In 2015, the U.S. witnessed more than 9,600 homicides committed with a firearm — an average of more than one every hour for the entire year. At the same time, police departments have been struggling to clear these cases. In Chicago, for instance, where gun violence has surged to levels not seen since the late ’90s, only about one-third of homicides are solved.
Professor Lawrence Wein, the Jeffrey S. Skoll Professor of Management Science at Stanford Graduate School of Business, decided to take on this problem of gun violence using his deep expertise in operations. He found that small, often costless adjustments to the procedure of ballistics analysis could dramatically improve crime-solving capabilities.
The National Integrated Ballistic Information Network (NIBIN) maintains a national database of images from cartridge cases that were either recovered at a crime scene as evidence or test-fired from confiscated guns. In theory, the database allows U.S. cities to match cartridge cases from specific guns with specific crimes. In practice, about 72% of “hits” come from only 20% of cities — those that are diligent about entering recovered cartridges into NIBIN.
“Some cities process all of the cartridge cases that they get; other cities process very few,” Wein says. “So the question is: What’s the relationship between hit rate and the proportion of all the evidence that comes into the police department and actually gets processed?” By analyzing five years of NIBIN data from Stockton, California, Wein revealed that small increases in processing actually provide big gains in hit rate.
This fact is critical, Wein noted. Many cities are entering few cartridges into the system and getting few matches as a result. Projecting from this, police departments may assume that greater effort and resources will provide only marginal gains. “Their thinking goes linearly,” he says. “But the improvement actually goes up quadratically.” Doubling the percentage of cartridges processed will improve the hit rate fourfold, not twofold. Over a decades-long career studying operations, this is the first time Wein has seen this kind of relationship.
“If you go to any manufacturing operation, or any service operation, like McDonald’s or the supermarket, if it is capacity-constrained then when you double the number of cashiers, you’ll double the amount of people going out of the system,” he says. “This was the first operation I’d encountered where the relationship is not linear.”
The implication for police departments is that minor investment in improved capacity to analyze cartridges returns outsized gains. But even if police departments don’t have the resources to increase the number of cartridges they process, Wein found a costless way to improve the match rate.
Investigators recover cartridges from bullets of different calibers at crime scenes. (In Stockton, for example, bullets of 12 different calibers make up the majority of evidence.) What if cartridges were prioritized in different ways once they arrive at the police station, Wein wondered. He designed and tested three allocation policies. In the first one, cartridges were analyzed randomly. (They might be processed in the order they arrived at the station, for example, or chosen randomly from the entire pool.) In the second policy, cartridges recovered at crime scenes were prioritized over those from the test fire of recovered guns. The third policy, like the second, prioritized cartridges taken as evidence over test-fire cartridges, but it also grouped them by caliber. So, for instance, all 12-gauge cartridges would be processed together, and then all .357 cartridges, and so on.
Wein found that the last option of grouping cartridges by type — a procedure that, importantly, is free — dramatically improved the hit rate. “This is a very simple policy that produces much better results,” Wein says. “Most cities can’t even process half of their cartridges, but they could increase their hits three-, four-, or even fivefold without spending any money.”