What would actually be the content of such a page as
http://www.example.com/{sport-name}/{category}/{category}/{team-name}? I can conceive of a team roster and statistics page, but only for a professional team. A sports club would be more geared toward needing to see the league schedule (time and location of next game), and perhaps win/loss record to feed into the playoff computation.
Do you really need a CPT? Are you coding some functionality to go into it? If not, just use pages to show the various sports, their schedules, costs, rules, and contact info for signing up. Then each category can have a page for the current league’s game schedule and it will be easy to update with the win/loss results after each game day.