There is definitely something wrong on your math: since wipe, I have NEVER deal 100 damage on a BA with an avenger without crits (and I have BRD)
Also, an avenger which supposed to be highiest tier in this game, with highest cost for weapon and ammo, which deal less damage than LSW because no appropriate perk... Beuargh.
I have 2x BRD and 25 critic chance.
Critical Hit for 69 damage to BA from Avenger and Critical Hit for 145 damage to BA from LSW
As Crazy, i never had damage arroud 100 with Avenger.
There is something wrong with your math. Also you have "tested" it on paper and i have tested it in combat.
Well I don't know bullets from burst to hit %, so probably avenger deals less damage, because atleast 40th (14th in central hex) bullet will miss, if each bullet has penalty from 95%, not from your skill (for example you have 150% to hit, and every bullet will give penalty X% to 150%, so you'll have 95%, 95%, 95% etc for few fist bullets, then you need really high skill), if it gives penalty to 95%, then you need skill only to have 95% on the first bullet and then damage will be affected only by real life luck, because sometimes all 14 can hit, sometimes only half of them, sometimes only 1 or 2 bullets. While for LSW it's only 10 bullets, 10 much less than 40, so you have much more % that all bullets will hit, you need only 4 for central hex, so LSW requires less real life luck or... less BG skill, if each bullet gives penalty to it, not to 95%.
Probably you know better ToHit% for bursting weapon, and you know how much % removed from each next bullet in burst, then you can calculate it yourself.
All I can say with my math, that I think not all 14 bullets hits your target, try to test it in point blank, I think it's harder to miss all 40 bullets and all 10 bullets... may be, as I said I don't know from what to reduce % and how much.
For example every bullet gives -4% to hit from your skill or base ToHit% before setting it to 95%.
Then you need 4x40=160% skill only to have all bullets from avenger hit with 95%.
+95% for 95% for first bullet.
+4% per hex between you and target.
-8% for every PE higher than 2.
So with 7 PE, it's 5x8=40%.
For example at range of 10 it negates 7 PE bonus, because of 40-40=0.
so it's 160+95=255% BG skill to 0 AC target.
And if target has like 30 AC, it's 285% BG skill.
*Again it was an example, if each bullet reduces ToHit on 4%, it can be 2% or 5%, I don't know, also if it reduces from 95%, then you don't need to high skill, but you need your real life luck, so 2nd bullet will have 91%, 3rd 87%, etc. so you may hit only with first few bullets, again, depending on how much % each bullet reduces.