The statistic Ultimate Zone Rating (UZR) measures three components of outfield defense: range, arm, and error, and assigns a run value to each component. The sum of the parts gives a cumulative run value, or UZR. For instance, outfielder X could be very sure handed, with an ErrorUZR of 10; have a very strong arm, with an ArmUZR of 8; but not cover a lot of ground, with a RangeUZR of -20. So, in total, he has a UZR of -2, which means his fielding cost his team about 2/10 of a win with the glove.
The hardest of these three parts to observe is range. When a player drops a ball, it's an issue of ErrorUZR, and everyone notices. When Juan Pierre throws home, but the ball doesn't make it into the infield, it's an issue of ArmUZR, and everyone notices. Raul Ibanez not getting to a ball 10 feet to his left that Carl Crawford gets to every time, however, is virtually impossible to notice, because we don't see the field as a GPS map with grid lines.
In other words, everyone and their mom notices when Daniel Murphy drops a ball that costs the Mets the Marlins game. But when he glides to a deep ball without sliding, no one says, "wow 8 yards from his original position in just 3.1 seconds of hangtime."
Besides the rotation, Daniel Murphy's fielding has been often identified as one of the weakness of the Mets in the early going. It's understandable: he's dropped two easy flyballs and has had to throw to the cutoff man from the edge of the infield. Every observable, fundamental aspect of his defense has looked bad. Thus, the excuse of "he's just learning" is convenient and probably does explain some of his trouble so far. Checking UZR, however, Murphy has been a defensive asset for the Mets so far. In fact, according to UZR, he's the rangiest left fielder in the majors, narrowly edging out a little-known Seattle fielder named Endy Chavez:
It's funny that Murphy, whose defense is now associated with one terrible non-catch, is ahead the guy who made the most iconic catch in Mets history. Granted, he probably won't lead Endy for much longer.
Still, all the players below Murphy (except maybe Holliday) are your prototypical speedsters, which suggests either Murphy's much faster than we thought or a very good route runner. Although he ranks last among the group in both ErrorUZR and Arm, he leads the majors in Range. His UZR/150, or UZR extrapolated over 150 games, is 26.6. That figure, roughly +2.7 wins, would probably make him the most valuable defensive player on the team. While it's too early to make that conclusion based on the small sample size, it's a far cry from how many in the media regard his defense.
While his arm probably won't suddenly improve, his ErrorUZR certainly could, given some better fundamental play. While many rightfully think "firstbaseman of the future" is a stretch for Murphy, maybe "centerfielder of the future" should be considered.