After a few attempts at drafting on tappedout.com today I can advise, don't waste your time here.
The lag is terrible, and most people get disconnected shortly. The bots are terrible and don't draft realistically at all. There is something weird with the program where I get passed strange numbers of cards, I think this happens when people start disconnecting mid pick.
I like the way the draft simulator organizes my picks. I can choose MD, SB, hate, or money for my picks and see what cards are in those piles at any time. I have seen cool logs of completed drafts that show what every player pickd and in what order, but I have yet to successfully complete a draft without crashing.