This is an ongoing debate. One that requires serious study and more empirical studies. One that is very important given the money and time pour society spends on sports. As CPA, CFA and MBA tutors our focus is on helping students with finance, accounting, statistics, etc but we also want to help them truly evolve as individuals. So we do encourage sports as we believe it builds various aspects of personality in individuals.
Here is an excellent article on this topic. It does not provide any statistics or facts but is an excellent and entertaining read drawing on the authors own experience and some classic history. Recommended read for all tutors and not just CPA, CFA and MBA tutors.