The team announced Tuesday that manager Kirk Gibson and the rest of his staff will return for next season. Nagy, a three-time All-Star in 14 seasons in the majors, had been Arizona's pitching coach the past three seasons.
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Sax, a five-time All-Star in 14 big-league seasons, returned to baseball after nearly two decades when the Diamondbacks hired him before the 2013 season.
Arizona finished 81-81 for the second straight season to miss the playoffs for the second straight year after winning the NL West in 2011.