If there’s any good to come out of the 2014 fatal police shooting of Ashley DiPiazza in Madison, it might be the light shed on police procedures during the federal civil trial that ended Thursday with a verdict against two officers.

Having agreed to spend up to $400,000 on a study of police but resisted the adoption of police body cameras, the City Council in particular could have plenty to learn.

DiPiazza’s death didn’t get as much attention from police-reform advocates and their council allies as the 2012 fatal police shooting of Paul Heenan, in part because of the outspokenness of Heenan’s supporters.

As a white woman, DiPiazza also didn’t fit the mold of victims in the national Black Lives Matter movement, such as black 19-year-old Tony Robinson, whose 2015 fatal shooting by Madison police continues to reverberate.

DiPiazza, unlike Robinson and Heenan, also had a gun, although it’s not clear that made her a threat to anyone but herself.

All three were intoxicated when they were killed, but police allege Heenan struggled with and tried to disarm an officer and that Robinson attacked one, and the two were shot seconds after police arrived on the scene.

By contrast, police were told before arriving on the scene that DiPiazza was distraught and armed, and it was some 30 minutes before she did the thing that police say justified their decision to open fire: For the second time during the course of the call, she came out of her bedroom with a gun pointed at her head.

In other words, not only was she not pointing the gun at police, but police had refrained from firing on her once, and they had time to come up with a plan for taking better cover should she decide to come out again.

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Officers testified Wednesday they’d been trained to fire on a suspect holding a gun to his head if he refused orders to put it down — which goes to a longtime question in law enforcement: whether an armed suspect can aim and fire a gun more quickly than a police officer with gun already aimed can fire in response.

“In the abstract, action is quicker than reaction. That’s what police training tends to emphasize,” said Seth Stoughton, a cop-turned-law-professor at the University of South Carolina who wasn’t commenting specifically on the DiPiazza case.

But the officer’s location and the suspect’s strength can influence this, he said, and “unfortunately, most of the timing studies of suspect movement and officer responses are methodologically flawed.”

Stoughton said time is critical in a situation like this and “officers use distance, cover and concealment, for example, to increase the amount of time that it takes for a subject’s actions to present an imminent threat.”

The officers in the Heenan, Robinson and DiPiazza cases were cleared of criminal wrongdoing, and families of the former two won multimillion-dollar settlements without police admitting any fault. A jury awarded DiPiazza’s family $7 million.

You can’t blame grieving families for taking settlements, but an open, adversarial forum, like a trial, comes closer to achieving truth and justice.

It can be more valuable than any study, and almost as valuable as video evidence.

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Contact Chris Rickert at 608-252-6198 or crickert@madison.com, as well as on Facebook and Twitter (@ChrisRickertWSJ). His column appears Tuesday, Thursday, Saturday and Sunday.