Jim Litke AP columnist

One of the four or five best coaching jobs in football is open, beginning Monday. Lloyd Carr could have stayed on at Michigan for as long as he wanted, yet at age 62, what he wanted to do was leave now. That says as much about the state of the college game as it does about Carr.

At a time when some members of the profession cheat to hang onto average jobs and some lie to lock up good ones — see Saban, Nick, and the University of Alabama — Carr walked away from one of the finest on his own terms. No one was holding the door open for him. Carr reworked his contract last winter so he could retire as coach after this season, accept another job at the university and collect deferred compensation. Then, he secured a deal guaranteeing his assistants will be paid through next season, whether Carr’s successor keeps them around or not.

No surprise there. Michigan’s administration is to college football what the Rooney family is to the NFL’s Pittsburgh Steelers, patient and loyal almost to a fault, just as committed to doing things right as it is to doing them better than anyone else.

(Full disclosure: My older son graduated from Michigan in 2003 and believe me, few things will sort out how you feel about a school and its mission faster than mailing out-of-state tuition checks there every month for four years.)

The winningest program in the sport’s history has had a total of 10 coaches since 1901 just five since 1948, and the continuity has paid dividends. The Wolverines’ last losing season was 1967 — two seasons before Bo Schembechler arrived and stamped his personality on the program — and they’ve avoided a prolonged slide into mediocrity that has tripped up rival powerhouses ranging from Nebraska and Notre Dame to Oklahoma, Southern California and Miami at one time or another.

Even so, it’s not like Carr had to rely on anyone’s good will or a connection to Schembechler dating back more than 25 years to keep his job. He’ll be remembered, fair or not, for being on the wrong end of a monumental upset by Appalachian State in this season’s opener and six times in his past seven games against Ohio State. But since taking over from Gary Moeller in 1995, Carr won a national championship, five Big Ten titles and 75 percent of his games.

That figure kept the Wolverines solidly planted among the top 10 programs in winning percentage during Carr’s tenure and placed him seventh among active coaches, sandwiched between Florida State’s Bobby Bowden and South Carolina’s Steve Spurrier, before he retired.

Yet critics argued the game had passed him by after 13 seasons, and based on the Wolverines’ record in the big ones late in Carr’s career, they had a point. Despite rising through the ranks as a defensive coach, Carr’s teams remained vulnerable to mobile quarterbacks and spread offenses to the very end. Despite helping to develop such potent offensive stars as quarterback Tom Brady and wide receiver Braylon Edwards and relying on the pass more than Schembechler, when games got tight, he often lapsed into the same cautious play-calling that finally dated his mentor.

Carr remained so devoted, in fact, that he refused to enter Schembechler’s office just down the hall, or let anyone move even a single item from where Bo left it when he died in November 2006. Successful as Carr was, it’s hard to think of him as a caretaker. But maybe that’s how he saw himself. Ten years after winning the championship Schembechler never could, Carr looked around and realized coaching had become a younger man’s racket.

Whether Carr’s successor draws as heavily on Schembechler’s legacy, he better bring some energy of his own. He’ll definitely have the same advantages Carr did: a national recruiting network, a track record of developing NFL talent, a tradition that practically sells itself — winged helmets, the Big House — and access to deep pockets that are about to get even deeper.

Michigan Stadium, which already boasts the largest seating capacity in the sport, is adding luxury boxes as part of a controversial $226 million renovation. Considering that investment, Carr’s successor should have considerable leverage in negotiating a salary package. So the $1.25 million that LSU coach Les Miles would have to pay his current employer to get out of his contract and return to Michigan, where he played, met his wife and worked as an assistant under Schembechler, might not be much of an obstacle.

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But Baton Rouge won’t be the only pin on the map in whatever office Michigan’s search committee has already commandeered.

Among college coaches, Iowa’s Kirk Ferentz and Stanford’s Jim Harbaugh, a former Michigan QB, are generating some buzz. The list of NFL candidates ranges from Carolina Panthers assistant Mike Trgovac, who played for the Wolverines, on through head coaches Bobby Petrino in Atlanta and Jon Gruden in Tampa Bay.

The most intriguing rumor, perhaps, has former Steelers coach Bill Cowher cutting short retirement to take the job. At least he’s had plenty of rest.