Critical Hit
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Critical hits are otherwise normal weapon strikes that randomly deal increased damage on enemies. When a weapon critically hits (or "crits"), the damage is displayed as a yellow number on the HUD instead of the usual white coloring (though crits on shields 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 like weapons), rolls its own chance to critically hit.
Contrary to common belief, melee attacks against unalerted enemies are not guaranteed to crit. Invisibility and Smoke Screen only grant a stealth damage bonus; actual crits when stealthed or attacking unalerted enemies will simply apply the critical damage multiplier on top of the stealth damage bonus.
Critical Hit ChanceEdit
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 do not give percentage points nor stack multiplicatively.
CritChance = Weapon Crit Chance × (1 + Mod Crit Chance)
- Weapon Crit Chance: Each weapon has its own listed chance to critically hit. Currently, weapons range from 0% to 50% (Amprex, Dread, Synapse).
- Mod Crit Chance: This is the total of all equipped mod bonuses added together. If you have a Rank 5 Point Strike giving +150% (1.50) and a Rank 5 Critical Delay giving +48% (0.48) equipped, your Mod Crit Chance totals to 1.98.
This means that if a hypothetical rifle with a weapon crit chance of 10% has a Rank 5 Point Strike equipped, its new crit chance is 25%.
Critical Damage MultiplierEdit
When a weapon attack is determined to result in 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.
Crit Multiplier = Weapon Crit Multiplier × (1 + Mod Crit Multiplier)
- Weapon Crit Multiplier: Most weapons have either a 1.5x or a 2.0x damage multiplier to their critical hits. Currently, weapons range from 0x (Miter, Panthera, Seer) to 4.0x (Nukor).
- Mod Crit Multiplier: This is the total of all equipped mod bonuses added together. Equipping both Vital Sense and Hammer Shot 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. Plainly and simply, a weapon's damage on crit is as follows:
Critical Damage = Damage × Crit Multiplier
Red CritsEdit
If the critical hit chance for a weapon exceeds 100%, not only will every shot be a critical, but there is a chance for a red crit to occur. Red crits are critical hits that deal even more damage than normal crits, and are called such because their damage is displayed with red numbering. Once a weapon's critical chance exceeds 200% every attack is displayed in red but the multiplier varies based on the level of critical. The crit level starts at 1 for yellow "normal" 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%.
Modded Crit Chance | Crit Level | ||
0.01% − 100% | 1 | ||
100.01% − 200% | 2 | ||
200.01% − 300% | 3 | ||
300.01% − 400% | 4 | ||
400.01% − 500% | 5 | ||
500.01% − 600% | 6 | ||
600.01% − 700% | 7 | ||
700.01% − 800% | 8 | ||
• • • | • • • | ||
n% < CritChance ≤ (n% + 100%) | (n% + 100%) ÷ 100 |
The chance for a red crit to occur is equal to the critical hit chance of the weapon in excess of 100%:
Red Crit Chance = Crit Chance − 1
For Basic Red Crits (Level 2 Crits) the critical damage multiplier can be determined from the formula:
Red Crit Multiplier = 2 × (Crit Multiplier − 1) + 1
More generally, the critical damage multiplier of any hit can be determined from the following formula:
Red Crit Multiplier = Crit Level × (Crit Multiplier − 1) + 1
For example, a melee weapon with a base 3.0x crit multiplier and Organ Shatter installed would have a multiplier of 5.7x for level 1 (yellow) crits. If that weapon were to have a Critical Chance over 100% it would be capable of achieving level 2 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.
Critical HeadshotsEdit
Certain body parts 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 that listed damage!
Critical Headshot Damage = Damage × Critical Multiplier × Headshot Multiplier × 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 "fanny pack" which normally receives 3.0x damage, but does not seem to receive an additional multiplier beyond that and your weapon's listed crit multiplier when actually crit. The Jordas Golem, 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.
Redhead Damage = Damage × Red Crit Multiplier × Headshot Multiplier × 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.
CritzoneEdit
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, because headcrits provide a greater damage bonus than a 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 sustained DPS can be assimilated into the general damage gain by using an estimate 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:
Avg Damage Per Shot = Damage × (1 + Crit Chance × (Crit Multiplier − 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.
Avg Damage = Headcrits + Headshots + Crits + Hits
- Headcrits = Crit Chance × Headshot Rate × 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.
- Headshots = (1 − Crit Chance) × (Headshot Rate) × 2 × Damage
- Crits = Crit Chance × (1 − Headshot Rate) × Crit Damage
- Hits = (1 − Crit Chance) × (1 − Headshot Rate) × 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:
- Headcrits = 0.1 × 0.8 × 8.0 × 100 = 64
- Headshots = 0.9 × 0.8 × 2.0 × 100 = 144
- Crits = 0.1 × 0.2 × 2.0 × 100 = 4
- Hits = 0.9 × 0.2 × 100 = 18
So, your average damage per shot is actually:
Avg Damage = 64 + 144 + 4 + 18 = 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 — critical hit statistics and headshots synergize highly.
