Constantly put in games that have started.

I’ll add to this a problem where I get put into games and the other team already has 80% or more of the score to win. You join and lose two minutes later. Screw that. 

That's how matchmaking works. People get frustrated when the team is losing and when they die too much. So they leave the game prematurely. That means there's free slots on those servers and then you get matchmade into the losing team on that server to fill it back up again.

They could in theory track match completion rate based on the amount of tickets/time left and then prevent you from joining those servers, but it would also mean that once people start leaving, the team won't fill up anymore and that you'll have even less chance to come back from a battle that you were previously losing.

So the trick is simple, don't leave once you're in a server. Wait it out until the new map loads. That's the only way to guarantee joining in from the start.

After the game ends, they put me in the next almost finished game. 

Yeah, that's not exactly a secret.  People quit when they're losing, especially stat padders who want their win ratio in the top %.  

Yeah, just let the game collapse and not force people into the loss.  That's really a garbage thing to do to a player by handing them a loss in a game they didn't really contribute to, especially if there's no hope of recovering a win in the game.  

Yeah DICE keeps throwing me in matches that have already started and I’m on the team that’s losing by 300+. 

Nice try DICE! I immediately leave every single time. If I’m bringing a party I pull my party out EVERY SINGLE TIME. We’re not your fodder for the unbalanced steamroll.