When congressional Democrats staged a sit-in on the House floor last month to demand a vote on gun control measures, many of them touted a familiar policy solution: universal background checks.

Federal law already requires background checks for anyone purchasing a gun through a licensed dealer. But the law exempts private sales, a category that accounts for 40 percent of gun sales, according to one 1997 study. (Researchers are now working to update that figure.) That means there are few practical barriers keeping guns from people legally prohibited from owning them, usually because of a prior criminal record.

Background checks wouldn’t have prevented the Orlando mass shooting that prompted the Democrats’ protest, nor most other recent high-profile attacks. Omar Mateen, like other recent mass shooters, was allowed to carry firearms and apparently bought his guns through a licensed dealer.

But researchers believe background checks could have an impact on homicides of women by their partners and of young men by other young men. Both types of violence are frequently committed by people with prior criminal histories that prevent them from owning guns legally — and both kill far more people each year than mass shootings.

Assessing the impact of background checks is difficult, in part because federal law prohibits the government from tracking gun ownership and sales. There is no comprehensive data on how criminals obtain their guns, or even a reliable tally of gun crimes committed by people prohibited from owning firearms. Instead, researchers are forced to scrutinize selected cases or rely on surveys of inmates. One 13-state study published in 2012 found that, among inmates incarcerated for gun crimes, 40 percent were prohibited from owning firearms; nearly all obtained their guns through a private seller.

Background checks almost certainly wouldn’t have prevented all of those sales; black markets for guns exist even in cities and states with strict background-check requirements, such as Chicago and Massachusetts. But there is evidence that requiring background checks makes it more difficult for criminals to obtain guns and, even more significantly, can reduce gun homicides.

The best evidence comes from Missouri, which in 2007 repealed a decades-old law requiring background checks for all gun purchases. A 2013 study from researchers at Johns Hopkins found that the repeal led to a 23 percent increase in gun homicide, the equivalent of 55 to 63 additional gun deaths per year. (Non-gun homicides, which shouldn’t have been as affected by the law, didn’t increase.)

Gun rights groups have criticized the study’s methods, but other evidence from Missouri and other states supports its findings. A separate peer-reviewed study found that when, in 1995, Connecticut adopted a background check law similar to the one Missouri repealed, gun homicides there fell by 40 percent. (Related research found the Missouri and Connecticut laws had a smaller but still significant impact on gun suicides.) Meanwhile, the gun control advocacy group Everytown for Gun Safety last year found that since the Missouri law’s repeal, more guns used to commit crimes there were purchased in state, and more were bought shortly before the crime was committed, a key measure of gun trafficking. Both trends suggest it has become easier for criminals to get guns in Missouri.

“All of these signals are telling you that guns sold in the state of Missouri are more readily available for criminal misuse,” said Daniel Webster, one of the authors of the Missouri and Connecticut studies. “You had a system that wasn’t perfect, but it was blocking a lot of risky transactions, and then you said, ‘OK, no more accountability.’ ”

Kansas City Mayor Sly James said that since the repeal of the 2007 permitting law, illegal guns have become more readily available in his city. (Last month, Gov. Jay Nixon vetoed a bill that would have expanded gun rights in Missouri, including making it easier for Missouri residents to obtain concealed-carry permits. Republican lawmakers in the state have vowed to override the veto.)

“The state of Missouri has totally taken away the ability of cities to have any impacts at all on the number of guns on the street,” James said. “It makes it easier for people to get guns in this city, and from my perspective as the mayor of the city … it’s absolutely the worst thing in the world to have more guns on the street.”

Before its repeal, Missouri’s law had been one of the strictest in the nation, requiring not just a simple background check but a “permit to purchase” — potential buyers had to go in person to their local law-enforcement agency, which ran a check and then issued a 30-day permit to buy a gun. Connecticut’s new law is similar.

Federal background checks, by contrast, are performed by sellers, who run a buyer’s name and other identifying information through an FBI database. Most proposals for universal background checks would apply the existing federal system to private sales — buyers and sellers would have to go to a licensed dealer to complete their transactions. Researchers don’t know whether that approach would have the same impact as the stricter permit-to-purchase rules. (Webster and his colleagues are now studying this question.)

Still, the push for universal background checks has more momentum than most other gun control measures. They are supported by large majorities in most polls, including by many gun owners. In 2013, a bipartisan background check bill won support from a majority of senators, though it failed to garner enough votes to overcome a filibuster. President Obama recently announced a series of executive actions intended to narrow that loophole, though gun rights groups are suing to block the new rules.

This article is part of our project exploring the more than 33,000 annual gun deaths in America and what it would take to bring that number down.

Ben Casselman was a senior editor and the chief economics writer for FiveThirtyEight.