I have an extremely hard time motivating myself to go to the gym , but i will play soccer for 2 hours given the chance by kids + SO. The latter effect of complete body exhaustions/soreness is glorious validation you play hard.
Theres also tennis which i dont even tolerate watching. But give me a loving friend of similar skill level, and a racket, and I'll play as long as she/he wants to. I dont do basketball, but i suspect a good chunk of HN would have a ball doing a 1:1 eith a friend.
Competitive sports are the salvation of the extrovert.
I don't know what the introvert should do, but generally should be the same. You should feel like you are recharging your soul, even though you are putting energy into the endeavor. For this reason i suspect meditation is a better fit for mental health to the introvert. However that does not solve the issue of exercise requirements for the body.
Its a chance to shut down your adult brain and go back to cavemen bliss. Simple problems (hit the ball, etc) are relaxing - they silence the monkey on your head.
Note: I'm not sure if sports are a good solution for exercise to competitive folk. It may not end up being as relaxing to you... or your sport friends.