PIR sensors basically rely on the difference in temperature between the background and an object in the field of view. In other words, people and animals emit heat. Your basket ball is generally going to be near the same temperature as the background.
This is not a trivial problem, those with a lot of money to throw at the problem would probably use a few cameras, and do a lot of image processing in real time(think of the way an optical mouse works, but in three dimensions)
One possibility would be to set up a "curtain" in a horozontal plain at the level of the bottom of the hoop. The curtain is effectively a slice in space, through which the ball must fall. There would be two regions, the over all region records every shot, and the specific region where the hoop is would record a ball passing through the hoop.
Kevin's idea of an ultrasonic system might work, range and beam pattern are two issues you would have to investigate. You would probably need two or three transceivers on the back board for it to work.
I used to use holographic laser scanners, and high and speed photo detectors to collect the reflected light to set up an optical curtain. It is possible that. You may be able to set up a two D curtain by means of an extended frame attached to the base board, and use directed LED light and photo detectors to set up a curtain through which the ball falls.
Recording a shot that goes through the hoop is the easy part, the need to record all shots, missed or not, is where the problem lies.
Hope that all makes sense,
Richard
