Draft your all-time NFL roster and chase a perfect run

Each roll lands on a random team and season from 2001 to today (the 2007 Patriots, the 2013 Seahawks, this year's contenders) and reveals that roster. Draft one real player to an open spot and the next team rolls automatically. Fill all 15 (offense, defense and a kicker), then play a full 17-game season and chase a playoff run. Go undefeated and win the Super Bowl for the perfect season.