Games : How can I detect a player's score against other players?

I'm creating a PvP map in Minecraft and I'd like to track how many times a player has hit other players on a scoreboard. I'm not tracking kills; I'm tracking hits. How can I do this?

I'm not tracking the number of times player1 has hit player2, I'm tracking how many times player1 has hit anyone. Also, I'm only using projectiles. I am fine with using any projectile needed in order to track this.