In looking at the backstops, it seems to me that there are two choices:
1. Replace only the 4x8 plywood front on each of the 6 backstops (12 sheets of plywood total). These are the critical wall-ball surfaces and in the most need of repair. They seem to be held on by nails (no glue) so would be easy to remove. The 2x4 frames behind the plywood are in decent shape, and though they are rotted in some places they would probably support the plywood just fine with enough wood screws around the perimeter. This would be the quick, cheap solution.
2. Replace everything. This would include notching and joining about 42 eight-foot-long 2x4s and possibly replacing the 18 12-foot-long 2x4s that are used to attach the frames to the fence. With a good coat of paint (or if we could somehow get synthetic boards like the material used in the raised bed garden), this option would be more time consuming, more expensive, but would last many more years.
Just my opinions!
JB Morch