Peter Gray:

Other research has assessed relationships between the amount of time children have to direct their own activities and psychological characteristics predictive of future mental health. Such research has revealed significant positive correlations between the amount of self-structured time (largely involving free play) young children have and (1) scores on tests of executive functioning (ability to create and follow through on a plan to solve a set of problems); (2) indices of emotional control and social ability; and (3) scores, 2 years later, on a measure of self-regulation.

Moreover, two retrospective studies with adults have shown that those who recall more instances of independent play when they were children are, by various indices, happier and more successful in adulthood than those who recall less such independence. And research with college students reveals that those with over-controlling parents (as assessed with questionnaires) fare more poorly psychologically than those whose parents are less controlling. These and other correlational studies all point in the same direction. Opportunities to take more control of your own life when young predict better future well-being. 

See also this essay by Gray: “Why Adult-Directed Sports Are No Substitute for Kid-Directed Play.” Sports, in our context, are very nearly the opposite of play.