The source of toxicity is typically people tilting off the face of the earth via plays turned bad.
You can make good plays and good shotcalling in attempts to untilt them.
####Case study: ####
Kayle and Heimer were both doing decently well and have gotten a few kills in laning phase and had decent CS. Our MF and Kayn were not the best, as they were feeding and had poor positioning, hence they weren't contributing at all . Kayle and Heimer started blame them for being bad and started to tilt.
I said: "Kayle, Heimer, don't tilt on me now. We have 3 people whom are better than the enemy team, so let's ignore MF and kayn play around you two and we'll dominate fights together."
I (Leona) started grouping around kayle and Heimer and they didn't disappoint. We won mid-game skirmishes 3v4 sometimes even 3v5, trading only my life for 4 of the enemy's. Kayle and Heimer was quiet during this time and we even managed to push the enemy into their inhibs.
Unfortunately, Heimer decided to try to stay for inhib instead of resetting when the enemy respawns and killed Heimer. They rushed down mid lane and Kayle that just respawned wanted to get red buff, but MF whom was "split pushing" decided to rotate back into our jungle and took red buff.
You can see Kayle was tilted off the face of earth again because MF took the red as Kayle stop in her tracks and not pay attention to the map, when I engaged on the enemy. As Kayle didn't rotate to mid lane as soon as she saw MF taking red, her follow up to my engage was delayed and we lost the fight and the game.
For a period of time, I was able to bring them back into the game. Just that other bad plays tilted them off the face of the earth, which weren't in position to recover.
It's possible to untilt people, but it doesn't always work. Those tilted people are also very prone to go back into tilt if anything goes against their expectations, but they aren't impossible to untilt.
