this no joke -- i have one delay pedal with an odd power connector preventing me from chaining it in with my other stuff (just a onespot). it sounds fine with a brand new battery but starts getting noisy after about 20-30 mins when the battery starts losing juice.
so i found a 9v 500ma wallwart in a box, however my meter reports that it's providing 13.5v. i hardwired/soldered it to this delay pedal and it sounds GREAT, even better than with a new battery.
and i also have a distortion pedal that sounds AMAZING when the battery is so dead that you can barely see the indicator light.