The clarity of rules (rugby not included; why there are 2 systems in place? Union and league? Is there anyone not confused with this?) versus the uniqueness of people following them.
The commitment, the need to participate, to do something together, to act out (a play is a play), to have fun, to release endorphins, to laugh, to get tired, to feel better about oneself.
While I tend to follow individual route, this is - let's face it - my decision of necessity, not of choice. If there were enough people around me who I know, who I could hang out, I would enjoy it much more than lonely walks (not bad either, quite a release and reshaping moment in between fascinating playground endeavors).
I think we're more animals then we tend to admit. We like to describe everything with sophisticated words and elaborated descriptions. But it all is much simpler.
Everyone of us has one life. One.
And whether we spend it alone, or with someone, it's up to us.
We can have it all, we can stick to one option throughout our lives.
But it's up to us.
So, when your choice of loneliness is something bothering you, and there seems to be no one to ease it up, team sport might work. Not on all levels, and not in a long term.
But as a quick pick-me-up - it's great.