Depends on the power of the gun and it's configuration.
Regular Bulldogs usually shoot 3 or 4 inches at 100 yards, convert one to a Pitbull and get 1 or 1-1/2, WITH the right slug.
I have a .357 and .457 Texan and both will do 1" at 100 IF tuned for the right bullet at the right pressure. Depends on the shooter too of course. Airguns are harder and different to shoot then centerfires. Lots of guys I've seen at the range where quite a few airgunners shoot only get 3 or 4 inches with their Texans but they just don't shoot enough to master the gun I think.
Got a custom WAR .357 FLEX rifle that shoots 150gr bullets at 980 FPS and I shoot it at a 6" steel gong at 300 yards and hit it 90% if the time, the missed shots scare it really badly, haha.
And the ultimate that I just got one of and others have done amazingly well with is the .357 Slayer, three different friends Slayers are MOA rifles
https
://americanairarms.com/product/slayer-hi-power-bullpup/ But the couple of .357 PELLET rifles I have that can only shoot 81gr Diablo pellets group good to 50, 60 or sometimes 70 yards then their accuracy falls off. Had an Ataman that was a fine rifle except pellet only and just not powerful enough for my hunting needs.... Might fit someone else's so I sold it.
The Winchester .357 and 457 are basically pellet rifles and the couple guys I know with them had only OK accuracy. Not very powerful either so only pellets and similar weight slugs. Read about multiple people who took deer with them this last hunting season. Got a guy in Florida called Bullfrog who regularly takes deer with a .30 caliber and swears by it. (Makes great videos too, check out his YouTube channel)
So your questions answer is both "It's complicated" and "It depends". When I was growing up a lot of guys and their rifles (and ammunition) only got around 3" at 100yards and we killed and kept meat on the table just fine.
Kind of depends on what you are hunting too. Lots of guys have taken deer or hogs with some low FPE guns with precision shots. Like Tim Allen the comedian, I like "More power" so that if I'm off just a bit the bigger caliber and highest FPE I can get makes for a humane kill.
I've hunted and killed 140 pound hogs with a .25 Marauder and 33gr pellets but I now ALWAYS tell people they shouldn't because it's just too minimal, everything has to be perfect and too much can go wrong.
Finally, I cast my own Big Bore bullets and pellets too and I DO plink with them. Of course, owning my own SCUBA compressor so I have unlimited air helps immensely, hahahaha
Mostly cast 128gr to 152gr bullets/slugs but I do have this .357 pellet mold and it is an accurate projectile with the deep and medium base pin (don't even try the flat base pin, they shoot terrible)
http://noebulletmolds.com/NV/index.php?cPath=35_586 Now my small and medium (up to 50 lbs) predator gun is a .257 Texan fitted with a Maddog Recon stock shooting the NSA 85gr BTHP at 1050 FPS/208 FPE and I get 1/2", yes ONE HALF INCH groups at 100 yards.
https://nielsenspecialtyammo.com/products/85-grain-swaged-257-caliber-sized-257-100-count