For your .44 revolver, buy .454 or .457 inch balls.
I know ... I know ... the loading manuals tell you to buy .451 inch balls but best accuracy will be found with the slightly larger balls.
The larger ball will ensure a tight fit in the chamber. With the .44s and their heavier recoil, this will ensure that the ball doesn't move under the heavier recoil.
But most of all a slightly larger ball, when swaged down in the chamber, will create a longer bearing surface for the rifling to grip. With more of an area for the rifling to grip, accuracy is improved.
Speer sells .454 and .457 inch balls. Once in a while I buy Hornady balls but I always seem to find four or five out-of-round balls in each Hornady box. Therefore, I suggest you buy Speer balls.
An out-of-round ball may not affect accuracy but it irks me. When I buy a box of "round balls" (as opposed to square or rectangular balls?) I expect to have them ROUND.
When they're not, I lapse into "Grumpy ol' desert cat" mode. :evil: