My school used large foam balls (Nerf type) when we played Dodgeball. Made it far more fun. When it was going to be an hour of it in gym class, we just went to town!
We used billiard balls, but that was back in the ‘50s.
Riffing from your post, Nerf Battles in the Corporate world...
https://www.youtube.com/watch?v=pVKnF26qFFM
Warning: Simulated violence