When trying to evaluate outfield defense, it's all about measuring on the margins. Every professional outfielder can catch the lazy pop fly right to where they're standing. No outfielder is going to be able to do much about a 420-foot drive off the center-field wall. Ideally, you can identify the balls that have some chance of being caught without being total no-brainers, and figure out who does the best at actually turning those into outs.
With Statcast™, we're at the beginning of being able to do that in a meaningful way, especially now that we have two months of 2016 data to compare to a full season of '15 data. So let's do exactly that, by taking all non-home run line drives and fly balls that traveled between 200 and 400 feet. These are the kind of batted balls that should in theory give the outfield at least a chance to make a play, and we can see what teams are doing better (or not) compared to what they did last year.
Happily for us, the Major League average on such balls in play in the Statcast™ era is .499 on nearly 50,000 batted balls, which is to say it's just about exactly a 50/50 proposition, and that's exactly the type of ball that should allow for defensive talent to stand out. This isn't a perfect analysis, not without controlling for positioning or direction, but it's a hopefully interesting start. In the future, we can build on this and do more.
The list, through games of Monday, showing the year-to-year average and difference between 2015 and '16 for all 30 teams:

What's helping (or ailing) teams this year? Let's look at three doing better, and three who may wish it was still 2015.
THREE UP 

 Dodgers
The Dodgers may have improved the most this year, but that doesn't make them No.1 in hit prevention here. The Rays were the best last year, and even despite Kevin Kiermaier's injury, they're still the best this year. But Los Angeles, by this accounting, has gone from below average to above. Why?
While the cast of characters has changed somewhat with Andre Ethier and Scott Van Slyke injured, and Joc Pederson has remained constant, the big difference here appears to be Yasiel Puig, who has managed to markedly increase his defensive game even as he struggles to do the same with his bat. To choose just one data point of many, he's made four catches this year where he had to travel at least 95 feet, after not doing so once all of last year.

  Cubs
Is this where Jason Heyward's vaunted sterling defensive reputation has really paid off? Heyward hasn't hit much in his first year with Chicago, but his defense has certainly lived up to its reputation. We know that changed outfield positioning has been a big deal for the Cubs this year, particularly benefiting Dexter Fowler, and it may have helped save Jake Arrieta's no-hitter. This may be the only area where the unfortunate injury to Kyle Schwarber hasn't hurt the Cubs so badly, as the converted catcher was still a work-in-progress in left field last year, though his bat is missed.
Gif: Jason Heyward's diving catch

  Braves
In the midst of a long and trying season for Atlanta, it feels nice to be able to focus on something they're doing really well. Part of why the Shelby Miller trade was seen as such a great deal for the Braves wasn't just because of the prospect haul they received, but because Ender Inciarte was such a valuable player for the D-backs last year, finishing second behind only Kiermaier with 29 Defensive Runs Saved.
Inciarte has lived up to expectations when healthy this year, but the real star has been rookie Mallex Smith, who worked with Braves legend Andruw Jones in spring and has made a slew of outstanding plays with the glove. Back in 2014 when he was in the Padres' organization, MLBPipeline.com called out Smith's game-changing speed, which we've seen plenty of in the outfield for Atlanta .
* * * * *
THREE DOWN

  Mets
For all of Matt Harvey's struggles, one that never seemed to get enough attention was the lack of help he was getting from his defense. At his low point, when he didn't make it out of the third inning in a 9-1 loss to Washington on May 19, it wasn't just allowing hard-hit balls, though it was that, too -- it was that Michael Conforto, Yoenis Cespedes and Asdrubal Cabrera all misplayed balls that may have helped save Harvey some damage.
Though both Conforto and Cespedes have proven themselves to be excellent hitters, the outfield defense is an uncertain combination. Cespedes is far better in left than in center, but Conforto doesn't play right, and Curtis Granderson looks like he's taken a step back this year. With Cespedes in center, the plus glove of Juan Lagares remains on the bench, and that plus a limited Granderson means more balls fall for hits. Of course, if Conforto and Cespedes keep hitting, no one will worry.

  D-backs
Arizona's outfield issues are part by design, and part by completely unforeseen bad luck. Inciarte was so good last year that trading him was always going to weaken the outfield defense somewhat, especially since his presumed replacement, Yasmany Tomas, impressed few with the glove in 2015. But A.J. Pollock was an underrated star in center, and David Peralta was useful enough in a corner, so the D-backs felt they'd be good enough, if somewhat lesser.
Unfortunately, Pollock's broken elbow and Peralta's wrist injury have thrown things into disarray. Tomas and converted shortstop Chris Owings (who has been surprisingly good, considering his lack of experience) have played the most outfield innings, and the D-backs have had to patch and fill with players better known as infielders (Brandon Drury, Rickie Weeks) or catchers (Chris Herrmann). Only two teams have allowed a higher percentage of these balls to drop, though recent import Michael Bourn has helped; the one saving grace, perhaps, is that an infield led by Nick Ahmed and Paul Goldschmidt is solid.

  Giants
San Francisco has allowed the highest non-Coors Field batting average on these types of balls. What's that look like? Let's compare the Giants to the Rays, who have the most efficient defense so far, with red being outs and green being hits:

There's a lot less red on the Giants' side, isn't there? Outfield defense wasn't a strength for San Francisco last year, but it was supposed to have been improved when Denard Span signed, pushing incumbent center fielder Angel Pagan to left, joining a presumably healthier Hunter Pence. It hasn't really worked out that way, so far.
There's good news for the Giants, however. Baseball's hottest team -- they've won 15 of their past 18 to take a commanding lead in the National League West -- is showing defensive improvement. Two weeks ago, they'd allowed the highest Batting Average on Balls In Play in all of baseball, a good indicator of a defense that wasn't making plays. Over the past two weeks, they've had the third-lowest BABIP, meaning more balls are finding gloves. Better pitching? Improved luck? Sure. You don't make outs by accident, though. In the smallest of samples, the defense is doing better.