I always see streamers on Twitch listen to music while they play, but is that really good while playing League? I have tried listening to music while playing and at times it may be a little distracting depending on you song choice. I don't know what is actually better, play League with music or without. Comment your feedback and say whether you listen to music or not while playing or if it helps or not.
Personally, I listen to Classical Music(Especially Tchaikovsky. Man, he uses cannons as instruments. You know his music is going to be awesome!) while playing League but yeah, loud music can be distracting but I lower my music volume right below my character's voice levels.... I mean, yeah... you're pretty gonna be distracted if you're playing erotic music while playing 
or 
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A lot of it has to do with sound levels and music choice (as you hinted towards). Your brain unconsciously gives attention to whatever is most obviously sensed. That being the case, music that's loud enough to drown out in-game effects or that you aren't accustomed to can pose as a distraction.
But listening to comfortable music, which varies with your tastes (ie. Classical for MRH4DES), at a decent volume can actually can sometimes be beneficial as it helps drown out the stress from in-game interactions (if you just died for example). Just low enough to be able to clearly make out in-game effects is recommended, maybe lower if the music is naturally interpreted as loud.
