Replace single shower/tub faucet

[alissa23]

4 years ago, I moved into my house and almost immediately the faucet handle in my shower fell off, apparently never really on there, and I was never able to reinstall. So, since then I have simply been using the lever that was there sort of like a computer joystick. Now, the tub spout has begun to leak. I figure it just needs a new washer, but decided maybe it was time to replace the faucet itself. My problem is I can't seem to figure out how. Looking at my local Home Dopey all the faucets seemed like they wouldn't work with my design. I don't know what faucet I should be looking for, and wonder if it isn't easier to simply start from scratch with a new assembly as what I have looks pretty worn and battered. Probably it's more than 30 years old, the age of the house. This is a single faucet that uses a plastic ball type assembly with the metal rod. I can't even figure out how to attach a faucet to it.

[LazyPup]

Some tub faucets have an allen wrench type set screw on the underside to hole them in place but most are simply screwed onto a male thread adapter on the end of the spout stub out. I am attaching a drawing of a tub shower mixer assembly so you can see how it all fits.

[alissa23]

Thanks this helps!