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A little bit of cheating can go a long way.

A new study, published in the Academy of Management Journal, suggests that when “high-reputation” institutions -- colleges and universities ranked among the top 50 institutions by U.S. News & World Report -- run afoul of National Collegiate Athletic Association rules, they actually see an initial increase in support from alumni. But that surge in alumni support declines as a program racks up more violations, and nonalumni are less likely to donate after even a single infraction.

“If you have a lot of very loyal supporters, what our study suggests is that it may not be bad to cheat a little,” said Rhonda Reger, co-author of the study and a professor of strategic management and entrepreneurship at the University of Tennessee at Knoxville. “When institutions had a small amount of NCAA violations, alumni donations went up significantly. Those that had a high emotional connection to the college increased their support. Now, if you cheat a lot, however, even the alumni will begin to turn on you.”

For the study, the researchers examined NCAA violations at 658 institutions between 1999 and 2009. Those data were then compared to donor information those institutions provided to the annual Council for Aid to Education survey. The researchers measured the “volume of wrongdoing” as the sum of the specific NCAA rules -- or legislative references -- cited in each infraction. The negative effect of too many violations is felt most at high-reputation colleges, compared to NCAA institutions that are not ranked among the top 50 by U.S. News & World Report.

The researchers said that they cannot "definitively claim causality," but the findings suggested that a high-reputation university that engaged in a major infraction with just one legislative reference -- essentially breaking one NCAA rule -- experienced, on average, a $162,503, or 4.1 percent, decrease in nonalumni donations. Lower-reputation institutions, meanwhile, had a $12,995, or 1.1 percent decrease.

“This indicates that a high reputation is a burden when considering support from low-identification stakeholders,” the researchers wrote.

It’s a different story for alumni donors, however. After an institution committed an NCAA violation, alumni donations actually increased by $201,324, on average, at high-reputation institutions.

“Some schools saw increases in the hundreds of thousands and even millions of dollars after an infraction,” Reger said. “But there is a threshold. Three or four violations is where you see that increase. At about seven is where the alumni donations start falling back to where they were when there was no violation. More than seven is where even those who are most loyal start to feel hurt by the cheating.”

While the study was focused on NCAA infractions, the researchers -- drawing on their previous work studying how high-profile companies weather crises such as product recalls -- said that their conclusions would likely apply to other college athletics scandals, as well.

In 2012, Pennsylvania State University received more than $208 million in donations, despite the arrest and conviction of the football team’s former defensive coordinator Jerry Sandusky on 45 counts of child sexual abuse. The arrest rocked the campus and led the university to oust both its president and its longtime head football coach over allegations that they covered up the abuse. The NCAA fined the institution $60 million and enacted a series of historic and controversial sanctions.

But the $208 million Penn State received in the wake of the scandal was the second-highest fund-raising amount in the university’s history. Giving to the football program skyrocketed to $9.7 million that year, compared to $2.1 million the previous year.

An analysis of the donations by the university’s senior vice president for development found that donors who had previously given $5,000 or more to Penn State were the most likely to continue supporting the university during the scandal. Many of those donors had already donated more than $25,000 to the university. 

“People who highly identify with an institution, they leap to its defense in times of scandal,” Reger said.

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