I think there can be, and it can be either a positive relationship or a negative one, and the key is consciousness.
If we desire to do harm, we use sports as training for killing. This is part of their history, as in medieval jousting competitions and military martial arts competitions.
If we are not conscious, then sports partially works out, and partially encourages, our destructive and hateful impulses.
If we are very conscious, we can use sports to channel energy that would otherwise be destructive into fun, wise, and healing activity. I am a pacifist and meditator (practitioner of loving awareness and mindfulness) who practices martial arts in this way (though I don't fight others). In the move Ip Man 2, the character Ip Man (played by Donnie Yen) says, “By fighting this match, I’m not trying to prove that Chinese martial arts is better than western boxing. What I really want to say is, that, while people have different positions in life, everybody’s dignity … we are all the same. I hope that from this moment on, we can all start to respect one another.”
That, I believe, is the highest conscious transformation of our destructive desires through the medium of sports.