Bamboo ⺮ on top tells the material: baskets were woven bamboo strips. 监 lends the sound it also gives to 蓝 'blue'. A 篮 was the market basket on every arm for two thousand years before it became a hoop bolted ten feet up.
篮球 arrived in China in 1895, four years after basketball was invented, via YMCA missionaries in Tianjin — making China one of the first countries outside America to play. Today it's the most-played ball game in the country, and 菜篮子 'the vegetable basket' is still the government's codename for food-supply policy.
A bamboo ⺮ container you inspect 监 at the market — your BASKET.
Basketball is 打篮球 'hit basketball' but football is 踢足球 'kick football' — Chinese verbs sort every sport by the body part that touches the ball.