}} 3.4}}

Therefore, the combined crit & zone modifier is:

{{MathText|2.25 {{mul}} 3.4 {{eql}} 7.65}}

This means the weapon will on average deal '''665%''' more damage before hit zones and critical hits were taken into consideration.

===Calculating Yellow Critzone Modifiers===
In this special case where critical chance exactly equals 100%, the formula is simplified even further, as there can only be yellow strikes—no white non-crits nor any red crits.

{{MathText|Critzone Modifier {{eql}} Crit Damage Multiplier {{mul}} (1 + 3 {{mul}} Headshot Rate)}}

==Comparing Benefit of Crit Mods==
When considering installing critical hit mods on a weapon, it is important to compare the relative benefit of these mods as an increase in damage potential to that of the other mods in question. The easiest way to do this is by calculating damage both before and after installing the critical hit mods in question using the following formula:

{{MathText|Relative Benefit {{eql}} (Critzone Modifier{{ind|new}} {{div}} Critzone Modifier{{ind|old}}) {{sub}} 1}}

It is important to note that critical chance and critical damage mods show strong synergy, which means that using them together will provide a greater benefit than individually. '''It is therefore advised to either use critical chance and critical damage mods together, or to not use them at all.'''

As an example, consider installing [[Punto de impacto]] and/or [[Sentido vital]] into the [[Vulkar]], which has a 20% crit chance and 2.0x crit damage multiplier, and assume the player has a headshot accuracy of 80%. Using the previous formulas, the relative benefit of [[Punto de impacto]] alone would be roughly '''+53.57%''', that of [[Sentido vital]] would be around '''+58.29%''', and that of both combined would be close to '''+199.29%'''&mdash;which is significantly higher than if both would only scale multiplicatively with each other (that would only be '''+143.09%''').

===Synergy Explanation===
The direct general solution to the formula above illustrates how this strong synergy comes about. To recognize the elements comprising the benefit equation solution, here is the critzone modifier equation in a slightly altered and color-coded form:
[[File:Czm.jpg|none|thumb|619x619px]]
* '''CZM''' is the '''Critzone Modifier'''.
* '''H''' is the '''Headshot Rate''', where 1.00 means every shot you land is on an enemy head, and 0 means they all land onto other body parts without bonus damage.
* '''NCC''' is the '''Net Crit Chance''', which is the '''Base Crit Chance {{mul}} (1 + Crit Chance Bonus)'''.
* '''NCD''' is the '''Net Crit Damage Multiplier''', which is the '''Base Crit Damage Multiplier {{mul}} (1 + Crit Damage Multiplier Bonus)'''.
This is equal to the previous Critzone Modifier formulas from previous sections. The term {{MathText|(3 {{sub}} 2 {{div}} (1 + h))}} is just the properly condensed form of {{MathText|((1 + 3h) {{div}} (1 + h))}}, which has been re-extended here for clarity about how it is comprised. The direct solution for the relative benefit is then:
[[File:Ben.jpg|none|thumb|800x800px]]
* '''Base Crit Chance (BCC)''' is the crit chance value of the unmodded weapon.
* '''Base Crit Damage (BCD)''' is the crit damage value of the unmodded weapon.
* '''Crit Chance Bonus (CCB)''' is the value of any crit chance mod in question, expressed as a decimal to two places.
* '''Crit Damage Bonus (CDB)''' is the value of any crit damage mod in question, expressed as a decimal to two places.
* '''Net Crit Chance (NCC)''' is your weapon's modified crit chance. If it is below 100% (1.00), use the upper equation; else, use the lower equation.

====''Upper Equation''====
The strong synergy comes from each of the bonuses and the product of both adding up altogether. The benefit gained from the '''CCB''' alone is low, when compared to the benefit given by the '''CDB''' and the product of both together. This is because the '''CCB''' is multiplied by a factor that is always between 0 and 1, and the closer that factor is to 1, the greater the base crit damage multiplier of the weapon is.

A higher '''headshot accuracy (H)''' also improves the weighted impact of the crit chance bonus, as is apparent when '''NCC''' is less than 100% (the '''NCC < 1''' case), as yellow over red ranges from '''1 when H = 0''' to '''0.5 when H = 1'''.

====''Lower Equation''====
When the net crit chance is greater than 100% (the '''NCC ≥ 1''' case), a new value to add in (a ''summand'') appears here, containing only base values and headshot accuracy. This summand comes about because the '''CCB''' must be high enough to raise the crit chance to or over 100%; it is a corrective remainder of the formula rearrangement. The '''CCB''' doesn't appear in this summand because any more crit chance bonus than is necessary to reach when '''NCC = 1''' will not increase this component of benefit any further.

Since one factor in it, orange over red, ranges from '''0 when H = 0''' to '''0.5 when H = 1''' (it is the complement of yellow over red; both together always add up to 1 regardless of '''H'''), the headshot accuracy increases the weighted impact of crit chance bonuses in the '''NCC ≥ 1''' case too.

The crit chance bonus is actually "hidden" in this summand: '''(1 / BCC {{sub}} 1)''' is the value the crit chance bonus must have to set '''NCC''' to exactly 1. As '''NCC''' has been defined as equal to or greater than 1 in this case, the crit chance bonus must be equal to or greater than this term to fulfill that criteria. Therefore, this term at this position should be regarded as the portion of the '''CCB''' that raises the '''NCC''' to 1.

====''Both Equations''====
Apart from that transition summand and the different coefficients of '''CCBs''', the two cases are the same, especially in that the sum of all these benefit components is reduced to below its nominal value by the same denominator, a denominator that is always greater than 1.00. As '''H''', '''BCC''', and '''BCD''' all contribute inversely to this denominator, the greater they are, the smaller the whole denominator. If the denominator is smaller, the actual benefit is greater, converging against '''CCB + CDB + CCB × CDB''' for base crit chances very close to 100% and very large base crit damage multipliers. Note however that the range of base values of all weapons currently implemented into the game all yield denominators far greater than 1, so one shouldn't think of this convergence as a reasonable approximation for practical purposes.

To get an idea of the magnitude: Picking up on the previously used example of the Vulkar, a weapon with already comparatively favorable base crit stats, the denominator for this weapon at the assumed headshot accuracy of 80% is '''~ 2.06''', so the bonuses are roughly halved, and the individual '''CCB''' component is multiplied with '''~0.735''', i.e. reduced by ~26.5%, on top of that.

Even for the current best of critical chance weapons ([[Dread]], [[Amprex]], [[Lenz]] and [[Synapse]]) and assuming 100% headshot accuracy, the denominator is still 1.25, the transition summand 0.25, and the crit chance bonus coefficient 0.5 or 0.75 (depending on whether or not it raises the net crit chance to/above 100%). All of these are far away from their respective maximums and minimums of 1.00, 0.00, and 1.00.

Perhaps counter-intuitively, a higher base crit damage multiplier will increase the impact of crit chance mods more than that of crit damage mods, relative to each other, while different base crit chances affect the impact of both stat bonuses indiscriminately. When experimenting with crit builds, focus first on weapons with high crit multipliers.

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[[en:Critical Hit]]