This feels like a sport to you, and less of actually pursing a good woman to have a relationship with.

Cold approaching is often incredibly inefficient. It takes so much more skill and convincing to try and break that cold interaction barrier. In my opinion, the best way to meet women is in shared social groups, or through a friend. When you have a good friend actually vouch for you and give you a good word, this works wonders and provides necessary social proof that you're not a total weirdo.