The shallow crossing routes have become very popular recently. A recurring question is how to use the running back on the play. Send him to the side the shallow is going, or where he came from?
For an earlier discussion of the shallow cross, see my article on how Mike Martz uses the shallow cross in various ways here. Martz is a pretty comprehensive guy and this covers most of the bases.
But here are some thoughts on how to use the runningback in the route:
Depends what you're doing on the play.
The Airraid (Mike Leach/Texas Tech, I think Kansas with Mark Mangino, Troy St., Hal Mumme) guys let him "leak" out to the side the shallow came from. This creates a nice "triangle" for their hunt route coming over the middle and works as a nice hi/lo read. They look at the shallow first.
Some other coaches will send a shoot/swing/wheel to the side the shallow is going. Petrino used to do this at Louisville a lot (especially with a no-back protection, shallow came from trips side, single rec side (TE or split end) would run a post or a square-in).
The reason is that the RB will pull the flat defender on that side out. That way the shallow will come open in the void he has created.
Another good option is to have the RB run an angle route to the side the shallow came from. Mike Martz often does this. Any hesitation by the Mike backer can create a nice void for the RB to get into. The "crease" concept is built around this.
Purdue and the Airraid guys will also send the running back on a full swing or shoot to the side the shallow came from. Both will usually have the outside receiver run a curl. (This also relates to the drive or "stem" concept but without the rubs.) The reason for this is that the curl essentially fits into the same void as the "leak" or "short hook" RB just outside the tackle, but obviously he's farther downfield. But it's the same passing window. There they just use the RB to widen the flat defender out.
So the point is there is no one right way, just different ways to attack the defense. This gets back to the notion of "concepts." In other words, the "shallow" is not a concept, it is a route to be used within those various concepts.
While a pro team may use each of these and more, a high school team may only have room for one. But each affects the defense differently so what you choose to do may depend on what you already do, what defenses you see, and what you can fit in well.