The National Rifle Association donates millions of dollars every year to Republican lawmakers in Congress. And those same Republicans line up uniformly to block proposed gun control legislation.

The implication of these two facts appears obvious: Politicians are refusing to stem the bloodshed of gun violence because they’re getting what amounts to a legal bribe from lobbyists.

Indeed, this familiar refrain was widely echoed again after a 15-hour Senate filibuster to force a gun vote and House Democrats’ unauthorized sit-in on the Capitol floor — both were high-profile responses from politicians in the wake of the deadliest mass shooting in US history.

And it wasn’t just politicians. Lefty observers all over the place pushed this narrative:

"One big reason the latest gun bills failed: Gun-rights groups have in recent years given much more money to sympathetic politicians than gun-control advocates have," writes Rolling Stone.

Samantha Bee clearly thinks so.

Adds Igor Volsky of the Center for American Progress Action Fund:

.@RepGoodlatte got $9,900 from @NRA in 2014. He won't do anything to stop terrorists from easily getting guns https://t.co/0z2EJcNTHs — igorvolsky (@igorvolsky) June 12, 2016

But when you talk to experts who study the way money influences our political system, they say this account is wrong — or, at least, often badly oversimplified. The NRA may exert a massive and real influence on Washington, DC, but its campaign contributions can’t possibly be the corrupting agent singlehandedly thwarting meaningful action on gun control, as many of the analyses above suggest.

And, they say, we can come pretty close to proving it.

How we know gun control isn’t crushed by NRA money

If you wanted to cook up a perfect laboratory experiment to test whether the NRA’s donations really bought blanket opposition to gun control, you’d want to try neutralizing the effect of NRA money on politicians’ campaign coffers. To do that, you could eliminate corporations’ contributions to Congress. Or you could create a counterweight group that would match NRA funding to campaigns of lawmakers who decide to instead support gun control.

Luckily, we don’t have to imagine what that second route would look like — someone’s already trying it. Back in 2014, former New York City mayor and billionaire media magnate Michael Bloomberg started "Everytown for Gun Safety." Its goal was as clear as its method: Get gun control passed by erasing Republicans’ financial incentives to stick by the NRA.

"Those who favor gun control convinced enough elements of the donor community that the problem was money," says Matt Grossmann, a political scientist at Michigan State University, in an interview. "They went about trying to solve that problem by matching the gun rights lobby’s funding."

Two years later, and the shifting financial landscape hasn’t changed much: America still can’t enact meaningful gun legislation.

"Michael Bloomberg offering to give money to Republicans hypothetically makes a clear case," says Lee Drutman, a senior fellow at the think tank New America and the author of several books on money in politics (and a Vox contributor). "If the theory is that they’re selling their votes to the highest bidder, it has to be something else."

That’s not to say Everytown is a failure, or close to it. Everytown has provided a platform for the cause of gun reform, and it has worked to help craft legislation with some centrist Republicans — including Pennsylvania Sen. Pat Toomey, who proposed an ultimately doomed compromise to the current Senate fight. It’s also been effective at working with local lawmakers and shepherding through gun legislation at the state level.

But in terms of breaking Republican senators’ opposition to gun control, the organization’s influx of countervailing money just hasn’t made the difference. "There’s not much to show for it," Grossmann says.

NRA funding reflects a tiny fraction of the Republican fundraising apparatus

Shortly after Sen. Chris Murphy’s 15-hour filibuster on gun control, the Washington Post published a graphic about how the NRA has donated close to $4 million to congressional races since 1998.

That sure sounds like a lot. But when you really look at how that money fits into the grand scheme of congressional fundraising, it looks much less likely to actually be playing a crucial role.

One of the most prominent critics of Democrats’ gun control measure was Texas Sen. John Cornyn, a Republican and reliable NRA ally since before his 2002 election. The NRA has given Cornyn about $30,000 over the past decade. In 2014, the NRA gave him $9,900 — more than it gave to any other Republican senator that election cycle.

But it was a drop in his much bigger ocean of donations. In 2014 he raised $14 million, including $57,000 from Exxon alone. The NRA was nowhere near his top 15 biggest donor contributors.

All of the money the NRA has given Cornyn for more than a decade might pay for about 1 percent of his fundraising for one election cycle — and Cornyn is one of the biggest recipients of NRA cash in Congress. Overall, though the NRA does help pump money into outside spending groups, Republican lawmakers could fund their campaigns just fine if the NRA bowed out.

According to the Center for Responsive Politics, the NRA gave close to $1 million to Republican senators’ PACs in 2014 — or about 1 percent of the $67 million they raised that year.

"In the broader scheme of things, it’s not that much money," Drutman says.

Research shows money doesn’t factor in the highest-priority congressional votes

Money does have a real influence on policymaking in Washington. But it doesn’t tend to change how politicians vote on big, high-profile issues that garner national attention, according to the political scientists.

"There’s a whole lot of evidence on the relationship of money in politics, and the least persuasive evidence is that you can buy vote on final passage of legislation on issues of high public importance," Grossmann says.

Some people (including Donald Trump) like to imagine that the campaign finance system creates a quid pro quo in which businesses are transactionally rewarded for their gifts. Instead, the money has two key but subtler effects: 1) It systematically elevates the priorities of the rich by forcing politicians to spend more time with them than they do with the poor; and 2) it helps businesses grease the legislative wheel.

The second one tends to apply primarily to issues well out of the public eye. Drutman likened campaign donations to bringing a nice bottle of wine to an exclusive dinner party: The wine won’t itself get you through the door, but it may help you strike up a conversation you wouldn’t have been able to otherwise.

Now, Drutman acknowledges there’s a meaningful argument that Republicans and their voters have come to be pro-gun in part because of the influence of the NRA’s money. But the donations themselves are clearly not the reason Republican lawmakers fear opposing the NRA — the much bigger threat the gun rights group poses is its ability to mobilize and excite huge numbers of voters, Drutman says.

"The way you rise up in Republican politics is by supporting gun rights issues, and you do that because there a lot of Republican voters in the coalition who care very deeply about gun rights," Drutman says.

Of course, none of this means that it wouldn’t be good to try to root money out of politics. It just means that doing so wouldn’t lead to the sweeping gun control so many liberals hope is only being held back by our campaign finance system.

How fast 4 different guns can shoot and reload