Your guess is as good as anyone's. With the manager saying it's a committee, I don't think there will be a guy that runs away with the job. I mean, tonight Clippard gets it, and the manager was saying he was pretty dead set against him closing. About the only thing you can probably count on right now is that Rodriguez won't see the 9th for a few games.
If you really, really need a name, I think Burnett will get a decent chunk of the opportunities.