Continuing with throwing/overhead athletes. The core is important to throwing, swimming, volleyball etc in regards to performance and protecting the shoulder from pain and injury.
Research shows that throwing athletes with shoulder pain have a lower core stability than those without pain.
So what can you do? Train the core to do what it is supposed to do. It is a transmission for power to connect upper and lower body. It is reactive, so you have to teach it to fire with load.
I love the halo with a narrow stance to develop stability through the core.
Pogetti LS, Nakagawa TH, Conteçote GP, Camargo PR. Core stability, shoulder peak torque and function in throwing athletes with and without shoulder pain. Phys Ther Sport. 2018 Nov;34:36-42. doi: 10.1016/j.ptsp.2018.08.008. Epub 2018 Aug 17. PMID: 30145541