Core Crystal

Core Crystals are a type of item in Xenoblade Chronicles 2. Drivers can resonate with Core Crystals to awaken Blades.

Of the eight Drivers that can be in the player's party at any point, only four of them can resonate with new Core Crystals: Rex, Nia, Mòrag, and Zeke. The other four -, , Jin, and Malos - are all unable or unwilling to resonate.

Standard Core Crystals
The following Core Crystals will grant their driver a random Common Blade or Rare Blade.
 * Common Core Crystal
 * Rare Core Crystal
 * Legendary Core Crystal

Unique Core Crystals
The following Core Crystals are unique and will grant their driver a predetermined Common or Rare Blade.
 * Unnamed Core Crystal
 * Beastly Core Crystal
 * Sealed Core Crystal
 * Roc's Core Crystal
 * Vess's Core Crystal
 * Lucky Core Crystal
 * Praxis's Core Crystal
 * Theory's Core Crystal
 * Aegaeon's Core Crystal
 * Ebullient Core Crystal
 * Divine Core Crystal

Mechanics
When the player decides to resonate with a Core Crystal, the game iterates through every Rare Blade that the player does not currently possess, and makes an independent random roll for each one (explained below). Rare Blades that succeed this roll are added to a pool of potentials. Once every Rare Blade has been checked, another roll is made based on the Core Crystal.
 * For Rare and Legendary Core Crystals, one of the Rare Blades in the potential pool is chosen at random. If the pool is empty, a Common Blade appears.
 * For Common Core Crystals, an additional 25% chance is rolled. If this roll fails, a Common Blade appears no matter how many Rare Blades are in the pool. If it succeeds, a Rare Blade is picked as above.

If the player chooses to view the awakening (as opposed to skipping it), the game generates two additional resonances of the same inputs. The Blades selected by these "dummy" resonances appear as the two silhouette flashes before the third, which is the Blade acquired.

The method of choosing whether to add each Rare Blade to the pool is straightforward but complex, having four main compoments.

Base rate
Each Rare Blade has a set of five different base probabilies for being selected, known as "groups". The game randomly selects which group to use when the player first begins the game, which cannot be changed in the same save file. Previously-released Blades are available for selection without any special consideration, even if they were originally obtained from a guaranteed source. Certain Blades are also not available until some condition is met, such as being in.

The five groups have equal chance of being selected.

Crystal modifier
Much like Pokéballs, the rarity of a Core Crystal is a straight multiplier to the "catch" rate of a Rare Blade.
 * Common Core Crystal: 1.0x
 * Rare Core Crystal: 1.5x
 * Legendary Core Crystal: 3.0x

Idea modifier
Every Driver has four idea levels: Bravery, Truth, Compassion, and Justice. Whichever of these is the greatest has an effect on Rare Blades of the matching s, with ties broken at random. For example, say a Driver has a Bravery of level 4, a Truth of level 3, a Compassion of level 4, and a Justice of level 2. The Bravery and Compassion levels are equal, so one is selected randomly for each Core Crystal used. It picks Bravery, so the chances of Rare Blades that are Fire or Water being selected is increased.

Using boosters during resonance temporarily increases a Driver's matching idea level for this try only, in addition to forcing it to be used even if it is not the highest.

Each idea level grants a +5% chance to Rare Blades of the matching elements, up to the maximum idea level of 15 being a boost of 1.75x.

Luck modifier
Luckier Drivers are more likely to get Rare Blades. The input used is based on the square root of the Driver's luck stat, meaning that the boost in rate has diminishing returns as luck increases: going from 100 to 400 luck is an increase of +13%, but going from 400 to 700 is only about +8.4%.

The formula used for the luck modifier is. At the maximum luck of 999, the boost in rate to all Rare Blades is approximately 1.36x. Humourously, a Driver with a luck of less than 15 would have a luck modifier of less than 1.0x.

Complete formula
probability% = baseRate * crystalMod * ((selectedIdeaRank * 5 + 100) / 100) * ((sqrt(luckStat) / 100 * 1.3) + 0.95)

Pity system
Disregarding all the above, the game has a method for guaranteeing that the player receives three specific Rare Blades based on the chosen group.

When a Core Crystal is used without receiving a Rare Blade, a pity counter is increased based on the Core Crystal used.
 * Common Core Crystal: 5 points
 * Rare Core Crystal: 25 points
 * Legendary Core Crystal: 50 points

Upon reaching 100 points, the next Core Crystal to be opened is guaranteed to have one of three "pity Blades", determined by which base probability group was selected. The point total is then reset, and the required point for the next one increases: the second pity Blade is earned at 200 points, and the third at 300. After this, the pity system no longer has any effect. If the player happens to already have all their group's pity Blades, the pity is "wasted", and a Common Blade appears instead.

Due to a bug, being in pity group 5 will result in the Blades for pity group 1 being generated instead. Therefore, the Blades from group 1 are twice as likely to be given as pity Blades, and those in group 5 cannot be generated via the pity system.

Takeaways
As a result of all the above:
 * The maximum possible boost to the chances of getting a specific Rare Blade is about 7.14x. This requires a Legendary Core Crystal, an idea level of 15 in the correct idea (which requires the natural max of 10 plus the max of 5 boosters per use), and a luck of 999.
 * While the chances of getting any specific Rare Blade do not change over time, the chance of getting any Rare Blade are higher at the start of the game simply due to there being more to pick from.
 * Common Core Crystals essentially add an extra "dud rate" of 75%, so their modifier is more like 0.25x than 1.0x (not exactly but it's similar in practice).
 * The DLC content contains many Rare and Legendary Core Crystals, which due to the pity system are an excellent way to guarantee multiple Rare Blades very early in a playthrough.

Gallery
Cristalli nucleici