I think problem drinking comes often from a bad mental place, and I think regular excercise is one of the first things to go when your mental health starts to decline. Of course excercise can help raise your mood too, helping again.
There is plenty of nuance to all that which can't be quickly captured in a comment.
This is a good point. Exercise is probably correlated with a general effort to take care of yourself for either health or appearance reasons. Many people enjoy sports and exercise for recreation, but health is probably at least a secondary reason for those individuals to exercise.
There is plenty of nuance to all that which can't be quickly captured in a comment.