The head coach of the Cincinnati Bengals might be one of the best gigs in the NFL. Seriously.
Think about it. What's the average head-coaching life for an NFL head coach these days? 2-3 years? Well, if you're the head coach of the Cincinnati Bengals you'll get that. Heck, unlike Al Davis, your owner will wait and not fire you until your contract is up and you will get ALL OF YOUR MONEY!
If you win, you're a genius, because you have won in spite of Mike Brown and his bass-ackwards organization. Luck your way into winning 10-11 games and they might name a street after you. You are the savior! 8-8 and you get an extension and the city thinks you're the next Lombardi!
If you lose, it's Mike Brown's fault and there was nothing you ever could have done to insure winning anyway.
If you lose bad, you still get your money and probably complete your time. Then the media comes to your defense saying how impossible it is for anyone to coach in that environment....blah...blah...blah and next thing you know you're one of the top candidates to move on to another organization in some capacity. There is no guilt by association to worry about.
So, in summary...
You get paid.
If you happen to win, you're a genius.
If you lose, it wasn't your fault anyway.
People feel sorry for you.
Move on to another gig.
Being head coach of the Cincinnati Bengals is a no-lose (except for on the field) situation.