The careers of Arthur Rhodes and Darren Oliver span a period of change in the use of lefthanded relievers, from the days when lefty one-out guys (LOOGYs) were relatively new to the game to that being the only role available to southpaw relief pitchers.
In 1990, the season before Rhodes debuted, 27 lefties threw at least 40 innings without starting a game. Of those, just three averaged fewer than one inning per appearance. A decade later, in 2000, 31 southpaws were full-time relievers with at least 40 innings pitched; 21 of them went less than an inning each time out. By last season LOOGYs had taken over: Of the 26 full-time lefthanded relievers just three averaged at least an inning per appearance.
Consider Rhodes's path: In 1997, his first season as a full-time reliever, he made 53 appearances and pitched 95 1/3 innings. Three years later he averaged less than an inning per outing and has been above that figure, barely, just twice in the past 10 years. It's not as if Rhodes had a large platoon split. He has, in fact, held righthanded batters to a respectable .243 batting average in his career. He could do more—the game simply won't allow him to.
This is a problem. Baseball is forcing pitchers into roles that keep them from contributing to the best of their ability, while actively hurting pitchers who, by mechanics and repertoire, are ill-suited for get-the-lefty work. Renyel Pinto (formerly with the Marlins) and Rafael Perez (now with the Indians) are two lefthanded relievers of recent vintage who struggled to establish themselves because their skill at retiring righthanded batters—and relatively small or even backward platoon splits—isn't valued by an industry that isn't asking lefties to go two innings.
In terms of managing their resources, teams would be wise to move away from fitting all square pegs into round holes. Rhodes and Oliver, Pinto and Perez, Tim Collins and Aroldis Chapman can all do more than face lefthanded sluggers in big spots. Let them.