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Virtually all of the nominees here have already been covered, in one or more of the previous awards, which is fine by me, as I just get to copy/paste the paragraphs from those nominations!
Welington Castillo
Castillo saved the Diamondbacks from perhaps the ultimate Gurgling Vortex of Suck offensively from the catcher position: on Opening Day, we were looking at Tuiffy Gosewisch (career OPS+ 41), with backup up from Gerald Laird (74). But Mark Trumbo proved useful after all, turning into a couple of prospects and a catcher who hit the snot out of the ball. Beef had 17 homers in only 80 games for us, and only Buster Posey - who played 150 times - had more HR among National League catchers. It was also one off the franchise all-time high by a catcher, and again, in 2011 Miguel Montero appeared 60 more times than Castillo, while hitting just a single additional home-run.
Paul Goldschmidt
This is likely the most superfluous paragraph I will ever write, because I hardly need to sing Goldy's praises to anyone reading this site. By some measures, his 2015 campaign was the best individual season by any position player in Diamondbacks history, and among the very best by a first baseman in the 145-year history of the league. He became, entirely legitimately, the first Arizona player elected to start consecutive All-Star games, and also picked up a Gold Glove, Silver Slugger and was second in the league's MVP voting. There wasn't an aspect of his game that was a weakness, and you couldn't ask for a nicer guy off the field earlier. Truly, the all-round package.
David Peralta
Had a monster season and took over the cleanup spot which was dreadful at the time. Peralta truly was a beast hitting #4 in the Diamondbacks' order this year: over 80 games and 317 PAs there, he batted .345, with a .952 OPS. Everyone else combined for an .870 OPS out of the clean-up position. Overall, Peralta's 139 OPS+ for the year trailed only Goldie among Arizona hitters with 100 or more PA, and David became the first NL batter since Bobby Abreu and Vladimir Guerrero in 2000, to hit better than .310 with 15+ HR as well as double-digits in triples. Not bad at all for a failed pitcher!
A.J. Pollock
Likely overshadowed by Goldschmidt's season, Pollock's performance was hardly any less impressive, combining top-quality defense, great base-running (39 stolen bases at an 85% success-rate) and excellent offense. His value of 7.4 bWAR was far and away the most at his position in the NL, more than two and a half wins ahead of the next-best player (Andrew McCutchen, 4.8). A.J. accompanied Goldschmidt to the All-Star Game, won his first Gold Glove, and picked up MVP mentions, all while he was earning little more than major-league minimum, truly putting the "value" into "Most Valuable".
Brad Ziegler
We'd never had a reliever with a sub-two ERA before this year? We had two in 2015, and the best of them all was Brad, with a 1.85 ERA. The resulting ERA+ of 221 made him the sixth-best reliever in all of baseball, and his career figure for Arizona of 161 is far and away the best by any bullpen pitcher. He took over the closer's job in late May, and was all but automatic thereafter. He ended the year with an active streak of 28 consecutive saves, tying the franchise record set by J.J. Putz. In 36 save situations, Ziegler had a 1.50 ERA, and held all batters below the Uecker Line, to a .198 average and miniscule .524 OPS on the season.