If you have a ball go off the table, chances are it is going to land well beyond the size of your rug, unless you have a rug that is quite a bit larger than your table, IMHO.
Yes they make them super big and that is the size I would recommend. Along with saving the backs and knees, it will also save the balls, and whatever hard flooring you might have. It will also quiet the room down quite a bit.
Edit: I would just like to add something for the younger folks who like to go shoeless. Standing for long periods without arch supports will tend to lead to Planters Fasciitis, trust me! You don’t want that! Extremely painful and it can be a long process getting it corrected. Wear shoes with proper support.