Sure you could see why you got your #10 pick..
Imagine this visualization. On "draft day", the names of the players that you have ranked are revealed, so that you know that you have Joe Smith as your top rated player instead of Player No. 11.
Each team would have an avatar, and these would slide over by the picture of their #1 pick. If this was a unique matchup, the player would return with a smiling avatar to join his new team. The players would also be crossed off your draft list.
If there were multiple teams that had selected a player, there would be a drawing to decide which team would get the player, and the succesful team would take their pick back to their team. The other avatars would slide back to their team, with a disappointed expression.
Those who didn't get their first pick would slide over to their next pick, and the process would repeat, and so on.