Why do my lower back experience pain instead of legs after my sports?

Back pain exercise: Could be for a lot of reasons. The most common reason for back pain after running is probably related to a deconditioned back. Often your back will hurt if you have tight hamstrings which changes the tilt of your pelvis and puts strain on your back. Outside of that weak abdominal muscles will contribute to back pain. Adding hamstring stretching and core body exercise will help. Ie yoga, etc.

DOMS: Soreness in the lower back can be common after vigorous exercises that require extreme bending or twisting of your back. Delayed onset muscle soreness (doms) is a well-known physiologic condition that can cause pain in poorly conditioned muscles. If the pain does not subside after 72 hours following exercise, a more serious injury may be present. Consult with your physician if this is the case.