Bernie Sanders is right: Closed primaries, which exclude independent voters, are hurting him at the voting booth, according to a new analysis.

But just how much better would Bernie be doing if every state primary let independents vote? Luckily, Emory political scientist Alan Abramowitz agreed to run the numbers for us using a model he's built for Larry Sabato's Crystal Ball.

Controlling for other variables, Abramowitz found that closed primaries did penalize Sanders — by roughly 4.7 points. (The flip side of this, naturally, is that Hillary Clinton does about 4.7 points better in closed primaries than in open ones, according to Abramowitz.)

How Abramowitz calculated Bernie Sanders's closed primary penalty

For this analysis, Abramowitz used the model for the Democratic primary he had already created to predict the race's outcome.

It looks at three basic inputs — whether the state is in the South or North, what share of its 2008 voters were African American, and what share of its 2008 primary voters were Democrats.

So far, that model correctly explains more than 90 percent of Clinton's vote share — it accurately predicted who would win all five of Tuesday's primaries, for instance. And Abramowitz notes on the Center for Politics website that it's outperformed the RealClearPolitics polling averages.

To calculate the effect of the closed primary, Abramowitz found the difference in independents (which he calculated with registrations and exit polls) as a percentage of the vote share in open and closed primaries. In other words, he found the extent to which the different kinds of primaries are dominated by Democrats.

So far this year, self-described independents make up 7.5 percentage points more of the primary electorate in open primaries than they do in closed primaries. Abramowitz then multiplied that number by what his model found as the effect of the partisan composition of the electorate — giving him the 4.7 point figure.

So what does this mean for the Democratic primary?

A flip of nearly 5 percentage points sounds like a big effect, and in some ways it really is.

But it wouldn't meaningfully change the outcome of the race. Only six states — New York, Pennsylvania, Maryland, Connecticut, Delaware, and Florida — have held closed primaries since the race began.

Mathematically, if we changed all of the closed primaries to open primaries, we could generously assume Sanders would have done 5 points better in each of the six states. Because of the Democrats' proportional allocation rules, that would probably give Sanders around 5 percent more delegates in each of the six contests.

Add those up, and Sanders would have won 41 more delegates than he currently has. Clinton is currently leading Sanders by 293 delegates (without even counting the superdelegates).

Similarly, if you converted all of the open primaries into closed primaries, Clinton would net about 76 more delegates, according to Abramowitz.

"I think it just helps to show — it is important, it does make a difference, but it's not like if every state had an open primary then Bernie would be ahead," Abramowitz said. "Not even close."