It is very commonly thought that back pain is mainly caused by the degree of lumbar curvature (lumbar lordosis), pelvic rotation or leg length discrepancy. Whilst these might indeed play a role, the body is highly adaptable to these variables and can often perform very effectively in their presence.
Research has shown that the main factor behind back pain is actually the endurance of back extensor muscles. There are several back extensor muscle groups and they all have a role to play. For instance, muscles called multifidus provide very important spinal stabilisation and are considered part of your "intrinsic core".
Additionally, the other important factors are the length of the back extensor muscles, the strength of the hip flexor (muscles folding the hip), hip adductor (moving the thigh inwards towards the midline), and abdominal muscles.
All these muscle groups are targeted by various Pilates exercises which is why Pilates is so effective,