stat.damageDealt not working properly

I'm making an adventure map so whenever you hit a mob, you get points via scoreboard. I set it up using "/scoreboard objectives add ZombieHit stat.damageDealt" & setting the display using "/scoreboard objectives setdisplay sidebar ZombieHit" You gain 1 point every time you hit any mob but you don't get any points when you shoot them with an arrow from a bow. There is no other way to indicate whether you damaged a mob using a bow.

1st Picture: Before I hit the Zombie, score = 0
2nd Picture: When I hit the Zombie with an arrow from the bow, score = 0
3rd Picture: When I hit the Zombie with an iron sword, score = 1