Balls made of leather or fabric, stuffed with scraps of cloth, are known from early medieval archaeological finds and continued to be in use throughout the medieval period and beyond. Leather ones stitched like a baseball but filled with fabric scraps, known as "badanes," are still used in the Valencian game of Llargues (a kind of handball). In Renaissance France, a stuffed ball was called an "esteuf," and was probably used for the handball games that would (with the invention of the racket) evolve into modern tennis. Similar balls were probably also used in medieval England for the earliest ancestors of baseball and cricket as well.
This pattern is a simple one found in early medieval samples, and is very easy to make.
Step 1: Cut Pattern Pieces
First, assemble your pieces. You will need two circular pieces and one rectangular one. In this sample, the circles are 3 1/2" in diameter, and the rectangle is just over 10" long by 2 1/4" in width.
This is going to be close to the size of a modern baseball, which is a good size for your first esteuf, because the bigger pieces are a little easier to work with, but it's quite large by medieval standards; I like this or a bit smaller for stoolball (medieval baseball), while for pallacorda (medieval tennis) I find that a ball half this size or a bit larger works nicely.
For a half-size ball, don't just halve the size of the pieces - aim for a rectangle 5 1/4" x 1 3/8" and 2" circles. More generally, if you ignored seam allowances you would want your rectangle to have an aspect ratio of 5.5 and a length equal to the circumference of the circles (and the desired circumference of the ball); figure out the size of your pattern pieces based on that and add 1/2" to the diameter of the circles and to each dimension of the rectangle to leave room for 1/4" of seam on each part. Add a smidge to the length of the rectangle for good measure.
The way I actually size my pieces is to find a cup or other object with a flat round end that's about the same circumference as the ball I'm making, measure around it, and calculate the size of the rectangle from there. Conveniently, the mouth of the average American pint glass gives the size shown here.
Finally, cut a slit along the middle of the rectangular piece. This should run approximately 1/3 of its length, or a little less is good for larger balls such as this one.
Step 2: Sew the Casing
Sew one of the long sides of the rectangle to the outside edge of one of the circles. Trim the end of the rectangle if necessary so that the two ends meet after you've gone all the way around the circle.
Stitch the two ends of the rectangle together, and finally sew the second circle to the rectangle in the same way as you did the first. All of this will be done with the wrong sides together, if your material has a particular right and wrong side.
Note that when you don't leave as big a seam allowance as you budgeted for when cutting the leather, the stitches will be visible from the outside and the ball will be weaker. It's easy to make this kind of mistake when sewing the circles to the rectangle, because stitching curves is not intuitive for most of us. (I am far from a skilled tailor myself, but do not find these sorts of balls at all challenging except for that pitfall.)
Step 3: Invert and Stuff the Ball.
Turn the ball inside out by pulling it through the slit in the rectangle. Then, through the same slit, stuff it with scraps of fabric.
If you wish to reinforce the seams, after you invert the ball but before you stuff it, whip stitch along each seam. I like to do this with artificial sinew when I'm sewing leather balls, but with cloth ones I don't usually bother. You can also do this after you stuff the ball to fix weak spots in the seams if you have anywhere where they are too close to the edge of the material, but it's a lot harder after the ball is stuffed.
A fifteenth-century French law forbade balls stuffed with anything other than cloth, specifically banning the use of moss and sawdust as materials, so we know they were sometimes used - but we also know they preferred scraps of fabric back then, so those are clearly the stuffing of choice. Pack them in until you're not sure you can fit any more, and then find a way to fit more even so.
Finally, whip stitch the slit closed. (Again, I like to use artificial sinew when working in leather.) Your ball is ready for use.
Over time, the ball will get softer; if you want to restore it to its original state, take an exacto knife and cut the stitching on the slit, stuff more fabric in, and then stitch it closed again.
Step 4: Play Ball!
This ball should be just soft enough that you don't mind being struck by it when it's thrown somewhat forcefully. (Test this before playing sports with it, though!) This makes it perfect for all sorts of games you might not want to play with a baseball. You can invent your own, but since this is a medieval ball design you can also use it for medieval sports. http://sports.lilleypress.com/index.php?title=Stoolball has a good description of stoolball, the ancestor of both baseball and cricket, as played by Canadian reenactors. This ball design is quite likely to have been used for it back in the day.