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It is not only the inning in which a reliever enters the game that counts. The quality of the batters he faces is important. Bobby Parnell had the best success against the best hitters in 2013.
A lot of attention is given to the closer role. The last three outs are always the toughest, or so the saying goes. What is often overlooked is the place in the order where a reliever is asked to get outs. Assuming the best hitters are stacked in the middle-of-the-lineup, we can see how Mets relievers performed strictly against the 3-6 batters in the lineup to understand who gets the toughest outs. In 2013, it was Bobby Parnell who found the most success against the opposing team's best hitters.