To put it simply. You don't have a stuttering problem. You only stutter sometimes right? Then why is it when you're playing sports you don't stutter? That's because when you stutter, you've created (over a long period of time) a state of panic/fear/anxiety. This state of fear and everything that comes with it is so deeply woven into your mind and nervous system that it literally has a mind of its own. Once you're in that immense state of fear it kind of has you doesn't it? I do have some good news for you, if you speak fluently in one context then you can speak fluently in all contexts. I know how it sounds but there is hope.