The three best hitters are Big Papi and two out of Youkilis, Drew, Bay, and Pedroia. Papi's got huge power and is a sloth, so he bats fourth. Youkilis has a slight edge over the other three guys in production and projects to have the highest OBP, so he bats second. Who should lead off? Well, Bay's a big homerun guy, so he's out. Both Drew and Pedroia are solid options, but given that Drew projects to have a higher OBP and a lower SLG, he's the guy. For now the lineup is Drew -- Youk -- XXX -- Ortiz.
The next two best hitters are Bay and Pedroia. This one's easy, as Bay hits homeruns and Pedroia's a base-stealing threat -- Bay goes third with Pedroia fifth. Another benefit of putting Drew at the top of the order instead of either third or fifth is that he and Ortiz are separated by a righty. The top five are: Drew -- Youk -- Bay -- Ortiz -- Pedroia.
Ellsbury and Lowell project to be equally productive, with Ellsbury more OBP-friendly and Lowell having more power. I'd prefer to have Lowell after Ellsbury, I think, although he might be needed in the sixth spot to drive home Big Papi -- it's tough to know for sure. Then we round out the lineup with Lowrie and Varitek. Varitek doesn't project to be bad enough to make it worth batting him eighth, like a pitcher. The end result against righties:
From my moderate knowledge of what's going on in Boston, that lineup is not very likely to be seen in a regular season game, the biggest mistake being Ellsbury at the top of the lineup, when he doesn't even project to be an above-average hitter. Whatever lineup they go with, a weighted total puts them in the +110 runs above average range.