Basketball or other sports ball sleeve sized to put around a basketball or another sports ball that can be used as a purse and/or that can be used as a basketball or another sports ball holder; Basketball or another sports ball holder that is attachable to resistance bands and/or weight machine cables and is usable for exercises that emulate the movements specific to basketball training or to the movements specific to another sports ball training; Matable first and second exercise ball half bodies such as hemispheres or hemi-footballs that in their mated condition provide an exercise ball emulating a sports ball such as a basketball or football and attachable in their mated condition to resistance bands and/or weight machine cables and usable for exercises that emulate the movements specific to the emulated sports ball such as the movements specific to basketball training or to the movements specific to football or another sports ball training and that in their unmated condition provide freestanding first and second hemispheres or hemi-footballs or other exercise ball half bodies having curved, metastable surfaces that can be stood upon for balance and/or other training exercises