We're using WAR to quantify calling Peralta the most valuable shortstop over 2014-15, because it accounts for contributions on both sides of the ball. Peralta's been 25 percent better than the average hitter over that span, and despite the fact that he doesn't "look like a shortstop is supposed to," he's been worth approximately 11 fielding runs above average. Though he gets dinged for below-average baserunning, when you put that all together, you get:
Shortstop WAR leaders, 2014-15
1. Peralta, 6.6
2t. Crawford, 5.1
2t. Tulowitzki, 5.1
Obviously, no one considers Peralta to be "more talented" than Tulowitzki, who lags on this list because of his regular time missed due to injury, but health is a skill as well, and Peralta has started 196 of the 210 St. Louis games since he arrived prior to last season. (Interestingly enough, if you push the range back to 2011, Peralta and Tulowitzki are essentially tied on the WAR leaderboards, though it's taken Peralta nearly 600 additional plate appearances to make that happen.)
While a large part of Peralta's value comes from his underrated defense, we can also look at Statcast™ and see just how much the ball is jumping off his bat. Peralta's second double on Friday night, this one coming in the seventh inning off of Juan Nicasio to drive in Kolten Wong with the game's final run, came off the bat at 103.8 mph. That's the sixth-hardest tracked non-homer ball of the season for Peralta, who appears near the top of the leaderboards for hardest-hit average ball among shortstops:
Shortstop batted-ball average velocity leaders, 2015
1. Crawford, 91.97 mph
2. Tulowitzki, 90.83 mph
3. Jean Segura, 90.07 mph
4. Peralta, 89.19 mph
While we don't have that kind of data for previous years, what we can show is that Peralta has taken the interesting path of making himself into a better player as he's gotten older. In his age-27 to age-29 seasons, he was worth 6.7 WAR; from 30-32, that was 11.4. Now, 200 plate appearances into his age-33 season, he's off to the best offensive start of his career.
When the Cardinals gave Peralta a four-year deal worth $53 million coming off of the suspension that cut short his 2013 season, it raised more than a few eyebrows across the sport. So far, it's been a bargain. As the Cardinals have continued to succeed despite the loss of Adam Wainwright and the struggles of Jason Heyward, their underappreciated shortstop is a huge reason why.