WEST LAFAYETTE, Ind. — Members of the band, a few cheerleaders and the costumed Purdue Pete filed into a large suite at Ross-Ade Stadium on Monday to participate in one of college football’s archetypal pageants: the introduction of the new football coach.

The coach, Jeff Brohm, arrived shortly afterward, along with Mitch Daniels, the university president, and Mike Bobinski, the athletic director.

One could make a good case that Purdue, which had two winning seasons in the past 10, got its man. After a career in professional football in the N.F.L. and the short-lived X.F.L., Brohm spent the past three years rejuvenating Western Kentucky, leading the Hilltoppers to a 30-10 record and consecutive Conference U.S.A. championships.

The high-powered offense developed by Brohm — a former quarterback whose mentors include Bobby Petrino, Marc Trestman and Mike Shanahan — was the second-most potent in the Football Bowl Subdivision this season. It was also a perfect fit for a Purdue program that fancies itself “the cradle of quarterbacks” because of its incubation of luminaries such as Len Dawson, Jim Everett and Drew Brees.

“I’m 100 percent committed to restoring the gloried past of Purdue football, while upholding the values and integrity that Purdue represents,” Brohm said.

Stories like the ones at those smaller programs have been amplydocumented, and rightly so: They represent how the structure of college sports, a nominally “equitable” enterprise (according to the N.C.A.A.’s mission statement), prevents certain teams in certain sports — above all football — from sustainably competing at the highest level. The reason is simple economics: The 65 members of the so-called Power 5 conferences receive comparatively colossal annual payouts connected to TV contracts and the College Football Playoff compared with their less-well-off peers.

Purdue’s story is the obverse. Compared with those smaller programs, it swims in cash. It barely had to pause before firing its coach, Darrell Hazell, after less than four full seasons of profoundly losing football, costing a nearly $5 million buyout, before reportedly pledging to pay Brohm, in his first major-conference head coaching job, $20 million over six years.

This is not because of geography. Ask a football coach whether he would prefer his recruiting base to be Central Indiana (Purdue) or the Gulf Coast of Texas (Houston), and he would laugh. Nor is it because of past or recent accomplishment. While Purdue has had its glory years, there are a half-dozen Big Ten teams with superior football pedigrees. The last time the Boilermakers finished a season in the top 10 of the Associated Press rankings was after the 1979 campaign.

Rather, the difference between programs like Cincinnati and Purdue is about $30 million per year. And much of that comes not from anything Purdue did in the past five years or 25 years, but what it did more than 100 years ago, when it was a charter member — by most accounts the singular founder — of what became the Big Ten.

Being a large, old land-grant university in a sizable state certainly helps, as do Purdue’s nearly half-million living alumni, but that does not tell the whole story, especially with a recent annual donation mark of around $17 million (or less than half that of division rival Nebraska), per USA Today’s financial database, or the Boilermakers’ league-worst attendance. One Purdue-centric blog calculated that Purdue last year easily had the lowest football earnings in the conference — $7 million lower than even hapless Rutgers.

Morgan Burke, who recently stepped down after 24 years as Purdue’s athletic director, spoke about Purdue’s blessed situation Monday night.

“Are you fortunate these schools have stuck together?” he asked. “Sure.”

Asked about the would-be football powers who make up the so-called Group of 5 conferences, whose competitive ceiling is financially imposed, Burke referred to Purdue’s status as an athletic department that, according to the typical accounting methods, does not require any subsidy from the rest of the university. That is a rare distinction it shares with several other Big Ten programs, thanks to lucrative conference payouts.

If there is a catch, it is that Purdue’s monetary advantage is canceled out for the nine games of its regular football season that it plays against other Big Ten members. Western Michigan managed to beat two Big Ten teams, on the road, in going 13-0 this season, but it also got to play Kent State and Buffalo, which had losing seasons against lesser competition. By contrast, Purdue must play Wisconsin and Nebraska every year, and it frequently finds Michigan, Ohio State, Michigan State and Penn State on its schedule.

Brohm took the challenges his new program faces in stride.

“I understand it’s had its struggles recently,” he said, “but that’s what they pay me for.”

[IMAGE: CreditJohn Terhune/Journal & Courier, via Associated Press]
© 2016 The New York Times Company.

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