By Steve Eder

New York Times News Service

In late 2012, Arkansas hired Bret Bielema as its football coach, paying him a salary of $3.2 million per year, plus bonuses, making him one of the best-compensated coaches in his industry and his state’s highest-paid employee.

During Bielema’s first season, the Razorbacks won their first three games before losing their last nine, prompting some fans to wonder whether Arkansas had overpaid him. One fan took to Facebook to sarcastically thank the coach for the three wins: “Good job, Bielema, here’s $3 million dollars for that.” Another posted on Twitter that the coach should share his paycheck with his players who “get paid nothing but bring $ to the university.”

But, according to a new study by researchers at Vanderbilt, coaches like Bielema who command what are widely seen as robust salaries are worth the money because of the value they bring to their universities. The Vanderbilt study, which included 947 contracts from 2005 to 2013, benchmarked coaching salaries against those of chief executive officers at public companies — another group that is often accused of being paid too much.

“Coaches are running large programs that have tremendous value,” said Randall S. Thomas, a law and business professor and one of the authors of the study. “They are creating great value, and they are being paid for creating that value. They contrast quite directly to public company CEOs.”

In universities’ zest to compete, many routinely court coaches as if they were recruiting a new chief executive: offering millions of dollars, the power to hire and fire others, and even the use of a private jet. A result is that big paydays are hardly unusual in college football, in which head coaches, win or lose, have been among the biggest financial beneficiaries of the ballooning amount of cash flowing into the industry.

The increasing demands to win and billion-dollar television deals have combined to cause the average pay for coaches at the top level of Division I football to double since 2005 to $1.5 million, the Vanderbilt study found.

Like chief executives, numerous coaches make more than $3 million a year and enjoy special perks, the researchers found.

Nick Saban, the coach at Alabama, receives personal use of a private jet each year, in addition to his pay. Les Miles at LSU has a provision in his deal that will automatically make him the highest-paid coach in the Southeastern Conference, by $1,000, should he coach his squad to another national championship.

“If one believes that CEO compensation is set by the market at an appropriate level, and that employment contracts reflect this equilibrium, then one should reach the same conclusion about football coaches,” wrote Thomas and co-author R. Lawrence Van Horn, an associate professor of economics and management. The professors shared with The New York Times a draft of their report, which has not been published or peer-reviewed.

To be sure, there are significant differences between a football coach and a chief executive, some of them acknowledged by the authors. One divergence is that coaches often have higher fixed salaries, while compensation for chief executives tends to be heavily influenced by performance. In addition, executive pay is also supposed to be closely monitored by experts on company boards. In some cases, the boards even have the power to take back pay that was promised to executives in previous awards. And the chief executives are often paid a substantial part of their compensation in company stock — which can fall in value if the firm underperforms — something that does not exist in college football, at least as it stands.

The debate over the pay of football coaches at big public institutions is especially in focus at a time when critics are piling on the NCAA.

Some contend that the sizable coaching salaries are enabled by what critics call the exploitative nonpayment of college football players. Others believe the coaches’ compensation packages are evidence that the universities are overly invested in athletics, spending to keep up in sports, with academics and budget cuts at large public universities in the backdrop.

“It has gotten out of whack,” said David Ridpath, a former athletics administrator at Marshall who has been critical of the NCAA. Runaway salaries, Ridpath said, have “caused and fueled greater problems in college athletics.”

But others say that a reality of big-time college athletics is that top-level coaches are special talents with huge jobs, and the market demands that they be highly compensated. The jobs are often short-lived, and the stress level is high.

“They are worth every penny,” said Martin J. Greenberg, a Milwaukee-based sports lawyer who has represented coaches in contract negotiations for 25 years. Greenberg said that coaches nowadays suffer from what he called “role strain,” meaning they have a broad range of responsibilities, including fundraising, recruiting, academics, being public figures and meeting with alumni.

“They are asked to do just about everything under the guise of being the football coach,” Greenberg added.