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15 / 370 = effecitvely a 4% increase. That can be noticable for sure, but it's not going to have the proportional effect of your first 10 syringes.
Sticky increases in damage and chance, so it just keeps scaling forever.
No hardcoded caps, but sometimes there are effective caps, often absurdly large.
Teddy bears give 15% chance to block per stack, but in a 10+ bear run, I was still getting hit.
I'm pretty sure there are diminishing returns. It's 15% extra, but 15% of what? There might be a hidden value or something, but it's calculated to give less as you go. The rates aren't flat.
I remember my friend looking it up and saying if you want 100% block chance, you'll need an absurd amount of bears, like about thousand
its called diminishing returns and even with 10 quadrillion bears you still wouldnt have 100% block chance
Proc coefficient doesn't actually affect chance, just damage. (Also I think MUL-T's nail gun is 0.4, not 0.2, but I could be wrong).
So if MUL-T's Nail gun has a coefficient of 0.2, he'll still Bleed an enemy 100% of the time with 10 Daggers, it'll just do 0.2x the damage that it usually would.