James Brent Cox is former college teammate of Taylor Teagarden at Texas where they won the College World Series in 2005. Cox was the closer for that team and the Yankees took him in the second round that same year. He's not as good a prospect as the guy he replaced as closer for the Longhorns (Huston Street), but he ain't chopped liver either.
Cox isn't a premium prospect and he won't be a lights-out guy in the way that somebody like Billy Wagner has been. But he has a solid resume and he's a solid young pitcher. He has 2 pitches, a low 90's fastball and a slider. The slider is the out pitch. He has 2 things going for him. 1. He has solid command and control. 2. He keeps the ball down, producing a lot of ground balls and very few home runs.
This isn't the profile of a future closer, but it's a pretty well established sabermetric tenant to say that there is nothing particularly special about 9th inning specialists and that non-traditional closer options should be taken seriously. Any pitcher capable of being a competent reliever can theoretically handle the 8th or 9th inning. If a World Series team can employ Todd Jones as their capital C closer when he doesn't really strike anybody out anymore, then somebody with Cox's modest stuff shouldn't be written off as a late inning reliever either.
That being said, expect Cox to settle in as a 4th or 5th man in the bullpen for the Yankees or somebody else (presuming they include him in a trade). With a 2-1 groundball-flyball rate, the Yankee infield defense as it is currently constructed isn't likely to do him any favors.
Cox is a nice example of the improvement in the Yankee system in recent years. They have a bit of depth now to go with Phil Hughes. If their pitching staff starts to melt down due to age and injuries like it has the last few years, they have pitchers like Cox who can step into the breach and give solid production. That isn't to say that the Bronx Brass is going to be any more patient with young players than they have been in the past or that they won't pass up these guys in order to give innings to some 30-something stuff whose name Joe Torre recognizes. But at least it is there in case the opportunity presents itself.