When choosing to record and broadcast racquetball, a stable shot is important. Viewers do not continue to watch when the camera is moving up and down in unpredictable ways. I will recommend always using a gimbal (if you must be handheld), a tripod (if there is room), or a suction cup mount.
When placing cameras/phones for recording and broadcasting racquetball, you want as few things between the camera and action as possible.
If you are local to the event, there are frequently $30-40 tripods available from Best Buy and Amazon that will do a great job.
If you are only going to have 1 camera/phone, or you are traveling, then you will want to use a suction cup mount designed for a vehicle. The one linked below will easily fit into a racquet bag without being bulky enough that you have to skimp on anything else you want to have with you.
For larger cameras:
Delkin Devices Fat Gecko Dual Suction Camera Mount
ivoler windshield mount
This is my preferred tripod, as the basic extension is exactly the right height to get above any painted lines on the back glass and the max height is enough to get over the heads of any players in between the tripod and the action.
Joilcan Tripod 81″