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 above scenario, 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 above equations can be condensed into the following:
Critzone Modifier = (1 + Headshot Rate) × (1 + Crit Chance × (Crit Multiplier × (3 − 2 ÷ (1 + Headshot Rate)) − 1))
Calculating Red Critzone ModifiersEdit
Perhaps unintuitively, calculating the redzone modifier is simpler than when critical chance lies below 100%. This is because the headcrit modifier applies to all headshots. This by no means relaxes the dependency of average damage output on headshot rate, though.
Critzone Modifier = (1 + 3 × Headshot Rate) × (1 + Critical Chance × (Crit Multiplier − 1))
In this case, headshot accuracy and average crit modifier are indeed two independent factors and can be examined and treated separately, as:
Crit Modifier = 1 + Crit Chance × (Crit Damage Multiplier − 1)
Zone Modifier = 1 + 3 × Headshot Rate
For example, a weapon with 125% crit chance and 2x crit damage multiplier has an average crit modifier of:
Average Crit Modifier = 1 + 1.25 × (2 − 1)
Average Crit Modifier = 1 + 1.25
Average Crit Modifier = 2.25
At a player's headshot accuracy of 80%, the zone modifier is:
Average Zone Modifier = 1 + 3 × 0.8
Average Zone Modifier = 3.4
Therefore, the combined crit & zone modifier is:
2.25 × 3.4 = 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 Edit
In this special case where critical chance exactly equals 100%, the formula simplifies even further, as there can only be yellow strikes—no white non-crits nor any red crits.
Critzone Modifier = Crit Damage Multiplier × (1 + 3 × Headshot Rate)
Comparing Benefit of Crit Mods Edit
When considering to install critical hit mods into a weapon, it is important to compare these mods' relative benefit as an increase in damage potential to that of 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, then use them with the following formula:
Relative Benefit = (Critzone Modifier_{new} ÷ Critzone Modifier_{old}) − 1
It is important to note that critical chance and critical damage mods show strong synergy, which means that using them combined will provide a greater benefit than the product of their individual benefits. It is therefore advised on any weapon to either use critical chance and critical damage mods together, or to not use them at all.
As an example, consider installing Point Strike and/or Vital Sense into the Vulkar, which has a 20% crit chance and 2.0x crit damage multiplier, and assume a player headshot accuracy of 80%. Using the previous formulas, the relative benefit of Point Strike alone would be roughly +53.57%, that of Vital Sense alone would be around +58.29%, and that of both combined would be close to +199.29%—which is significantly higher than if both would only scale multiplicatively with each other (that would only be +143.09%).
Synergy Explanation Edit
The direct general solution to the above formula 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:
- 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 × (1 + Crit Chance Bonus).
- NCD is the Net Crit Damage Multiplier, which is the Base Crit Damage Multiplier × (1 + Crit Damage Multiplier Bonus).
This is equal to the previous Critzone Modifier formulation from a previous section. The term (3 − 2 ÷ (1 + h)) is just the properly condensed form of ((1 + 3h) ÷ (1 + h)), which has been re-extended here for clarity about how it is comprised. The direct solution for the relative benefit is then:
- 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 Edit
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 either the benefit given by the CDB or the product of both together. This is because the CCB is multiplied by a factor that is always between 0 and 1, and that 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 Edit
When 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 − 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 criterion. Therefore, this term at this position should be regarded as the portion of the CCB that raises the NCC to 1.
Both Equations Edit
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, 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.
See AlsoEdit
Damage Mechanics | ||
---|---|---|
Offense | Critical Hit • Damage • Enemy Body Parts • Multishot • Punch Through | |
Defense | Armor • Health • Shield | |
Damage Types | ||
Physical | Impact • Puncture • Slash • Finishing | |
Elemental | Cold • Electricity • Heat • Toxin | |
Combined | Blast • Corrosive • Gas • Magnetic • Radiation • Viral |
Mechanics | |||
---|---|---|---|
Currencies | Credits • Ducats • Platinum • Standing | ||
General | Affinity • Clan • Daily Tribute • Focus • Foundry • Fusion • Key Bindings • Mastery Rank • Mods (Damaged) • Orbiter • Polarization • Trade System • Transmutation | ||
Gameplay | Mission | Air Support • Alert (Tactical) • Archwing • Cell • Challenge Reward • Death • Death Mark • Enemy Behavior • HUD • Maneuvers (Archwing) • Matchmaking • One-Handed Action • Tile Sets • Mission | |
Stealth | Hacking • Noise Level • Stealth | ||
Attributes | Weapons | Accuracy • Ammo • Attack Speed • Critical Hit • Damage • Fire Rate • Melee • Multishot • Projectile Speed • Punch Through • Recoil • Reload Speed • Status • Zoom | |
Warframe | Attributes • Armor • Health • Passives • Powers • Shield • Threat Level | ||
Mathematical | Enemy Level Scaling • Maximization (Duration • Efficiency • Range • Strength) • User Research |