It sounds like you're trying too hard to characterize your job in a way that it isn't.
You were a professional athlete, a basketball player. Not a product manager in a cubicle. Trying too hard to make your job sound like a "business job" frankly will make you look silly. Sort of like a QB on a football team talking about "managing stakeholders on conference calls with team members" and "incentivizing and marshaling resources" or "identifying synergies in the game plan" or "initiated a process to elicit buy in from project team members".
Just write down what you did. What position or positions you played, notable stats (FG%, PPG, rebounds, assists, 3-pt, free throw %, etc), and so forth. Your team win-loss record. As for whether you break it out into six separate sections for each team or have one section is a matter of clutter and personal choice. Don't over think it.
You played pro basketball in Europe. Most adcoms will think that is pretty damn cool. Don't sell yourself short by trying too hard to make your job sound like it's a business job.
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