Basic HA lock-on/success concepts:
-Facing opponent has slightly larger attack range then starting the HA with your back to your opponent.
-I'm pretty sure it is dependent on where the homing attack launches from, not where it starts (in other words canceling can make or break whether or not it "locks-on" to your opponent's current position)
-The move does not home on the center of your opponent's body. If you drew a rectangle around your opponent the attack always tries to pass through a specific corner depending on your location (thus you sometimes are on a path to hit and other times you are not)
-If an opponent is in invincibility frames from their own moves, spot dodging, air dodging, rolling or rolling up from an edge as the HA attempts to lock-on will result in a complete miss.
-Opponents moving towards you: attack from below.
-Opponent moving away from you: attack from above. This explains why snake is so easy to hit and why a character as slow and sluggish as Ike when below the stage is next to impossible to hit with a HA. You can attempt to jump past your opponent and initiate one of these if they are really low. You may be fortunate enough to force a stage spike. Be careful though. This move can get you into trouble.
-The more vertically you are aligned with your opponent, the more likely you will connect.
-The more horizontal distance between you and your opponent you will likely miss. Miss here = locking on... but zipping past your opponent. This is why you need to be careful if you use this move when recovering. You will find yourself flying just over your opponent and probably landing with lag right behind them, begging to be punished by your careless recovery.
I tried to make a chart for this move but it's so difficult to make an accurate one, plus it's better to understand how it behaves when your opponent is moving (as described above).
*GREEN=Best Chance
*YELLOW=Very situational see above tips
*RED=Won't lock-on at all