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Here are the teams that have gone worst to first in the last 10 years (which is when the current division structure started), and the number of games behind they were when they were worst.
2003 KC 3, CAR 5
2004 SD 9, ATL 6
2005 CHI 5, TB 6
2006 PHI 5, NO 8
2007 TB 6
2008 MIA 15
2009 NO 4
2010 KC 9
2011 DEN 6
2012 WAS 4
The Chiefs were 11 games behind last season, and it seems like a similar situation to Miami's 2008 season would be necessary to go worst to first.
Interestingly, going worst to first (14 times in 10 years) was more common than going worst to wildcard (11 times).
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