Here’s a study of one-batter pitchers from the Hardball Times. The one-out guy is a modern phenomenon, and Clearly the teams that are good at using one-out guys last season were the Cards (54 PAs, 54 outs - wow. Thank goodness Steve Kline was left off the WS roster), the Marlins (31 PAs, 32 outs - the count includes pickoffs, caught stealings, and GIDPs), the Royals (28 PAs, 30 outs), and the Orioles (27 PAs, 27 outs).
Interestingly enough, the AL East on the whole was pretty terrible with one-out guys (or rather one-batter guys, since more than any other division the AL East didn’t get the one out they were looking for): the Sox had a 78% out percentage from their one-batter pitchers, which is worse than every other team in MLB except for the Blue Jays (76%), the D-Rays (74%), the Giants (73%), and the Yankees (61% - thank you Felix Heredia). Yup, 4 of the worst 5 teams at using one-out guys were from the AL East, which probably just shows nothing other than the fact that the AL East clearly didn’t opt to spend its riches on LOOGYs(“Lefty One-Out Guys”) - Mike Myers and Trever Miller weren’t very good in their roles, and Felix Heredia was clearly atrocious.