RES area of influence is 20km spherical.
Not sure the exact bonus but I know its a very significant bonus, probably around 300-400% bonus to yield outside of a RES.
I know that my python's battery of mining lasers barely breaks a sweat on an untagged roid but can only power three lasers to 30% left roid depletion before switching to two lasers
No idea about inside of RESes, aside from knowing that apparently higher risk RESes have greater bonuses, as I haven't been in one since mining in a dropship - which I haven't done since helping to build Obsidian Dock.
20km? That's interesting because I did comparisons with a mate's fragment numbers from outside of a res site about 4 weeks back and was still getting more fragments over 70km away from the haz res marker. If it is genuinely supposed to be 20m it would appear to be bugged.
As for it being 300% to 400% greater, it just isn't, at all. Seriously, stop trying to work things out from how long your guns are firing and just count the fragments in contacts - you don't need to estimate it, it is quantifiable.
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