An exercise typically recommended for runners and other athletes was described as follows in a popular magazine. Lie on your side and bend the lower leg but keep the top leg straight, in line with the body. Then “tighten your abs and extend your top leg behind you. Raise your top leg 30-degrees and hold for one second.”
The directions here are not only contradictory but the movement does not involve the glutes, except for the gluteus minimus and medius that raise and hold the leg up. When you bring the leg behind the body, you use the erector spinae muscles to rotate the pelvis, creating an arch in the lumbar spine. The hip flexors which are typically fairly tight, do not allow your leg to go behind the body. The pelvis must rotate to allow this range of “leg” movement.
The recommendation to tighten your abs before extending the leg behind you is also incorrect as tightening the abs will not allow you to arch the lower back making it impossible to bring the leg back. To do this you must relax the abdominals and contract the erectors.
Perhaps even more important is that when you bring the leg behind you in a lying position, you do not work against gravity. You work against gravity only when you raise the leg upward and hold it up while the leg moves forward and back. Thus, there is mainly static strengthening of the hip abductors but not of the gluteus maximus, a major muscle involved in running. This exercise, however, may be effective for preventing iliotibial band syndrome (ITBS).
See Explosive Running for more details.