Lines in the afternoon can depend on many factores - the primary being what time of year you come to Rome. In season, lines will often extend past 2 PM.
Also, what day of the week you go can be a factor. Mondays always have longer lines because the VM is usually closed on Sundays. Wednesdays are always busy when the Pope is in town and doing his 10:30 AM address. Saturdays are a day off for many Italians and they come to Rome. And of course, the last Sunday of the month, the VM is free so there WILL BE A LINE! So if I had to play the odds, I would go on Tues(2), Thurs(1), or Friday(3).
Special events, for example Holy Week and XMAS, always lead to longer lines at the VM. And even the weather can impact the line!
Tour Group pre-bookings also influence the line. My tour buddies tell me that 1,300 pre-bookings are allowed in each hour. These groups primarily book between 9:30 - 12:30 at the VM. More pre-bookings leads to later pre-bookings and a longer line!