does the psp battery...

[kp_assman]

drain even though the psp is off? i'm asking cuz sometimes the charge level seems to have magically dropped since i last used it

 

[cochesecochese]

Just like all batteries: Yes.

 

[Cthulhu8u]

It drains much more slowly if you turn the PSP off completely (hold power button for 3-5 seconds). Drawback is it takes a little longer to boot up, and loses the spot where you left off in movies/sound files.
If you do leave it in quick-power off mode, then at least make sure the Wifi switch is off.