Proc Coefficient

The proc coefficient is the factor by which an item's effect, trigger chance, duration, or any combination of the three is scaled (multiplied).

This affects how certain "hits" can be "worse" or "better" at activating on-hit effects, depending on how high (or low) the proc coefficient is. If something hits very frequently, it may have a lower proc coefficient to lower the power of the ability to not outclass other abilities. Conversely, an infrequent, hard-hitting ability may have a higher proc coefficient to make up for the fact that it doesn't hit too often.

This also means that a character may need more than 100% "chance" from a collection of items to guarantee that desired proc.

In Hopoo Games Development Thoughts #1, the developers introduced the concept of proc coefficient like so:

"MUL-T’s nailgun has a low proc coefficient per nail of 0.4 compared to most character’s 1.0, so he isn’t proccing stuff a ton faster than other characters." - Quote from NaKyle, 03/30-2019.

(Note: Since the 1.0 update, MUL-T's nailgun has a proc coefficient of 0.6 rather than 0.4. The quote is given primarily as rationale for the proc coefficient system.)

It is worth noting that proc coefficients do not affect critical strike chance from items such as Lens-Maker's GlassesLens-Maker's Glasses
Gain 10% chance for hits to 'Critically Strike', dealing double damage.
Your attacks have a 10% (+10% per stack) chance to 'Critically Strike', dealing double damage.. All attacks are guaranteed to deal critical damage once 100% critical chance is reached.

Examples

Example 1

Suppose that a bullet has a proc coefficient of 0.5, and we have 1 Tri-Tip DaggerTri-Tip Dagger
Gain +10% chance to bleed enemies on hit.
10% (+10% per stack) chance to bleed an enemy for 240% base damage.. The dagger normally contributes a +10% chance to inflict BleedBleed (Debuff)
Damage over time.Deals 240% damage over time [3 x proc coefficient] (20% per tick, 4 ticks per second).
(stackable) on the victim for 3 seconds. However, with a proc coefficient of 0.5, the chance to inflict Bleed is halved (since we multiply that chance by 0.5), so the bullet's chance to inflict Bleed is only 5%. Additionally, the duration of Bleed is also halved, so even if the bullet does successfully roll the 5% infliction chance, the Bleed status will only last 1.5 seconds instead of 3.

Example 2

Suppose we have the same bullet with a proc coefficient of 0.5, but this time we have 18 Tri-Tip DaggerTri-Tip Dagger
Gain +10% chance to bleed enemies on hit.
10% (+10% per stack) chance to bleed an enemy for 240% base damage., totaling +180% bleed chance. With the proc coefficient of 0.5, this makes the bullet have a 90% chance to inflict Bleed, instead of 100%. This means that we will need at least 20 daggers to guarantee Bleed from this bullet. Additionally, the duration will still be halved (1.5 seconds), no matter how many daggers we have.

Key Points

A character with skills that have lower proc coefficients will require more items to reach a similar effect than skills with higher coefficients, but those caps for effects with linear stacking can still be reached.
Skills and effects with low proc coefficients often hit faster than normal or hit more than one target. Because of this, those skills and effects may tend to be more effective at utilizing item effects with linear stacking for their trigger chance (notably Bleed effects) than those with higher coefficients but that hit slower or hit fewer targets. The caveat is, of course, that these skills require a greater investment required to reach their maximum potential. Exceptions also exist; for instance, many of Commando'sCommandoThe Commando is a jack-of-all-trades character that is reliable in all situations of the game.
Class: Unknown
HP: 110 (+33 per level)
Damage: 12 (+2.4 per level)
Armor: 0
Umbra: Cornered Gunslinger skills hit very quickly but also have very high coefficients.
Critical strike chance is not affected by the proc coefficient.

For more information on item stacking mechanics and strategies, see Item Stacking.