How to get maximum premier ball for boss raid?

I still haven't figured out what Gym control means. I have tried every proposed permutation. Team color of gym, own mon in gym, full motivation team color gym, full motivation of own mon in gym, none seem to be consistent. Unless, from that picture, it means ONLY members from that team are in the fight for properly colored gyms (that's something I haven't tried).

Also, I would imagine that the damage bonus is individual (since you already get a team bonus underneath). What the cut off is, I don't know, but you do still get the bonus if you have to rejoin the battle. I got a +2 bonus when I died and rejoinned during a lugia raid (I used 9 mons in one battle since everyone else had at least one blissey going).

Gym control has been wonky for me too. Back when there was a two hour warning and then one hour to raid, I found that if I captured a gym during the warning, I didn't get gym control bonuses. I don't remember if I raided where my team held the gym for all of the two hours but I never remember getting a gym bonus then at all; even owning the only mon in the gym, it was messed up. I think the shift to two hour raids may have fixed that, so I'm starting that data collection over.

Damage:

If you take out less than 5% of the boss' max HP, you get 0.

If you take out 5–10% of the boss' max HP, you get 1.

If you take out 10–20% of the boss' max HP, you get 2.

If you take out more than 20% of the boss' max HP, you get 3.

Gym control means that the gym is owned by your team

crazy, i got 14 balls in a raid b4.. so 13 isn't max

Does anyone wonder whether gym control maybe infers who has controlled the gym for the longest period of time in regards to team? i mean usually our gym badges tell us how long we've each controlled a gym. i'm not sure if the game is intricate enough to identify that one team has controlled the gym longer than the others using that information