To hit a home run, a batter must accomplish two main goals.
First, he has to hit the ball hard. Or, in the parlance of Statcast™, he has to generate a high exit velocity. The second piece of the puzzle is perhaps less sexy but, as we have learned, no less important. The batter also must strike the pitch at the proper angle.
On every batted ball, Statcast™ provides the launch angle, which is the vertical angle at which the ball leaves the player's bat. It might sound a bit complicated, but the lesson is fairly simple. As a general rule, balls hit at an angle of less than 10 degrees turn into grounders, those hit between 10-25 degrees turn into line drives, those hit between 25-50 degrees turn into fly balls, and anything higher than that tends to be a pop fly.
As a result, most homers fall into a relatively narrow range of launch angles. It takes an extremely rare set of circumstances for a batter to drive the ball out of the ballpark if he connects at an angle of less than 16 degrees or more than 45, as can be seen in this chart of all homers Statcast™ tracked successfully in 2015 (data via MLB.com's Daren Willman).

So what about those outliers? Here is a look at last season's homers that featured the five lowest and five highest launch angles, according to Statcast™. This list focuses on balls that left the yard, so inside-the-park homers are excluded.
LOWEST LAUNCH ANGLES
1. 13.5 degrees -- Giancarlo Stanton
Who else were you expecting to lead a list of extreme homers? On April 23 at Philadelphia, the Marlins slugger jumped on a 91.5-mph fastball from Phillies right-hander Justin De Fratus, and in a blink of an eye, the ball was over the left-field wall. Stanton's 118.5-mph exit velocity was the third hardest of the season -- trailing two of his own hits -- and the hardest on a home run. The two-run shot got only 38 feet off the ground at its apex and remained in the air for a grand total of 3.1 seconds. Fortunately, the fans in the left-field bleachers got out of the way in time.
2. 14.1 degrees -- Maikel Franco
The Phillies' rookie third baseman impressed during his age-22 season, slamming 14 homers with an .840 OPS over 80 games. Franco certainly showed off his skill with the bat on June 16 at Camden Yards, connecting on a pitch from the Orioles' Chris Tillman at 108.9 mph and driving it out to left-center field. The ball never got higher than 42 feet off the ground as it traveled a projected distance of 366 feet.

3. 14.6 degrees -- Stanton
Here's that man again. Stanton was responsible for three of the eight homers with the lowest launch angles last season, and he managed six that were lower than 19 degrees. The lesson: If you hit the ball incredibly hard, it can get over the wall even with a low angle. In this case, on June 11, Stanton crushed a meaty offering from the Rockies' Chris Rusin at 114.6 mph, resulting in a three-run shot that rocketed over Marlins Park's left-field wall in about 3.5 seconds.

4. 15.1 degrees -- Mark Trumbo
He since has moved on to Seattle and now Baltimore, but Trumbo enjoyed quite a day as a member of the D-backs on May 12 against the Nationals at Chase Field. In the fourth inning, he whacked a three-run shot off Stephen Strasburg that was projected to go 451 feet. Two innings later, Trumbo added a solo shot off lefty Sammy Solis that soared a projected 428 feet out to left-center field despite the low angle and a maximum height of 48 feet. At 115.5 mph, it was the hardest-hit big fly of the year for Trumbo, who ranked seventh in MLB in average exit velocity (minimum 100 balls in play).

5. 15.4 degrees -- Evan Gattis
His season stands out most for his shockingly large collection of triples, but Gattis also went deep a career-best 27 times for the Astros. The damage included a pair of line-drive shots against the Mariners on May 3, as Gattis took advantage of Minute Maid Park's friendly left-field Crawford Boxes for his two lowest-angled homers of the year. First, he launched a three-run blast off J.A. Happ at 18.2 degrees, then topped himself with an eight-inning solo job against Carson Smith to break a 6-6 tie. The latter homer, struck at 107.7 mph, reached a peak of 41 feet before landing in the first row.
HIGHEST LAUNCH ANGLES
1. 49.7 degrees -- J.D. Martinez
The Tigers slugger ranked seventh last season in highest average launch angle (minimum 300 balls in play), so it's not a huge surprise to see him top this list. On May 15 at Busch Stadium, Martinez hit what initially appeared to be a playable fly ball to left field off Cardinals righty Mitch Harris. But Matt Holliday drifted back … and back .. and back … and eventually ran out of room as the ball dropped just over the wall and inside the foul pole. The solo shot reached an impresive height of 173 feet and had a projected hang time of longer than 7 seconds.

2. 49.0 degrees -- Bryce Harper
This probably was the oddest of the National League Most Valuable Player Award winner's 42 dingers, courtesy of the famous Wrigley Field wind. Harper didn't launch any of his other long balls at an angle higher than 38.7 degrees, and he clearly didn't think this solo shot off the Cubs' Kyle Hendricks was going to have enough distance when he struck it at 100.9 mph. After contact, Harper watched the ball for a second before tossing his bat away in apparent frustration at a missed opportunity. But the ball caught the breeze as it sailed to the opposite field, carrying a few rows into the seats to tie the game in the seventh inning.

3. 47.8 degrees -- Yoenis Cespedes
His stretch-run heroics for the Mets featured 14 home runs, including this solo job off Washington's Max Scherzer on Sept. 7 at Nationals Park. The ball, carrying well on a warm afternoon, fooled left fielder Jayson Werth, who kept drifting back until he suddenly ran out room. His leap came up just a bit short, as the ball dropped into the flower bed right beyond the wall. Peaking at 175 feet, this homer was nearly 43 feet higher than any other one Cespedes hit in 2015.

4. 46.3 degrees -- Brett Lawrie
Now a member of the White Sox following an offseason trade, Lawrie burned his future club with a solo shot off lefty John Danks on Sept. 14 at U.S. Cellular Field. Getting around on an up-and-in pitch, Lawrie pulled a towering drive into a favorable wind and watched it sail over the left-field bullpen. The 155-foot apex was about 40 feet higher than that of any of Lawrie's 15 other big flies.

5. 46.0 degrees -- Martinez
As Stanton was to low-angled homers in 2015, Martinez was to high-angled ones. Like Harper's, this blast came at Wrigley Field, as the Tigers took the Cubs deep five times on Aug. 19. In the ninth inning, Martinez got a pitch over the middle of the plate from lefty James Russell and connected at 107 mph, hooking it into the first row of the left-field bleachers. This long ball peaked at 162 feet off the ground and again achieved a projected hang time of more than 7 seconds.