based on the name attribute of your select, you will want to have a parameter named "leagueSelection" in you controller's action. Assuming that your select is contained within a form element that posts to controller name/Submit.
public ActionResult Submit(int leagueSelection)
{
// do what ever you want
}
you can also post with query string parameters
$.ajax({
type: 'POST',
url: '/controller/submit?leagueSelection=' + $('#leagueIdDrop').val()
});