If you replaced the lower ball joint and are still getting massive movement out of the wheel, I'd suggest your wheel bearing is bad. With the strut suspension, you shouldn't be having that much movement on the vertical, even with a bad ball joint. A bad ball joint will only give you movement at the bottom, where you should only see maybe 1-2 degrees of deflection. The other areas of the suspension where you might see any type of deflection are the bushings at the base of the lower A-arm, where it meets the frame rail. Secondly, there should be a hard rubber piece at the top of the strut. Either of these places would not allow for as much deflection as you are suggesting, again 1-2 degrees, if you could even get it to move with your hands. Which leads me back to the wheel bearing(s). These are the ones in the hub (depending on the vehicle, it could be one or two sets there).
EDIT:
To detect the ball joint deflection, look at the below image. You'll see movement between these two pieces in your lower A-arm and spindle (where the two arrows are):

If there is any lateral movement here, it's bad, and needs replaced. The ball joint should allow free twisting movement, but should not allow lateral movement. In order to see if this is deflecting, you need to do the following:
- Jack the front end off of the ground
- Support the car on a jack stand while leaving the A-arm with the ball joint completely unsupported, and the tire about 3-4" off the ground
- Place a board (2x4 over 4 feet in length - or some such which is similar) under the tire from the front of the vehicle, with about 6-8" of board to the back side of the tire (board should be inline with the vehicle at this point)
- Using the board as a cantilever, lift the board so the tire becomes supported
- Move the board to the left and right while observing the ball joint area
- Check for deflection