It’s a logical connection. Jon Lester, Clay Buchholz and Daniel Bard had their best seasons when John Farrell was the Red Sox pitching coach. So, in the four months since the Sox hired Farrell as their manager, it has been widely presumed that his mere presence will somehow cure Lester, Buchholz and Bard of all the problems they had during a nightmarish 2012. Of course, it isn’t that simple. As manager, Farrell’s job extends beyond being a pitcher whisperer. He’s responsible for overseeing an entire 25-man roster, from the catchers to the closer, and delegating to a coaching staff, to say nothing of holding the twice-daily press briefings and weekly radio appearances that make him the most prominent in-season spokesman for the organization. Supervising bullpen sessions? That’s for new pitching coach Juan Nieves. But the Red Sox would be lying if they said they don’t expect that a reunion with Farrell will spark at least some improvement from his former proteges. It may not have been the primary reason they pried him from the final year of his contract with the Toronto Blue Jays, but team president Larry Lucchino said the Red Sox liked Farrell for “the familiarity, the continuity and the relationships in place.” And it’s no coincidence that Farrell made offseason trips to see Lester in Georgia, Bard in Mississippi and John Lackey in Dallas, while he left it to new hitting coach Greg Colbrunn to visit with several position players, including Jacoby Ellsbury and Dustin Pedroia in Arizona. “The manager’s job is not one where he can sort of solely focus on a certain demographic,” general manager Ben Cherington said after Red Sox pitchers concluded another voluntary workout here. “John’s job is much bigger than trying to help one player or two players get better because of some history he has with them. I think the players know that, too.