Everything I am about to write assumes that you are using a SOFT, pure lead ball.
If the ball is suited to the ACTUAL diameter of your barrel- you measure it-- DON't rely on what is stamped on the barrel, or what someone told you--- and is .020" Smaller in diameter( or more) than your BORE DIAMETER, you should be able to thumb start the ball with a Patch that is well greased, and no more than .020" Thick. I start with a patch that is .015" thick, and work up in thickness from there.
REMEMBER, that a ball that diameter has a LOT OF lead to expand when the gun fires it, to press the patching into the walls of the bore. For that reason, Bores that are not pitted, or rusted, and in good condition generally, will usually shoot tight groups with smaller ball diameters, and thicker patches, than would be used in Any Rifle.
Also remember that unlike a rifled barrel, There is NO PLACE for the fabric to compress Into( ie. grooves) so that its fairly easy to determine what thickness patch material will work in that barrel by taking a length of it, centering the ball over the material at the muzzle, and pushing the barrel into the barrel with the fabric. You can then pull on the strips to pull both the fabric and Lead Ball out of the barrel.
With smoothbores, if you have to use a short starter, or worse, a mallet, to start a ball into the barrel pushing on some thick patching, the ONLY way that ball is going down your barrel is by distorting its shape, and elongating that ball a bit. The larger ball diameter, the more force is going to be needed to distort that ball into the muzzle, if that ball diameter/patch thickness combination is too tight for the barrel.
Without seeing your gun, and how you load it, I can't possibly know if you will be ever capable of putting 5 shots into a 4" circle at 70 yards. No offense is intended. There simply are too many variables to consider when it comes to smoothbore "accuracy".
What I can observe from my own experience, and watching other shooters over the years is that most are able to shoot small groups that you are seeking with a thumb started RB in their guns, provided the patching is properly greased, and the right thickness.
One experience I learned here, from CoyoteJoe, is that I may be trying to use too much powder in my 20 gauge load- 75 grains of FFg Goex. He shoots some amazing 50 yd. groups using on 60 grains FFg powder. I am going to have to try that in my gun....... :grin: Until I saw Joe's targets here, I was very proud of the groups I got with what I thought was a rather light load of powder. At the short ranges we are talking about, That huge, heavy ball is going to go right through any deer you shoot, so the difference in MV is not that big a concern, IMHO.
Those are the BIG "ifs" that keep us all practicing, and trying out different combinations, as well as staying up nights using micrometers, or calipers to measure, and scales to weigh and sort our cast lead balls. :grin: :surrender: :thumbsup: Most of us will grin broadly when asked if we ever have tried a "different " Lube on our patches. :bow: :grin: Its not a question of "if", for most of us, but when was the last time I did that! :shocked2: :blah: :surrender: :thumbsup: :thumbsup: