Critical Chance is a derived statistic in Fallout, Fallout 2, Fallout 3, Fallout: New Vegas, Fallout Tactics and Fallout: Brotherhood of Steel.
Fallout, Fallout 2 and Fallout Tactics
An Aimed Shot has a critical chance bonus equal to the chancetohit penalty of the targeted body part^{[1]}. In Fallout Tactics, the Science skill also has an effect on critical chance against robotic enemies.
 $ \text{Initial level}=\text{Luck}\times1\% $
The Chance to Hit adds a slight bonus to critical chance if the attack hits the intended target. The formula used to determine whether an attack hits or misses is (Chance to Hit)  (RandomNumberBetween1and100). If the remainder is 0 or more, the attack is a hit. If it's negative, the attack is a miss.
If the attack hits its target, the same random number that was subtracted from the chance to hit is used to calculate the critical chance bonus of the successful hit. This bonus is equal to (ChanceToHit  RandomNumberBetween1and100)/10 rounded down. Thus if a successful attack's chance to hit was 49%, this critical chance bonus could be anything between 0% (random number is between 40 and 49) and 4% (random number is between 1 and 9).
A successful hit whose chance to hit was 95% has a critical chance bonus ranging from 0% to 9%. The average critical chance bonus of a successful hit with a 95% hit chance is (5x9 + 10x8 + 10x7 + 10x6 + 10x5 + 10x4 + 10x3 + 10x2 + 10x1 + 10x0) / 95 = 4.26%
 The Finesse trait increases the critical chance by 10%.
 The More Criticals perk increases the critical chance by 5% per rank.
 The Sniper perk increases the critical chance to 10*Luck for ranged weapons, but never above 95%.
 The Slayer perk increases the critical chance to 100% for melee weapons.
Fallout 3
Base Chance
Luck is the main base factor that determines the chances of a critical strike on an opponent.
 $ \text{Initial level}=\text{Luck}\times1\% $
Example: A starting Luck of 5.
 $ 5~(\text{Luck}) \times 1\%=5\%~(\text{Base chance}) $
Notes:
 Maximum initial base is capped at 10%.
 Ninja perk can increase this limit by another +15% for Melee and Unarmed weapons.
 Finesse perk can increase this limit by another +5%.
 Survival Guru perk can increase this limit by another +3%.
 Strikes dealt in V.A.T.S have additional +15% critical chance added.
 Some weapons have 0% chance of a critical strike (see Critical Multiplier for detail of effects).
player.getav critchance.
You can also check your critical chance with the console commandCritical Multiplier
All weapons have a critical multiplier that modifies the player character's base critical hit chance. This may improve or hinder the ability to score a critical hit depending on the weapon's Critical multiplier.
 $ \text{Base chance}\times\text{Critical multiplier} $
Example: A starting Luck of 5 and using a sniper rifle, which has a x5 Critical Multiplier.
 $ 5\%~(\text{Base chance})\times5~(\text{Critical multiplier})=25\%~(\text{Critical chance}) $
Notes
 The critical multiplier for fullyautomatic weapons is much lower than for singleshot weapons.
 There are a few weapons that have a x0 multiplier, making it impossible to score a critical hit.
 For a detailed list of weapon critical multipliers, see here.
Weapon Condition
The final critical chance is also modified by weapon condition.^{[2]}
 $ \mbox{Critical chance} \times \mbox{Condition} $
For example, a character with 5 Luck and using a sniper rifle in 50% condition would have,
 $ 25\%~(\text{Critical chance})\times\frac{50}{100}~(\text{Condition})=12.5\%~\text{Critical chance} $
Fallout: New Vegas
The formulas for critical chance seem unchanged from Fallout 3. You receive 1% of critical chance for each point placed into Luck. During character creation, you can add an additional 3% for all weapons by choosing the Built to Destroy trait.
 Attributes, perks and traits that increase critical chance include
 Luck (permanent +110%)
 Built to Destroy (permanent +3%)
 Light Touch¹ (temporary +5% while wearing any light armor)(Dead Money)
 Finesse (permanent +5%)
 Ninja² (permanent 15% increase for melee and unarmed weapons)
 Laser Commander¹ (permanent +10% with lasers).
 Set Lasers for Fun¹ (permanent +2/4% with energy weapons)
 Meat of Champions (+1 Luck for 60 seconds after eating a fresh corpse)
 Intense Training (permanent +1 Luck if selected)
 Luck Implant (permanent +1 Luck if purchased)
 ¹ The critical chance added by these perks is a flat bonus and is not affected by your weapon's critical multiplier.
 ² Ninja multiplies your total critical chance after all modifiers by 1.15; thus it adds 15% of your normal critical chance, not a flat 15% boost.
 Items that increase critical chance
 1st Recon beret (+5%)
 Naughty nightwear (+1 Luck, effective +1%)
 True Police Stories (temporary +5% (+10% with Comprehension))
 VaultTec Assisted Targeting System¹ (temporary +5% critical hit chance when using V.A.T.S.)
 Lucky shades (+1 Luck, effective +1%)
 Armor of the 87th Tribe (+3%)(Lonesome Road)
 Elite riot gear (+5%)(Lonesome Road)
 Ulysses' duster (+5%)(Lonesome Road)
 Joshua Graham's armor (+3%) (Honest Hearts)
 SaltUponWounds' helmet (+2%) (Honest Hearts)
 Marked beast face helmet (+2%) (Lonesome Road)
 ¹ The critical chance added by V.A.T.S. is a flat bonus and is not affected by your weapon's critical multiplier.
Currently, the highest possible critical chance that will be affected by your multiplier is 38% (10 Luck, Finesse, Built to Destroy, 1st Recon Beret, Elite riot gear/Ulysses' Duster, True Police Stories with Comprehension). As mentioned above, Light Touch, Laser Commander, Set Lasers for Fun, Ninja, and V.A.T.S. can further increase your chance.
Fallout: Brotherhood of Steel
In Fallout: Brotherhood of Steel, a critical hit allows to exceed the maximum limit of damage for a weapon.
Some weapons are very powerful with a high critical chance, such as the doublebarrel shotgun or The Slugger and also the weapons in bursts.
An energy weapon with the skill Energy Charge or a Melee weapon with the skill Special Attack can be extremely powerful if the charged attack is a critical hit.
The chance to cause a critical hit in combat is increased by
Initial Level: Each character starts with a 1% critical chance.
 The Butcher skill (only Cain) increases the critical chance by 5% only for blades for each ranks until a total of 25%.
 The Desert Soldier skill (only female character) increases the critical chance by 5% only for conventional weapons (weapon that uses 9mm) for each ranks until a total of 25%.
 The Future Woman skill (only female character) increases the critical chance by 5% only for energy weapons for each ranks until a total of 25%.
 The Heavy Hitter skill (only human male character) increases the critical chance by 5% only for Blunt weapon (Gloves, Clubs and Hammers) for each ranks until a total of 25%.
 The Pyromaniac skill (only Cain) increases the critical chance by 5% when using a firebased weapon (like the frag grenade, flamer, etc.) for each ranks until a total of 25%.
 The Slayer skill increases the critical chance by 5% for each ranks until a total of 25%.
 The Wastelander skill (only human male character) increases the critical chance by 10% only when using homemade weapons for each ranks until a total of 50%.
The type of weapon with a maximum critical chance with the skill required is the homemade weapons with a total of 75%.
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