Modded controllers have absolutely nothing to do with your internet connection. If you are experiencing connection issues then you should check your network settings and make sure they are set properly for XBL and the game you
are playing. Of course some games, no matter what you do on your end, will always have a degree of lag. One such game is Black Ops due to its poor net coding.
If you believe someone is cheating then use the tools on your console to
file a complaint against them. Then be patient as enforcement action is not instant like many people believe it is.
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