(throw a frisbee, golf, bowl, throw a football, etc...)
That is great that you do this, I was once told by a pro golfer that if you start from an early age, or when learning to gold or other sports using the other hand you will have better control. When golfing people use the hand that is stronger to give distance but this means the weak hand is the one that is controlling aim. So if you reverse this you will have better aim.
Ok for myself I am a rightie, though all you lefties do not hate me, I was raised in a left handed house. My parents and sister are left hinders. I could never do well in computers at school because the teachers always put the mouse on the Wrong Side. I finally had to break down and start using a laptop though with the touch pad I use my right.
Though keep in mind that your dom hand is not just about what hand you Wright with, but also what side of your brain you think with. In most cases if you are right handed you think with you left side, if you are left you think with your right.
Though there are those of us that are messed up and have been tested to thing with the same side as their dom hand. This can sometimes combine with other "issues" to make you unique: dyslexia, short term memory....
Though it also may lean you to a more mathematical or artistic side depending on your side.
Though I do not know how the ambidextrous individuals (use both hands) work.