As Baton Rouge law enforcement deployed in force this past week to protests after the police shooting of Alton Sterling, city officers responded to less than half the number of reports of crime than in the week before Sterling died.

Records also show that in recent days Baton Rouge police have made few arrests unrelated to demonstrations.

Baton Rouge police did not answer specific questions about deployment and non-protest policing, but insisted the city is protected even as many officers are working demonstration duty.

"Most of the arrests lately have appeared to be a result of protest-related crimes. At no point in time during these unexpected protests have the citizens of Baton Rouge been neglected in our committed service to them," said Sgt. Don Coppola Jr., a BRPD spokesman, in a brief statement. "We will continue to perform our duties to the fullest."

State Police: Video shows projectile thrown at officers during Sterling protest A video captured by a WWL-TV reporter appears to show a brick being thrown at officers durin…

Criminal justice professor John DeCarlo of the University of New Haven noted that police may have their hands tied by the current situation, forced to deploy a large share of officers to protest duty. That could be true even if not many protesters materialize.

On Tuesday evening there was a peaceful protest of about 100 people across the street from the main Baton Rouge Police Department station. A helicopter circled overhead, while more officers waited on the grounds of the old Women's Hospital, where the police are now headquartered, but none of the demonstrators were arrested in the hours they spent outside.

During an even longer period, in the 12 hours between 12:30 p.m. on Tuesday and 12:30 a.m. Wednesday morning, city police only booked four people citywide, according to jail records. Those four include a suspected thief and a fugitive as well as one person accused of domestic battery and another accused of stealing a car.

In comparison, the same time period between Tuesday afternoon and Wednesday morning the week before the Sterling shooting, city police made 12 arrests.

Last weekend, when there were protests that grew tense on Friday, Saturday and Sunday, city officers arrested very few people who did not appear to be related to protests around Baton Rouge, though Zachary police and East Baton Rouge Parish sheriff deputies made a few other arrests.

Police also responded to far fewer incidents, which are stops initiated by a police officer or following up on a 911 call which may lead to an arrest or multiple arrests. The city's online database of these calls does not differentiate between the two kinds of responses.

On the Saturday and Sunday before Sterling was shot, police responded to 213 incidents, according to the city's online records. Last weekend they responded to 99. Both numbers may rise slightly since a police supervisor must sign off on officers' reports before they are recorded.

Various agencies, including the Louisiana State Police and multiple sheriffs' offices, have backed up Baton Rouge police in the wake of the Sterling shooting, though it's unclear if those other agencies have helped respond to 911 calls or provide law enforcement to parts of the city where people are not demonstrating. A State Police spokesman said only that troopers were helping city police as needed, but declined to comment how they were being deployed, and an East Baton Rouge sheriff's spokeswoman did not return several messages seeking comment.

The demonstrations began the night of July 5, the day Sterling was shot by a Baton Rouge police officer in the early morning hours outside the Triple S Food Mart near North Foster Drive and Fairfields Avenue. The shooting kicked up a firestorm as cellphone videos of officers initially Tasing and tackling Sterling went public. In the videos, officers are seeing pinning Sterling to the ground before one fires a gun into his chest.

Advocates for Sterling have called the shooting unjustified. A recently released police search warrant said that officers saw Sterling reach for a gun in his pocket before he was shot.

When the protests were held in the neighborhood where Sterling was shot, the police presence was minimal. But it grew on Friday, when the protests moved to outside police headquarters. Many police officers were deployed and local officials said they needed to keep protesters off of busy Airline Highway, both to keep traffic flowing and keep demonstrators safe.

Professor Joseph Pollini, of the John Jay College of Criminal Justice, said there are practical concerns when dealing with large demonstrations when many officers are needed on the streets.

"What is paramount at this point in time is safety," and there is safety in numbers, Pollini said.

That means officers are generally better able to protect each other in a big group. More broadly, a large police presence can keep a demonstration from turning into a riot, explained Pollini, a former New York City police detective. It's a concern for all large-scale protests, regardless of the issue, he added.

DeCarlo, the New Haven university professor who was a former police officer in Connecticut, also speculated that Baton Rouge may be experiencing the first stage of the so-called "Ferguson effect." Named for the Missouri city where teenager Michael Brown was killed by police in 2014, the concept -- disputed by some criminal justice observers -- posits that when a police department comes under scrutiny, officers pull back law enforcement efforts, possibly clearing the way for more crime.

Like any person, officers have a self-preservation instinct and may be fearful at a time when members of the community express anti-police sentiment, DeCarlo continued.

After the immediate aftermath of an incident has passed, communities are better able to see if officers are shirking their duties, he said.

Both DeCarlo and Pollini said it can be hard to tell how long a law enforcement agency might need to stay at high alert. In addition to the facts of the case at hand, respected politicians can sway crowds with calls for unity or demands for reform. Rain or extreme temperatures can also keep demonstrators home.

"Weather is one of the best police officers," Pollini said.

In the mean time, police will have to calibrate their response to crowds, striking a balance between the militarized reaction in places like Missouri -- where officers in Ferguson deployed wearing military-style garb -- and an approach that is too laid back at a time when social media can "foment civil unrest" much more quickly than in the past, DeCarlo said.

"That's a tough situation to be in," he said.