I like you're average. But if i can screen shot every game i play in gb. I'll honestly tell you 75% of BB5s don't even get 100k attack/ BB6s get around 150k at best, unless its an armored QV. You're average seems legit to me. I've seen over 50 games where i get a good 250k or so attack to only find the next best player has 70K or less, sometimes 2 BB6s are involve lol.

You are talking about at-level crew here, so let's get a more realistic picture:

BB1/BB2/BB3 - At level crew, in most cases (95%+), you can reach ability cap with only 1 aspect, Acc or Reload, which means either your Acc sucks, or your Reload sucks, let alone to say your range disadvantage against BB4+ ships, and there's no way you can reach repair cap, speed cap or have a long OH time, and your scout is pure food of enemy fighters. In such case, a most optimal estimat on damage would be:
BB1 - Avg 15k (and most damage came from hitting DD/CL/DA, etc)
BB2 - Avg 25k
BB3 - Avg 35k

Now, BB4, with at-level crew, you may reach Acc and Reload cap, but since Acc cap is level-related, your actuall Acc will still suck. Depending on your nation and the ship of your choice, you may reach speed cap, and you will have moderately good repair as well. But since you can't effectively scout because you don't have Lv115 scouts, a most optimal estimate on damage would be:
BB4 - Avg 50k (meaning sometimes you can get a 100k+ game, but sometimes you get little, becausae as a BB4 you start to draw attention from enemy's SS and bomber CVs) 

BB5, with at-level crew, your Acc will still suck a little bit, but everything gets better once all sailors reach Lv115 and now you finally have your T5 scout. Now the lack of your OH time will start to be your last bottleneck because you will lose most of your OH on line-fighting, dodgeing torpedos/dive bombers.  In most cases (95%+), even if you have finished off all your enemies in sight, but you won't be able to get the rest of them because you are out of OH already. A skilled B5 player with such crew can expected:
BB5 -  Avg 100k

An avg attack of 200k from BB6 seems to be the only reasonable estimate from you. Although sometimes a good BB6 can easily get 300k + damage, sometimes the SSs/CVs on your team may be just so bad which don't give you any effective support at all.

An average battle has a team attack of 500 to 800k all in all.
There are 10 BBs on one side.
Even without considering any other shipclass making damage you'll easily see that your numberts are far above the possibility of beeing average. 

Your damage rates  would mean you have 3 "average" BB 5/6 and the rest are noobs doing nothing.
That's probably not how "average" is defined.

Funny how you post a thread about skill estimate after flaming me several weeks ago in a CL. Pretty sure I had 280-300k attack in a BB. Can't carry all the leechers. 

What i use to do, with crew 120, usually the minimum supports for reaching 900 SD, only for leveling sailors and always choosing good ships in its tier.

BB1 Average 20-30k (Frenchy one, courbert i think is the name)

BB2/PBB Average 60-65k (Andrea Doria mainly)

BB3 Average Around 100k (Gulio Cesare or opro2)

BB4 Average Around 100k too, that's why i don't use them for leveling.

BB5 Average Around 150k (L2 unarmored or h44 AW)

BB6 Average Around 200k (QV charle or the italian one)

Also you have to see one thing, attack sometimes is not related with skill. You can hold with a BB4 three enemy BB5s with bad sight, team wins thanks to you but you did a poor attack record.

After reading this thread, I did a mini statistical sampling, looking at 16 random people in 16 games playing BB5 montana and noted their attacks. The results indicate that "averages" quoted in this thread is overly optmistic, or the skill level of players is below "average".

In 16 games, the average attack for BB5 Montana came out to be 60,238, the max attack is 140,301, and the min attack is 105.

Of course, with only 16 games, it's not very representative of true skill level of player base. Take from the stats what you will.