A recent study concludes that collegiate men’s basketball officials are more likely to whistle teams with fewer fouls or make a call on a team that is leading.

The authors say the pattern rewards aggressive teams.

The study examined 365 Division I conference games during the 2004-05 season. Co-author Kyle Anderson, a professor of business economics at Indiana’s Kelley School of Business and a former basketball player at Division III Knox College, said he had observed the phenomenon as a player and fan. He said he wasn’t surprised to find a pattern: The larger the foul differential between two teams, the greater the likelihood that the next call would be made against the team with fewer fouls.

What did surprise him was the strength of the pattern. For example, if the home team has three or more fouls than the visiting team, the probability that the next foul will be called against the visiting team is more than 60 percent. If the differential increases to five, the probability rises to 69 percent. The same trend occurs even in neutral-court games.

Anderson said his co-author, David Pierce, who has done some officiating himself, also acknowledged that he felt that officials did want to make calls, consciously or subconsciously, that would help the visiting or trailing team or the team with fewer fouls.

“It didn’t surprise me that we found a pattern, but it was a lot more significant than I ever expected going into it,” Anderson said. “A lot of officials want to feel like they are being objective, not favoring a team. They will almost go to an extreme to show they are not favoring a team. … But obviously, if you get into a situation where you’re actively trying to call fouls on one team and not the other, you’re trying to be fair but you’re actually not.”

The authors said the effect benefits aggressive teams that get called for fouls early since they are less likely to incur a whistle later in the game. The study also found that the crowd isn’t always a factor; the effect will benefit the visiting team if it accumulates more fouls early in the game.

Anderson said the pattern may already have affected play at the collegiate level.

“Every year the NCAA in its points of emphasis warns against physical and aggressive play,” he said. “However, this officiating pattern actually encourages more physical and aggressive play.”

In their introduction to the study, Anderson and Pierce cited the 2005 Final Four matchup between Illinois and Louisville. Officials called the first seven fouls on Illinois, which was playing an aggressive defense. Five of the next six whistles went against Louisville, and at the end of the game, the Cardinals had one more foul.

As a fan of college basketball, Anderson hopes that just raising awareness to these tendencies will help officials address it.

“They might say, ‘Hey, I’m OK with calling eight fouls on one team and two on the other in the first half because that’s what happened,’ ” Anderson said.

Anderson’s usual research centers on online pricing and decisions that firms make in competitive situations. While the study of basketball officiating was part of a mathematics course he was taking, he sees it as more than just something he did “for fun.”

“In business schools in general, people are interested in how we make decisions in uncertain situations. Referees are making that very kind of decision 25 times a night,” he said. “This is broader than just basketball. How do we make decisions? How do previous decisions affect future decisions? There is a relationship that goes beyond what we see on the court on Saturday afternoons.”