If you watch a baseball game these days, you can almost guarantee that launch angle and exit velocity will be mentioned multiple times. While exit velocity is relatively easy to understand, there's often very little description of what launch angle is and why it matters
Once the ball initially leaves the bat, the launch angle will determine how much of the ball's speed is vertical and how much is horizontal. From that point forward, air resistance will work to slow the ball down while gravity will bring the ball back towards the ground. The launch angle and corresponding combination of vertical and horizontal velocity will determine if the ball is able to travel far enough before gravity brings the ball back down.
Below are a few scenarios to show how this could play out if a ball with an exit velocity of 102.5 mph left the bat at different vertical angles in the direction of center field. As a note, there are other factors that would impact the distance in reality; these would include the back and side spin on the ball, humidity, elevation, wind, and many others. To make this easier, I've assumed that there is no side-spin and that all other values were average. I've used Alan Nathan's calculator at the below link as an aid in this process.
Examining Upper and Lower Limits
If hit at 36 degrees the ball reaches a max height of just over 125 feet, hangs in the air for 6.07 seconds, and strikes the wall just below the top. Decreasing this to just 35 degrees changes the result - the ball reaches 121 feet, and is in the air for 6.0 seconds before it goes over the fence for a home run. The explanation for the different results from such a small change is due to the corresponding horizontal and vertical velocities.
At 36 degrees, the velocity is separated into 82.9 mph horizontal (forward) and 60.2 mph vertical (up). These change to 84.0 and 58.8 respectively when the angle changes to 35 degrees. Even though the ball goes 4 feet less vertically and hangs is in the air for slightly less time, the increased forward speed allows the ball to travel further before getting back below 10 feet.
We see a similar scenario if we compare a 22 degree launch angle vs a 23 degree angle. At 23 degrees, the ball reaches only 73 feet but is still able to hang in the air for 4.8 seconds before going over the wall for a home run. At 22 degrees the ball no longer had enough vertical velocity - it reaches 69 feet and hangs for only 4.7 seconds before striking the wall. Even though the ball is moving forward faster, in this scenario it doesn't reach high enough to provide enough time for the horizontal velocity to travel 400 feet.
Based on this analysis, we know that in the scenario above a ball would have to be hit between approximately 23 and 35 degrees in order to achieve a home run; those values provide the right combinations of vertical energy to counteract gravity and horizontal velocity/energy to travel the distance quickly enough. It also opens the door for other analysis - for example, in the scenarios above we'd likely prefer the 22 degree option vs 36 degrees because the outfielder has over a second less to reach the spot where the ball strikes the wall.
There are plenty of avenues for coaches and analysts to look at, but hopefully this post at least helps to provide some context the next time the broadcasters are talking about (or criticizing) launch angles.