Dennis Allen inherited a Saints team coming off 5 straight winning seasons.
Virtually no new coach steps into such a position. That's a pretty good hand! The only better situation I could envision in today's NFL involves either Andy Reid's health making him retire, or the Steelers (idiotically IMHO) firing Mike Tomlin. Bowles with the Bucs stepping in for Arians after the latter retired is the only similar new coach situation recently I can think of off the top of my head.