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Mike Brown is hardly the Stephen Hawking of owners. He has been criticized in the past for being cheap, stupid, and stubborn. And I remain to be sold on Marvin Lewis. Not only has he had some really poor seasons, but even when the Bengals win, they are one and done in the playoffs. Their current success is built as much upon low draft choices (like A.J. Green) garnered over the 2006-2011 period when they went 42-51-1, as it is upon the patience of staying with Lewis.
I agree that is one reason for their success, and acknowledge that the Bengals haven't exactly been a top franchise either. However, looking at the Bengals franchise history, it is fair to say they have turned the corner and are certainly an above average team now; in fact, they've had a top 10 team for a few years. Not sure how much I blame Lewis for the playoffs; Dalton sure has played like absolute garbage. Either way, I didn't say Lewis was a great coach, just that the Bengals benefit for the team's continuity, which should not be underestimated. You mentioned their low draft choices, but many of them are now at market value and many other teams have also had a bunch of low draft choices and still remain in the cellar. If you are drafting a player in 2009 who you expect to be a franchise player, but your coaching staff is constantly changing (cover 2, 4-3, 3-4, zone vs press man, west coast offense, power running game), etc etc, there's a good chance that a guy like that will not fit at some point between then and now. For many years the Steelers have kept the same systems and coaches, though they recently changed it up, but it worked for a long time. So many teams in the NFL bring in one coach, fail, then bring in another coach with an opposite philosophy, so they are not just remodeling the team but rebuilding it instead.
Although the Patriots have changed from a 3-4 base to more sub packages and a 4 linemen, that has more to do with the changing league than their philosophy. They have benefited tremendously from continuity, and I think it was Brady who brought that up in a recent interview. While other teams are constantly shuffling around, changing how they evaluate players, changing the values of players, changing their systems, changing their priorities, panicking and hitting the reset button every 2-3 years, the Patriots have used the same methods for the last fifteen years (there are changes, but more adaptive ones than major ones.) They look for the same type of players on the offensive line, at wide receiver, valuing intelligence over straight line speed, and they are very strict about ball security; on defense, they value versatility in linebackers and linemen; at cornerback, they typically look for quickness and fluidity; they tend to keep guys who can also play well on special teams. Overall, their player evaluation remains the same year-to-year. A guy they draft in 2009 is going to bring value year in and year out as long as Belichick is here, whereas that guy would be changing systems and teams constantly had he been drafted by team in constant flux.
When a coach fails, I think it would be intelligent to replace him with another coach who has similar ideas about players, schemes, and football philosophy. That way, you can at least keep a lot of the same continuity and your players will still fit. However, teams typically adopt the opposite approach. When a 3-4 coach fails, they bring in someone who will run a 4-3, as an example, thinking that they need an entirely new coach, system, style, set of players, etc. It is a silly way to do things because it presumes that everything about the team's roster is a liability, whereas smart teams would leverage their assets and make changes but not completely blow it up. There is very little long-term thinking here and a lot of kneejerk reactions.