It's really odd. 5/16 = .3125 so why the problem??
I shot with a .031 ball and .010 patch. That combo shoots well but does seem a little lose going down. Once I double patched. Much tighter but did not see any difference in how it shoot.
Molly- one usually needs to shoot more than one shot to see a difference in shooting ability.
Len and I used my .32 for the squirrel rifle shoot at Rendezvous BC last week. it has a .32 bore and very narrow, .008" deep rifling. I used.320"X.320" balls from a DC Lee mould marked .319".
We used an .018" patch.
Just for a lark, I thumb started it into the bore, but used both thumbs on the starter bulb, with the short peg swaging and pushing the patched ball some 1/4" below the crown. LOL
Unlike many of the rifles used here by ALR members, this one likes tight combinations along with 35gr. 3F GOEX with a water based lube (WWWF+NOil), and .40gr. 3f with an oil base, like Track's Mink Oil or Neetsfoot Oil.
After loading and shooting 52 shots, the rifle loaded as easily as the first - once into the bore- 2 fingers only needed on the rod to push it down to the powder.
It NEVER needed wiping of any sort.
I used to use both the .311" Lee mould ball & the .320" ball with a .0235" mattress ticking patch but we've run out of a source for that patching and I am hording it for my .45 rifle for use with .445" balls.
Tight loading (& NO wiping) is VERY easy with smaller sized small balls - compared to moving lead in a large one like a .684". with tight combinations and large balls, more strength is required as MORE lead is being moved when forming to the bore and grooves.