Checkpoint64 has a preset for League of Legends: it already knows where the config folder is, backs it up automatically and keeps every version. Everything this site has on League of Legends:
League of Legends
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Config file location
Windows:
C:\Riot Games\League of Legends\Config -
Backup guide
Competitive games keep your progress on their servers — what's on your disk is the config. Checkpoint64 versions the settings folder for 67 games and 16 dedicated servers, so a reinstall or a file verification can't cost you your binds. Free download.