The king radical 王 here is really 玉 jade: 球 originally named a perfectly rounded piece of fine jade. The flawless sphere was the treasure; only later did the word roll onto leather, rubber, and every ball a foot or hand could play.
Every sport in Chinese is just 球 with a prefix: 足球 foot-ball, 篮球 basket-ball, 乒乓球 ping-pong, 羽毛球 feather-ball (badminton). Learn 球 once and you've learned half the sports section.
A jade 王 so round you'd SEEK 求 it anywhere — the perfect BALL.
地球 'earth-ball' is the planet, 全球 'whole-ball' means global — Chinese made Earth a ball in its vocabulary long before you could see it from space.