The Object(s) of Billy's Affection

Billy, the cat that thinks he is a dog, loves to chase a bouncing rubber sphere, leap upon it, kick it with his hind legs and bite it a bit before trotting back to you with it between his teeth. He then lies down expectantly at your feet like an enthusiastic retriever, hoping for an encore.
The object of choice is a Red Nose purchased on the occasion of Red Nose Day for Comic Relief. A close inspection of the photograph will readily reveal which of the two red noses Billy likes best. Little bits of disintegrating red rubber are strewn around on the carpet. It is just as well that Comic Relief 2014 is not too far in the future.