This is a really recent problem that happened this afternoon.
Whenever i unplug my laptop from the wall, my fps drops dramatically - about half. This happened after, as usual, I left my laptop on for the night running ffxi. I unplugged my laptop, carried it into the living room, and plugged it in. I noticed i was getting shit for fps, so I tried reinstalling graphics card drivers, which didnt solve it. I then realized the plug wasn't plugged all the way into the back of the laptop, so i pushed it all the way in and then everything works fine >.>
Plugged in: my usual 25+ fps
Unplugged: 11ish fps
Battery issue? I have no idea
XI Wiki

