The perversion of shotgun barrel length

[Wapiti]

Can I get some help from the shotgun shooters out there on a question I have?
Why do some shotguns have 28, 30, 32" barrels?
Is it solely the sighting plane length? And is it a myth?
I mean, it's not like a rifle where you align the front and rear sight for precision. There is no rear sight on fast aiming shotguns.

I ask because of this observation of my own use case.
My wife has a Buckmaster PB12-M. It's got a 16" barrel, and is super-short overall, great for stashing or tight situations.
It was not bought to shoot clays. It was bought for around the farmhouse at night, for things that go bump.
It is extremely simple to use from a repeating shotgun perspective for multiple shots, in cat A & B anyway.
It has screw in chokes with it, to adjust the pattern I imagine.
With a full choke, and 9-pellet buckshot, the groups are so tight at house long hallway length, the hole is one hole from all nine pellets.
With the more open chokes, the pattern opens up like the cylinder bore of my Remington 870 pump.
It has a green dot reflex sight that turns on when you pick it up.

So I guess what I want to know is, Does barrel length make a better tighter pattern at a given distance? Because from what I see, the pattern at a given distance when choked the same is pretty much identical to a 30" barrel O/U Beretta.
But the sight radius has been changed from a cheek at one end, a tiny steel dot at the other, to a dot that has no parralax to throw you off.
So why the mega long barrels? That long sight radius?

[Zach]

I believe it's largely to smooth out the swing when tracking birds or clays that travel in a predictable path. When you've got the gun moving in an arc, having some mass out away from the pivot (you) will diminish the effect of muscle twitches and inconsistencies

[No1Mk3]

Barrel length makes no difference to pattern, that is solely a consequence of velocity, wad type and choke. Some ammo gains from a longer barrel, but every test I have seen seems to indicate max velocity by about 26". I really don't feel barrels longer than this add anything at all other than perhaps sighting.

[Wapiti]

Thanks for the replies fellas. Yeah, it's gotta be the open-sight plane and fit, and the swing consistency and follow-through I guess.
Something I am completely inexperienced at doing. I never shoot into the air.
The fact that I do OK at our farm shoots is just plain arse.

I guess that velocity could be chrony'd, but I wouldn't use an old screen type chrony. Wouldn't make it through the session i'd reckon.

[Fester]

Yeah, it's a debate that will go on forever.
As said, it's just the 30'' for swinging on birds and clays.
20'' for a great brush gun for pigs, snakes, or anything up close.

Patterning and testing whatever shot you use is the key.

The only personal results for me was the 20" Dicko did hit some clays, surprisingly.
It also shot slugs with more accuracy than I ever expected.
I used the choke that was 1 size tighter than open as a bloke did all the testing, and was keener than me.
He used a scope and shot it from a bench lol
I put a smaller Bushy red dot on and leaned against a pole.
The red dot gives me an OK cheekweld, but hard to see in sunlight so not that great.

It has been a safe queen, but I love it as a handy light shotty.
I would love to shoot a meaty deer with it before it gets crushed with so little use.
I tried once, left the pack in the car and carried the Tikka on the shoulder.
You guessed it, seen deer at about 200 and used the deer rifle.