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Getting rid of all AFK players in League of Legends is near impossible to find, but Riot is working hard to make having an AFK player on your team more bearable by introducing new LP and surrender options.
With Patch 10.24, teams with an AFK player will be able to initiate a surrender vote after 10 minutes. This change currently only applies to Summoner's Rift and must be unanimously voted.
If voting is not unanimous, teams will have the option to vote again after 15 minutes. Only the majority will need to agree for the second ballot.
When a player leaves a match or is found to be AFK, their team's LP loss can also be reduced. Players in their premade and temporary series who have been disconnected or are AFK members will be excluded from this rating reduction. This means that if you get an AFK or a breakout during the series, you'll still get a loss.
Changes will be open to feedback, and things can change drastically during the preseason as Riot has indicated that it will be very careful with the LP to avoid any negative LP trends.
While Riot didn't provide further details with the 10.24 patch notes, it did mention that the LP fix will be limited from week to week. The LP fix will take into account variables throughout the game to set an LP value to avoid victimizing players affected by an AFK on their team in the game; this means that there is no fixed percentage of discounts that everyone will get when there is a breakout in the game.