FPS Drop, near positive it's not on my end

Hello, For the past couple of weeks I have been experiencing FPS Drops. It seemed really weird at first and I assumed it was on my end so I started with the basics and worked my way through possibilities on my end. I started with resetting my router, then restarting my comp, checked that my drivers were up to date, switched ISPs from my home to work, rolled back my drivers to when it was normal, checked for viruses (both manually and with tools), and finally today I even wiped my entire computer and still I have had the same problem. What happens is when I start a game my FPS is normally ranging from 290-330. Then at about the 3minute mark it starts to drop all the way down to 117-140ish. It usually hangs in that range until a team fight or large amount of character movement, then it will drops to 30ish, and sometimes as low as 15. The main thing that is annoying is that it always drops when a team fight happens (basically when you need fps the most) and screen tearing becomes unreal. example - http://imgur.com/a/BEmmJ Any solutions? I'm really doubting that this is on my end anymore, especially after the wipe. I literally only have the basics and League installed at this point.
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