Ok, let's look at the math calmly.
It obviously won't do too much with shotguns, BFGs, and stuff like that, but the boosts it gives to Chainguns and plasma rifles are absolutely rediculous
In my experience with the beta, this actually gives a fair amount of help to shotguns; it's still not as handy as being able to reload while moving, but it gives a noticeable boost such that you won't need to be quite as close to land a killing blow. Obviously, a person using shotguns primarily will have more important trait picks first, but the effect from SoB is appreciable as it pads the effect of distance some.
With Chaingun, you get +5 armor piercing damage per attack per level, meaning that at SoaB(3) you'd get +15 armor piercing damage per attack. This means that against unarmored monsters your average damage would be rising from 17.5 per attack to 32.5 per attack- that's almost twice as much damage! And that's without thrwing armor into the mix. Against an enemy with level 2 armor, you'd be going from an average of 7.5 damage to an average of 22.5 damage- a 200% increase.
Your first figure on the armor math is wrong; the lowest amount of damage from a hit that is at all possible, including things not normally called hits like acid and lava damage, is 0 (as far as everything I've ever seen indicates), and I'm about 99% sure that gunshots/punches/the like have to do at least 1 point of damage on a successful hit, thus it would not be 7.5 damage but 12.5 damage (((1+4)/2)*5). But I know the response already; an 80% increase still seems like too much of a change, and granted, the possibility that I'm wrong about the single point of necessary damage would up that to 125%. The trouble with giving percentage changes is that when the numbers are low, so's the effect; the number difference, for conservative arguments' sake is 0-4 versus 2-7. It's not clear just from that that things are going to suddenly turn into a cakewalk. Before we go ahead and declare that SoB's gotta get removed, or perhaps changed such that it makes hits less accurate, or that it makes only a decimal increase in the damage, let's see what the wiki says about HP totals...
O = 40 HP, 1 Armor
B = 50 HP, 1 Armor
B = 60 HP, 2 Armor
A = 50 HP, 2 Armor
V = 70 HP, 2 Armor
..and compare the number of times you'd have to shoot our most notorious foes (assuming all bullets hit their mark and that armor can reduce a hit to 0 damage) before they go down, since that's what will ultimately determine the change in the usefulness of the chaingun and the level of difficulty in the game (plasma rifle ignored for the moment, simply because the chaingun uses *the* most plentiful ammo type in the whole game and is the most powerful weapon using said ammo):
Before SoB:
O - worst case: never, average case: 4 times, best case: 2 times.
B - worst case: never, average case: 4 times, best case: 2 times.
B - worst case: never, average case: 6 times, best case: 3 times.
A - worst case: never, average case: 5 times, best case: 2.5 times (halfway through the third).
V - worst case: never, average case: 7 times, best case: 3.5 times (halfway through the fourth).
After SoB 3:
O - worst case: 3 times, average case: 2 times, best case: 1 time (8*5=40; ouch).
B - worst case: 4 times, average case: 2 times, best case: 2 times.
B - worst case: 6 times, average case: 3 times, best case: 2 times.
A - worst case: 5 times, average case: 3 times, best case: 2 times.
V - worst case: 7 times, average case: 4 times, best case: 2 times.
With results like these, I gotta admit there's a balance problem. I think the best way to fix things while keeping the spirit of SoB is to change SoB so that it affects either the min or the max damage of hits but not both; I'm not totally sure which one would be better but I'm inclined towards the min damage as mods already cover the max damage portion.