So why don’t hockey teams enjoy a lift on home ice?

The prevailing view among economists and statisticians is that home advantage in all sports exists mainly because of referee bias. Mr. Moskowitz and others have written that noisy fans and announcers do not have much impact in terms of distracting or demoralizing visiting players. But statistically, they do cause officials to make calls that favor the home team in tricky situations, including many pivotal ones.

“Obviously the referees play a role, and it’s subconscious on their behalf,” Aaron Schatz, the editor in chief of Football Outsiders, said. “They don’t mean to favor the home team.”

Eric Tulsky, the manager of hockey analytics for the Carolina Hurricanes, said: “You have to be really sure of yourself when you know that everybody around you thinks one thing to say, ‘No, it’s actually the opposite.’ So the home team ends up getting some borderline calls, just because hearing other people’s opinions influences you.”

If officials can be swayed by their surroundings when making tough decisions, one key difference may be the way that fouls are called in basketball and hockey.

“In an N.B.A. game, a referee could literally call a foul on every play if they wanted to,” Mr. Moskowitz said. “Their influence on the game is definitely higher.”

Michael Lopez, an assistant professor of statistics at Skidmore College, said there was a cumulative effect to foul calls within a basketball game.

“On an individual play level, the magnitude of the home bias is very small, but when you add up all those small plays across the course of the game, that’s where you get a pretty big, dramatic effect,” he said. “In hockey, just by the nature of the sport, they can’t make that many calls in a game.”

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