I too, have also experienced a battery drain while my rMBP (late 2013) running Mavericks some time after Avast was installed. I have logged the issue for the past 3 months, believing it to be a Address Book Contacts issue with no results...
Until this past weekend, when I restored my rMBP back to the original OS and re-installed all programs except avast for Mac. Since then, I have had zero instances of battery drain and when in Sleep, my rMBP actually sleeps with only about 1%/hr batter discharge. When using the rMBP with avast, i would regularly experience a dead battery after leaving the rMBP overnight in Sleep mode. (approx 15%/hr discharge rate during Sleep)
I can't explicitly tie this issue to Avast, but the evidence is overwhelming. My immediate recovery in battery performance points to Avast since I've already re-installed ALL programs and apps used prior to restoring the OS - with the exception of Avast for Mac.