So, if it pleases the court (and BK), I'd like to dig into this 2013 pitching performance a bit deeper. I'll start by disclosing that I'm coming from the perspective that Farrell is not at fault for the team's pitching performances over the past few years.
First, the Sox were not simply middle of the pack in 2013. They were 4th in the AL in ERA+, and 7th in FIP. However, their FIP was only a meaningless 0.01 behind Oakland and KC, who were tied for 5th. In any event, they were far closer to 5th in FIP than to the league average FIP of 3.97. Also, both KC and Oakland play half their games in very pitcher friendly parks (full disclosure: I should have done a road/home split analysis here to see if the park factors were at play; my bad).
Now it appears that the theory is that the Sox pitching stats should have even been better given that they had Lester, Lackey, and Buchholz as their top 3 starters. But upon closer look, we see the following:
Lester: Jon came off a terrible 2012 (Farrell had nothing to do with that). After a strong start, he went through a difficult stretch over 6 or starts in May/June, a period in which his BABIP exploded to 0.394. However, he quickly recovered, and had a strong end of season and finished a respectable 17th in FIP. He then dominated that postseason, which is relevant if we are to attribute Lester's performance to Farrell's presence in the dugout.
Lackey: Lackey was coming off TJ surgery, and only pitched twice in April, both times being on a fairly stringent pitch count limit. But starting in May he was very consistent throughout the rest of the season and finished an unexpected 23rd in the AL in FIP. He never had a difficult stretch after April aside perhaps from one game against the Yankees in September where he gave up 7 runs after being BABIP'ed aorund.
Buchholz: He was very good if not dominant. However, he missed most of the month of June and did not pitch at all in July or August. Which means his production was replaced by the #6 starter during that period.
Felix Doubront: His FIP of 3.78 was right around the team's FIP of 3.84. Good for 20th in the league. This was by far his best season.
Ryan Dempster: Originally the #5 starter, he became the #4 when Buchholz went on the shelf. His 4.68 FIP pretty closely matched his performance; while below league average, he was probably better than average as a 5th starter. Dempster was at the end of his career and retired the following season.
Jake Peavy: His 3.79 FIP with Boston closely matched the team's FIP.
Remaining starters: Allan Webster, Alfredo Aceves, Brandon Workman, Franklin Morales, and one Steven Wright combined for 18 starts, 84 innings pitched, 53 earned runs, 5.68 ERA, 5.55 FIP. Workman was by far the best of this bunch, but he was moved to the pen where he performed admirably that season.
Starters overall: 985 IP, 420 ER, 3.84 ERA, 3.96 FIP
Bottom line is that the starting pitching performed about as well as could be expected given the situations. Lester's stats were hit by his subpar stretch in June of that year. Losing Buchholz for nearly 3 months hurt the team's overall numbers. But I see nothing to pin on Farrell here, unless we also want to give him credit for Doubront, Peavy, Workman's 3.43 FIP, and Lester's playoff run.