When Baltimore fired Lee Mazzilli and replaced him with Sam Perlozzo, it was the first time in MLB history a manager with two "z's" in his name replaced another manager with two "z's" in his name, a piece of trivia which I just pulled out of my ass but which is probably true. The Orioles have gone 2-0 under Perlozzo; while I haven't been paying close attention to the sports media's take on it, if a team does well under a new manager, usually writers and the BBTN guys go off about how the team's trying to impress their new manager, and/or there's a "fresh start" which allows the players to "clear their heads and begin anew". I've always assumed that was BS, but never bothered to look it up. That is, until this morning, when I had some important stuff to do at work which I've been trying to avoid.
Since the 2002 season, managers have been replaced midseason 14 times; three times this year (Mazzilli, Tosca, Pena), twice last year (Brenly and Jimy), twice in 2003 (Torborg, Boone), and seven times in 2002 (Manuel, Garner, Muser, Martinez, Baylor, Bell, Lopes). [I'm not counting the two times KC named an interim manager for less than 20 games.] The 14 new managers went a combined 8-6 in their managerial debut; over the course of their first 5 games (2 in the case of Perlozzo), they went a combined 37-30. Not bad given that all came into teams at or below .500 (the 2004 Astros were 44-44 when Jimy was fired), but my guess is those winning records are statistically insignificant.
In only 3 of those cases are the new managers considered to have "turned the team around": Tony Pena for KC in early 2002, Jack McKeon for the Marlins in early 2003, and Phil Garner for the Astros in mid-2004. Given that that list includes the names "McKeon" and "Garner", I have serious doubts as to whether the new managers had anything to do with the teams' turnarounds, but in any case, those three went a combined 1-2 in their debuts, and 6-9 in their first 5 games.