To answer your question, it doesn’t matter from where you’re going to player1. HTTP being a stateless protocol, doesn’t care if you’re going from announcements or teams or even if by typing directly to the address bar. So what you’re asking is not possible without some kind of coding
Now when we have the same content at 2 different urls, wordpress favors just one of those urls & that is a very good thing if you ask me, else search engines will penalize your site for duplicate content.
I recommend leaving it as it is, but if you just want to do it no matter what, you’ll need to store the previous pages information somewhere(typically a cookie or session variables). Then you’ll need to use this information together with your breadcrumbs generating code in your theme to favor one of the trees.