This ball was most certainly wrapped in leather, deerskin or pigskin. The core may have been either an inflated bladder, catgut wound into a ball, or a ball of wool or feathers. The first two, of course, would bounce, and would have been used for those games requiring bounce, such as Expulsim Ludere (handball) or Roman Ball.
The size of the ball appears to be somewhere between 10 cm and 16 cm, based on comparison with the heights and hand sizes of the women. Romans were much shorter than modern Europeans, and therefore the balls appear larger in their hands than they would in ours. Furthermore, Roman ball manufacturing techniques may have placed limitations on how small a ball they could make, necessitating larger balls than they would perhaps have liked to use.
Modern technology has no limits on adapting ball size or the degree of bounce, and therefore we can improve upon the design and so improve the game. The aesthetics of the ball's appearance, however, cannot be improved upon, and should be preserved.
Ergonomic factors can be incorporated into the modern redesigned Roman Ball. A smaller ball, approaching the size of a baseball, is ideal for throwing very hard. A larger ball, near the size of a full-size softball, is better for catching. An intermediate size, about that of a small softball, would probably be ideal. Another good reason for not making the ball as proportionally large to us as it was to the Romans is the fact that children would find such a large ball less manageable. Adults, however, can handle the smaller ball with no problem.
Considering these factors, the ideal Roman Ball for the modern version of the game should be about 10 or 11 cm in diameter. It would be made of the same dense foam rubber that typical rubber balls are made of today. A professional version of this ball would have a leather cover stitched in four sections like the original. Our playing experience, however, has shown that leather-wrapped rubber core baseballs do not stand up indefinitely to being slammed into the concrete -- the covers eventually rip off. Therefore, the non-professional version should simply be solid rubber with a painted surface.