I don't think catharsis means what you two think it means.
The term is Greek for "purifying" or "purging". In the dramatic arts, it is used to signify an emotional
cleansing, and generally comes about
after moments of intense anger or other emotions. It is an incredibly hotly debated term due to its use in Aristotle's
Poetics, under the following paragraph (using Preston H. Epps's translation):
Tragedy, then, is an imitation, through action rather than narration, of a serious, complete, and ample action, by means of language rendered pleasant at different places in the constituent parts by each of the aids [used to make language more delightful], in which imitation there is also effected through pity and fear its catharsis of those and similar emotions.
Epps has a lengthy footnote about this one, and he suggests checking out D. W. Robertson, Jr.'s "A Preliminary Survery of the Controversy over Artistotle's Doctrine of Tragic Catharsis" (1937). I've never followed up on it, though.
The definition is always the actual "release" (though that's still not accurate: it's a cleansing, which may come about due to a release), not the method by which this is done. The always-cited
Oedipus Rex's catharsis is not Oedipus gouging out his eyes, it is the loss of control when he sees his mother-wife has killed herself. The eye-gouging is a side-effect of the catharsis, and not the other way around.
I wandered over to Wikipedia to see if there is another definition I am missing. It appears there is! It has been adopted by Freudian psychologists, who live in constant proximity to the term "Catharsis" as a result of Freud's interests in ancient literature and theatre (where the term was coined). This is probably where you got your idea of what the term means, Vector, but the catharsis is not the cause of the release of the anger and violence, but rather the side effect of releasing pent up aggression.
From what is mentioned on "Cathartic Aggression", it doesn't seem like taking up a sport actually
would increase violent and angry behaviours. The downside to it is that it acts as a reward and encourages releasing emotion in this manner again. I feel like consistently wanting to release anger on a football field instead of on a parent is a good thing, but send me some documentation saying otherwise and I will give it a look.