Plumbing Questions? Ask a Plumbing Expert.
Welcome to Just Answer. I will do my best to fully answer your question(s).
You may be able to retrieve it with the use of a "closet auger". Normally used to rod the trap-way of a toilet. The tool has a "pig tail" type of end that will snag the rubber ball and bring it back towards the clean-out. This tool is short length though so about 6-8 ft would be the max. If that doesn't work the next step is an actual rodding machine (electric snake). You will want to use a cable of at least 1/2" - 3/4" diameter. anything smaller in that large of pipe has a tendency to wrap around itself and cause even more problems for you. local home improvement stores do rent these.