Core behavior of OG is that every Content type defines it's own relationship to OG. They might be barred from a group relationship, a group node, or a group post. There is nothing in that base configuration to specify the relationship between a content type and each group type individually.
However, there are a few tricks you could put in place to try to facilitate something.
Cheap Trick
For example, if you hide the navigation to create a node of a given content type, you've cut off the obvious approach.
OG User Roles
Probably the most conventional trick I can think of would be to carve up the different content types on a permissions level. I'm not entirely positive this will work, so it will bear some experimentation.
- Create a Sports Writer role, limit the ability to create and edit Basketball nodes to it.
- Use OG User Role to automatically promote members of the Sports group types into the Sports Writer role.
Cutting Edge Shenanigans
You can also use the Spaces module to toggle content type availability by Feature. In fact, the implementation of spaces_menu_alter() might show you how you could programmatically build out the functionality you are looking for. Sounds like it would be useful.