You don't have to be a stats freak to see what's wrong with the Red Sox. As was said, just look at the team offensive and pitching leaders in the AL. The Sox are near the top in offense, and near the bottom in pitching. The Yankees are near the top in offense and in the top half in pitching. Pitching is the difference.
And it's mainly the starting pitching, from the ERA numbers, though I think the back end of the bullpen was screwed up by Bailey's injury and moving Bard to starter. Aceves is not a closer--he has too many losses and blown saves. And they don't have a setup guy.
Aside from that, I think their biggest problem is the Front Office. The turf war with the manager which is affecting team personnel (eg, Iglesias) and maybe a lot of the lineup and moves on the field (they still don't steal bases). When you hear somebody called Hazen from the FO saying Iggy will never get called up until he becomes an "offensive" player, we like offense on this team--well that's a pretty stupid remark and reflects serious competence and turf issues in the FO. When you consider there has been a brain drain from the FO the past few years, losing a few top people, it appears the leftovers have been promoted to their level of incompetence.
It's amazing how little is known of front offices--considering the power they wield on teams like the Red Sox. It's the FO that determines the personnel, and maybe even who starts and who sits. As for the lineup and how the pitchers are handled, it's an open question as to what is the FO and what is Valentine.
The problem of course is Lucchino/Henry, who have mishandled the team. Creating turf wars. What's needed is a new VP to oversee baseball operations--somebody from the outside with experience. A guy like John Hart. That is what is needed to turn this team around--some real baseball leadership--that is currently lacking.