Also:

basketball -> handball

hockey -> stickball

volleyball -> handball

rugby -> handegg

baseball -> stickball

cricket -> stickball

golf -> stickball

Hopefully this will finally appease the football literalists and make things simpler for you all to understand :)

I like the basketball, volleyball, and baseball way where the noun before ball has some leeway but should be clearly identified with an aspect of the sport.

football -> tackleball rugby -> tossball cricket -> paddleball golf -> clubball hockey -> icepuck