In the first quarter of a scoreless 2016 AFC Championship game against the New England Patriots, Peyton Manning and the Denver Broncos faced third-and-6 from their own 44-yard line. Wide receiver Demaryius Thomas ran a 15-yard out, breaking toward the Broncos’ sideline. He did not catch Manning’s wobbly throw, but there was contact on the play, and Denver’s players and coaching staff appealed to the official for a pass interference call on Patriots cornerback Logan Ryan. They got one, and the Broncos got a first down, scoring the game’s opening touchdown four plays later.

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On the ensuing drive, the Patriots faced third-and-3 at their own 27-yard line. Rob Gronkowski ran a wheel route up the Broncos’ sideline with T.J. Ward in coverage. As the Patriots tight end turned to look back for the ball, the defender made contact and shoved him, preventing a catch. Both Gronk and Tom Brady yelled for a penalty. The flag did not come, and the Patriots were forced to punt.

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Similar plays led to different outcomes that benefited the team on the sideline closest to the on-field action. Most NFL refs would likely say they are immune any sideline bias. “If I make a call because a coach is screaming at me on one side of the field and it’s wrong, that’s a bad day for me,” former NFL official Scott Green told us. (The NFL declined to comment.)

But as it turns out, a sideline bias in the NFL is real, and it’s spectacular. To prove it, we looked at the rates at which refs call the NFL’s most severe penalties, including defensive pass interference, aggressive infractions like personal fouls and unnecessary roughness, and offensive holding calls, based on where the offensive team ran its play.

For three common penalties, the direction of the play — that is, whether it’s run toward the offensive or defensive team’s sideline — makes a significant difference. In other words, refs make more defensive pass interference calls on the offensive team’s sideline but more offensive holding calls on the defensive team’s sideline. What’s more, these differences aren’t uniform across the field — the effect only shows up on plays run, roughly, between the 32-yard lines, the same space where coaches and players are allowed to stand during play.

The following graphs show the penalty rates per 1,000 plays for defensive pass interference and aggressive defensive penalties, which include unnecessary roughness, personal fouls, unsportsmanlike conduct, and horse-collar tackles.

Refs throw flags for defensive infractions at significantly higher rates when plays are run in the direction of the offensive team’s sideline; near midfield, defensive penalties are called about 50 percent more often on the offensive team’s sideline than the defensive team’s. Close to the end zone, where the sidelines are supposed to be free of coaches and players, these differences are negligible.

For offensive flags, that association is reversed, at least on holding penalties. Here’s the rate of holding calls made on outside run plays, which shows how the defensive team’s sideline can help draw flags on the offense. Around midfield, offensive holding gets called about 35 percent more often on plays run at the defensive team’s sideline.

So what could be causing this phenomenon?

Refs are faced with a near-impossible task. They make judgment calls in real time, relying on just their eyes and their experience. Deprived of the advantages, like instant replay, that we enjoy from the couch, refs have less information to help them resist the normal subconscious urge to draw on external cues for assistance in making borderline calls. In psychology terms, this process is called cue learning. It’s why we laugh longer in the presence of other humans laughing, why we eat more in the presence of overweight company, and why our judgment of persuasive speeches is influenced by the audience’s reaction.

The most common cue in sports is crowd noise, and because crowd noise almost always supports the home team, the way the fans sway the referees is the No. 1 driver of home-field advantage in sports. And one notable experiment suggests that how loud a crowd is helps refs decide whether an interaction should be penalized. A pair of German researchers showed actual referees old video clips of possible soccer infractions, with crowd noise played at high or low volume. Refs looking at the exact same interactions were more likely to hand out a yellow card when they heard a lot of crowd noise than when the volume was low.

It follows, then, that screaming and hat-throwing football personnel may also have an effect on referee choices. In football, this sideline bias even seems to supersede refs’ tendency to support the home team: The differences in the penalty rates from sideline to sideline are several times larger than the differences in penalty rates between the home and away teams.

That bias can affect the outcome even when officials have time to confer. In a 2015 playoff game between the Dallas Cowboys and the Detroit Lions, Matthew Stafford threw a third-and-1 pass to Brandon Pettigrew. Officials initially called defensive pass interference on the Cowboys’ Anthony Hitchens.

But the flag occurred right in front of the Cowboys sideline. This led to some confusion. It also led to a helmetless Dez Bryant yelling at the official.

After conferring with each other, the officials picked up the flag, a decision that Mike Pereira, Fox Sports’ rules analyst and the NFL’s former vice president of officiating, said was incorrect. Brian Burke of Advanced Football Analytics calculates that when the official picked up the flag, the Lions’ chances of winning that game dropped by 12 percentage points.

Dallas won 24-20.

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