I got this gem from Dean Somerset, the one observation I would add is: If an individual can perform a great swing, this person likely has a solid squat and deadlift. Both movements revolve around controlling the hips, and a swing is as pure a hip exercises as it gets. 

When watching a person squat, if their feet pronate or arches collapse, most coaches will go to the "tight calves" diagnosis. While this isn't incorrect, if you've been rolling away massaging your calves and haven't found any relief then this might do the trick here. 

While I recommend always performing your push up on your feet, I would say there are a few things I would watch out for such as:

  • Proper retraction and protraction of the scapula
  • Tight core and glutes to try to maintain a straight-line from head to toes. 
  • A 45 degree angle at the arm pit, no 90 degree elbows out push ups. 
  • Leading with the chest and not the hips. 

A properly designed program should include single leg work. It should also include:

  • Hip dominant
  • Quad dominant
  • Vertical Pull
  • Vertical push
  • Loaded carry
  • Anti-extension core work
  • Anti-rotation core work